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• Probability distribution of species' extinction time derived for a neutral model. • The distribution nearly always gives overestimates of tree species ages. • Probability distributions of species richness derived for two neutral models. • The distributions show that species richness has low variation in large communities. • Formulae derived for immigration and extinction curves from a neutral model. In community ecology, neutral models make the assumption that species are equivalent, such that species abundances differ only because of demographic stochasticity. Despite their ecological simplicity, neutral models have been found to give reasonable descriptions of expected patterns of biodiversity in communities with many species. Such patterns include the expected total number of species and species-abundance distributions describing the expected number of species in different abundance classes. However, the expected patterns represent only the central tendencies of the full distributions of possible outcomes. Thus, ecological inferences and conclusions based only on expected patterns are incomplete, and may be misleading. Here, we address this issue for the spatially implicit neutral model, by using classic results from birth–death processes to derive (1) the probability distribution of extinction time of a species with given abundance for the metacommunity; (2) the probability distributions of total species richness and number of species with given abundance for both the metacommunity and local community; and (3) the probability distributions of the average immigration and extinction rates in the local community, across different values of total species richness. We illustrate the utility of these probability distributions in providing greater ecological insight via statistical inference. Firstly, we show that under the neutral metacommunity model, there is only 2.65 × 10 − 9 probability that the age of a common tree species in the Amazon is ≤ 3 × 108 yr, which is approximately the oldest estimated age of the first angiosperm. Thus, species ages from the model are unrealistically high. Secondly, for a tree community in a 50 ha plot at Barro Colorado Island in Panama, we show that the spatially implicit model can be fitted to observed species richness and an independent estimate of the immigration parameter, with the fitted model predicting a species-abundance distribution close to the observed distribution. Our results complement those using sampling formulae that specify the multivariate probability distribution of species abundances from neutral models. [ABSTRACT FROM AUTHOR]

Canopy gaps are widely recognized as being crucial for maintaining the diversity of forest tree communities. But empirical studies have found mixed results because the differences in diversity between individual gaps and non-gaps are often small and statistically undetectable. One overlooked factor, however, is how small individual gap versus non-gap differences may accumulate across sites and potentially have a large effect on forest diversity at the plot scale. Our study investigated sapling richness, density, and composition in 124 treefall gaps, and 200 non-gap sites in the 50-ha tropical forest plot at Barro Colorado Island (BCI), Panama. Additionally, we analyzed species accumulation curves to understand how species richness increases with increasing stem numbers. We observed that sapling richness and density were only slightly higher in gaps 7 years after formation and statistically indistinguishable from non-gaps after 12 years. However, species accumulation curves across multiple gaps were substantially higher than those across non-gaps. Species composition showed small differences between individual gaps and non-gaps but differed significantly between collections of gaps and non-gaps. Specifically, 55 species specialized in 7-year-old gaps compared with 24 in non-gaps; of these, 23 gap-specialized species and zero non-gap species were pioneers. Our results indicate that tree species richness is higher in gaps because of both higher stem density and the presence of gap-specialized species. Our study has finally provided compelling evidence to support the idea that gaps enhance the overall diversity of tropical forest tree communities., (© 2024 The Author(s). Ecology published by Wiley Periodicals LLC on behalf of The Ecological Society of America.)

To estimate species loss from habitat destruction, ecologists typically use species-area relationships, but this approach neglects the spatial pattern of habitat fragmentation. Here, we provide new, easily applied, analytical methods that place upper and lower bounds on immediate species loss at any spatial scale and for any spatial pattern of habitat loss. Our formulas are expressed in terms of what we name the 'Preston function', which describes triphasic species-area relationships for contiguous regions. We apply our method to case studies of deforestation and tropical tree species loss at three different scales: a 50 ha forest plot in Panama, the tropical city-state of Singapore and the Brazilian Amazon. Our results show that immediate species loss is somewhat insensitive to fragmentation pattern at small scales but highly sensitive at larger scales: predicted species loss in the Amazon varies by a factor of 16 across different spatial structures of habitat loss., (© 2018 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.)

The neutral theory of community ecology can predict diversity and abundances of tropical trees, but only under the assumption of steady input of new species into the community. Without input, diversity of a neutral community collapses, so the theory's predictions are not relevant unless novel species evolve or immigrate. We derive analytically the species input needed to maintain a target tree diversity, and find that a rate close to 1.0 x 10(-4) per recruit would maintain the observed diversity of 291 species in the Barro Colorado 50-ha tree plot in Panama. We then measured the rate empirically by comparing species present in one complete enumeration of the plot to those present five years later. Over six census intervals, the observed rate of input was 0.6 x 10(-4) to 1.8 x 10(-4) species per recruit, suggesting that there is adequate immigration of novel species to maintain diversity. Species interactions, niche partitioning, or density-dependence, while they may be present, do not appear to enhance tree species richness at Barro Colorado.

In the classic spatially implicit formulation of Hubbell's neutral theory of biodiversity a local community receives immigrants from a metacommunity operating on a relatively slow timescale, and dispersal into the local community is governed by an immigration parameter m. A current problem with neutral theory is that m lacks a clear biological interpretation. Here, we derive analytical expressions that relate the immigration parameter m to the geometry of the plot defining the local community and the parameters of a dispersal kernel. Our results facilitate more rigorous and extensive tests of the neutral theory: we conduct a test of neutral theory by comparing estimates of m derived from fits to empirical species abundance distributions to those derived from dispersal kernels and find acceptable correspondence; and we generate a new prediction of neutral theory by investigating how the shapes of species abundance distributions change theoretically as the spatial scale of observation changes. We also discuss how our main analytical results can be used to assess the error in the mean-field approximations associated with spatially implicit formulations of neutral theory.