A comment on Hubbell's zero‐sum ecological drift model

Demographic analysis of Hubbell's neutral theory of biodiversity

In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by Hidden-Markov-Model (HMM) literature is used to compute exact sample allele frequency spectra for three demographic scenarios: single changes in (effective) population size, boom-bust dynamics, and stochastic fluctuations in (effective) population size. An approach for fully agnostic demographic inference from these sample allele spectra is explored, and sufficient statistics for stepwise changes in population size are found. Further, convergence behaviours of the polymorphic sample spectra for population size changes on different time scales are examined and discussed within the context of inference of the effective population size. Joint visual assessment of the sample spectra and the temporal coefficients of the spectral decomposition of the forward diffusion process is found to be important in determining departure from equilibrium. Stochastic changes in (effective) population size are shown to shape sample spectra particularly strongly.

Hubbell's unified neutral theory is a zero-sum ecological drift model in which population sizes change at random in a process resembling genetic drift, eventually leading to extinction. Diversity is maintained within the community by speciation. Hubbell's model makes predictions about the distribution of species abundances within communities and the turnover of species from place to place (beta diversity). However, ecological drift cannot be tested adequately against these predictions without independent estimates of speciation rates, population sizes, and dispersal distances. A more practical prediction from ecological drift is that time to extinction of a population of size N is approximately 2N generations. I test this prediction here using data for passerine birds (Passeriformes). Waiting times to speciation and extinction were estimated from genetic divergence between sister populations and a lineage-through-time plot for endemic South American suboscine passerines. Population sizes were estimated from local counts of birds in two large forest plots extrapolated to the area of wet tropical forest in South America and from atlas data on European passerines. Waiting times to extinction (ca. 2 Ma) are much less than twice the product of average population size (4.0 and 14.4 x 10(6) individuals in South America and Europe) and generation length (five and three years) for songbirds, that is, 40 and 86 Ma, respectively. Thus, drift is too slow to account for turnover in regional avifaunas. Presumably, other processes, involving external drivers, such as climate and physiographic change, and internal drivers, such as evolutionary change in antagonistic interactions, predominate. Hubbell's model is historical and geographic, and his perspective importantly links local and regional process and pattern. Ecological reality can be added to the mix while retaining Hubbell's concept of continuity of communities in space and time.

For a Wright-Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.

We studied the waterbird population at Lashihai Lake, Yunnan Province, China, which is a Ramsar Site (Wetland of International Importance), to determine seasonal variation in the species composition and size of the waterbird population. The study was conducted at five selected spots along Lashihai Lake at the same time each week from August 2011 to September 2013. In total, 62 waterbird species were recorded, of which 38.71%, 35.48%, 16.13%, and 9.68% were winter migrants, passage visitors, residents, and summer migrants, respectively. We found important seasonal changes in waterbird species composition and population size. Waterbird species richness was highest from September to the following April, with the total species numbers peaking in December. Total individual numbers peaked twice from late November to early December and mid-to-late February. However, waterbird species and individual numbers were comparatively lower from May to August. The change in species composition was determined by the arrival and departure dynamics of winter migrants and passage visitors. Winter migrants primarily caused the periodic changes in population size. Of concern, species and overall waterbird numbers seemed to be lower than the numbers in historical records. The decline of waterbird numbers implies that environmental changes caused by the implementation of the dam upstream of Lashihai Lake may have had adverse effects on this waterbird population. This study confirms the existence of major seasonal changes in species composition and size of the waterbird population at Lashihai Lake. Furthermore, the findings demonstrate that this wetland is of high conservation importance for waterbirds using the Central Asian–Indian and Asian–Pacific migratory routes.

Population size and population growth rate respond to changes in vital rates like survival and fertility. In deterministic environments change in population growth rate alone determines change in population size. In random environments, population size at any time t is a random variable so that change in population size obeys a probability distribution. We analytically show that, in a density-independent population, the proportional change in population size with respect to a small proportional change in a vital rate has an asymptotic normal distribution. Its mean grows linearly at a rate equal to the elasticity of the long-term stochastic growth rate λS while the standard deviation scales as \(\sqrt t\). Consequently, a vital rate with a larger elasticity of λS may produce a larger mean change in population size compared to one with a smaller elasticity of λS. But a given percentage change in population size may be more likely when the vital rate with smaller elasticity is perturbed. Hence, the response of population size to perturbation of a vital rate depends not only on the elasticity of the population growth rate but also on the variance in change in population size. Our results provide a formula to calculate the probability that population size changes by a given percentage that works well even for short time periods.

In human populations, the relative levels of neutral diversity on the X and autosomes differ markedly from each other and from the naïve theoretical expectation of 3/4. Here we propose an explanation for these differences based on new theory about the effects of sex-specific life history and given pedigree-based estimates of the dependence of human mutation rates on sex and age. We demonstrate that life history effects, particularly longer generation times in males than in females, are expected to have had multiple effects on human X-to-autosome (X:A) diversity ratios, as a result of male-biased mutation rates, the equilibrium X:A ratio of effective population sizes, and the differential responses to changes in population size. We also show that the standard approach of using divergence between species to correct for male mutation bias results in biased estimates of X:A effective population size ratios. We obtain alternative estimates using pedigree-based estimates of the male mutation bias, which reveal that X:A ratios of effective population sizes are considerably greater than previously appreciated. Finally, we find that the joint effects of historical changes in life history and population size can explain the observed X:A diversity ratios in extant human populations. Our results suggest that ancestral human populations were highly polygynous, that non-African populations experienced a substantial reduction in polygyny and/or increase in the male-to-female ratio of generation times around the Out-of-Africa bottleneck, and that current diversity levels were affected by fairly recent changes in sex-specific life history.

Monitoring changes in animal population size is rarely possible through complete censuses; frequently, the only feasible means of monitoring changes in population size is to use counts of animals obtained by skilled observers as indices to abundance. Analysis of changes in population size can be severely biased if factors related to the acquisition of data are not adequately controlled for. In particular, we identify two types of observer effects: these correspond to baseline differences in observer competence and to changes through time in the ability of individual observers. We present a family of models for count data in which the first of these observer effects is treated as a nuisance parameter. Conditioning on totals of negative binomial counts yields a Dirichlet compound multinomial vector for each observer. Quasi-likelihood is used to estimate parameters related to population trajectory and other parameters of interest; model selection is carried out on the basis of Akaike's information criterion. An example is presented using data on Wood thrush from the North American Breeding Bird Survey.

Recently, new methods have been developed for estimating the current and recent changes in effective population sizes. Based on the methods, the effective population sizes of Korean populations were estimated using data from the Korean Association Resource (KARE) project. The overall changes in the population sizes of the total populations were similar to CHB (Han Chinese in Beijing, China) and JPT (Japanese in Tokyo, Japan) of the HapMap project. There were no differences in past changes in population sizes with a comparison between an urban area and a rural area. Age-dependent current and recent effective population sizes represent the modern history of Korean populations, including the effects of World War II, the Korean War, and urbanization. The oldest age group showed that the population growth of Koreans had already been substantial at least since the end of the 19th century.

Understanding and predicting population abundance is a major challenge confronting scientists. Several genetic models have been developed using microsatellite markers to estimate the present and ancestral effective population sizes. However, to get an overview on the evolution of population requires that past fluctuation of population size be traceable. To address the question, we developed a new model estimating the past changes of effective population size from microsatellite by resolving coalescence theory and using approximate likelihoods in a Monte Carlo Markov Chain approach. The efficiency of the model and its sensitivity to gene flow and to assumptions on the mutational process were checked using simulated data and analysis. The model was found especially useful to provide evidence of transient changes of population size in the past. The times at which some past demographic events cannot be detected because they are too ancient and the risk that gene flow may suggest the false detection of a bottleneck are discussed considering the distribution of coalescence times. The method was applied on real data sets from several Atlantic salmon populations. The method called VarEff (Variation of Effective size) was implemented in the R package VarEff and is made available at https://qgsp.jouy.inra.fr and at http://cran.r-project.org/web/packages/VarEff.

Climate-induced phenological shifts may have serious consequences for organisms and populations, but it is challenging to link such shifts to demographic change. Here, we present an overview of current methodological approaches for studying the demographic consequences of phenological shifts, based on a literature survey of 62 studies on diverse taxa. The majority of these studies (66%) were conducted using an approach that linked phenological shifts to demography through the measurement of vital rates (survival, growth, and fecundity). About 18% of the studies used a population-based approach that linked the phenological shifts to changes in population size, and 16% took a combined approach by considering changes in both vital rates and population size. Birds and mammals were overrepresented in studies of the demographic consequences of phenological shifts, compared to their occurrence in nature, while insects were heavily underrepresented. The effects of phenological shifts often varied according to the particular vital rate under consideration, in many cases even within a single species. In the few studies that examined changes in phenology together with both vital rate and population data, the changes in vital rates did not always predict changes in population size. To better understand the ultimate causes of population-level effects we argue that further study is needed on density-dependent aspects of population dynamics and on the sensitivity of population dynamics to perturbations in vital rates. We encourage re searchers to observe multiple vital rates throughout organisms' life-cycles in order to enable more meaningful examination of the consequences of phenological shifts for population dynamics. (Less)

Past environmental changes have shaped the evolutionary and ecological diversity of extant organisms. Specifically, climatic fluctuations have made environmental conditions alternatively common or rare over time. Accordingly, most taxa have undergone restriction of their distribution to local refugia during habitat contraction, from which they could expand when suitable habitat became more common. Assessing how past restrictions in refugia have shaped species distributions and genetic diversity has motivated much research in evolutionary biology and biogeography. But there is still lack of clear synthesis on whether and how the taxonomic, functional and phylogenetic composition of extant multispecies assemblages retains the imprint of past restriction in refugia. We devised an original eco-evolutionary model to investigate the temporal dynamics of a regional species pool inhabiting a given habitat today, and which have experienced habitat reduction in the past. The model includes three components: (i) a demographic component driving stochastic changes in population sizes and extinctions due to habitat availability, (ii) a mutation and speciation component representing how divergent genotypes emerge and define new species over time, and (iii) a trait evolution component representing how trait values have changed across descendants over time. We used this model to simulate dynamics of multispecies assemblages that occupied a restricted refugia in the past and could expand their distribution subsequently. We characterized the past restriction in refugia in terms of two parameters representing the ending time of past refugia, and the extent of habitat restriction in the refugia. We characterized extant patterns of taxonomic, functional and phylogenetic diversity depending on these parameters. We found that extant relative abundances reflect the lasting influence of more recent refugia on demographic dynamics, while phylogenetic composition reflects the influence of more ancient habitat change. Extant functional diversity depends on the interplay between diversification dynamics and trait evolution, offering new options to jointly infer current trait adaptation and past trait evolution dynamics.

In this paper an adaptive differential evolution algorithm with dynamic changes of population size is presented. In proposed algorithm an adaptive selection of control parameters of the algorithm are introduced. Due to these parameters selection, the algorithm gives better results than differential evolution algorithm without this modification. Also, in presented algorithm dynamic changes of population size are introduced. This modification try to overcome limitations connected with premature convergence of the algorithm. Due to dynamic changes of population size, the algorithm can easier get out from local minimum. The proposed algorithm is used to train artificial neural networks. Results obtained are compared with those obtained using: adaptive differential evolution algorithm without dynamic changes of population size, method based on evolutionary algorithm, error back-propagation algorithm, and Levenberg-Marquardt algorithm.

Intraspecific variation is a major component of biodiversity, yet it has received relatively little attention from governmental and nongovernmental organizations, especially with regard to conservation plans and the management of wild species. This omission is ill‐advised because phenotypic and genetic variations within and among populations can have dramatic effects on ecological and evolutionary processes, including responses to environmental change, the maintenance of species diversity, and ecological stability and resilience. At the same time, environmental changes associated with many human activities, such as land use and climate change, have dramatic and often negative impacts on intraspecific variation. We argue for the need for local, regional, and global programs to monitor intraspecific genetic variation. We suggest that such monitoring should include two main strategies: (i) intensive monitoring of multiple types of genetic variation in selected species and (ii) broad‐brush modeling for representative species for predicting changes in variation as a function of changes in population size and range extent. Overall, we call for collaborative efforts to initiate the urgently needed monitoring of intraspecific variation.

In response to environmental change, species may decrease or increase in population size across their range, expand or contract their range limits, or alter how sites are occupied within their existing range. Shifts in range limits and widespread changes in population size have been documented in birds especially in response to changes in climate. Range occupancy, or how patchily or continuously a species is distributed within their range, has been studied less in the context of anthropogenic changes but may be expected to decrease with range-wide population size if abundance-occupancy relationships are generally positive. Determining which properties of species are related to range expansion or contraction or increased range occupancy or decreased range occupancy is useful in developing an understanding of which species become “winners” or “losers” under global change. Species with broader climatic niches may be more likely to successfully expand to new sites as climate changes. Range occupancy can be related to habitat preferences of species, and habitat specialization may predict how species fill in sites within their range. To examine how species niche breadth may explain changes in species distributions, we modeled how changes in range-wide population size, range extent, and range occupancy from 1976 to 2016 were predicted by species’ climate, habitat, and diet niche breadth for 77 North American breeding bird species. We found that climate generalists were more likely to be increasing in range area, while species with declining population trends were likely to be contracting in range area and in occupancy within their range. Understanding how different dimensions of specialization relate to shifts in species distributions may improve predictions of which species are expected to benefit from or be vulnerable to anthropogenic change.