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Comparing distance-independent and distance-dependent competition indices for Picea abies
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Ecosystems Services and Management Program, International Institute for Applied Systems Analysis.
Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Competition between individual trees is important for forest growth. Modeling the underlying interactions is difficult and sometimes not possible. Consequently, simplified competition indices are often used as a proxy. Several studies have shown that including competition indices into growth models will improve accuracy. However, there is no consensus on which or what type of indices work well. Here, we compare several indices of two qualitatively different types: distance-independent and distance-dependent indices. These indices are incorporated into a log-linear growth model and tested against 5-year diameter growth data collected from three Norway spruce plots that each have different fertilization treatments. We find that although distance-dependent indices performed better, distance-independent indices can also perform well; R2adj = 0.66 vs. 0.62 for the best indices in each category. We find that Bella’s index to be the best distance-dependent index (the index depends on distance between competitors and their diameters) and Reineke’s index to be the best distance-independent index (this index depends on the mean quadratic diameter and density in the stand). We also find that the performance ranking of indices is consistent across three different fertilization treatments.

Keywords [en]
Competition index, Modelling, Picea abies, Diameter growth
National Category
Forest Science
Identifiers
URN: urn:nbn:se:umu:diva-156737OAI: oai:DiVA.org:umu-156737DiVA, id: diva2:1291701
Funder
Swedish Research Council Formas, 2012-1008Available from: 2019-02-26 Created: 2019-02-26 Last updated: 2019-03-19
In thesis
1. Optimal thinning: a theoretical investigation on individual-tree level
Open this publication in new window or tab >>Optimal thinning: a theoretical investigation on individual-tree level
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Paper I: In paper I, we asked how a tree should optimally allocate its resources to maximize its fitness. We let a subject tree grow in an environment shaded by nearby competing trees. The competitors were assumed to have reached maturity and had stopped growing, thus creating a static light environment for the subject tree to grow in. The light environment was modeled as a logistic function. For the growth model we used the pipe model as a foundation, linking tree width and leaf mass. This allowed us to construct a dynamic tree-growth model where the tree can allocate biomass from photosynthesis (net productivity) to either stem-height growth, crown-size growth, or reproduction (seed production). Using Pontryagin's maximum principle we derived necessary conditions for optimal biomass allocation, and on that built a heuristic allocation model. The heuristic model states that the tree should first invest into crown-size and then switch to tree height-growth, and lastly invest into crown-size before the growth investments stop and all investments are allocated to reproduction. To test our heuristic method, we used it to determine the growth in several different light environments. The results were then compared to the optimal growth trajectories. The optimal growth was determined by applying dynamic programming. Our less computationally demanding heuristic performed very well in comparison. We also found there exist a critical crown-size: if the subject tree possessed a larger crown-size, the tree would be unable to reach up to the canopy height.

Paper II: One of the most important aspects of modelling forest growth, and modelling growth of individual trees in general, is the competition between trees. A high level of competition pressure has a negative impact on the growth of individual trees. There are many ways of modelling competition, the most common one is by using a competition index. In this paper we tested 16 competition indices, in conjunction with a log-linear growth model, in terms of the mean squared error and the coefficient of determination. 5 competition indices are distance-independent (i.e. distance between the competitors are not taken into consideration) and 11 are distance-dependent. The data we used to fit our growth model, with accompanying competition index, was taken from an experimental site, in northern Sweden, of Norway spruce. The growth data for the Norway spruce comes from stands which were treated with one of two treatments, solid fertilization, liquid fertilization, or no treatment (control stand). We found that the distance-dependent indices perform better than the distance-independent. However, both the best distance-dependent and independent index performed overall well. We also found that the ranking of the indices was unaffected by the stand treatment, i.e. indices that work well for one treatment will work well for the others.

Paper III: In this paper we studied how spatial distribution and size selection affect the residual trees, after a thinning operation, in terms of merchantable wood production and stand economy. We constructed a spatially explicit individual-based forest-growth model and fitted and validated the model against empirical data for Norway spruce stands in northern Sweden. To determine the cost for the forest operation we employed empirical cost functions for harvesting and forwarding. The income from the harvested timber is calculated from volume-price lists. The thinnings were determined by three parameters: the spatial evenness of residual trees, the size selection of removed trees, and the basal area reduction. In order to find tree selections fulfilling these constraints we used the metropolis algorithm. We varied these three constrains and applied them for thinning of different initial configurations of Norway spruce stands. The initial configurations for the stands where collected from empirical data. We found that changing the spatial evenness and size selection improved the net wood production and net present value of the stand up to 8%. However, the magnitude of improvement was dependent on the initial configuration (the magnitude of improvement varied between 1.7%—8%).

Paper IV: With new technology and methods from remote sensing, such as LIDAR, becoming more prevalent in forestry, the ability to assess information on a detailed scale has become more available. Measurements for each individual tree can be more easily gathered on a larger scale. This type of data opens up for using individual-based model for practical precision forestry planning. In paper IV we used the individual-based model constructed in paper III to find the optimal harvesting time for each individual tree, such that the land expectation value is maximized. We employed a genetic algorithm to find a near optimal solution to our optimization. We optimized a number of initial Norway spruce stands (data obtained from field measurements). The optimal management strategy was to apply thinning from above. We also found that increasing the discount rate will decrease the time for final felling and increase basal area reduction for the optimal strategy. Decreasing relocation costs (the cost to bring machines to the stand) led to an increase in the number of optimal thinnings and postponed the first thinning. Our strategy was superior to both the unthinned strategy and a conventional thinning strategy, both in terms of land expectation value (>20% higher) and merchantable wood production.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2019. p. 32
Series
Research report in mathematics, ISSN 1653-0810 ; 65/19
Keywords
Forest management, Simulation, Optimization, Spatially explicit model, Individual-based model
National Category
Computational Mathematics Forest Science
Identifiers
urn:nbn:se:umu:diva-156741 (URN)978-91-7855-031-9 (ISBN)
Public defence
2019-03-29, MA121, MIT-huset, Umeå, 09:00 (English)
Opponent
Supervisors
Available from: 2019-03-08 Created: 2019-02-26 Last updated: 2019-03-04Bibliographically approved

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Fransson, Peter

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