Modeling spatial aggregation of finite populations.

Accurate description of spatial distribution of species is essential for correctly modeling macroecological patterns and thus to infer mechanisms of species coexistence. The Poisson and negative binomial distribution (NBD) are most widely used to respectively model random and aggregated distributions of species in infinitely large areas. As a finite version of the Poisson distribution, the binomial distribution is used to model random distribution of species populations in finite areas. Despite that spatial aggregation is the most widespread pattern and no species in nature are distributed in infinitely large areas, no model is currently available to describe spatial aggregation for species distributed in finite areas. Here we develop a finite counterpart of the NBD to model aggregated species in finite landscapes. Similar to the NBD, this new model also has a parameter k measuring spatial aggregation. When k --> infinity, this model becomes the binomial distribution; when study area approaches infinite, it becomes the NBD. This model was extensively evaluated against the distributions of over 300 tree species in a 50-ha stem-mapping plot from Barro Colorado Island, Panama. The results show that when sampling area is small (relative to the study area), the new model and the NBD are of little difference. But the former correctly models spatial distribution at the finite limit at which the NBD fails. We reveal serious theoretical pathologies by using infinite models to approximate finite distribution and show the theoretical and practical advantages for using the new finite model for modeling species-area relationships, species occupancy and spatial distribution of rare species.

[1]  J. Connell.  On the role of the natural enemies in preventing competitive exclusion in some marine animals and in rain forest trees , 1971 .

[2]  J. Illian,et al.  Ecological information from spatial patterns of plants: insights from point process theory , 2009 .

[3]  B. D. Coleman.  On random placement and species-area relations , 1981 .

[4]  O. Arrhenius,et al.  Species and Area , 1921 .

[5]  Kevin J Gaston,et al.  Estimating Species Abundance from Occurrence , 2000, The American Naturalist.

[6]  C. D. Kemp,et al.  Random Counts in Models and Structures. , 1971 .

[7]  Stephen P. Hubbell,et al.  Beta-Diversity in Tropical Forest Trees , 2002, Science.

[8]  F. Chapin,et al.  Competition causes regular spacing of alder in Alaskan shrub tundra , 1989, Oecologia.

[9]  Stephen P. Hubbell,et al.  Habitat associations of trees and shrubs in a 50‐ha neotropical forest plot , 2001 .

[10]  J. Andrew Royle,et al.  ESTIMATING SITE OCCUPANCY RATES WHEN DETECTION PROBABILITIES ARE LESS THAN ONE , 2002, Ecology.

[11]  Jessica Green,et al.  ENDEMICS–AREA RELATIONSHIPS: THE INFLUENCE OF SPECIES DOMINANCE AND SPATIAL AGGREGATION , 2003 .

[12]  R. Condit,et al.  Tree species distributions and local habitat variation in the Amazon: large forest plot in eastern Ecuador , 2004 .

[13]  Joshua B Plotkin,et al.  Seed Dispersal and Spatial Pattern in Tropical Trees , 2006, PLoS biology.

[14]  S. Hubbell,et al.  Spatial patterns in the distribution of tropical tree species. , 2000, Science.

[15]  J. Andrew Royle,et al.  Modelling occurrence and abundance of species when detection is imperfect , 2005 .

[16]  David Kenfack,et al.  A general framework for the distance–decay of similarity in ecological communities , 2008, Ecology letters.

[17]  D. Janzen.  Herbivores and the Number of Tree Species in Tropical Forests , 1970, The American Naturalist.

[18]  Ian P. Woiwod,et al.  THE DENSITY-DEPENDENCE OF SPATIAL BEHAVIOUR AND THE RARITY OF RANDOMNESS , 1978 .

[19]  S. Hubbell,et al.  The unified neutral theory of biodiversity and biogeography at age ten. , 2011, Trends in ecology & evolution.

[20]  Joshua B. Plotkin,et al.  SAMPLING THE SPECIES COMPOSITION OF A LANDSCAPE , 2002 .

[21]  Annette Ostling,et al.  A THEORY OF SPATIAL STRUCTURE IN ECOLOGICAL COMMUNITIES AT MULTIPLE SPATIAL SCALES , 2005 .

[22]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[23]  Stephen P. Hubbell,et al.  Tree Dispersion, Abundance, and Diversity in a Tropical Dry Forest , 1979, Science.

[24]  Pierre Legendre,et al.  Distribution patterns of tree species in a Malaysian tropical rain forest , 1997 .

[25]  C. I. Bliss,et al.  FITTING THE NEGATIVE BINOMIAL DISTRIBUTION TO BIOLOGICAL DATA AND NOTE ON THE EFFICIENT FITTING OF THE NEGATIVE BINOMIAL , 1953 .

[26]  H. Howe.  Scatter-and clump-dispersal and seedling demography: hypothesis and implications , 1989, Oecologia.

[27]  F. He,et al.  Spatial distributions of tree species in a subtropical forest of China , 2009 .

[28]  Andreas Huth,et al.  Recruitment in Tropical Tree Species: Revealing Complex Spatial Patterns , 2009, The American Naturalist.

[29]  J. Harte,et al.  Maximum entropy and the state-variable approach to macroecology. , 2008, Ecology.

[30]  Xiangcheng Mi,et al.  Species-area relationships explained by the joint effects of dispersal limitation and habitat heterogeneity. , 2009, Ecology.

[31]  S. Hurlbert.  Spatial distribution of the montane unicorn , 1990 .

[32]  J. Fragoso,et al.  LONG‐DISTANCE SEED DISPERSAL BY TAPIRS INCREASES SEED SURVIVAL AND AGGREGATES TROPICAL TREES , 2003 .

[33]  Joshua B Plotkin,et al.  A statistical theory for sampling species abundances. , 2007, Ecology letters.

[34]  Pierre Legendre,et al.  SPECIES DIVERSITY PATTERNS DERIVED FROM SPECIES–AREA MODELS , 2002 .

[35]  K. Gaston,et al.  Species-range-size distributions: patterns, mechanisms and implications. , 1996, Trends in ecology & evolution.