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  • 1.
    Andersson, Bea
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Zhao, Wei
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Haller, Benjamin C.
    Department of Computational Biology, Cornell University, NY, Ithaca, United States.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Advancing Systems Analysis Program, International Institute for Applied Systems Analysis, Laxenburg, Austria; Complexity Science and Evolution Unit, Okinawa Institute of Science and Technology Graduate University, Kunigami, Japan.
    Wang, Xiao-Ru
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Inference of the distribution of fitness effects of mutations is affected by single nucleotide polymorphism filtering methods, sample size and population structure2023In: Molecular Ecology Resources, ISSN 1755-098X, E-ISSN 1755-0998, Vol. 23, no 7, p. 1589-1603Article in journal (Refereed)
    Abstract [en]

    The distribution of fitness effects (DFE) of new mutations has been of interest to evolutionary biologists since the concept of mutations arose. Modern population genomic data enable us to quantify the DFE empirically, but few studies have examined how data processing, sample size and cryptic population structure might affect the accuracy of DFE inference. We used simulated and empirical data (from Arabidopsis lyrata) to show the effects of missing data filtering, sample size, number of single nucleotide polymorphisms (SNPs) and population structure on the accuracy and variance of DFE estimates. Our analyses focus on three filtering methods—downsampling, imputation and subsampling—with sample sizes of 4–100 individuals. We show that (1) the choice of missing-data treatment directly affects the estimated DFE, with downsampling performing better than imputation and subsampling; (2) the estimated DFE is less reliable in small samples (<8 individuals), and becomes unpredictable with too few SNPs (<5000, the sum of 0- and 4-fold SNPs); and (3) population structure may skew the inferred DFE towards more strongly deleterious mutations. We suggest that future studies should consider downsampling for small data sets, and use samples larger than 4 (ideally larger than 8) individuals, with more than 5000 SNPs in order to improve the robustness of DFE inference and enable comparative analyses.

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  • 2.
    Andersson, Bea
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Umeå University, Faculty of Science and Technology, Umeå Plant Science Centre (UPSC).
    Zhao, Wei
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Umeå University, Faculty of Science and Technology, Umeå Plant Science Centre (UPSC).
    Haller, Benjamin
    Department of Computational Biology Cornell University Ithaca New York USA.
    Wang, Xiao-Ru
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Umeå University, Faculty of Science and Technology, Umeå Plant Science Centre (UPSC).
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Effects of self-fertilization on DFE inferenceManuscript (preprint) (Other academic)
  • 3.
    Aye, Tin Nwe
    et al.
    Division of Applied Mathematics, Mälardalen University, Box 883, 721 23 Västerås, Sweden; Department of Mathematics, Kyaukse University, Kyaukse 05151, Myanmar.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Advancing Systems Analysis Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, Laxenburg, Austria.
    Carlsson, Linus
    Division of Applied Mathematics, Mälardalen University, Box 883, 721 23 Västerås, Sweden.
    Prediction of tree sapwood and heartwood profiles using pipe model and branch thinning theory2022In: Tree Physiology, ISSN 0829-318X, E-ISSN 1758-4469, Vol. 42, no 11, p. 2174-2185Article in journal (Refereed)
    Abstract [en]

    Estimates of tree heartwood and sapwood profiles are important in the pulp industry and for dynamic vegetation models, in which they determine tree biomechanical stability and hydraulic conductivity. Several phenomenological models of stem profiles have been developed for this purpose, based on assumptions on how tree crown and foliage distributions change over time. Here, we derive estimates of tree profiles by synthesizing a simple pipe model theory of plant form with a recently developed theory of branch thinning that from simple assumptions quantifies discarded branches and leaves. This allows us to develop a new trunk model of tree profiles from breast height up to the top of the tree. We postulate that leaves that are currently on the tree are connected by sapwood pipes, while pipes that previously connected discarded leaves or branches form the heartwood. By assuming that a fixed fraction of all pipes remain on the trunk after a branching event, as the trunk is traversed from the root system to the tips, this allows us to quantify trunk heartwood and sapwood profiles. We test the trunk model performance on empirical data from five tree species across three continents. We find that the trunk model accurately describes heartwood and sapwood profiles of all tested tree species (calibration; R2: 84-99%). Furthermore, once calibrated to a tree species, the trunk model predicts heartwood and sapwood profiles of conspecific trees in similar growing environments based only on the age and height of a tree (cross-validation/prediction; R2: 68-98%). The fewer and often contrasting parameters needed for the trunk model make it a potentially useful complementary tool for biologists and foresters.

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  • 4.
    Bodin, Mats
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Dieckmann, U.
    Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361, Laxenburg, Austria.
    A systematic overview of Harvesting-Induced Maturation Evolution in Predator-Prey systems with three different Life-History Tradeoffs2012In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 74, no 12, p. 2842-2860Article in journal (Refereed)
    Abstract [en]

    There are concerns that anthropogenic harvesting may cause phenotypic adaptive changes in exploited wild populations, in particular maturation at a smaller size and younger age. In this paper, we study the evolutionarily stable size at maturation of prey subjected to size-selective harvesting in a simple predator-prey model, taking into account three recognized life-history costs of early maturation, namely reduced fecundity, reduced growth, and increased mortality. Our analysis shows that harvesting large individuals favors maturation at smaller size compared to the unharvested system, independent of life-history tradeoff and the predator's prey-size preference. In general, however, the evolutionarily stable maturation size can either increase or decrease relative to the unharvested system, depending on the harvesting regime, the life-history tradeoff, and the predator's preferred size of prey. Furthermore, we examine how the predator population size changes in response to adaptive change in size at maturation of the prey. Surprisingly, in some situations, we find that the evolutionarily stable maturation size under harvesting is associated with an increased predator population size. This occurs, in particular, when early maturation trades off with growth rate. In total, we determine the evolutionarily stable size at maturation and associated predator population size for a total of forty-five different combinations of tradeoff, harvest regime, and predated size class.

  • 5. Brush, Eleanor
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Dieckmann, Ulf
    Indirect reciprocity with negative assortment and limited information can promote cooperation2018In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 443, p. 56-65Article in journal (Refereed)
    Abstract [en]

    Cooperation is ubiquitous in biological and social systems, even though cooperative behavior is often costly and at risk of exploitation by non-cooperators. Several studies have demonstrated that indirect reciprocity, whereby some members of a group observe the behaviors of their peers and use this information to discriminate against previously uncooperative agents in the future, can promote prosocial behavior. Some studies have shown that differential propensities of interacting among and between different types of agents (interaction assortment) can increase the effectiveness of indirect reciprocity. No previous studies have, however, considered differential propensities of observing the behaviors of different types of agents (information assortment). Furthermore, most previous studies have assumed that discriminators possess perfect information about others and incur no costs for gathering and storing this information. Here, we (1) consider both interaction assortment and information assortment, (2) assume discriminators have limited information about others, and (3) introduce a cost for information gathering and storage, in order to understand how the ability of discriminators to stabilize cooperation is affected by these steps toward increased realism. We report the following findings. First, cooperation can persist when agents preferentially interact with agents of other types or when discriminators preferentially observe other discriminators, even when they have limited information. Second, contrary to intuition, increasing the amount of information available to discriminators can exacerbate defection. Third, introducing costs of gathering and storing information makes it more difficult for discriminators to stabilize cooperation. Our study is one of only a few studies to date that show how negative interaction assortment can promote cooperation and broadens the set of circumstances in which it is know that cooperation can be maintained.

  • 6.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Modelling animal populations2004Doctoral thesis, comprehensive summary (Other academic)
    Abstract [sv]

    This thesis consists of four papers, three papers about modelling animal populations and one paper about an area integral estimate for solutions of partial differential equations on non-smooth domains. The papers are:

    I. Å. Brännström, Single species population models from first principles.

    II. Å. Brännström and D. J. T. Sumpter, Stochastic analogues of deterministic single species population models.

    III. Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology.

    IV. Å. Brännström, An area integral estimate for higher order parabolic equations.

    In the first paper we derive deterministic discrete single species population models with first order feedback, such as the Hassell and Beverton-Holt model, from first principles. The derivations build on the site based method of Sumpter & Broomhead (2001) and Johansson & Sumpter (2003). A three parameter generalisation of the Beverton-Holtmodel is also derived, and one of the parameters is shown to correspond directly to the underlying distribution of individuals.

    The second paper is about constructing stochastic population models that incorporate a given deterministic skeleton. Using the Ricker model as an example, we construct several stochastic analogues and fit them to data using the method of maximum likelihood. The results show that an accurate stochastic population model is most important when the dynamics are periodic or chaotic, and that the two most common ways of constructing stochastic analogues, using additive normally distributed noise or multiplicative lognormally distributed noise, give models that fit the data well. The latter is also motivated on theoretical grounds.

    In the third paper we approximate a spatially explicit individual-based model with a stochastic coupledmap lattice. The approximation effectively disentangles the deterministic and stochastic components of the model. Based on this approximation we argue that the stable population dynamics seen for short dispersal ranges is a consequence of increased stochasticity from local interactions and dispersal.

    Finally, the fourth paper contains a proof that for solutions of higher order real homogeneous constant coefficient parabolic operators on Lipschitz cylinders, the area integral dominates the maximal function in the L2-norm.

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  • 7.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Carlsson, Linus
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Rossberg, Axel
    School of Biological Sciences, Queen’s University Belfast, Belfast, BT9 7BL UK.
    Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces2011In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 3, p. 575-592Article in journal (Refereed)
    Abstract [en]

    Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

  • 8.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Carlsson, Linus
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria.
    Simpson, Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria.
    On the convergence of the Escalator Boxcar Train2013In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, no 6, p. 3213-3231Article in journal (Refereed)
    Abstract [en]

    The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical biology to investigate the dynamics of physiologically structured population models, i.e., models in which individuals differ by size or other physiological characteristics. The method was developed more than two decades ago, but has so far resisted attempts to give a formal proof of convergence. Using a modern framework of measure-valued solutions, we investigate the EBT method and show that the sequence of approximating solution measures generated by the EBT method converges weakly to the true solution measure under weak conditions on the growth rate, birth rate, and mortality rate. In rigorously establishing the convergence of the EBT method, our results pave the way for wider acceptance of the EBT method beyond theoretical biology and constitutes an important step towards integration with established numerical schemes.

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  • 9.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Dieckmann, Ulf
    Evolutionary dynamics of altruism and cheating in social ameobas2005In: Proceedings of the Royal Society London Series B, Vol. 272, p. 1609-1616Article in journal (Refereed)
  • 10.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Gross, Thilo
    Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
    Blasius, Bernd
    Institute for Chemistry and Biology of Marine Environment, Oldenburg University, 26111 Oldenburg, Germany.
    Dieckmann, Ulf
    Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria.
    Consequences of fluctuating group size for the evolution of cooperation2011In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 2, p. 263-281Article in journal (Refereed)
    Abstract [en]

    Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner’s dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the ‘tragedy of the commune’. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.

  • 11.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Loeuille, Nicolas
    Kristensen, Nadiah
    Troost, Tineke A
    Lambers, Reinier Hille Ris
    Dieckmann, Ulf
    Modelling the ecology and evolution of communities: a review of past achievements, current efforts, and future promises2012In: Evolutionary Ecology Research, ISSN 1522-0613, E-ISSN 1937-3791, Vol. 14, no 5, p. 601-625Article in journal (Refereed)
    Abstract [en]

    Background: The complexity and dynamical nature of community interactions make modelling a useful tool for understanding how communities develop over time and how they respond to external perturbations. Large community-evolution models (LCEMs) are particularly promising, since they can address both ecological and evolutionary questions, and can give rise to richly structured and diverse model communities.

    Questions: Which types of models have been used to study community structure and what are their key features and limitations? How do adaptations and/or invasions affect community formation? Which mechanisms promote diverse and stable communities? What are the implications of LCEMs for management and conservation? What are the key challenges for future research?

    Models considered: Static models of community structure, demographic community models, and small and large community-evolution models.

    Conclusions: Large community-evolution models encompass a variety of modelled traits and interactions, demographic dynamics, and evolutionary dynamics. They are able to reproduce empirical community structures. They have already generated new insights, such as the dual role of competition, which limits diversity through competitive exclusion yet facilitates diversity through speciation. Other critical factors determining eventual community structure are the shape of trade-off functions, inclusion of adaptive foraging, and energy availability. A particularly interesting feature of LCEMs is that these models not only help to contrast outcomes of community formation via species assembly with those of community formation via gradual evolution and speciation, but that they can furthermore unify the underlying invasion processes and evolutionary processes into a single framework.

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  • 12.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Lund University.
    von Festenberg, Niels
    The Hitchhiker’s Guide to Adaptive Dynamics2013In: Games, E-ISSN 2073-4336, no 4, p. 304-328Article in journal (Refereed)
    Abstract [en]

    Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

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  • 13.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Loeuille, Nicolas
    Laboratoire Ecologie & Evolution, Université Pierre et Marie Curie, Paris, France .
    Loreau, Michel
    Department of Biology, McGill University, Montreal, Canada.
    Dieckmann, Ulf
    International Institute for Applied Systems Analysis (IIASA), Evolution and Ecology Program, Laxenburg, Austria.
    Emergence and maintenance of biodiversity in an evolutionary food-web model2011In: Theoretical Ecology, ISSN 1874-1738, Vol. 4, no 4, p. 467-478Article in journal (Refereed)
    Abstract [en]

    Ecological communities emerge as a consequence of gradual evolution, speciation, and immigration. In this study, we explore how these processes and the structure of the evolved food webs are affected by species-level properties. Using a model of biodiversity formation that is based on body size as the evolving trait and incorporates gradual evolution and adaptive radiation, we investigate how conditions for initial diversification relate to the eventual diversity of a food web. We also study how trophic interactions, interference competition, and energy availability affect a food web’s maximum trophic level and contrast this with conditions for high diversity. We find that there is not always a positive relationship between conditions that promote initial diversification and eventual diversity, and that the most diverse food webs often do not have the highest trophic levels.

  • 14.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Advancing Systems Analysis Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Sjödin, Henrik
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health.
    Rocklöv, Joacim
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health.
    A Method for Estimating the Number of Infections From the Reported Number of Deaths2022In: Frontiers In Public Health, ISSN 2296-2565, Vol. 9, article id 648545Article in journal (Refereed)
    Abstract [en]

    At the outset of an epidemic, available case data typically underestimate the total number of infections due to insufficient testing, potentially hampering public responses. Here, we present a method for statistically estimating the true number of cases with confidence intervals from the reported number of deaths and estimates of the infection fatality ratio; assuming that the time from infection to death follows a known distribution. While the method is applicable to any epidemic with a significant mortality rate, we exemplify the method by applying it to COVID-19. Our findings indicate that the number of unreported COVID-19 infections in March 2020 was likely to be at least one order of magnitude higher than the reported cases, with the degree of underestimation among the countries considered being particularly high in the United Kingdom.

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  • 15.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Sumpter, David J.T.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Coupled map lattice approximations for spatially explicit individual-based models of ecology2005In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 67, no 4, p. 663-682Article in journal (Refereed)
    Abstract [en]

    Spatially explicit individual-based models are widely used in ecology but they are often difficult to treat analytically. Despite their intractability they often exhibit clear temporal and spatial patterning. We demonstrate how a spatially explicit individual-based model of scramble competition with local dispersal can be approximated by a stochastic coupled map lattice. The approximation disentangles the deterministic and stochastic element of local interaction and dispersal. We are thus able to understand the individual-based model through a simplified set of equations. In particular, we demonstrate that demographic noise leads to increased stability in the dynamics of locally dispersing single-species populations. The coupled map lattice approximation has general application to a range of spatially explicit individual-based models. It provides a new alternative to current approximation techniques, such as the method of moments and reaction–diffusion approximation, that captures both stochastic effects and large-scale patterning arising in individual-based models.

  • 16.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Sumpter, David J.T.
    Stochastic analogues of deterministic single-species population models2006In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 69, no 4, p. 442-451Article in journal (Refereed)
    Abstract [en]

    Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models—additive normally distributed noise and multiplicative lognormally distributed noise—generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.

  • 17.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Sumpter, David J.T.
    The role of competition and clustering in population dynamics2005In: Proceedings of the Royal Society London Series B, p. 2065-2072Article in journal (Refereed)
  • 18. Chen, Xiaojie
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.
    Dieckmann, Ulf
    Parent-preferred dispersal promotes cooperation in structured populations2019In: Proceedings of the Royal Society of London. Biological Sciences, ISSN 0962-8452, E-ISSN 1471-2954, Vol. 286, no 1895, article id 20181949Article in journal (Refereed)
    Abstract [en]

    Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth-death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.

  • 19. Chen, Xiaojie
    et al.
    Sasaki, Tatsuya
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Dieckmann, Ulf
    First carrot, then stick: how the adaptive hybridization of incentives promotes cooperation2015In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 12, no 102, article id 20140935Article in journal (Refereed)
    Abstract [en]

    Social institutions often use rewards and penalties to promote cooperation. Providing incentives tends to be costly, so it is important to find effective and efficient policies for the combined use of rewards and penalties. Most studies of cooperation, however, have addressed rewarding and punishing in isolation and have focused on peer-to-peer sanctioning as opposed to institutional sanctioning. Here, we demonstrate that an institutional sanctioning policy we call 'first carrot, then stick' is unexpectedly successful in promoting cooperation. The policy switches the incentive from rewarding to punishing when the frequency of cooperators exceeds a threshold. We find that this policy establishes and recovers full cooperation at lower cost and under a wider range of conditions than either rewards or penalties alone, in both well-mixed and spatial populations. In particular, the spatial dynamics of cooperation make it evident how punishment acts as a 'booster stage' that capitalizes on and amplifies the pro-social effects of rewarding. Together, our results show that the adaptive hybridization of incentives offers the 'best of both worlds' by combining the effectiveness of rewarding in establishing cooperation with the effectiveness of punishing in recovering it, thereby providing a surprisingly inexpensive and widely applicable method of promoting cooperation.

  • 20.
    Coder Gylling, Kira
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, 2361 Laxenburg, Austria.
    Effects of Relatedness on the Evolution of Cooperation in Nonlinear Public Goods Games2018In: Games, E-ISSN 2073-4336, Vol. 9, no 4Article in journal (Refereed)
    Abstract [en]

    Evolution of cooperation has traditionally been studied by assuming that individuals adopt either of two pure strategies, to cooperate or defect. Recent work has considered continuous cooperative investments, turning full cooperation and full defection into two opposing ends of a spectrum and sometimes allowing for the emergence of the traditionally-studied pure strategies through evolutionary diversification. These studies have typically assumed a well-mixed population in which individuals are encountered with equal probability. Here, we allow for the possibility of assortative interactions by assuming that, with specified probabilities, an individual interacts with one or more other individuals of the same strategy. A closely related assumption has previously been made in evolutionary game theory and has been interpreted in terms of relatedness. We systematically study the effect of relatedness and find, among other conclusions, that the scope for evolutionary branching is reduced by either higher average degree of, or higher uncertainty in, relatedness with interaction partners. We also determine how different types of non-linear dependencies of benefits and costs constrain the types of evolutionary outcomes that can occur. While our results overall corroborate the conclusions of earlier studies, i.e. higher relatedness promotes the evolution of cooperation, our investigation gives a comprehensive picture of how relatedness affects the evolution of cooperation with continuous investments.

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  • 21. Colon, Celian
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied System Analysis, Laxenburg, Austria.
    Rovenskaya, Elena
    Dieckmann, Ulf
    Fragmentation of production amplifies systemic risks from extreme events in supply-chain networks2020In: PLOS ONE, E-ISSN 1932-6203, Vol. 15, no 12, article id e0244196Article in journal (Refereed)
    Abstract [en]

    Climatic and other extreme events threaten the globalized economy, which relies on increasingly complex and specialized supply-chain networks. Disasters generate (i) direct economic losses due to reduced production in the locations where they occur, and (ii) to indirect losses from the supply shortages and demand changes that cascade along the supply chains. Firms can use inventories to reduce their risk of shortages. Since firms are interconnected through the supply chain, the level of inventory hold by one firm influences the risk of shortages of the others. Such interdependencies lead to systemic risks in supply chain networks. We introduce a stylized model of complex supply-chain networks in which firms adjust their inventory to maximize profit. We analyze the resulting risks and inventory patterns using evolutionary game theory. We report the following findings. Inventories significantly reduce disruption cascades and indirect losses at the expense of a moderate increase in direct losses. The more fragmented a supply chain is, the less beneficial it is for individual firms to maintain inventories, resulting in higher systemic risks. One way to mitigate such systemic risks is to prescribe inventory sizes to individual firms—a measure that could, for instance, be fostered by insurers. We found that prescribing firm-specific inventory sizes based on their position in the supply chain mitigates systemic risk more effectively than setting the same inventory requirements for all firms.

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  • 22. Cornforth, Daniel M
    et al.
    Sumpter, David J T
    Brown, Sam P
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Synergy and group size in microbial cooperation2012In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 180, no 3, p. 296-305Article in journal (Refereed)
    Abstract [en]

    Abstract Microbes produce many molecules that are important for their growth and development, and the exploitation of these secretions by nonproducers has recently become an important paradigm in microbial social evolution. Although the production of these public-goods molecules has been studied intensely, little is known of how the benefits accrued and the costs incurred depend on the quantity of public-goods molecules produced. We focus here on the relationship between the shape of the benefit curve and cellular density, using a model assuming three types of benefit functions: diminishing, accelerating, and sigmoidal (accelerating and then diminishing). We classify the latter two as being synergistic and argue that sigmoidal curves are common in microbial systems. Synergistic benefit curves interact with group sizes to give very different expected evolutionary dynamics. In particular, we show that whether and to what extent microbes evolve to produce public goods depends strongly on group size. We show that synergy can create an "evolutionary trap" that can stymie the establishment and maintenance of cooperation. By allowing density-dependent regulation of production (quorum sensing), we show how this trap may be avoided. We discuss the implications of our results on experimental design.

  • 23. Dieckmann, U.
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    HilleRisLambers, R.
    Ito, H.C.
    The adaptive dynamics of community structure2007In: Mathematics for Ecology and Environmental Sciences, p. 145-177Article in journal (Refereed)
  • 24.
    Falster, Daniel
    et al.
    Department of Biological Sciences, Macquarie University, NSW 2109, Sydney, Australia.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Dieckmann, Ulf
    Evolution and Ecology Program, International Institute for Applied Systems Analysis, Schlossplatz 1, 2361 Laxenburg, Austria.
    Westoby, Mark
    Department of Biological Sciences, Macquarie University, NSW 2109, Sydney, Australia.
    The influence of four major plant traits on average height, leaf area cover, net primary productivity, and standing biomass in single-species forests: a theoretical investigation2011In: Journal of Ecology, ISSN 0022-0477, E-ISSN 1365-2745, Vol. 99, no 1, p. 148-164Article in journal (Refereed)
    Abstract [en]

    Numerous plant traits are known to influence aspects of individual performance, including rates of carbon uptake, tissue turnover, mortality and fecundity. These traits are bound to influence emergent properties of vegetation because quantities such as leaf-area cover, average height, primary productivity and density of standing biomass result from the collective behaviour of individuals. Yet, little is known about the influence of individual traits on these emergent properties, despite the widespread use in current vegetation models of plant functional types, each of which is defined by a constellation of traits.

    We examine the influence of four key traits (leaf economic strategy, height at maturation, wood density, and seed size) on four emergent vegetation properties (average height of leaf area, leaf-area index, net primary productivity and biomass density). We employ a trait-, size- and patch-structured model of vegetation dynamics that allows scaling up from individual-level growth processes and probabilistic disturbances to landscape-level predictions. A physiological growth model incorporating relevant trade-offs was designed and calibrated based on known empirical patterns. The resulting vegetation model naturally exhibits a range of phenomena commonly observed in vegetation dynamics.

    We modelled single-species stands, varying each trait over its known empirical range. Seed size had only a small effect on vegetation properties, primarily because our metapopulations were not seed-limited. The remaining traits all had larger effects on vegetation properties, especially on biomass density. Leaf economic strategy influenced minimum light requirement, and thus total leaf area and basal area. Wood density and height at maturation influenced vegetation mainly by modifying individual stem mass. These effects of traits were maintained, and sometimes amplified, across stands differing in productivity and mean disturbance interval.

    Synthesis: Natural trait variation can cause large differences in emergent properties of vegetation, the magnitudes of which approach those arising through changes to site productivity and disturbance frequency. Our results therefore underscore the need for next-generation vegetation models that incorporate functional traits together with their effects on the patch and size structure of vegetation.

  • 25. Falster, Daniel S.
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, A-2361 Laxenburg, Austria.
    Westoby, Mark
    Dieckmann, Ulf
    Multitrait successional forest dynamics enable diverse competitive coexistence2017In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 114, no 13, p. E2719-E2728Article in journal (Refereed)
    Abstract [en]

    To explain diversity in forests, niche theory must show how multiple plant species coexist while competing for the same resources. Although successional processes are widespread in forests, theoretical work has suggested that differentiation in successional strategy allows only a few species stably to coexist, including only a single shade tolerant. However, this conclusion is based on current niche models, which encode a very simplified view of plant communities, suggesting that the potential for niche differentiation has remained unexplored. Here, we show how extending successional niche models to include features common to all vegetation-height-structured competition for light under a prevailing disturbance regime and two trait-mediated tradeoffs in plant function-enhances the diversity of species that can be maintained, including a diversity of shade tolerants. We identify two distinct axes of potential niche differentiation, corresponding to the traits leaf mass per unit leaf area and height at maturation. The first axis allows for coexistence of different shade tolerances and the second axis for coexistence among species with the same shade tolerance. Addition of this second axis leads to communities with a high diversity of shade tolerants. Niche differentiation along the second axis also generates regions of trait space wherein fitness is almost equalized, an outcome we term "evolutionarily emergent near-neutrality." For different environmental conditions, our model predicts diverse vegetation types and trait mixtures, akin to observations. These results indicate that the outcomes of successional niche differentiation are richer than previously thought and potentially account for mixtures of traits and species observed in forests worldwide.

  • 26. Falster, Daniel S.
    et al.
    FitzJohn, Richard G.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institutefor Applied Systems Analysis, Schlossplatz 1, A-2361 Laxen burg, Au stria.
    Dieckmann, Ulf
    Westoby, Mark
    plant: A package for modelling forest trait ecology and evolution2016In: Methods in Ecology and Evolution, E-ISSN 2041-210X, Vol. 7, no 2, p. 136-146Article in journal (Refereed)
    Abstract [en]

    Population dynamics in forests are strongly size-structured: larger plants shade smaller plants while also expending proportionately more energy on building and maintaining woody stems. Although the importance of size structure for demography is widely recognized, many models either omit it entirely or include only coarse approximations. Here, we introduce the plant package, an extensible framework for modelling size- and trait-structured demography, ecology and evolution in simulated forests. At its core, plant is an individual-based model where plant physiology and demography are mediated by traits. Individual plants from multiple species can be grown in isolation, in patches of competing plants or in metapopulations under a disturbance regime. These dynamics can be integrated into metapopulation-level estimates of invasion fitness and vegetation structure. Because fitness emerges as a function of traits, plant provides a novel arena for exploring eco-evolutionary dynamics. plant is an open source R package and is available at . Accessed from R, the core routines in plant are written in C++. The package provides for alternative physiologies and for capturing trade-offs among parameters. A detailed test suite is provided to ensure correct behaviour of the code. plant provides a transparent platform for investigating how physiological rules and functional trade-offs interact with competition and disturbance regimes to influence vegetation demography, structure and diversity.

  • 27.
    Farooq, Zia
    et al.
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health.
    Sjödin, Henrik
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health.
    Rocklöv, Joacim
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Optimizing case fatality ratio estimates in ongoing pandemics through case-to-death time distribution analysisManuscript (preprint) (Other academic)
  • 28. Franklin, Oskar
    et al.
    Harrison, Sandy P.
    Dewar, Roderick
    Farrior, Caroline E.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. International Institute for Applied Systems Analysis, Laxenburg, Austria..
    Dieckmann, Ulf
    Pietsch, Stephan
    Falster, Daniel
    Cramer, Wolfgang
    Loreau, Michel
    Wang, Han
    Mäkelä, Annikki
    Rebel, Karin T.
    Meron, Ehud
    Schymanski, Stanislaus J.
    Rovenskaya, Elena
    Stocker, Benjamin D.
    Zaehle, Söenke
    Manzoni, Stefano
    van Oijen, Marcel
    Wright, Ian J.
    Ciais, Philippe
    van Bodegom, Peter M.
    Peñuelas, Josep
    Hofhansl, Florian
    Terrer, Cesar
    Soudzilovskaia, Nadejda A.
    Midgley, Guy
    Prentice, I. Colin
    Organizing principles for vegetation dynamics2020In: NATURE PLANTS, ISSN 2055-026X, Vol. 6, no 5, p. 444-453Article in journal (Refereed)
    Abstract [en]

    Plants and vegetation play a critical-but largely unpredictable-role in global environmental changes due to the multitude of contributing processes at widely different spatial and temporal scales. In this Perspective, we explore approaches to master this complexity and improve our ability to predict vegetation dynamics by explicitly taking account of principles that constrain plant and ecosystem behaviour: natural selection, self-organization and entropy maximization. These ideas are increasingly being used in vegetation models, but we argue that their full potential has yet to be realized. We demonstrate the power of natural selection-based optimality principles to predict photosynthetic and carbon allocation responses to multiple environmental drivers, as well as how individual plasticity leads to the predictable self-organization of forest canopies. We show how models of natural selection acting on a few key traits can generate realistic plant communities and how entropy maximization can identify the most probable outcomes of community dynamics in space- and time-varying environments. Finally, we present a roadmap indicating how these principles could be combined in a new generation of models with stronger theoretical foundations and an improved capacity to predict complex vegetation responses to environmental change. Integrating natural selection and other organizing principles into next-generation vegetation models could render them more theoretically sound and useful for earth system applications and modelling climate impacts.

  • 29. Franklin, Oskar
    et al.
    Johansson, Jacob
    Dewar, Roderick C.
    Dieckmann, Ulf
    McMurtrie, Ross E.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Dybzinski, Ray
    Modeling carbon allocation in trees: a search for principles2012In: Tree Physiology, ISSN 0829-318X, E-ISSN 1758-4469, Vol. 32, no 6, p. 648-666Article, review/survey (Refereed)
    Abstract [en]

    We review approaches to predicting carbon and nitrogen allocation in forest models in terms of their underlying assumptions and their resulting strengths and limitations. Empirical and allometric methods are easily developed and computationally efficient, but lack the power of evolution-based approaches to explain and predict multifaceted effects of environmental variability and climate change. In evolution-based methods, allocation is usually determined by maximization of a fitness proxy, either in a fixed environment, which we call optimal response (OR) models, or including the feedback of an individual's strategy on its environment (game-theoretical optimization, GTO). Optimal response models can predict allocation in single trees and stands when there is significant competition only for one resource. Game-theoretical optimization can be used to account for additional dimensions of competition, e.g., when strong root competition boosts root allocation at the expense of wood production. However, we demonstrate that an OR model predicts similar allocation to a GTO model under the root-competitive conditions reported in free-air carbon dioxide enrichment (FACE) experiments. The most evolutionarily realistic approach is adaptive dynamics (AD) where the allocation strategy arises from eco-evolutionary dynamics of populations instead of a fitness proxy. We also discuss emerging entropy-based approaches that offer an alternative thermodynamic perspective on allocation, in which fitness proxies are replaced by entropy or entropy production. To help develop allocation models further, the value of wide-ranging datasets, such as FLUXNET, could be greatly enhanced by ancillary measurements of driving variables, such as water and soil nitrogen availability.

  • 30.
    Fransson, Peter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Franklin, Oskar
    International Institute for Applied Systems Analysis.
    A tree’s quest for light: optimal height and diameter growth under a shading canopy2021In: Tree Physiology, ISSN 0829-318X, E-ISSN 1758-4469, Vol. 41, no 1, p. 1-11Article in journal (Refereed)
    Abstract [en]

    For trees in forests, striving for light is matter of life and death, either by growing taller toward brighter conditions or by expanding the crown to capture more of the available light. Here, we present a mechanistic model for the development path of stem height and crown size, accounting for light capture and growth, as well as mortality risk. We determine the optimal growth path among all possible trajectories using dynamic programming. The optimal growth path follows a sequence of distinct phases: (i) initial crown size expansion, (ii) stem height growth toward the canopy, (iii) final expansion of the crown in the canopy and (iv) seed production without further increase in size. The transition points between these phases can be optimized by maximizing fitness, defined as expected lifetime reproductive production. The results imply that to reach the canopy in an optimal way, trees must consider the full profile of expected increasing light levels toward the canopy. A shortsighted maximization of growth based on initial light conditions can result in arrested height growth, preventing the tree from reaching the canopy. The previous result can explain canopy stratification, and why canopy species often get stuck at a certain size under a shading canopy. The model explains why trees with lower wood density have a larger diameter at a given tree height and grow taller than trees with higher wood density. The model can be used to implement plasticity in height versus diameter growth in individual-based vegetation and forestry models.

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  • 31.
    Fransson, Peter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Franklin, Oskar
    Ecosystems Services and Management Program, International Institute for Applied Systems Analysis.
    Lindroos, Ola
    Department of Forest Biomaterials and Technology, Swedish University of Agricultural Sciences.
    Nilsson, Urban
    Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    A simulation-based approach to a near optimal thinning strategy: allowing for individual harvesting times for individual trees2020In: Canadian Journal of Forest Research, ISSN 0045-5067, E-ISSN 1208-6037, Vol. 50, no 3, p. 320-331Article in journal (Refereed)
    Abstract [en]

    As various methods for precision inventories, such as LiDAR, are becoming increasingly common in forestry, individual-tree level planning is becoming more viable. Here, we present a method for finding the optimal thinning times for individual trees from an economic perspective. The method utilizes an individual tree-based forest growth model that has been fitted to Norway spruce (Picea abies (L.) Karst.) stands in northern Sweden. We find that the optimal management strategy is to thin from above, i.e. harvesting trees that are larger than average. We compare our optimal strategy with a conventional management strategy and find that it results in approximately 20% higher land expectation value. Furthermore, we find that increasing the discount rate will, for the optimal strategy, reduce the final harvest age and increase the basal area reduction. Decreasing the cost to initiate a thinning (e.g., machinery-related transportation costs) increases the number of thinnings and delays the first thinning.

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  • 32.
    Fransson, Peter
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Nilsson, Urban
    Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences, Alnarp, Sweden.
    Lindroos, Ola
    Department of Forest Biomaterials and Technology, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Franklin, Oskar
    Ecosystems Services and Management Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Model-based investigation on the effects of spatial evenness, and size selection in thinning of Picea abies stands2019In: Scandinavian Journal of Forest Research, ISSN 0282-7581, E-ISSN 1651-1891, Vol. 34, no 3, p. 189-199Article in journal (Refereed)
    Abstract [en]

    Size and spatial distribution of trees are important for forest stand growth, but the extent to which itmatters in thinning operations, in terms of wood production and stand economy, has rarely beendocumented. Here we investigate how the choice of spatial evenness and tree-size distribution ofresidual trees impacts wood production and stand economy. A spatially explicit individual-basedgrowth model was used, in conjunction with empirical cost functions for harvesting andforwarding, to calculate net production and net present value for different thinning operations inNorway spruce stands in Northern Sweden. The in silico thinning operations were defined by threevariables: (1) spatial evenness after thinning, (2) tree size preference for harvesting, and (3) basalarea reduction. We found that thinning that increases spatial evenness increases net productionand net present value by around 2.0%, compared to the worst case. When changing the spatialevenness in conjunction with size preference we could observe an improvement of the netproduction and net present value up to 8.0%. The magnitude of impact differed greatly betweenthe stands (from 1.7% to 8.0%) and was highest in the stand with the lowest stem density.

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  • 33. Gephart, Jessica A.
    et al.
    Rovenskaya, Elena
    Dieckmann, Ulf
    Pace, Michael L.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Vulnerability to shocks in the global seafood trade network2016In: Environmental Research Letters, E-ISSN 1748-9326, Vol. 11, no 3, article id 035008Article in journal (Refereed)
    Abstract [en]

    Trade can allow countries to overcome local or regional losses (shocks) to their food supply, but reliance on international food trade also exposes countries to risks from external perturbations. Countries that are nutritionally or economically dependent on international trade of a commodity may be adversely affected by such shocks. While exposure to shocks has been studied in financial markets, communication networks, and some infrastructure systems, it has received less attention in food-trade networks. Here, we develop a forward shock-propagation model to quantify how trade flows are redistributed under a range of shock scenarios and assess the food-security outcomes by comparing changes in national fish supplies to indices of each country's nutritional fish dependency. Shock propagation and distribution among regions are modeled on a network of historical bilateral seafood trade data from UN Comtrade using 205 reporting territories grouped into 18 regions. In our model exposure to shocks increases with total imports and the number of import partners. We find that Central and West Africa are the most vulnerable to shocks, with their vulnerability increasing when a willingness-to-pay proxy is included. These findings suggest that countries can reduce their overall vulnerability to shocks by reducing reliance on imports and diversifying food sources. As international seafood trade grows, identifying these types of potential risks and vulnerabilities is important to build a more resilient food system.

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  • 34.
    Harrison, Sandy P.
    et al.
    Department of Geography and Environmental Science, University of Reading, Reading, United Kingdom; Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing, China.
    Cramer, Wolfgang
    Institut Méditerranéen de Biodiversité et d’Ecologie Marine et Continentale, Aix Marseille Université, CNRS, IRD, Avignon Université, Technopôle Arbois-Méditerranée, Aix-en-Provence Cedex 04, France.
    Franklin, Oskar
    International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg, Austria; Department of Forest Ecology and Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
    Prentice, Iain Colin
    Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing, China; Department of Life Sciences, Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, United Kingdom; Department of Biological Sciences, Macquarie University, NSW, North Ryde, Australia.
    Wang, Han
    Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing, China.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg, Austria.
    de Boer, Hugo
    Copernicus Institute of Sustainable Development, Environmental Sciences, Faculty of Geosciences, Utrecht University, Vening Meinesz Building, Princetonlaan 8a, Utrecht, Netherlands.
    Dieckmann, Ulf
    International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg, Austria; Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies (Sokendai), Kanagawa, Hayama, Japan.
    Joshi, Jaideep
    International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg, Austria.
    Keenan, Trevor F.
    Climate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, CA, Berkeley, United States; Department of Environmental Science, Policy and Management, University of California Berkeley, CA, Berkeley, United States.
    Lavergne, Aliénor
    Department of Physics, Imperial College London, South Kensington Campus, London, United Kingdom.
    Manzoni, Stefano
    Department of Physical Geography and Bolin Centre for Climate Research, Stockholm University, SE-106 91, Stockholm, Sweden.
    Mengoli, Giulia
    Department of Life Sciences, Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, United Kingdom.
    Morfopoulos, Catherine
    Department of Life Sciences, Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, United Kingdom.
    Peñuelas, Josep
    CSIC, Global Ecology, CREAF-CSIC-UAB, Bellaterra, Catalonia, Barcelona, Spain; CREAF, Cerdanyola del Valles, Catalonia, Barcelona, Spain.
    Pietsch, Stephan
    International Institute for Applied Systems Analysis, Schlossplatz 1, Laxenburg, Austria; BOKU - University of Life Sciences and Natural Resources, Gregor-Medel-Strasse 33, Vienna, Austria.
    Rebel, Karin T.
    Copernicus Institute of Sustainable Development, Environmental Sciences, Faculty of Geosciences, Utrecht University, Vening Meinesz Building, Princetonlaan 8a, Utrecht, Netherlands.
    Ryu, Youngryel
    Department of Landscape Architecture and Rural Systems Engineering, Seoul National University, Seoul, South Korea.
    Smith, Nicholas G.
    Department of Biological Sciences, Texas Tech University, 2901 Main Street, TX, Lubbock, United States.
    Stocker, Benjamin D.
    Department of Environmental System Science, ETH, Universitätstrasse 2, Zürich, Switzerland; Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Zrcherstrasse 111, Birmensdorf, Switzerland.
    Wright, Ian J.
    Department of Biological Sciences, Macquarie University, NSW, North Ryde, Australia.
    Eco-evolutionary optimality as a means to improve vegetation and land-surface models2021In: New Phytologist, ISSN 0028-646X, E-ISSN 1469-8137, Vol. 231, no 6, p. 2125-2141Article, review/survey (Refereed)
    Abstract [en]

    Global vegetation and land-surface models embody interdisciplinary scientific understanding of the behaviour of plants and ecosystems, and are indispensable to project the impacts of environmental change on vegetation and the interactions between vegetation and climate. However, systematic errors and persistently large differences among carbon and water cycle projections by different models highlight the limitations of current process formulations. In this review, focusing on core plant functions in the terrestrial carbon and water cycles, we show how unifying hypotheses derived from eco-evolutionary optimality (EEO) principles can provide novel, parameter-sparse representations of plant and vegetation processes. We present case studies that demonstrate how EEO generates parsimonious representations of core, leaf-level processes that are individually testable and supported by evidence. EEO approaches to photosynthesis and primary production, dark respiration and stomatal behaviour are ripe for implementation in global models. EEO approaches to other important traits, including the leaf economics spectrum and applications of EEO at the community level are active research areas. Independently tested modules emerging from EEO studies could profitably be integrated into modelling frameworks that account for the multiple time scales on which plants and plant communities adjust to environmental change.

  • 35.
    Hellström, Lars
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.
    Carlsson, Linus
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.
    Falster, Daniel S.
    Westoby, Mark
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Branch Thinning and the Large-Scale, Self-Similar Structure of Trees2018In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 192, no 1, p. E37-E47Article in journal (Refereed)
    Abstract [en]

    Branch formation in trees has an inherent tendency toward exponential growth, but exponential growth in the number of branches cannot continue indefinitely. It has been suggested that trees balance this tendency toward expansion by also losing branches grown in previous growth cycles. Here, we present a model for branch formation and branch loss during ontogeny that builds on the phenomenological assumption of a branch carrying capacity. The model allows us to derive approximate analytical expressions for the number of tips on a branch, the distribution of growth modules within a branch, and the rate and size distribution of tree wood litter produced. Although limited availability of data makes empirical corroboration challenging, we show that our model can fit field observations of red maple (Acer rubrum) and note that the age distribution of discarded branches predicted by our model is qualitatively similar to an empirically observed distribution of dead and abscised branches of balsam poplar (Populus balsamifera). By showing how a simple phenomenological assumptionthat the number of branches a tree can maintain is limitedleads directly to predictions on branching structure and the rate and size distribution of branch loss, these results potentially enable more explicit modeling of woody tissues in ecosystems worldwide, with implications for the buildup of flammable fuel, nutrient cycling, and understanding of plant growth.

  • 36. Hochrainer-Stigler, Stefan
    et al.
    Colon, Celian
    Boza, Gergely
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Linnerooth-Bayer, Joanne
    Pflug, Georg
    Poledna, Sebastian
    Rovenskaya, Elena
    Dieckmann, Ulf
    Measuring, modeling, and managing systemic risk: the missing aspect of human agency2020In: Journal of Risk Research, ISSN 1366-9877, E-ISSN 1466-4461, Vol. 23, no 10, p. 1301-1317Article in journal (Refereed)
    Abstract [en]

    It is problematic to treat systemic risk as a merely technical problem that can be solved by natural-science methods and through biological and ecological analogies. There appears to be a discrepancy between understanding systemic risk from a natural-science perspective and the unresolved challenges that arise when humans with their initiatives and interactions are included in systemic-risk considerations. It is therefore necessary to investigate possible fundamental differences and similarities of systemic risk with and without accounting for human involvement. Focusing on applied and implementation aspects of measuring, modeling, and managing systemic risks, we identify three important and distinct features characterizing such fundamental differences: indetermination, indecision, and responsibility. We contend that, first, including human initiatives and interactions in systemic-risk considerations must emphasize a type of variability that is especially relevant in this context, namely the role of free will as a fundamental source of essential indetermination in human agency. Second, we postulate that collective indecision generated by mutual uncertainty often leads to the suspension or alteration of rules, procedures, scripts, and norms. Consequently, the associated systemic risks cannot be incorporated into explanatory models, as the new causal rules cannot be predicted and accounted for. Third, analogies from biology and ecology, especially the idea of ‘contagion,’ downplay human agency, and therefore human responsibility, promoting the false belief that systemic risk is a merely technical problem. For each of these three features, we provide recommendations for future directions and suggest how measuring, modeling, and managing approaches from the natural-science domain can best be applied in light of human agency.

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  • 37. Hochrainer-Stigler, Stefan
    et al.
    Pflug, Georg
    Dieckmann, Ulf
    Rovenskaya, Elena
    Thurner, Stefan
    Poledna, Sebastian
    Boza, Gergely
    Linnerooth-Bayer, Joanne
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.
    Integrating Systemic Risk and Risk Analysis Using Copulas2018In: International Journal of Disaster Risk Science, ISSN 2095-0055, Vol. 9, no 4, p. 561-567Article in journal (Refereed)
    Abstract [en]

    Systemic risk research is gaining traction across diverse disciplinary research communities, but has as yet not been strongly linked to traditional, well-established risk analysis research. This is due in part to the fact that systemic risk research focuses on the connection of elements within a system, while risk analysis research focuses more on individual risk to single elements. We therefore investigate how current systemic risk research can be related to traditional risk analysis approaches from a conceptual as well as an empirical point of view. Based on Sklar's Theorem, which provides a one-to-one relationship between multivariate distributions and copulas, we suggest a reframing of the concept of copulas based on a network perspective. This provides a promising way forward for integrating individual risk (in the form of probability distributions) and systemic risk (in the form of copulas describing the dependencies among such distributions) across research domains. Copulas can link continuous node states, characterizing individual risks, with a gradual dependency of the coupling strength between nodes on their states, characterizing systemic risk. When copulas are used for describing such refined coupling between nodes, they can provide a more accurate quantification of a system's network structure. This enables more realistic systemic risk assessments, and is especially useful when extreme events (that occur at low probabilities, but have high impacts) affect a system's nodes. In this way, copulas can be informative in measuring and quantifying changes in systemic risk and therefore be helpful in its management. We discuss the advantages and limitations of copulas for integrative risk analyses from the perspectives of modeling, measurement, and management.

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  • 38.
    Hofhansl, Florian
    et al.
    International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Chacón-Madrigal, Eduardo
    Escuela de Biología, Universidad de Costa Rica, San José, Costa Rica.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Dieckmann, Ulf
    International Institute for Applied Systems Analysis, Laxenburg, Austria; Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies (Sokendai), Hayama, Japan.
    Franklin, Oskar
    International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Mechanisms driving plant functional trait variation in a tropical forest2021In: Ecology and Evolution, E-ISSN 2045-7758, Vol. 11, no 9, p. 3856-3870Article in journal (Refereed)
    Abstract [en]

    Plant functional trait variation in tropical forests results from taxonomic differences in phylogeny and associated genetic differences, as well as, phenotypic plastic responses to the environment. Accounting for the underlying mechanisms driving plant functional trait variation is important for understanding the potential rate of change of ecosystems since trait acclimation via phenotypic plasticity is very fast compared to shifts in community composition and genetic adaptation. We here applied a statistical technique to decompose the relative roles of phenotypic plasticity, genetic adaptation, and phylogenetic constraints. We examined typically obtained plant functional traits, such as wood density, plant height, specific leaf area, leaf area, leaf thickness, leaf dry mass content, leaf nitrogen content, and leaf phosphorus content. We assumed that genetic differences in plant functional traits between species and genotypes increase with environmental heterogeneity and geographic distance, whereas trait variation due to plastic acclimation to the local environment is independent of spatial distance between sampling sites. Results suggest that most of the observed trait variation could not be explained by the measured environmental variables, thus indicating a limited potential to predict individual plant traits from commonly assessed parameters. However, we found a difference in the response of plant functional traits, such that leaf traits varied in response to canopy-light regime and nutrient availability, whereas wood traits were related to topoedaphic factors and water availability. Our analysis furthermore revealed differences in the functional response of coexisting neotropical tree species, which suggests that endemic species with conservative ecological strategies might be especially prone to competitive exclusion under projected climate change.

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  • 39.
    Isaksson, Hanna
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Advancing Systems Analysis Program, International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Complexity Science and Evolution Unit, Okinawa Institute of Science and Technology Graduate University, Japan.
    Libby, Eric
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Minor variations in multicellular life cycles have major effects on adaptation2023In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 19, no 4, article id e1010698Article in journal (Refereed)
    Abstract [en]

    Multicellularity has evolved several independent times over the past hundreds of millions of years and given rise to a wide diversity of complex life. Recent studies have found that large differences in the fundamental structure of early multicellular life cycles can affect fitness and influence multicellular adaptation. Yet, there is an underlying assumption that at some scale or categorization multicellular life cycles are similar in terms of their adaptive potential. Here, we consider this possibility by exploring adaptation in a class of simple multicellular life cycles of filamentous organisms that only differ in one respect, how many daughter filaments are produced. We use mathematical models and evolutionary simulations to show that despite the similarities, qualitatively different mutations fix. In particular, we find that mutations with a tradeoff between cell growth and group survival, i.e. "selfish" or "altruistic" traits, spread differently. Specifically, altruistic mutations more readily spread in life cycles that produce few daughters while in life cycles producing many daughters either type of mutation can spread depending on the environment. Our results show that subtle changes in multicellular life cycles can fundamentally alter adaptation.

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  • 40.
    Jang, Yun-Ting
    et al.
    Department of Biology, Lund University, Lund, Sweden.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Advancing Systems Analysis Program, International Institute for Applied Systems Analysis, Laxenburg, Austria; Complexity Science and Evolution Unit, Okinawa Institute of Science and Technology Graduate University, Kunigami, Japan.
    Pontarp, Mikael
    Department of Biology, Lund University, Lund, Sweden.
    The interactive effects of environmental gradient and dispersal shape spatial phylogenetic patterns2022In: Frontiers in Ecology and Evolution, E-ISSN 2296-701X, Vol. 10, article id 1037980Article in journal (Refereed)
    Abstract [en]

    Introduction: The emergence and maintenance of biodiversity include interacting environmental conditions, organismal adaptation to such conditions, and dispersal. To understand and quantify such ecological, evolutionary, and spatial processes, observation and interpretation of phylogenetic relatedness across space (e.g., phylogenetic beta diversity) is arguably a way forward as such patterns contain signals from all the processes listed above. However, it remains challenging to extract information about complex eco-evolutionary and spatial processes from phylogenetic patterns.

    Methods: We link environmental gradients and organismal dispersal with phylogenetic beta diversity using a trait-based and eco-evolutionary model of diversification along environmental gradients. The combined effect of the environment and dispersal leads to distinct phylogenetic patterns between subsets of species and across geographical distances.

    Results and discussion: Steep environmental gradients combined with low dispersal lead to asymmetric phylogenies, a high phylogenetic beta diversity, and the phylogenetic diversity between communities increases linearly along the environmental gradient. High dispersal combined with a less steep environmental gradient leads to symmetric phylogenies, low phylogenetic beta diversity, and the phylogenetic diversity between communities along the gradient increases in a sigmoidal form. By disentangling the eco-evolutionary mechanisms that link such interacting environment and dispersal effects and community phylogenetic patterns, our results improve understanding of biodiversity in general and help interpretation of observed phylogenetic beta diversity.

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  • 41. Johansson, Jacob
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Metz, Johan A. J.
    Dieckmann, Ulf
    Twelve fundamental life histories evolving through allocation-dependent fecundity and survival2018In: Ecology and Evolution, E-ISSN 2045-7758, Vol. 8, no 6, p. 3172-3186Article in journal (Refereed)
    Abstract [en]

    An organism's life history is closely interlinked with its allocation of energy between growth and reproduction at different life stages. Theoretical models have established that diminishing returns from reproductive investment promote strategies with simultaneous investment into growth and reproduction (indeterminate growth) over strategies with distinct phases of growth and reproduction (determinate growth). We extend this traditional, binary classification by showing that allocation-dependent fecundity and mortality rates allow for a large diversity of optimal allocation schedules. By analyzing a model of organisms that allocate energy between growth and reproduction, we find twelve types of optimal allocation schedules, differing qualitatively in how reproductive allocation increases with body mass. These twelve optimal allocation schedules include types with different combinations of continuous and discontinuous increase in reproduction allocation, in which phases of continuous increase can be decelerating or accelerating. We furthermore investigate how this variation influences growth curves and the expected maximum life span and body size. Our study thus reveals new links between eco-physiological constraints and life-history evolution and underscores how allocation-dependent fitness components may underlie biological diversity.

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  • 42. Joshi, Jaideep
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Dieckmann, Ulf
    Emergence of social inequality in the spatial harvesting of renewable public goods2020In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 16, no 1, article id e1007483Article in journal (Refereed)
    Abstract [en]

    Spatially extended ecological public goods, such as forests, grasslands, and fish stocks, are at risk of being overexploited by selfish consumers-a phenomenon widely recognized as the 'tragedy of the commons.' The interplay of spatial and ecological dimensions introduces new features absent in non-spatial ecological contexts, such as consumer mobility, local information availability, and strategy evolution through social learning in neighborhoods. It is unclear how these features interact to influence the harvesting and dispersal strategies of consumers. To answer these questions, we develop and analyze an individual-based, spatially structured, eco-evolutionary model with explicit resource dynamics. We report the following findings. (1) When harvesting efficiency is low, consumers evolve a sedentary consumption strategy, through which the resource is harvested sustainably, but with harvesting rates far below their maximum sustainable value. (2) As harvesting efficiency increases, consumers adopt a mobile 'consume-and-disperse' strategy, which is sustainable, equitable, and gives maximum sustainable yield. (3) A further increase in harvesting efficiency leads to large-scale overexploitation. (4) If costs of dispersal are significant, increased harvesting efficiency also leads to social inequality between frugal sedentary consumers and overexploitative mobile consumers. Whereas overexploitation can occur without social inequality, social inequality always leads to overexploitation. Thus, we identify four conditions that-while being characteristic of technological progress in modern societies-risk social inequality and overexploitation: high harvesting efficiency, moderately low costs of dispersal, high consumer density, and the tendency of consumers to adopt new strategies rapidly. We also show how access to global information-another feature widespread in modern societies-helps mitigate these risks.

    Author summary: Throughout history, humans have shaped ecological landscapes, which in turn have influenced human behavior. This mutual dependence is epitomized when human consumers harvest a spatially extended renewable resource. Simple models predict that, when multiple consumers harvest a shared resource, each is tempted to harvest faster than his/her peers, putting the resource at risk of overexploitation. It is unclear, however, how the interplay among resource productivity, consumer mobility, and social learning in spatial ecological public goods games influences evolved consumer behavior. Here, using an individual-based, spatially structured, eco-evolutionary model of consumers and a resource, we find that increasing resource productivity initially promotes efficient resource use by enabling mobile consumption strategies, but eventually leads to inequality and overexploitation, as overexploitative mobile consumers coexist with frugal sedentary consumers. When consumers are impatient (i.e., eager to imitate successful strategies) or myopic (i.e., unaware of conditions outside of their neighborhoods), inequality and overexploitation tend to aggravate.

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  • 43.
    Landi, Pietro
    et al.
    Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa; International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Minoarivelo, Henintsoa O.
    Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa; Centre of Excellence in Mathematical and Statistical Sciences, Wits University, Johannesburg, South Africa.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Hui, Cang
    Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa; African Institute for Mathematical Sciences, Muizenberg, South Africa.
    Dieckmann, Ulf
    International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Complexity and stability of adaptive ecological networks: a survey of the theory in community ecology2018In: Systems analysis approach for complex global challenges, Springer, 2018, p. 209-248Chapter in book (Refereed)
    Abstract [en]

    Background and Significance of the topic: The planet is changing at paces never observed before. Species extinction is happening at faster rates than ever, greatly exceeding the five mass extinctions in the fossil record. Nevertheless, human life is strongly based on services provided by ecosystems, thus the responses to global change of the planet's natural heritage are of immediate concern. Understanding the relationship between complexity and stability of ecosystems is of key importance for the maintenance of the balance of human growth and the conservation of all the natural services that ecosystems provide.

    Methodology: The concept of ecological networks and their characteristics are first introduced, followed by central and occasionally contrasting definitions of complexity and stability. The literature on the relationship between complexity and stability in different types of models and few real ecosystems is then reviewed, highlighting the theoretical debate and the lack of consensual agreement.

    Application/Relevance to systems analysis: This chapter uses ecological-network models to study the relationship between complexity and stability of natural ecosystems.

    Policy and/or practice implications: Mathematical network models can be used to simplify the vast complexity of the real world, to formally describe and investigate ecological phenomena, and to understand ecosystems propensity of returning to its functioning regime after a stress or a perturbation.

    Discussion and conclusion: The chapter concludes by summarising the importance of this line of research for the successful management and conservation of biodiversity and ecosystem services.

  • 44. Landi, Pietro
    et al.
    Minoarivelo, Henintsoa O.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Hui, Cang
    Dieckmann, Ulf
    Complexity and stability of ecological networks: a review of the theory2018In: Population Ecology, ISSN 1438-3896, E-ISSN 1438-390X, Vol. 60, no 4, p. 319-345Article, review/survey (Refereed)
    Abstract [en]

    Our planet is changing at paces never observed before. Species extinction is happening at faster rates than ever, greatly exceeding the five mass extinctions in the fossil record. Nevertheless, our lives are strongly based on services provided by ecosystems, thus the responses to global change of our natural heritage are of immediate concern. Understanding the relationship between complexity and stability of ecosystems is of key importance for the maintenance of the balance of human growth and the conservation of all the natural services that ecosystems provide. Mathematical network models can be used to simplify the vast complexity of the real world, to formally describe and investigate ecological phenomena, and to understand ecosystems propensity of returning to its functioning regime after a stress or a perturbation. The use of ecological-network models to study the relationship between complexity and stability of natural ecosystems is the focus of this review. The concept of ecological networks and their characteristics are first introduced, followed by central and occasionally contrasting definitions of complexity and stability. The literature on the relationship between complexity and stability in different types of models and in real ecosystems is then reviewed, highlighting the theoretical debate and the lack of consensual agreement. The summary of the importance of this line of research for the successful management and conservation of biodiversity and ecosystem services concludes the review.

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  • 45. Lindh, Magnus
    et al.
    Falster, Daniel S.
    Zhang, Lai
    Dieckmann, Ulf
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Latitudinal effects on crown shape evolution2018In: Ecology and Evolution, E-ISSN 2045-7758, Vol. 8, no 16, p. 8149-8158Article in journal (Refereed)
    Abstract [en]

    Large variations in crown shape are observed across the globe, from plants with wide and deep crowns to those with leaves clustered at the top. While there have been advances in the large-scale monitoring of forests, little is known about factors driving variations in crown shape with environmental conditions. Previous theoretical research suggests a gradient in crown shape with latitude, due to the effects of sun angle. Yet, it remains unclear whether such changes are also predicted under competition. Using a size-structured forest-growth model that incorporates self-shading from plants and competitive shading from their neighbors, we investigate how changes in site productivity and sun angle shape crown evolution. We consider evolution in two traits describing the top-heaviness and width-to-height ratio of crowns, shaped by trade-offs reflecting the costs and benefits of alternative architectures. In top-heavy trees, most of the leaves are at the top half of the trunk. We show that, contrary to common belief, the angle of sun beams per se has only a weak influence on crown shapes, except at low site productivity. By contrast, reduced site productivity has a strong effect, with trees growing in less productive sites keeping their leaves closer to the ground. The crown width-to-height ratio is generally higher at a lower site productivity, but this trait is not strongly influenced by any environmental factor. This theoretical analysis brings into question established beliefs about the effects of latitude on crown shapes. By introducing geometry-related growth constraints caused by shading from both the surrounding forest and the tree on itself, and costs for constructing and maintaining a three-dimensional crown, our analysis suggests crown shapes may vary with latitude, mostly via effects on overall site productivity, and less because of the angle of the sun.

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  • 46.
    Lindh, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Lund University.
    Bolmgren, Kjell
    SLU.
    Lundström, Niklas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Jonzén, Niclas
    Lund University.
    Constrained growth flips the direction of optimal phenological responses among annual plants2016In: New Phytologist, ISSN 0028-646X, E-ISSN 1469-8137, Vol. 209, no 4, p. 1591-1599Article in journal (Refereed)
    Abstract [en]

    Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory.

  • 47.
    Lindh, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Lund University.
    Falster, Daniel
    Macquarie University, Sydney, Australia.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Optimal tree-crown shapes and heights in a trade-off between light interception and crown-rise efficiency2016Manuscript (preprint) (Other academic)
    Abstract [en]

    How the shape of the tree crown is related to tree growth is still by and large unknown. Intuitively the crown shape should influence the loss of biomass during growth, as top-heavy crown shapes require the loss of branches at lower heights.

    Here we theoretically investigate how the loss of biomass during growth influences crown-rise efficiency based on the assumption that tree growth is isometric and that the leaf area is homogenously distributed with the crown. This implies that top-heavy tree crowns loose more biomass than bottom-heavy crowns. Based on this idea, we derive an analytic expression for tree crown-rise efficiency. We then investigate the trade-off between light-use efficiency and crown-rise efficiency for a range of possible crown shapes. To understand the effect of the light environment for this trade-off, we vary the sun angle and canopy vertical light gradient, and find for each such combination a range of trees that optimally balance both light-use and crown-rise efficiency, i.e., are Pareto efficient.

    Our main findings are: (1) For a stand-alone tree without external shading only a low bush-like tree is Pareto efficient. (2)We only find narrow elongated shapes when light gradient is weak and sun angle is low, but conical and spherical shapes are never found, indicating that these shapes are not light-use efficient. (3) Large variations in the Pareto efficient shapes are found in intermediate light gradients, suggesting a new mechanism for coexistence. (4) In steep light gradient we find mostly top-heavy crowns. (5)Surprisingly, hourglass shapes are found in many light conditions.

    Our results are largely consistent with field data from 36 datasets between Lat. 0 and Lat. 60, indicating that the tree crown length-to-height ratio is positively correlated to latitude, corroborating the common belief that top-heavy crowns are primarily found at high sun angles corresponding to low latitudes.

  • 48.
    Lindh, Magnus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zhang, Lai
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Falster, Daniel
    Franklin, Oskar
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Plant diversity and drought: The role of deep roots2014In: Ecological Modelling, ISSN 0304-3800, E-ISSN 1872-7026, Vol. 290, p. 85-93Article in journal (Refereed)
    Abstract [en]

    Extreme temperatures and droughts in the wake of climate change potentially threaten plant diversity. A strategy that plants use to improve survival during seasonal drought is to establish deep roots, aptly named tap roots for their ability to tap into groundwater. Little is known, however, about the role of deep roots in maintaining plant diversity. Here, we extend an established model of plants canopies by Iwasa et al. (1985), in which plants of different heights compete for light, to allow strategic investments in an optional tap root. We investigate how emerging diversity varies with water table depth, soil water gradient and drought-induced mortality rate. Having a tap root enables plants to reach deep water, thus reducing mortality, but also carries a construction cost, thus inducing a tradeoff. We find (1) that tap roots maintain plant diversity under increasing drought mortality, (2) that tap roots evolve when ground water is accessible at low to intermediate depths, (3) no viable strategies at high drought mortality and deep water table, and (4) Red Queen evolutionary dynamics in mixed communities with and without tap root.

  • 49.
    Liu, Haoqi
    et al.
    Institute of Arid Ecology and Environment, Xinjiang University; Evolution and Ecology Program, International Institute for Applied Systems Analysis.
    Wickman, Jonas
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hui, Cang
    Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University; Mathematical and Physical Biosciences, African Institute for Mathematical Sciences.
    Dieckmann, Ulf
    Evolution and Ecology Program, International Institute for Applied Systems Analysis.
    How species characteristics affect extinction through habitat lossManuscript (preprint) (Other academic)
    Abstract [en]

    With an increasing number of species at risk of extinction because of habitat loss, and extinction risks varying across species with different characteristics, it becomes essential to understand which and how species with different characteristics respond to habitat loss so as to prevent species loss. Although there exists a substantive literature on this subject, studies have so far not taken into account that natural communities have been formed through evolution, and that habitat loss is both heterogeneous in space and dynamic in time. Here, we design a spatially explicit evolving food-web model and expose the evolved communities to both random and spatially contagious habitat loss. We show that: (1) species that are large, rare, at high trophic levels, with small biomass energy intake, or having small spatial distribution differences with the autotrophic species are particularly susceptible to habitat loss. (2) Large species or species at high trophic level are more vulnerable to random habitat loss, while small species or species at low trophic levels are more vulnerable to contagious habitat loss. (3) Food webs are less robust for random habitat loss than for contagious habitat loss. (4) Reduction of body sizes is warning signal for food-web collapse. Taken together, these results facilitate identifying the most vulnerable species and the most damaging kinds of habitat loss.

  • 50.
    Liu-Helmersson, Jing
    et al.
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Epidemiology and Global Health.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Sewe, Maquins
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health.
    Rocklöv, Joacim
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health.
    Estimating past, present and future trends in the global distribution and abundance of the arbovirus vector Aedes aegypti2019In: Frontiers In Public Health, ISSN 2296-2565, Vol. 7, article id 148Article in journal (Refereed)
    Abstract [en]

    Background: Aedes aegypti is the principal vector for several important arbovirus diseases, including dengue, chikungunya, yellow fever, and Zika. While recent empirical research has attempted to identify the current global distribution of the vector, the seasonal, and longer-term dynamics of the mosquito in response to trends in climate, population, and economic development over the twentieth and the twenty-first century remains to be elucidated.

    Methods: In this study, we use a process-based mathematical model to estimate global vector distribution and abundance. The model is based on the lifecycle of the vector and its dependence on climate, and the model sensitivity to socio-economic development is tested. Model parameters were generally empirically based, and the model was calibrated to global databases and time series of occurrence and abundance records. Climate data on temperature and rainfall were taken from CRU TS3.25 (1901–2015) and five global circulation models (CMIP5; 2006–2099) forced by a high-end (RCP8.5) and a low-end (RCP2.6) emission scenario. Socio-economic data on global GDP and human population density were from ISIMIP (1950–2099).

    Findings: The change in the potential of global abundance in A. aegypti over the last century up to today is estimated to be an increase of 9.5% globally and a further increase of 20 or 30% by the end of this century under a low compared to a high carbon emission future, respectively. The largest increase has occurred in the last two decades, indicating a tipping point in climate-driven global abundance which will be stabilized at the earliest in the mid-twenty-first century. The realized abundance is estimated to be sensitive to socioeconomic development.

    Interpretation: Our data indicate that climate change mitigation, i.e., following the Paris Agreement, could considerably help in suppressing risks of increased abundance and emergence of A. aegypti globally in the second half of the twenty-first century.

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