A stochastic biodiversity model with overlapping niche structure

The niche is a fundamental ecological concept that underpins many explanations of patterns of biodiversity. The complexity of niche processes in ecological systems, however, means that it is difficult to capture them accurately in theoretical models of community assembly. In this study, we build upon simple neutral biodiversity models by adding the important ingredient of overlapping niche structure. Our model is spatially implicit and contains a fixed number of equal-sized habitats. Each species in the metacommunity arises through a speciation event; at which time, it is randomly assigned a fundamental niche or set of environments/habitats in which it can persist. Within each habitat, species compete with other species that have different but overlapping fundamental niches. Species abundances then change through ecological drift; each, however, is constrained by its maximum niche breadth and by the presence of other species in its habitats. Using our model, we derive analytical expressions for steady-state species abundance distributions, steady-state distributions of niche breadth across individuals and across species, and dynamic distributions of niche breadth across species. With this framework, we identify the conditions that produce the log-series species abundance distribution familiar from neutral models. We then identify how overlapping niche structure can lead to other species abundance distributions and, in particular, ask whether these new distributions differ significantly from species abundance distributions predicted by non-overlapping niche models. Finally, we extend our analysis to consider additional distributions associated with realized niche breadths. Overall, our results show that models with overlapping niches can exhibit behavior similar to neutral models, with the caveat that species with narrow fundamental niche breadths will be very rare. If narrow-niche species are common, it must be because they are in a non-overlapping niche or have countervailing advantages over broad-niche species. This result highlights the role that niches can play in establishing demographic neutrality.     

Sympatric speciation in birds is rare: insights from range data and simulations

Sympatric speciation is now accepted as theoretically plausible and a likely explanation for divergence in a handful of taxa, but its contribution to large-scale patterns of speciation remains contentious. A major problem is that it is difficult to differentiate between alternate scenarios of geographic speciation when species ranges have shifted substantially in the past. Previous studies have searched for a signal of the geographic mode of speciation by testing for a correlation between time since speciation and range overlap. Here we use simulations to show that the proportion of species showing zero or complete range overlap are more reliable indicators of the geography of speciation than is the correlation between time since speciation and overlap. We then apply these findings to the distributions of 291 pairs of avian sister species. Although 49% of pairs show some overlap in their ranges, our simulations show that this is not surprising under allopatric models of speciation. More revealingly, less than 2% show complete range overlap. Our simulations demonstrate that the observed patterns are most consistent with a model in which allopatric speciation is dominant but in which sympatric speciation is also present and contributes 5% of speciation events.     

Empirical phylogenies and species abundance distributions are consistent with preequilibrium dynamics of neutral community models with gene flow

Community characteristics reflect past ecological and evolutionary dynamics. Here, we investigate whether it is possible to obtain realistically shaped modeled communities–that is with phylogenetic trees and species abundance distributions shaped similarly to typical empirical bird and mammal communities–from neutral community models. To test the effect of gene flow, we contrasted two spatially explicit individual‐based neutral models: one with protracted speciation, delayed by gene flow, and one with point mutation speciation, unaffected by gene flow. The former produced more realistic communities (shape of phylogenetic tree and species‐abundance distribution), consistent with gene flow being a key process in macro‐evolutionary dynamics. Earlier models struggled to capture the empirically observed branching tempo in phylogenetic trees, as measured by the gamma statistic. We show that the low gamma values typical of empirical trees can be obtained in models with protracted speciation, in preequilibrium communities developing from an initially abundant and widespread species. This was even more so in communities sampled incompletely, particularly if the unknown species are the youngest. Overall, our results demonstrate that the characteristics of empirical communities that we have studied can, to a large extent, be explained through a purely neutral model under preequilibrium conditions.     

Neutral Models with Generalised Speciation

Hubbell’s neutral theory claims that ecological patterns such as species abundance distributions can be explained by a stochastic model based on simple assumptions. One of these assumptions, the point mutation assumption, states that every individual has the same probability to speciate. Etienne et al. have argued that other assumptions on the speciation process could be more realistic, for example, that every species has the same probability to speciate (Etienne, et al. in Oikos 116:241–258, 2007). They introduced a number of neutral community models with a different speciation process, and conjectured formulas for their stationary species abundance distribution. Here we study a generalised neutral community model, encompassing these modified models, and derive its stationary distribution, thus proving the conjectured formulas.     

Genetics of male nuptial colour divergence between sympatric sister species of a Lake Victoria cichlid fish

The hypothesis of sympatric speciation by sexual selection has been contentious. Several recent theoretical models of sympatric speciation by disruptive sexual selection were tailored to apply to African cichlids. Most of this work concludes that the genetic architecture of female preference and male trait is a key determinant of the likelihood of disruptive sexual selection to result in speciation. We investigated the genetic architecture controlling male nuptial colouration in a sympatric sibling species pair of cichlid fish from Lake Victoria, which differ conspicuously in male colouration and female mating preferences for these. We estimated that the difference between the species in male nuptial red colouration is controlled by a minimum number of two to four genes with significant epistasis and dominance effects. Yellow colouration appears to be controlled by one gene with complete dominance. The two colours appear to be epistatically linked. Knowledge on how male colouration segregates in hybrid generations and on the number of genes controlling differences between species can help us assess whether assumptions made in simulation models of sympatric speciation by sexual selection are realistic. In the particular case of the two sister species that we studied a small number of genes causing major differences in male colouration may have facilitated the divergence in male colouration associated with speciation.     

Phylogenies support out‐of‐equilibrium models of biodiversity

There is a long tradition in ecology of studying models of biodiversity at equilibrium. These models, including the influential Neutral Theory of Biodiversity, have been successful at predicting major macroecological patterns, such as species abundance distributions. But they have failed to predict macroevolutionary patterns, such as those captured in phylogenetic trees. Here, we develop a model of biodiversity in which all individuals have identical demographic rates, metacommunity size is allowed to vary stochastically according to population dynamics, and speciation arises naturally from the accumulation of point mutations. We show that this model generates phylogenies matching those observed in nature if the metacommunity is out of equilibrium. We develop a likelihood inference framework that allows fitting our model to empirical phylogenies, and apply this framework to various mammalian families. Our results corroborate the hypothesis that biodiversity dynamics are out of equilibrium.     

DYNAMICS OF SEXUAL SELECTION IN DIPLOID POPULATIONS

We describe results for a diploid, two-locus model for the evolution of a female mating preference directed at an attractive male trait that is subject to viability and/or fertility selection. Using computer simulation, we studied a large, random sample of parameter values, assuming additivity of alleles at the preference locus and partial dominance at the trait locus. Simulation results were classifiable into nine types of parameter sets, each differing in equilibria, evolutionary trajectories, and rates of evolution. For many parameters, evolutionary trajectories converged on curves within the allelic frequency plane and subsequently evolved along the curves toward fixation. Neutrally stable curves of equilibria did not occur in Fisherian models that assume only viability and sexual selection unless there is complete dominance at the trait locus. The Fisherian models also exhibited oscillation of allelic frequencies and unique polymorphic equilibria. “Sexy son” models in which attractive males had reduced fertility were much less likely to lead to increase in traits and preferences than were the Fisherian models. However, if less fertile males had increased viability, trait polymorphisms and fixation of rare “sexy” alleles occurred. In general, the behavior of the diploid model was much more complex than that of analogous haploid or polygenic models.     

ASSORTATIVE MATE CHOICE AND DOMINANCE MODIFICATION: ALTERNATIVE WAYS OF REMOVING HETEROZYGOTE DISADVANTAGE

In genetic polymorphisms of two alleles, heterozygous individuals may contribute to the next generation on average more or fewer descendants than the homozygotes. Two different evolutionary responses that remove a disadvantageous heterozygote phenotype from the population are the evolution of strictly assortative mate choice, and that of a modifier making one of the two alleles completely dominant. We derive invasion fitness of mutants introducing dominance or assortative mate choice in a randomly mating population with a genetic polymorphism for an ecological trait. Mutations with small effects as well as mutants introducing complete dominance or perfect assorting are considered. Using adaptive dynamics techniques, we are able to calculate the ratio of fitness gradients for the effects of a dominance modifier and a mate choice locus, near evolutionary branching points. With equal resident allele frequencies, selection for mate choice is always stronger. Dominance is more strongly selected than assortative mating when the resident (common) alleles have very unequal frequencies at equilibrium. With female mate choice the difference in frequencies where dominance is more strongly selected is smaller than when mutants of both sexes can choose without costs. A symmetric resource-competition model illustrates the results.     

The role of sex separation in neutral speciation

Neutral speciation mechanisms based on isolation by distance and assortative mating, termed topopatric, has recently been shown to describe the observed patterns of abundance distributions and species–area relationships. Previous works have considered this type of process only in the context of hermaphroditic populations. In this work, we extend a hermaphroditic model of topopatric speciation to populations where individuals are explicitly separated into males and females. We show that for a particular carrying capacity, speciation occurs under similar conditions, but the number of species generated is lower than in the hermaphroditic case. As a consequence, the species–area curve has lower exponents, especially at intermediate scales. Evolution results in fewer species having more abundant populations.     

PLOIDY AND EVOLUTION BY SEXUAL SELECTION: A COMPARISON OF HAPLOID AND DIPLOID FEMALE CHOICE MODELS NEAR FIXATION EQUILIBRIA

We compare the stability properties of haploid and diploid models of Fisherian sexual selection (with male contribution limited to sperm) by examining both models at equilibria for which a male trait is fixed or absent. Haploid and diploid two locus diallelic models share the property that the stability of such fixation equilibria is determined by the relationship between the harmonic mean of relative preference values for the common male trait, weighted by the frequency of the preferences, and the relative viability associated with the common male trait. When diploid females with heterozygotic-based preferences express preference strengths intermediate between homozygote-based preferences, then boundary equilibria of haploid and diploid models share many stability properties. However, even with intermediate heterozygote preferences, haploid and diploid models do differ: (1) for a particular frequency of the preference allele, both fixation boundaries can be stable for the diploid model, and (2) with over- or underdominance at the preference locus (a possibility precluded in the haploid model), a fixation boundary in the diploid model may show two switches in its stability state for increasing frequencies of one of the preference alleles. These differences are due not just to the impossibility of dominance in haploid models, but also to the larger number of diploid genotypes.     

The Maynard Smith model of sympatric speciation

The paper entitled "Sympatric speciation," which was published by John Maynard Smith in 1966, initiated the development of mathematical models aiming to identify the conditions for sympatric speciation. A part of that paper was devoted to a specific two-locus, two-allele model of sympatric speciation in a population occupying a two-niche system. Maynard Smith provided some initial numerical results on this model. Later, Dickinson and Antonovics (1973) and Caisse and Antonovics (1978) performed more extensive numerical studies on the model. Here, I report analytical results on the haploid version of the Maynard Smith model. I show how the conditions for sympatric and parapatric speciation and the levels of resulting genetic divergence and reproductive isolation are affected by the strength of disruptive selection and nonrandom mating, recombination rate, and the rates of male and female dispersal between the niches.     

The impact of species-neutral stage structure on macroecological patterns

Despite its radical assumption of ecological equivalence between species, neutral biodiversity theory can often provide good fits to species abundance distributions observed in nature. Major criticisms of neutral theory have focused on interspecific differences, which are in conflict with ecological equivalence. However, neutrality in nature is also broken by differences between conspecific individuals at different life stages, which in many communities may vastly exceed interspecific differences between individuals at similar stages. These within-species asymmetries have not been fully explored in species-neutral models, and it is not known whether demographic stage structure affects macroecological patterns in neutral theory. Here, we present a two-stage neutral model where fecundity and mortality change as an individual transitions from one stage to the other. We explore several qualitatively different scenarios, and compare numerically obtained species abundance distributions to the predictions of unstructured neutral theory. We find that abundance distributions are generally robust to this kind of stage structure, but significant departures from unstructured predictions occur if adults have sufficiently low fecundity and mortality. In addition, we show that the cumulative number of births per species, which is distributed as a power law with a 3/2 exponent, is invariant even when the abundance distribution departs from unstructured model predictions. Our findings potentially explain power law-like abundance distributions in organisms with strong demographic structure, such as eusocial insects and humans, and partially rehabilitate species abundance distributions from past criticisms as to their inability to distinguish between biological mechanisms.     

Biodiversity and the Lotka-Volterra theory of species interactions: open systems and the distribution of logarithmic densities

Theoretical interest in the distributions of species abundances observed in ecological communities has focused recently on the results of models that assume all species are identical in their interactions with one another, and rely upon immigration and speciation to promote coexistence. Here we examine a one-trophic level system with generalized species interactions, including species-specific intraspecific and interspecific interaction strengths, and density-independent immigration from a regional species pool. Comparisons between results from numerical integrations and an approximate analytic calculation for random communities demonstrate good agreement, and both approaches yield abundance distributions of nearly arbitrary shape, including bimodality for intermediate immigration rates.     

A deterministic genetic model for sympatric speciation by sexual selection

A deterministic haploid genetic model confirms and explores in more detail the results of our previous individual-based simulation model for sympatric speciation by sexual selection. With the deterministic model, we are able to elucidate parameter dependence by phase plane analysis. We clarify how and why sympatric speciation by sexual selection can happen in a number of ways: (1) Female preferences for or against particular types of males have different effects. Whereas the former affects how readily speciation is invoked, the latter changes the stability of speciation equilibrium. (2) When there is no cost on male ornamentations, speciation is triggered regardless of initial haplotype frequencies if sufficient female preference is provided. (3) There exists a threshold for female initial frequencies for speciation to be invoked, but male initial frequencies have little effect. (4) A small cost on female mate choice does not cancel speciation, but when large, it greatly reduces the possibility of speciation.     

Species abundance distributions and numerical dominance in gastrointestinal helminth communities of fish hosts

The abundances of different species in a parasite community are never similar: there is typically one or a few numerically dominant species and many species with low abundance. Here, we determine whether basic features of parasite communities are associated with strong dominance by one or a few species, among 39 component communities of gastrointestinal helminths in marine fishes from Brazil. First, we tested whether the shape of the species abundance distribution in these communities fits that predicted by several theoretical models, using a goodness-of-fit procedure. Only the canonical lognormal model could be rejected for 5 out of 39 communities; all other comparisons of observed and predicted abundance distributions showed no significant differences, although this may be due to limited statistical power. Second, we used the ratio between the abundance of the most abundant species and either the second or third most abundant species, as indices of dominance; these show, for instance, that the dominant species in a community is typically twice, but sometimes over ten times, as abundant as the next most abundant species. We found that these ratios were not influenced by either the community's species richness, the mean number of individual parasites per host, or the taxonomic identity of the dominant species. However, the abundance ratio between the first and third most abundant species in a community was significantly correlated with an independent index of species interactivity, based on the likelihood that the different parasite species in a component community co-occur in the same host individuals: the difference in abundance between the dominant and third most abundant species was greater in communities characterized by weak interactions. These findings suggest that strong interactions may lead to greater evenness in the abundance of species, and that numerical dominance is more likely to result from interspecific differences in recruitment rates.     

Testing the standard neutral model of biodiversity in lake communities

Hubbell's (2001) neutral model describes how local communities are structured if population dynamics are statistically identical among species in a constant, possibly patchy, environment with random speciation. Tests of this model have been restricted largely to terrestrial communities. Here we tested the fit of this neutral model to fish, zooplankton and phytoplankton species–abundance distributions from 30 well-studied lake communities varying widely in lake size and productivity. We measured the fit of the communities to the neutral model in three ways. All but two zooplankton (7 of 9) and all but three fish (9 of 12) communities were consistent with all three measures of fit. However, all nine phytoplankton communities did not fit the neutral model by at least one measure. This result for phytoplankton communities represents to date the most consistent failure of the standard neutral model to predict the shape of species-abundance distributions.     

The population genetics of synthetic lethals.

Synthetic lethals are variants at different loci that have little or no effect on viability singly but cause lethality in combination. The importance of synthetic lethals and, more generally, of synthetic deleterious loci (SDL) has been controversial. Here, we derive the expected frequencies for SDL under a mutation-selection balance for the complete haploid model and selected cases of the diploid model. We have also obtained simple approximations that demonstrate good fit to exact solutions based on numerical iterations. In the haploid case, equilibrium frequencies of carrier haplotypes (individuals with only a single mutation) are comparable to analogous single-locus results, after allowing for the effects of linkage. Frequencies in the diploid case, however, are much higher and more comparable to the square root of the single-locus results. In particular, when selection operates only on the double-mutant homozygote and linkage is not too tight, the expected frequency of the carriers is approximately the quartic root of the ratio between the mutation rate and the selection coefficient of the synthetics. For a reasonably wide set of models, the frequencies of carriers can be on the order of a few percent. The equilibrium frequencies of these deleterious alleles can be relatively high because, with SDL, both dominance and epistasis act to shield carriers from exposure to selection. We also discuss the possible role of SDL in maintaining genetic variation and in hybrid breakdown.     

Using species abundance models as indicators of habitat disturbance in tropical forests

1. In temperate communities, species abundance distributions have been used to detect ecosystem disturbance: in undisturbed habitats, distributions are claimed to generally fit log-normal models, whereas in disturbed habitats, distributions fit log-series models.
2. There is a growing literature on the effects of habitat disturbance in tropical ecosystems and several studies suggest that species abundance models may be useful in detecting disturbance, although data are lacking.
3. Nummelin (1998) claims that these models are not universal indicators of forest disturbance, but we highlight a number of problems with the data presented in Nummelin's study and conclude that it is too soon to dismiss these models. We discuss several important points arising from Nummelin's study which need to be considered if species abundance models are to be used appropriately.     

Community structure of vascular epiphytes: a neutral perspective

Vascular epiphytes form a diverse group of almost 30 000 species, yet theory concerning their community structure is still largely lacking. We therefore employed the simplest models of biodiversity, (near-)neutral models, to generate hypotheses concerning their community structure. With recently developed tools for (near-)neutral models we analyzed species abundance data from many samples in Central and South America which we divided into four metacommunities (Mesoamerica, Central America, Amazonia and Paraná), where for each metacommunity we considered two subsets differing in dispersal syndrome: an animal-dispersed guild and a wind-dispersed guild. We considered three models differing in the underlying speciation mode. Across all metacommunities, we found observed patterns to be indistinguishable from patterns generated by neutral or near-neutral processes. Furthermore, we found that subdivision in different dispersal guilds was often supported, with recruitment limitation being stronger for animal-dispersed species than for wind-dispersed species. This is the first time that (near-)neutral theory has been applied to epiphyte communities. Future efforts with additional data sets and more refined models are expected to further improve our understanding of community structure in epiphytes and will have to test the generality of our findings.