Abstract
Research on species interactions has generally assumed that species have a fixed interaction and therefore linear or non-linear parametric regression models (e.g. exponential, logistic) have been widely used to describe the species interaction. However, these models that describe the relationship between interacting species as a specific functional response might not be appropriate for real biological communities, for instance, in a chaotic system, when the species relationship varies among different situations. To allow a more accurate description of the relationship, we developed a species correlation model with varying coefficient analysis, in which a non-parametric estimation is applied to identify, as a function of related factors, variation in the correlation coefficient. This was applied to a fig-fig wasp model system. When the effect of the factors on the relationship can be described with parameters, the new method reduces to traditional parametric correlation analysis. In this way, the new method is more general and flexible for empirical data analyses, but different by allowing investigation of whether a species interaction varies with respect to factors, and of the factors that maintain or change the species interaction. This method will have important applications in both theoretical and applied research (e.g. epidemiology, community management).
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References
Li X C, Wang Z H, Wang W L. Biology Statistics (in Chinese). Beijing: Science Press, 2000
McCullagh P, Nelder J A. Generalized Linear Models (2nd ed). London: Chapman and Hall, 1989
Krebs J K. Ecology: The Experimental Analysis of Distribution and Abundance (2nd ed). New York: Harper and Row Press, 1978
May R M. Simple mathematical models with very complicated dynamics. Nature, 1976, 261: 459–467
Sun R Y. Fundamentals of Animal Ecology (in Chinese). Beijing: Beijing Normal University Press, 1992
Ma Z E. Theoretical Models of Population Ecology (in Chinese). Hefei: An-hui Education Press, 1996
Frank S A. The price equation. Fisher’s fundamental theorem, kin selection and causal analysis. Evolution, 1997, 51: 1712–1729
Molles M C. Ecology: Concepts and Applications. New York: McGraw-Hill Companies, 1999
Whittingham M J, Stephen P A, Bradbury R B, et al. Why do we still use stepwise modeling in ecology and behaviour? J Anim Ecol, 2006, 75: 1182–1189
Fisher R A. The Genetical Theory of Natural Selection. Clarendon: Oxford, 1930
Price G R. Selection and covariance. Nature, 1970, 227: 520–521
Queller D C. A general model for kin selection. Evolution, 1992, 46: 376–380
Stiling P D. Ecology: Theories and Applications. New Jersey: Prentice Hall, Upper Saddle River, 1996
Draper N R, Smith H. Applied Regression Analysis. New York: John Wiley and Sons, 1981
Raubenheimer D. Problems with ratio analysis in nutritional studies. Functional Ecol, 1995, 9: 21–29
Inouye B D. Response of surface experiment design for investigating interspecific competition. Ecology, 2001, 82: 2696–2706
Travis J, Trexler J C. Interactions among factors affecting growth, development and survival in experimental populations of Bufo terrestris (Anura: Bufonidae). Oecologia (Berlin), 1986, 69: 110–116
Trexler J C, McCulloch C E, Travis J. How can the functional response best be determined? Oecologia, 1988, 76: 206–214
Holling C S. Resilience and stability of ecological systems. Ann Rev Ecol Syst, 1973, 4: 1–23
May R M. Theoretical Ecology: Principles and Applications. Oxford: Blackwell Scientific Publishers, 1981
Nowak A M, Bonhoeffer S, May R. Spatial games and the maintenance of cooperation. Proc Natl Acad Sci USA, 1994, 91: 4877–4881
Jiang L, Morin P J. Temperature fluctuation facilitates coexistence of competing species in experimental microbial communities. J Anim Ecol, 2007, 76: 660–668
Hofbauer J, Sigmund K. Evolutionary Games and Population Dynamics. Cambridge: Cambridge University Press, 1998
Hanski I, Turchin P, Korpimaki E, et al. Population oscillations of boreal rodents: Regulation by mustelid predators lead to chaos. Nature, 1993, 364: 232–235
Ives A R. Predicting the response of populations to environmental change. Ecology, 1995, 76: 926–941
Gonzalez A, Descamps-Julien B. Population and community variability in randomly fluctuating environments. Oikos, 2004, 106: 105–116
Wang R W, Shi L, Ai S M, et al. Trade-off between the reciprocal mutualists: Local resource availability oriented interaction in fig/fig wasp mutualism. J Anim Ecol, 2008, 77: 616–623
Hassell M P, Comins H N, May R M. Spatial structure and chaos in insect population dynamics. Nature, 1991, 353: 255–258
Thompson J N, Fernandez C C. Temporal dynamics of antagonism and mutualism in a geographically variable plant-insect interaction. Ecology, 2006, 87: 103–112
Smith J M, White A, Sherratt A J, et al. Disease effects on reproduction can cause population cycles in seasonal environments. J Anim Ecol, 2008, 77: 378–389
Wang R W, Yang J X, Yang D R. Seasonal changes in the trade-off among the fig-supported wasps and viable seeds in figs and their evolutionary implications. J Integr Plant Biol, 2005, 47: 144–155
Frank S A. Genetics of mutualism: The evolution of altruism between species. J Theor Biol, 1994, 170: 393–400
Sun B F, Wang R W, Hu Z, et al. The relation between two non-pollinating wasps oviposition and the fruit abscission on Ficus racemosa. Acta Ecol Sin, 2009, 29: 1–6
Rudolf V H W. Consequences of size structure in the prey for predator-prey dynamics: The composite functional response. J Anim Ecol, 2008, 77: 520–528
Wang R W, Sun B F. The seasonal change in the structure of fig-wasp community of figs and its implication for conservation. Symbiosis, 2009, 47: 77–83
Wang R W, Ridley J, Sun B F, et al. Interference competition and high temperatures reduce the virulence of fig wasps and stabilize a fig-wasp mutualism. PLoS ONE, 2009, 4: e7802
Hastie T, Tibshirani R. Varying-coefficient models (with discussion). J Roy Stati Soc B, 1993, 55: 757–796
Epanechnikov V. Nonparametric estimates of a multivariate probability density. Theory Probab Appl, 1969, 14: 153–158
Haerdle W. Applied Nonparametric Regression. Berlin: Springer, 1994
Zhu L X. Nonparametric Monte Carlo Tests and Their Applications. New York: Springer, 2005
Janzen D H. How to be a fig. Ann Rev Ecol Syst, 1979, 10: 13–51
Wiebes J T. Co-evolution of figs and their insect pollinators. Ann Rev Ecol Syst, 1979, 10: 1–12
Bronstein J L, Hossaert-McKey M. Variation in reproductive success within a subtropical fig-pollinator mutualism. J Evol Biol, 1996, 23: 433–446
Anstett M C, Bronstein J L, Hossaert-McKey M. Resource allocation: A conflict in the fig-fig wasp mutualism. J Evol Biol, 1996, 9: 417–428
Herre E A, West S A. Conflict of interest in a mutualism: Documenting the elusive fig wasp-seed trade-off. Proc Roy Soc B, 1997, 264: 1501–1507
Maynard S J. Evolution and the Theory of Games. Cambridge: Cambridge University Press, 1982
Nowak A M, May M R. Evolutionary games and spatial chaos. Nature, 1992, 359: 826–829
Doebeli M, Knowlton N. The evolution of interspecific mutualisms. Proc Natl Acad Sci USA, 1998, 95: 8676–8680
Bronstein J L. Seed predator as mutualists: Ecology and evolution of the fig-pollinator interaction. In: Bernays E, ed. Insect-Plant Interaction. Boca Raton: CRC Press, 1992
Herre E A, Knowlton N, Mueller U G, et al. The evolution of mutualisms: Exploring the paths between conflict and cooperation. Trend Ecol Evol, 1999, 14: 49–53
Sugihara G, May R M. Non-linear forecasting as a way of distinguishing chaos from measurement error in time series. Nature, 1990, 344: 734–741
Wang R W, Sun B F, Zheng Q, et al. Asymmetric interaction and indeterminate fitness correlation between cooperative partners in the fig/fig wasp mutualism. J Roy Soc Interface, 2011, doi: 10.1098/rsif.2011.0063
Nefdt R J C, Compton S G. Regulation of seed and pollinator production in the fig-fig wasp mutualism. J Anim Ecol, 1996, 65: 170–182
Wang R W, Sun B F, Zheng Q. Diffusive co-evolution and mutualism maintenance mechanisms in a fig-fig wasp system. Ecology, 2010, 91: 1308–1316
Wang R W, Zheng Q. Structure of a figs wasp community: Temporal segregation of oviposition and larval diets. Symbiosis, 2008, 45: 113–116
Wang R W, Sun B F. The seasonal change in the structure of fig-wasp community of figs and its implication for conservation. Symbiosis, 2009, 47: 77–83
Nowak A M. An evolutionary stable strategy may be inaccessible. J Theor Biol, 1990, 142: 237–241
Wang R W, Shi L. The evolution of cooperation in asymmetric systems. Sci China Life Sci, 2010, 53: 139–149
Wang R W, He J Z, Wang Y Q, et al. Asymmetric interaction will facilitate the evolution of cooperation. Sci China Life Sci, 2010, 52: 1041–1046
Tilman D, Wedin D. Oscillation and chaos in dynamics of a perennial grass. Nature, 1991, 353: 653–655
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Shi, L., Wang, R., Zhu, L. et al. Varying coefficient analysis for indeterminate species interactions with non-parametric estimation, exemplifying with a fig-fig wasp system. Chin. Sci. Bull. 56, 2545–2552 (2011). https://doi.org/10.1007/s11434-011-4564-2
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DOI: https://doi.org/10.1007/s11434-011-4564-2