Tak Fung

Reproducing static and dynamic biodiversity patterns in tropical forests: the critical role of environmental variance

Ecological communities are subjected to stochasticity in the form of demographic and environmental variance. Stochastic models that contain only demographic variance (neutral models) provide close quantitative fits to observed species-abundance distributions (SADs) but substantially underestimate observed temporal species-abundance fluctuations. To provide a holistic assessment of whether models with demographic and environmental variance perform better than neutral models, the fit of both to SADs and temporal species-abundance fluctuations at the same time has to be tested quantitatively. In this study, we quantitatively test how closely a model with demographic and environmental variance reproduces total numbers of species, total abundances, SADs and temporal species-abundance fluctuations for two tropical forest tree communities, using decadal data from long-term monitoring plots and considering individuals larger than two size thresholds for each community. We find that the model can indeed closely reproduce these static and dynamic patterns of biodiversity in the two communities for the two size thresholds, with better overall fits than corresponding neutral models. Therefore, our results provide evidence that stochastic models incorporating demographic and environmental variance can simultaneously capture important static and dynamic biodiversity patterns arising in tropical forest communities.

Confidence intervals for population allele frequencies: the general case of sampling from a finite diploid population of any size.

The estimation of population allele frequencies using sample data forms a central component of studies in population genetics. These estimates can be used to test hypotheses on the evolutionary processes governing changes in genetic variation among populations. However, existing studies frequently do not account for sampling uncertainty in these estimates, thus compromising their utility. Incorporation of this uncertainty has been hindered by the lack of a method for constructing confidence intervals containing the population allele frequencies, for the general case of sampling from a finite diploid population of any size. In this study, we address this important knowledge gap by presenting a rigorous mathematical method to construct such confidence intervals. For a range of scenarios, the method is used to demonstrate that for a particular allele, in order to obtain accurate estimates within 0.05 of the population allele frequency with high probability (%), a sample size of is often required. This analysis is augmented by an application of the method to empirical sample allele frequency data for two populations of the checkerspot butterfly (Melitaea cinxia L.), occupying meadows in Finland. For each population, the method is used to derive % confidence intervals for the population frequencies of three alleles. These intervals are then used to construct two joint % confidence regions, one for the set of three frequencies for each population. These regions are then used to derive a % confidence interval for Josts D, a measure of genetic differentiation between the two populations. Overall, the results demonstrate the practical utility of the method with respect to informing sampling design and accounting for sampling uncertainty in studies of population genetics, important for scientific hypothesis-testing and also for risk-based natural resource management.

Species-abundance distributions under colored environmental noise

Natural communities at all spatiotemporal scales are subjected to a wide variety of environmental pressures, resulting in random changes in the demographic rates of species populations. Previous analyses have examined the effects of such environmental variance on the long-term growth rate and time to extinction of single populations, but studies of its effects on the diversity of communities remain scarce. In this study, we construct a new master-equation model incorporating demographic and environmental variance and use it to examine how statistical patterns of diversity, as encapsulated by species-abundance distributions (SADs), are altered by environmental variance. Unlike previous diffusion models with environmental variance uncorrelated in time (white noise), our model allows environmental variance to be correlated at different timescales (colored noise), thus facilitating representation of phenomena such as yearly and decadal changes in climate. We derive an exact analytical expression for SADs predicted by our model together with a close approximation, and use them to show that the main effect of adding environmental variance is to increase the proportion of abundant species, thus flattening the SAD relative to the log-series form found in the neutral case. This flattening effect becomes more prominent when environmental variance is more correlated in time and has greater effects on species’ demographic rates, holding all other factors constant. Furthermore, we show how our model SADs are consistent with those from diffusion models near the white noise limit. The mathematical techniques we develop are catalysts for further theoretical work exploring the consequences of environmental variance for biodiversity.

Maintenance of biodiversity on islands

MacArthur and Wilsons theory of island biogeography predicts that island species richness should increase with island area. This prediction generally holds among large islands, but among small islands species richness often varies independently of island area, producing the so-called ‘small-island effect’ and an overall biphasic species–area relationship (SAR). Here, we develop a unified theory that explains the biphasic island SAR. Our theorys key postulate is that as island area increases, the total number of immigrants increases faster than niche diversity. A parsimonious mechanistic model approximating these processes reproduces a biphasic SAR and provides excellent fits to 100 archipelago datasets. In the light of our theory, the biphasic island SAR can be interpreted as arising from a transition from a niche-structured regime on small islands to a colonization–extinction balance regime on large islands. The first regime is characteristic of classic deterministic niche theories; the second regime is characteristic of stochastic theories including the theory of island biogeography and neutral theory. The data furthermore confirm our theorys key prediction that the transition between the two SAR regimes should occur at smaller areas, where immigration is stronger (i.e. for taxa that are better dispersers and for archipelagos that are less isolated).

The potential for alternative stable states in nutrient-enriched invaded grasslands

Nutrient enrichment of native grasslands can promote invasion by exotic plant species, leading to reduced biodiversity and altered ecosystem function. Empirical evidence suggests that positive feedbacks may make such transitions difficult to reverse. We developed a mathematical model of grassland dynamics in which one group of species (native) is a better competitor for nitrogen (N) and another group (exotic) is a better competitor for light. We parameterized the model for a grassland community and reproduced observed transitions from a native- to an exotic-dominated state under N loading. Within known bounds of parameter values, both smooth and hysteretic transitions are plausible. The model also predicts that N loading alone is insufficient to achieve a transition to an exotic-dominated state on a timescale relevant to grassland management (a few decades), and that therefore some other disturbance (e.g., fire suppression or heaving grazing) must be present to accelerate it. The model predicts that to restore a grassland to a native-dominated state after N inputs have been reduced, fire and carbon supplements would be most effective. Further field research in N-enriched invaded grasslands is required to establish the strengths of positive feedbacks and, in turn, the consequences of anthropogenic modification of grasslands worldwide.

A robust nonparametric method for quantifying undetected extinctions

How many species have gone extinct in modern times before being described by science? To answer this question, and thereby get a full assessment of humanitys impact on biodiversity, statistical methods that quantify undetected extinctions are required. Such methods have been developed recently, but they are limited by their reliance on parametric assumptions; specifically, they assume the pools of extant and undetected species decay exponentially, whereas real detection rates vary temporally with survey effort and real extinction rates vary with the waxing and waning of threatening processes. We devised a new, nonparametric method for estimating undetected extinctions. As inputs, the method requires only the first and last date at which each species in an ensemble was recorded. As outputs, the method provides estimates of the proportion of species that have gone extinct, detected, or undetected and, in the special case where the number of undetected extant species in the present day is assumed close to zero, of the absolute number of undetected extinct species. The main assumption of the method is that the per-species extinction rate is independent of whether a species has been detected or not. We applied the method to the resident native bird fauna of Singapore. Of 195 recorded species, 58 (29.7%) have gone extinct in the last 200 years. Our method projected that an additional 9.6 species (95% CI 3.4, 19.8) have gone extinct without first being recorded, implying a true extinction rate of 33.0% (95% CI 31.0%, 36.2%). We provide R code for implementing our method. Because our method does not depend on strong assumptions, we expect it to be broadly useful for quantifying undetected extinctions.

Analytical formulae for computing dominance from species-abundance distributions.

The evenness of an ecological community affects ecosystem structure, functioning and stability, and has implications for biodiversity conservation. In uneven communities, most species are rare while a few dominant species drive ecosystem-level properties. In even communities, dominance is lower, with possibly many species playing key ecological roles. The dominance aspect of evenness can be measured as a decreasing function of the proportion of species required to make up a fixed fraction (e.g., half) of individuals in a community. Here we sought general rules about dominance in ecological communities by linking dominance mathematically to the parameters of common theoretical species-abundance distributions (SADs). We found that if a communitys SAD was log-series or lognormal, then dominance was almost inevitably high, with fewer than 40% of species required to account for 90% of all individuals. Dominance for communities with an exponential SAD was lower but still typically high, with fewer than 40% of species required to account for 70% of all individuals. In contrast, communities with a gamma SAD only exhibited high dominance when the average species abundance was below a threshold of approximately 100. Furthermore, we showed that exact values of dominance were highly scale-dependent, exhibiting non-linear trends with changing average species abundance. We also applied our formulae to SADs derived from a mechanistic community model to demonstrate how dominance can increase with environmental variance. Overall, our study provides a rigorous basis for theoretical explorations of the dynamics of dominance in ecological communities, and how this affects ecosystem functioning and stability.

Comment on “Plant diversity increases with the strength of negative density dependence at the global scale”

LaManna et al. (Reports, 30 June 2017, p. 1389) found higher conspecific negative density dependence in tree communities at lower latitudes, yielding a possible mechanistic explanation for the latitudinal diversity gradient. We show that their results are artifacts of a selective data transformation and a forced zero intercept in their fitted model. A corrected analysis shows no latitudinal trend.