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  • 1.
    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.

  • 2. 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.

  • 3.
    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.

  • 4.
    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.

  • 5.
    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.

  • 6.
    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)
  • 7.
    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.

  • 8.
    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.

  • 9.
    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
    Hille Ris Lambers, Reinier
    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 makemodelling a useful tool for understanding how communities develop over time and howthey respond to external perturbations. Large community-evolution models (LCEMs) areparticularly promising, since they can address both ecological and evolutionary questions, andcan give rise to richly structured and diverse model communities.Questions: Which types of models have been used to study community structure and what aretheir key features and limitations? How do adaptations and/or invasions affect communityformation? Which mechanisms promote diverse and stable communities? What are theimplications of LCEMs for management and conservation? What are the key challenges forfuture 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 andinteractions, demographic dynamics, and evolutionary dynamics. They are able to reproduceempirical community structures. They have already generated new insights, such as the dual roleof competition, which limits diversity through competitive exclusion yet facilitates diversitythrough speciation. Other critical factors determining eventual community structure arethe 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

  • 10.
    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, ISSN 2073-4336, 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.

  • 11.
    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.

  • 12.
    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.

  • 13.
    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.

  • 14.
    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)
  • 15. 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.

  • 16. 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.

  • 17.
    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, ISSN 2073-4336, 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.

  • 18. 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.

  • 19. 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)
  • 20.
    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.

  • 21. 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.

  • 22. 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, ISSN 2041-210X, 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.

  • 23. 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.

  • 24.
    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.
    Franklin, Oskar
    International Institute for Applied Systems Analysis.
    A tree’s quest for light: optimal height and diameter growth under a shading canopyManuscript (preprint) (Other academic)
    Abstract [en]

    In forests, striving for light is matter of life or death for a tree, either by growing taller towards brighter conditions or by expanding the crown to capture more of the available light. Here we present a model to predict plasticity in optimal growth paths in terms of height and crown-size under a shading canopy, as determined by fitness maximization. Based on a mechanistic tree growth model, we determine the optimal growth path among all possible trajectories using a numerical method (dynamic programming) for a range of different light environments. We then test whether this path can be understood and approximated by optimization-principles. The key findings are: (i) Maximization of net productivity based on local light conditions in each time step does not lead to an optimal growth path and may make it impossible for the tree to reach the canopy. Instead, the tree must account for the full range of expected future light levels up to the top of the canopy. (ii) This complex problem can however be solved with remarkable accuracy based on just three allocation switching points. (iii) The results can explain stratification into canopy and sub-canopy species and why canopy species often get stuck at certain size under a shading canopy. The model can be used to enable plasticity in height versus diameter growth in individual based vegetation and forestry models.  

  • 25.
    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.
    A simulation-based approach to a near optimal thinning strategy: allowing for individual harvesting times for individual treesManuscript (preprint) (Other academic)
    Abstract [en]

    As various methods for precision inventories, such as LiDAR, are becoming increasingly common the possibility of individual-tree level planning is becoming more viable. Previous studies have addressed stand management optimization, but not on an individual-tree based level. Here we present a procedure for finding, from an economic perspective, optimal number of thinning, timing for these and clear-cut, and finding for each individual tree in which thinning it should be harvested. The procedure utilizes an individual tree-based forest growth model that has been fitted to measurements of Norway spruce stands in northern Sweden. We find that the optimal management strategy is to thin from above. We test our optimal strategy against a conventional management strategy and find that it results in around 20% higher land expectation values than standard thinning regimes. Furthermore, we find that increasing the discounting rate will, for the optimal strategy, reduce the final clear-cutting age and increase the basal area reduction. Decreasing the machinery relocation cost (opening cost) increases the number of thinnings and delays the first thinning. While we focus on economic-oriented optimization, the same procedure can be applied to maximize other objectives, such as environmental goals, social goals, or even combinations of these goals.

  • 26.
    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.

  • 27. 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, ISSN 1748-9326, 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.

  • 28.
    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.

  • 29. 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 agency2019In: Journal of Risk Research, ISSN 1366-9877, E-ISSN 1466-4461Article 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.

  • 30. 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.

  • 31. 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, ISSN 2045-7758, 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.

  • 32. 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.

  • 33. 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, ISSN 2045-7758, 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.

  • 34.
    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.

  • 35.
    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.

  • 36.
    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.

  • 37.
    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.

  • 38.
    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 (Other academic)
    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.

  • 39.
    Liu-Helmersson, Jing
    et al.
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Epidemiology and Global Health.
    Rocklöv, Joacim
    Umeå University, Faculty of Medicine, Department of Public Health and Clinical Medicine, Section of Sustainable Health. Heidelberg University Medical School, Institute of Public Health, Heidelberg, Germany.
    Sewe, Maquins
    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. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Climate change may enable Aedes aegypti infestation in major European cities by 21002019In: Environmental Research, ISSN 0013-9351, E-ISSN 1096-0953, Vol. 172, p. 693-699Article in journal (Refereed)
    Abstract [en]

    Background: Climate change allows Aedes aegyptito infest new areas. Consequently, it enables the arboviruses the mosquito transmits - e.g., dengue, chikungunya, Zika and yellow fever – to emerge in previously uninfected areas. An example is the Portuguese island of Madeira during 2012–13.

    Objective: We aim to understand how climate change will affect the future spread of this potent vector, as an aidin assessing the risk of disease outbreaks and effectively allocating resources for vector control.

    Methods: We used an empirically-informed, process-based mathematical model to study the feasibility of Aedes aegypti infestation into continental Europe. Based on established global climate-change scenario data, we assess the potential of Aedes aegypti to establish in Europe over the 21st century by estimating the vector population growth rate for five climate models (GCM5).

    Results: In a low carbon emission future (RCP2.6), we find minimal change to the current situation throughout the whole of the 21st century. In a high carbon future (RCP8.5), a large parts of southern Europe risks being invaded by Aedes aegypti.

    Conclusion: Our results show that successfully enforcing the Paris Agreement by limiting global warming to below 2 °C significantly lowers the risk for infestation of Aedes aegypti and consequently of potential large-scale arboviral disease outbreaks in Europe within the 21st century.

  • 40.
    Lundström, Niklas L. P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Loeuille, Nicolas
    Meng, Xinzhu
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, China.
    Bodin, Mats
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. 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.
    Meeting yield and conservation objectives by harvesting both juveniles and adults2019In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 193, no 3, p. 373-390Article in journal (Refereed)
    Abstract [en]

    Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as "pretty good yields" (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured model and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, although our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g., basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and size structure, so that these later quantities can provide integrative signals to detect possible collapses.

  • 41.
    Lundström, Niklas L. P.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zhang, Hong
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Financial Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, PR China.
    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.
    Pareto-efficient biological pest control enable high efficacy at small costs2017In: Ecological Modelling, ISSN 0304-3800, E-ISSN 1872-7026, Vol. 364, p. 89-97Article in journal (Refereed)
    Abstract [en]

    Biological pest control is increasingly used in agriculture as an alternative to traditional chemical pest control. In many cases, this involves a one-off or periodic release of naturally occurring and/or genetically modified enemies such as predators, parasitoids, or pathogens. As the interaction between these enemies and the pest is complex and the production of natural enemies potentially expensive, it is not surprising that both the efficacy and economic viability of biological pest control are debated. Here, we investigate the performance of very simple control strategies. In particular, we show how Pareto-efficient one-off or periodic release strategies, that optimally trade off between efficacy and economic viability, can be devised and used to enable high efficacy at small economic costs. We demonstrate our method on a pest–pathogen–crop model with a tunable immigration rate of pests. By analyzing this model, we demonstrate that simple Pareto-efficient one-off and periodic release strategies are efficacious and simultaneously have profits that are close to the theoretical maximum obtained by strategies optimizing only the profit. When the immigration rate of pests is low to intermediate, one-off control strategies are sufficient, and when the immigration of pests is high, periodic release strategies are preferable. The methods presented here can be extended to more complex scenarios and be used to identify promising biological pest control strategies in many circumstances.

  • 42.
    Meng, Xinzhu
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Lundström, Niklas L.P.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Bodin, Mats
    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.
    Dynamics and management of stage-structured fish stocks2013In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 75, no 1, p. 1-23Article in journal (Refereed)
    Abstract [en]

    With increasing fishing pressures having brought several stocks to the brink of collapse, there is a need for developing efficient harvesting methods that account for factors beyond merely yield or profit. We consider the dynamics and management of a stage-structured fish stock. Our work is based on a consumer-resource model which De Roos et al. (in Theor. Popul. Biol. 73, 47-62, 2008) have derived as an approximation of a physiologically-structured counterpart. First, we rigorously prove the existence of steady states in both models, that the models share the same steady states, and that there exists at most one positive steady state. Furthermore, we carry out numerical investigations which suggest that a steady state is globally stable if it is locally stable. Second, we consider multiobjective harvesting strategies which account for yield, profit, and the recovery potential of the fish stock. The recovery potential is a measure of how quickly a fish stock can recover from a major disturbance and serves as an indication of the extinction risk associated with a harvesting strategy. Our analysis reveals that a small reduction in yield or profit allows for a disproportional increase in recovery potential. We also show that there exists a harvesting strategy with yield close to the maximum sustainable yield (MSY) and profit close to that associated with the maximum economic yield (MEY). In offering a good compromise between MSY and MEY, we believe that this harvesting strategy is preferable in most instances. Third, we consider the impact of harvesting on population size structure and analytically determine the most and least harmful harvesting strategies. We conclude that the most harmful harvesting strategy consists of harvesting both adults and juveniles, while harvesting only adults is the least harmful strategy. Finally, we find that a high percentage of juvenile biomass indicates elevated extinction risk and might therefore serve as an early-warning signal of impending stock collapse.

  • 43.
    Nonaka, Etsuko
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Department of Biology, University of New Mexico, Albuquerque, NM, USA.
    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.
    Svanbäck, Richard
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Department of Ecology and Genetics/Limnology, Uppsala University.
    Assortative mating can limit the evolution of phenotypic plasticity2014In: Evolutionary Ecology, ISSN 0269-7653, E-ISSN 1573-8477, Vol. 28, no 6, p. 1057-1074Article in journal (Refereed)
    Abstract [en]

    Phenotypic plasticity, the ability to adjust phenotype to the exposed environment, isoften advantageous for organisms in heterogeneous environments. Although the degrees ofplasticity appear limited in nature, many studies have reported low costs of plasticity invarious species. Existing studies argue for ecological, genetic, or physiological costs orselection eliminating plasticity with high costs, but have not considered costs arising fromsexual selection. Here, we show that sexual selection caused by mate choice can impede theevolution of phenotypic plasticity in a trait used for mate choice. Plasticity can remain low tomoderate even in the absence of physiological or genetic costs, when individualsphenotypically adapted to contrasting environments through plasticity can mate with eachother and choose mates based on phenotypic similarity. Because the non-choosy sex (i.e.,males) with lower degrees of plasticity are more favored in matings by the choosy sex (i.e.,females) adapted to different environments, directional selection toward higher degrees ofplasticity is constrained by sexual selection. This occurs at intermediate strengths of femalechoosiness we tested. Our results demonstrate that mate choice is a potential source of anindirect cost to phenotypic plasticity.

  • 44.
    Nonaka, Etsuko
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Department of Biology, University of New Mexico, Albuquerque, NM 87131, USA.
    Parvinen, Kalle
    Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland.
    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.
    Evolutionary suicide as a consequence of runaway selection for greater aggregation tendency2013In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 317, p. 96-104Article in journal (Refereed)
    Abstract [en]

    Aggregation of individuals is a common phenomenon in nature. By aggregating, individuals can reap benefits but may also be subject to associated costs from increased competition. The benefits of aggregation can depend on population density, which in turn can be affected by aggregation when it determines reproductive success of individuals. The Allee effect is often considered to be one of the factors that can explain the evolution of aggregation behavior. We investigated this hypothesis with a mathematical model which integrates population dynamics and evolution. Individuals gain synergistically from aggregation but suffer from scramble competition with aggregation tendency as an evolving trait. We found that aggregation behavior can stabilize the population dynamics and reduce population growth. The results show that the Allee effect alone is not sufficient for aggregative behavior to evolve as an evolutionarily stable strategy. We also found that weak local competition does not promote aggregation due to feedback from the population level: under low competition, the population can achieve high density such that aggregation becomes costly rather than beneficial. Our model instead exhibits an escalation of aggregation tendency, leading to the extinction of the population in a process known as evolutionary suicide. We conclude that for aggregation to evolve as an evolutionarily stable strategy we need to consider other factors such as inter-patch dispersal to new patches and avoidance of excessively large groups. 

  • 45.
    Nonaka, Etsuko
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Metapopulation Research Centre, Department of Biosciences, University of Helsinki, Helsinki, Finland.
    Svanbäck, Richard
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Department of Ecology and Genetics/Limnology, Uppsala University.
    Thibert-Plante, Xavier
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
    Englund, Göran
    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. Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria.
    Mechanisms by which phenotypic plasticity affects adaptive divergence and ecological speciation2015In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 186, no 5, p. E126-E143Article in journal (Refereed)
    Abstract [en]

    Phenotypic plasticity is the ability of one genotype to produce different phenotypes depending on environmental conditions. Several conceptual models emphasize the role of plasticity in promoting reproductive isolation and, ultimately, speciation in populations that forage on two or more resources. These models predict that plasticity plays a critical role in the early stages of speciation, prior to genetic divergence, by facilitating fast phenotypic divergence. The ability to plastically express alternative phenotypes may, however, interfere with the early phase of the formation of reproductive barriers, especially in the absence of geographic barriers. Here, we quantitatively investigate mechanisms under which plasticity can influence progress toward adaptive genetic diversification and ecological speciation. We use a stochastic, individual-based model of a predator-prey system incorporating sexual reproduction and mate choice in the predator. Our results show that evolving plasticity promotes the evolution of reproductive isolation under diversifying environments when individuals are able to correctly select a more profitable habitat with respect to their phenotypes (i.e., adaptive habitat choice) and to assortatively mate with relatively similar phenotypes. On the other hand, plasticity facilitates the evolution of plastic generalists when individuals have a limited capacity for adaptive habitat choice. We conclude that plasticity can accelerate the evolution of a reproductive barrier toward adaptive diversification and ecological speciation through enhanced phenotypic differentiation between diverging phenotypes.

  • 46. Ohlberger, Jan
    et al.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Dieckmann, Ulf
    Adaptive phenotypic diversification along a temperature-depth gradient2013In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 182, no 3, p. 359-373Article in journal (Refereed)
  • 47. Parvinen, Kalle
    et al.
    Brännstrom, 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.
    Evolution of Site-Selection Stabilizes Population Dynamics, Promotes Even Distribution of Individuals, and Occasionally Causes Evolutionary Suicide2016In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 78, no 8, p. 1749-1772Article in journal (Refereed)
    Abstract [en]

    Species that compete for access to or use of sites, such as parasitic mites attaching to honey bees or apple maggots laying eggs in fruits, can potentially increase their fitness by carefully selecting sites at which they face little or no competition. Here, we systematically investigate the evolution of site-selection strategies among animals competing for discrete sites. By developing and analyzing a mechanistic and population-dynamical model of site selection in which searching individuals encounter sites sequentially and can choose to accept or continue to search based on how many conspecifics are already there, we give a complete characterization of the different site-selection strategies that can evolve. We find that evolution of site-selection stabilizes population dynamics, promotes even distribution of individuals among sites, and occasionally causes evolutionary suicide. We also discuss the broader implications of our findings and propose how they can be reconciled with an earlier study (Nonaka et al. in J Theor Biol 317:96-104, 2013) that reported selection toward ever higher levels of aggregation among sites as a consequence of site-selection.

  • 48.
    Pontarp, Mikael
    et al.
    Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences. Department of Biology, Lund University, Lund, Sweden; Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.
    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.
    Petchey, Owen L.
    Inferring community assembly processes from macroscopic patterns using dynamic eco-evolutionary models and Approximate Bayesian Computation (ABC)2019In: Methods in Ecology and Evolution, ISSN 2041-210X, E-ISSN 2041-210X, Vol. 10, no 4, p. 450-460Article, review/survey (Refereed)
    Abstract [en]

    Statistical techniques exist for inferring community assembly processes from community patterns. Habitat filtering, competition, and biogeographical effects have, for example, been inferred from signals in phenotypic and phylogenetic data. The usefulness of current inference techniques is, however, debated as a mechanistic and causal link between process and pattern is often lacking, and evolutionary processes and trophic interactions are ignored.

    Here, we revisit the current knowledge on community assembly across scales and, in line with several reviews that have outlined challenges associated with current inference techniques, we identify a discrepancy between the current paradigm of eco-evolutionary community assembly and current inference techniques that focus mainly on competition and habitat filtering. We argue that trait-based dynamic eco-evolutionary models in combination with recently developed model fitting and model evaluation techniques can provide avenues for more accurate, reliable, and inclusive inference. To exemplify, we implement a trait-based, spatially explicit eco-evolutionary model and discuss steps of model modification, fitting, and evaluation as an iterative approach enabling inference from diverse data sources.

    Through a case study on inference of prey and predator niche width in an eco-evolutionary context, we demonstrate how inclusive and mechanistic approaches-eco-evolutionary modelling and Approximate Bayesian Computation (ABC)-can enable inference of assembly processes that have been largely neglected by traditional techniques despite the ubiquity of such processes.

    Much literature points to the limitations of current inference techniques, but concrete solutions to such limitations are few. Many of the challenges associated with novel inference techniques are, however, already to some extent resolved in other fields and thus ready to be put into action in a more formal way for inferring processes of community assembly from signals in various data sources.

  • 49.
    Poos, Jan Jaap
    et al.
    Evolution and Ecology Program, International Institute for Applied Systems Analysis, A-2361, Laxenburg, Austria.
    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, A-2361, Laxenburg, Austria.
    Harvest-induced maturation evolution under different life-history trade-offs and harvesting regimes2011In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 279, no 1, p. 102-112Article in journal (Refereed)
    Abstract [en]

    The potential of harvesting to induce adaptive changes in exploited populations is now increasingly recognized. While early studies predicted that elevated mortalities among larger individuals select for reduced maturation size, recent theoretical studies have shown conditions under which other, more complex evolutionary responses to size-selective mortality are expected. These new predictions are based on the assumption that, owing to the trade-off between growth and reproduction, early maturation implies reduced growth. Here we extend these findings by analyzing a model of a harvested size-structured population in continuous time, and by systematically exploring maturation evolution under all three traditionally acknowledged costs of early maturation: reduced fecundity, reduced growth, and/or increased natural mortality. We further extend this analysis to the two main types of harvest selectivity, with an individual's chance of getting harvested depending on its size and/or maturity stage. Surprisingly, we find that harvesting mature individuals not only favors late maturation when the costs of early maturation are low, but promotes early maturation when the costs of early maturation are high. To our knowledge, this study therefore is the first to show that harvesting mature individuals can induce early maturation.

  • 50.
    Rani, Raffaele
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Abramowicz, Konrad
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Falster, Daniel S.
    Sterck, Frank
    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.
    Effects of bud-flushing strategies on tree growth2018In: Tree Physiology, ISSN 0829-318X, E-ISSN 1758-4469, Vol. 38, no 9, p. 1384-1393Article in journal (Refereed)
    Abstract [en]

    Allocation of carbohydrates between competing organs is fundamental to plant development, growth and productivity. Carbohydrates are synthesized in mature leaves and distributed via the phloem vasculature to developing buds where they are consumed to produce new biomass. The distribution and mass-allocation processes within the plant remain poorly understood and may involve complex feedbacks between different plant functions, with implications for the emergent structure of the plant. Here, we investigate how the order in which dormant buds are flushed affects the development of tree size and reproductive output during the first 20 years of growth in full light and shaded canopy environments. We report the following findings: (i) Bud-flushing strategies strongly affect the temporal dynamics of height, mass and the size of reproduction pool, as well as the resulting architectures. (ii) Bud-flushing strategies affect tree growth by altering the rate of growth and final size of trees. (iii) No single bud-flushing strategy performs best when both the size and allocation for reproduction of the resulting trees are compared. However, we observe that the strategy that optimizes the net carbon gain for the entire tree architecture always results in a high reproduction output. (iv) Branch turnover and meristem regeneration enhance the performance of certain strategies with respect to the measured quantities. These results highlight the importance of employing generic models of architecture (i.e., non-species-specific) to identify general mechanisms of carbon allocation and the spatial distribution of newly formed biomass in growing trees.

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