The quest for a null model for macroecological patterns: geometry of species distributions at multiple spatial scales

Abstract

There have been several attempts to build a unified framework for macroecological patterns. However, these have mostly been based either on questionable assumptions or have had to be parameterized to obtain realistic predictions. Here, we propose a new model explicitly considering patterns of aggregated species distributions on multiple spatial scales, the property which lies behind all spatial macroecological patterns, using the idea we term 'generalized fractals'. Species' spatial distributions were modelled by a random hierarchical process in which the original 'habitat' patches were randomly replaced by sets of smaller patches nested within them, and the statistical properties of modelled species assemblages were compared with macroecological patterns in observed bird data. Without parameterization based on observed patterns, this simple model predicts realistic patterns of species abundance, distribution and diversity, including fractal-like spatial distributions, the frequency distribution of species occupancies/abundances and the species-area relationship. Although observed macroecological patterns may differ in some quantitative properties, our concept of random hierarchical aggregation can be considered as an appropriate null model of fundamental macroecological patterns which can potentially be modified to accommodate ecologically important variables.

Species abundance distribution results from a spatial analogy of central limit theorem

“…These models can produce quite realistic SADs, often close to lognormal distributions. However, the ubiquity of the SAD pattern (i.e., its independence of particular taxon specifics and other biological settings) indicates that the processes responsible are much more general, and perhaps of a statistical rather than a biological nature (7). Indeed, similar patterns have also been observed in many nonbiological systems (8).…”

“…Many such links have already been determined (7), and the mathematical connections to other macroecological patterns have been demonstrated (e.g., the species-area relationship) (25). Here, we have shown that abundance patterns can be derived using three assumptions: (i) that most species do not occur everywhere, (ii) that species abundances are positive (a trivial, but critical detail), and (iii) that these abundances are spatially autocorrelated.…”

Physiological tolerances account for range limits and abundance structure in an invasive slug

“…Indeed, recent work demonstrating that many macroecological patterns can be derived from spatial variation in aggregation (Storch et al 2008), and that human activities are fundamentally altering species ranges (Channell & Lomolino 2000;Parmesan 2006), has re-emphasized their importance. Much theory now exists concerning how range margins might be set by the interaction of ecological and evolutionary processes.…”

Can unified theories of biodiversity explain mammalian macroecological patterns?

“…The abundance of each species is described by a Gaussian bell-curve in two-dimensional space SAR; local SAD; ONR; SDR Fractal [10] simulation model of species presence/absence in hierarchically nested patches at multiple scales SAR; EAR; OAR; local SAD; global SAD MaxEnt [11] a Bayesian method taking minimal inputs (total number of species, individuals, total area and total energy) SAR; EAR; OAR; local SAD; global SAD; ONR Neutral [12] communities are made up of species with equal per capita birth and death rates. Immigration prevents mono-dominance SAR; local SAD; global SAD; SDR Metapopulation [13] each species has a characteristic population density, which contributes to its rate of migration between patches.…”

“…It is possible that the diverse range of macroecological patterns actually observed is generated by only a few common underlying mechanisms. The lack of unified theories has long been a shortcoming of ecology [7], and, excitingly, the last decade has seen the publication of at least six unifying hypotheses, unified theories of biodiversity (UTBs; table 1) [9][10][11][12][13][14]. These theories attempt to explain how a range of different macroecological patterns may be generated from the same underlying processes.…”