David Storch (Center for Theoretical Study)
Abstract. Looking for invariances proved to be very successful way of scientific inquiry, especially in physics. In ecology, little effort has been devoted to systematic exploration of invariances or to using invariances as a criterion to reveal generality of the patterns. There are several patterns in ecology that are assumed to be universal, namely (1) spatial scaling of biodiversity (the species-area relationship), (2) the frequency distribution of species’ abundances, or (3) large-scale climate-related trends of diversity (e.g. latitudinal decrease of species richness from the equator to the poles). The assumed universality of these patterns implies that they should be invariant against changes in taxonomic delimitation of the study group and/or spatial scale; otherwise they would apply only for a particular taxonomic category and/or particular location and spatial scale. However, I will show that classical forms of macroecological patterns (e.g. power-law species-area relationship or lognormal species-abundance distribution) cannot be invariant against changing taxonomic level or scale, so they cannot be really universal. Similarly, alternative patterns predicted using recent macroecological theories (e.g. Maximum Entropy theory) lack universality, i.e. they depend on particular delimitation of study groups. However, the universal form of macroecological patterns can be theoretically derived on the basis of their assumed invariance or their particular variation with scale or taxonomic scope. The decomposition of the patterns using variously delimited taxa and an analysis of taxonomic structure of the patterns provides important insights into their nature and possible causes, regardless of whether they are truly universal or not.
References
Šizling A.L., Kunin W.E. & Storch D. (2013). Taxon invariances, maximum entropy, and the species-area relationship. American Naturalist 181: 288-290.
Storch D., Keil P. & Jetz W. (2012). Universal species-area and endemics-area relationships at continental scales. Nature 488: 78-81.
Šizling A.L., Kunin W.E., Šizlingová E., Reif J. & Storch D. (2011). Between geometry and biology: the problem of universality of the species-area relationship. American Naturalist 178: 602-611.
Isaac N.J.B., Storch D. & Carbone C. (2011). Taxonomic variation in size-density relationships challenges the notion of energy equivalence. Biology Letters 7: 615-618.
Šizling A.L., Storch D., Reif J. & Gaston K.J. (2009): Invariance in species-abundance distribution. Theoretical Ecology, 2: 89-103.
Šizling A.L., Storch D., Šizlingová E., Reif J. & Gaston K.J. (2009): Species-abundance distribution results from a spatial analogy of central limit theorem. Proceedings of the National Academy of Sciences of the U.S.A., 106: 6691-6695.
Storch D. & Šizling A.L. (2008): The concept of taxon invariance in ecology: do diversity patterns vary with changes in taxonomic resolution? Folia Geobotanica, 43: 329-344.
Šizling A.L. & Storch D. (2004): Power-law species-area relationships and self-similar species distributions within finite areas. Ecology Letters 7: 60-68.