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Harnessing uncertainty to approximate mechanistic models of interspecific interactions. (English) Zbl 1405.92280
Summary: Because the Lotka-Volterra competitive equations posit no specific competitive mechanisms, they are exceedingly general, and can theoretically approximate any underlying mechanism of competition near equilibrium. In practice, however, these models rarely generate accurate predictions in diverse communities. We propose that this difference between theory and practice may be caused by how uncertainty propagates through Lotka-Volterra systems. In approximating mechanistic relationships with Lotka-Volterra models, associations among parameters are lost, and small variation can correspond to large and unrealistic changes in predictions. We demonstrate that constraining Lotka-Volterra models using correlations among parameters expected from hypothesized underlying mechanisms can reintroduce some of the underlying structure imposed by those mechanisms, thereby improving model predictions by both reducing bias and increasing precision. Our results suggest that this hybrid approach may combine some of the generality of phenomenological models with the broader applicability and meaningful interpretability of mechanistic approaches. These methods could be useful in poorly understood systems for identifying important coexistence mechanisms, or for making more accurate predictions.
MSC:
92D40 Ecology
92D25 Population dynamics (general)
Software:
zoverw
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[1] Anderson, G. W.; Guionnet, A.; Zeitouni, O., Real Wigner matrices: traces, moments and combinatorics, (An Introduction to Random Matrices, (2010), Cambridge University Press New York), 6-34
[2] Bairey, E.; Kelsic, E. D.; Kishony, R., High-order species interactions shape ecosystem diversity, Nature Commun., 7, 12285, (2016)
[3] Barabás, G.; Allesina, S., Predicting global community properties from uncertain estimates of interaction strengths, J. R. Soc. Interface, 12, (2015)
[4] Bates, D., Maechler, M., 2016. Matrix: Sparse and Dense Matrix Classes and Methods.
[5] Black, A. J.; McKane, A. J., Stochastic formulation of ecological models and their applications, Trends Ecol. Evol., 27, 337-345, (2012)
[6] Bolker, B. M.; Pacala, S. W., Spatial moment equations for plant competition: understanding spatial strategies and the advantages of short dispersal, Am. Nat., 153, 575-602, (1999)
[7] Carrara, F.; Giometto, M.; Seymour, A.; Rinaldo, A.; Altermatt, F., Inferring species interactions in ecological communities: a comparison of methods at different levels of complexity, Methods Ecol. Evol., 6, 895-906, (2015)
[8] Chesson, P., Macarthur’s consumer-resource model, Theor. Popul. Biol., 37, 26-38, (1990) · Zbl 0689.92016
[9] Chesson, P., Mechanisms of maintenance of species diversity, Annu. Rev. Ecol. Syst., 31, 343-366, (2000)
[10] Clark, A. T.; Lehman, C.; Tilman, D., Identifying mechanisms that structure ecological communities by snapping model parameters to empirically observed tradeoffs, Ecol. Lett., 21, 494-505, (2018)
[11] Detto, M.; Muller-Landau, H. C., Fitting ecological process models to spatial patterns using scalewise variances and moment equations, Am. Nat., 181, (2013)
[12] Dormann, C. F., On community matrix theory in experimental plant ecology, Web Ecol., 8, 108-115, (2008)
[13] Dormann, C. F.; Roxburgh, S. H., Experimental evidence rejects pairwise modelling approach to coexistence in plant communities, Proc. R. Soc. B, 272, 1279-1285, (2005)
[14] Gause, G. F., Experimental analysis of vito volterra’s mathematical theory of the struggle for existence, Science, 79, 16-17, (1934)
[15] Grilli, J.; Barabás, G.; Michalska-Smith, M. J.; Allesina, S., Higher-order interactions stabilize dynamics in competitive network models, Nature, (2017)
[16] Grimm, V.; Ayllón, D.; Railsback, S. F., Next-generation individual-based models integrate biodiversity and ecosystems: yes we can, and yes we must, Ecosystems, 20, 229-236, (2016)
[17] Grimmett, G.; Stirzaker, D., Probability and random processes, (2001), Oxford University Press Oxford, New York · Zbl 1015.60002
[18] Haygood, R., Coexistence in macarthur-style consumer-resource models, Theor. Popul. Biol., 61, 215-223, (2002) · Zbl 1037.92038
[19] Lehman, C. L.; Tilman, D., Biodiversity, stability, and productivity in competitive communities, Am. Nat., 156, 534-552, (2000)
[20] Levin, S. A., Community equilibria and stability, and an extension of the competitive exclusion principle, Am. Nat., 104, 413-423, (1970)
[21] Levine, J. M.; Bascompte, J.; Adler, P. B.; Allesina, S., Beyond pairwise mechanisms of species coexistence in complex communities, Nature, 546, 56-64, (2017)
[22] Litchman, E.; Klausmeier, C. A., Trait-based community ecology of phytoplankton, Annu. Rev. Ecol. Evol. Syst., 39, 615-639, (2008)
[23] Loreau, M., Does functional redundancy exist?, Oikos, 104, 606-611, (2004)
[24] Lotka, A., Growth of mixed populations, J. Wash. Acad. Sci., 22, 461-469, (1932)
[25] MacArthur, R. H., Population ecology of some warblers of northeastern coniferous forests, Ecology, 39, 599-619, (1958)
[26] MacArthur, R., Species packing and competitive equilibrium for many species, Theor. Popul. Biol., 1, 1-11, (1970)
[27] MacArthur, R. H.; Levins, R., Limiting similarity convergence and divergence of coexisting species, Am. Nat., 101, 377-385, (1967)
[28] Marsaglia, G., Ratios of normal variables, J. Stat. Softw., 16, (2006) · Zbl 0126.35302
[29] May, R. M., Stability and complexity in model ecosystems, (1973), Princeton University Press Princeton
[30] May, R. M.; Anderson, R. M., Transmission dynamics of HIV infection, Nature, 326, 137-142, (1987)
[31] Mayfield, M. M.; Stouffer, D. B., Higher-order interactions capture unexplained complexity in diverse communities, Nat. Ecol. Evol., 1, 0062, (2017)
[32] Meszéna, G.; Gyllenberg, M.; Pásztor, L.; Metz, J. A.J., Competitive exclusion and limiting similarity: A unified theory, Theor. Popul. Biol., 69, 68-87, (2006) · Zbl 1085.92048
[33] Michalet, R.; Chen, S.; An, L.; Wang, X.; Wang, Y.; Guo, P.; Ding, C.; Xiao, S., Communities: are they groups of hidden interactions?, J. Veg. Sci., 26, 207-218, (2015)
[34] Miller, T. E., Direct and indirect species interactions in an early old-field plant community, Am. Nat., 143, 1007-1025, (1994)
[35] Palamara, G. M.; Carrara, F.; Smith, M. J.; Petchey, O. L., The effects of demographic stochasticity and parameter uncertainty on predicting the establishment of introduced species, Ecol. Evol., 6, 8440-8451, (2016)
[36] Park, T., The effect of differentially conditioned flour upon the fecundity and fertility of tribolium confusum duval, J. Exp. Zool., 73, 393-404, (1936)
[37] Reich, P. B., The world-wide ‘fast-slow’ plant economics spectrum: a traits manifesto, J. Ecol., 102, 275-301, (2014)
[38] Roff, D. A.; Fairbairn, D. J., The evolution of trade-offs: where are we?, J. Evol. Biol., 20, 433-447, (2007)
[39] Roxburgh, S. H.; Wilson, J. B., Stability and coexistence in a lawn community: mathematical prediction of stability using a community matrix with parameters derived from competition experiments, Oikos, 88, 395-408, (2000)
[40] Schaffer, W. M., Ecological abstberaction: the consequences of reduced dimensionality in ecological models, Ecol. Monograph, 51, 383-401, (1981)
[41] Schoener, T. W., Some methods for calculating competition coefficients from resource-utilization spectra, Am. Nat., 108, 332-340, (1974)
[42] Tilman, D., (Resource Competition and Community Structure, (1982), Princeton University Press Princeton NJ), 190-204
[43] Tilman, D., Constraints and tradeoffs - toward a predictive theory of competition and succession, Oikos, 58, 3-15, (1990)
[44] Tilman, D., Competition and biodiversity in spatially structured habitats, Ecology, 75, 2-16, (1994)
[45] Tilman, D., Diversification, biotic interchange, and the universal trade-off hypothesis, Am. Nat., 178, 355-371, (2011)
[46] Vandermeer, J. H., The competitive structure of communities: an experimental approach with protozoa, Ecology, 50, 362-371, (1969)
[47] Wangersky, P. J., Lotka-Volterra population models, Annu. Rev. Ecol. Syst., 9, 189-218, (1978)
[48] Weigelt, A.; Schumacher, J.; Walther, T.; Bartelheimer, M.; Steinlein, T.; Beyschlag, W., Identifying mechanisms of competition in multi-species communities, J. Ecol., 95, 53-64, (2007)
[49] Wilbur, H. M., Competition, predation, and the structure of the ambystoma-rana sylvatica community, Ecology, 53, 3-21, (1972)
[50] Wright, I. J.; Reich, P. B.; Westoby, M.; Ackerly, D. D.; Baruch, Z.; Bongers, F.; Cavender-Bares, J.; Chapin, T.; Cornelissen, J. H.C.; Diemer, M.; Flexas, J.; Garnier, E.; Groom, P. K.; Gulias, J.; Hikosaka, K.; Lamont, B. B.; Lee, T.; Lee, W.; Lusk, C.; Midgley, J. J.; Navas, M.-L.; Niinemets, Ü.; Oleksyn, J.; Osada, N.; Poorter, H.; Poot, P.; Prior, L.; Pyankov, V. I.; Roumet, C.; Thomas, S. C.; Tjoelker, M. G.; Veneklaas, E. J.; Villar, R., The worldwide leaf economics spectrum, Nature, 428, 821-827, (2004)
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