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Neutral models in ecology assume that all species are demographically equivalent, such that their abundances differ ultimately because of demographic stochasticity rather than selection. In spite of their simplicity, neutral models have been found to accurately reproduce static patterns of biodiversity for diverse communities. However, the same neutral models have been found to exhibit species abundance dynamics that are far too slow compared to reality, resulting in poor fits to temporally dynamic patterns of biodiversity. Here, we show that one of the root causes of these slow dynamics is the additional assumption that a community has reached an equilibrium with a fixed community size, with species that have a net growth rate close to zero. We removed this additional assumption by constructing and analyzing a neutral model with an expected community size that can change over time and is not necessarily at equilibrium, which thus allows the historical formation of a community to be represented explicitly. Our analysis demonstrated that for the general scenario where a small community rapidly grows in size to a carrying capacity, representing recovery from ecological disturbance or assembly of a new community, the model produced much larger changes in species abundances and much shorter species ages than a neutral model at an equilibrium with fixed community size. In addition, the species abundance distribution was biphasic with a subset of abundant species arising from a founder effect. We confirmed these new results in applications of the new model to the specific scenario of recovery of the Amazon tree community after the end-Cretaceous bolide impact, which involved periods of increasing and decreasing community size. We conclude that incorporating transient dynamics in neutral models improves realism by allowing explicit consideration of how a community is formed over realistic time-scales. • Transient dynamics of a neutral model with varying community size are analyzed. • Formulae are derived specifying expected species richness and species age. • Formulae are derived specifying the species-abundance distribution. • Model gives a biphasic SAD with common species arising from a founder effect. • Model also gives realistic species ages for a tree community at an Amazon scale. [ABSTRACT FROM AUTHOR]

Abstract: Biogeography seeks to understand the mechanisms that drive biodiversity across long temporal and large spatial scales. Theoretical models of biogeography can be tested by comparing their predictions of quantities such as species ages against empirical estimates. It has previously been claimed that the neutral theory of biodiversity and biogeography predicts species ages that are unrealistically long. Any improved theory of biodiversity must rectify this problem, but first it is necessary to quantify the problem precisely. Here we provide analytical expressions for species ages in neutral biodiversity communities. We analyse a spatially implicit metacommunity model and solve for both the zero-sum and non-zero-sum cases. We explain why our new expressions are, in the context of biodiversity, usually more appropriate than those previously imported from neutral molecular evolution. Because of the time symmetry of the spatially implicit neutral model, our expressions also lead directly to formulas for species persistence times and species lifetimes. We use our new expressions to estimate species ages of forest trees under a neutral model and find that they are about an order of magnitude shorter than those predicted previously but still unrealistically long. In light of our results, we discuss different models of biogeography that may solve the problem of species ages. [Copyright &y& Elsevier]

Abstract: Previous research into the neutral theory of biodiversity has focused mainly on equilibrium solutions rather than time-dependent solutions. Understanding the time-dependent solutions is essential for applying neutral theory to ecosystems in which time-dependent processes, such as succession and invasion, are driving the dynamics. Time-dependent solutions also facilitate tests against data that are stronger than those based on static equilibrium patterns. Here I investigate the time-dependent solutions of the classic spatially implicit neutral model, in which a small local community is coupled to a much larger metacommunity through immigration. I present explicit general formulas for the eigenvalues, left eigenvectors and right eigenvectors of the models’s transition matrix. The time-dependent solutions can then be expressed in terms of these eigenvalues and eigenvectors. Some of these results are translated directly from existing results for the classic Moran model of population genetics (the Moran model is equivalent to the spatially implicit neutral model after a reparameterization); others of the results are new. I demonstrate that the asymptotic time-dependent solution corresponding to just these first two eigenvectors can be a good approximation to the full time-dependent solution. I also demonstrate the feasibility of a partial eigendecomposition of the transition matrix, which facilitates direct application of the results to a biologically relevant example in which a newly invading species is initially present in the metacommunity but absent from the local community. [Copyright &y& Elsevier]

Abstract: Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator–prey and competition models. The models exhibit three types of transition: the predator–prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator–prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems. [Copyright &y& Elsevier]

Abstract: Preston''s classic work on the theory of species abundance distributions (SADs) in ecology has been challenged by Dewdney. Dewdney contends that Preston''s veil-line concept, relating to the shape of sample SADs, is flawed. Here, I show that Preston''s and Dewdney''s theories can be reconciled by considering the differing mathematical properties of the sampling process on logarithmic (Preston) versus linear (Dewdney) abundance scales. I also derive several related results and show, importantly, that one cannot reject the log-normal distribution as a plausible SAD based only on sampling arguments, as Dewdney and others have done. [Copyright &y& Elsevier]

• Non-pharmaceutical interventions (NPIs) were enacted in COVID-19 pandemic. • We examine effect of NPIs on total disease burden of a non-target respiratory disease. • To do this, we mathematically analyse and simulate four models of varying complexity. • We show that NPIs over about a year have a negative effect on total disease burden. • The negative effect increased in magnitude with the rate at which immunity is lost. The recent global COVID-19 pandemic resulted in governments enacting non-pharmaceutical interventions (NPIs) targeted at reducing transmission of SARS-CoV-2. But the NPIs also affected the transmission of viruses causing non-target seasonal respiratory diseases, including influenza and respiratory syncytial virus (RSV). In many countries, the NPIs were found to reduce cases of such seasonal respiratory diseases, but there is also evidence that subsequent relaxation of NPIs led to outbreaks of these diseases that were larger than pre-pandemic ones, due to the accumulation of susceptible individuals prior to relaxation. Therefore, the net long-term effects of NPIs on the total disease burden of non-target diseases remain unclear. Knowledge of this is important for infectious disease management and maintenance of public health. In this study, we shed light on this issue for the simplified scenario of a set of NPIs that prevent or reduce transmission of a seasonal respiratory disease for about a year and are then removed, using mathematical analyses and numerical simulations of a suite of four epidemiological models with varying complexity and generality. The model parameters were estimated using empirical data pertaining to seasonal respiratory diseases and covered a wide range. Our results showed that NPIs reduced the total disease burden of a non-target seasonal respiratory disease in the long-term. Expressed as a percentage of population size, the reduction was greater for larger values of the basic reproduction number and the immunity loss rate, reflecting larger outbreaks and hence more infections averted by imposition of NPIs. Our study provides a foundation for exploring the effects of NPIs on total disease burden in more-complex scenarios. [ABSTRACT FROM AUTHOR]

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 community’s 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. [ABSTRACT FROM AUTHOR]

• Processing chain commensalism (PCC) is a type of resource conversion interaction. • Long-term outcomes of PCCs are invariant to the specification of functional responses. • SGH in PCCs requires leakage of the downstream resource to occur. • These findings are likely to apply to other resource conversion-type interactions. The stress-gradient hypothesis (SGH) in ecology predicts that the strength and frequency of positive interspecific interactions, including processing chain commensalisms (PCCs), increase with environmental stress. Although observed in some empirical PCC studies, a recent theoretical study of PCCs using a consumer–resource-type model found that, given the model's assumptions, the SGH never occurs. To investigate if this is a true reflection of PCCs or merely an artefact of the model, in this study, we modified this earlier model formulation by incorporating generalized, monotonically increasing resource uptake functions in place of linear functions, and added a term to represent the spontaneous leakage of the downstream resource to the environment. Mathematical analyses of the model revealed two key insights: 1) the specific algebraic forms of the functional responses of the species in a PCC do not affect the long-term behaviour of the system; 2) the SGH can occur in a facilitative interaction only if the consumer-independent leakage rate of the downstream resource exceeds the consumer-independent input rate. The first insight shows that the outcomes of consumer–resource interactions are robust to details of the functional responses when the functional responses are monotonically increasing, while the second insight shows that the SGH is not a universal feature of positive interactions but instead holds only under a well-defined set of conditions which may vary between PCC interactions and the environmental contexts in which they take place. [ABSTRACT FROM AUTHOR]

• 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]