Showing papers by "Nadav M. Shnerb published in 2020"

Mean growth rate when rare is not a reliable metric for persistence of species.

Abstract: The coexistence of many species within ecological communities poses a long-standing theoretical puzzle. Modern coexistence theory (MCT) and related techniques explore this phenomenon by examining the chance of a species population growing from rarity in the presence of all other species. The mean growth rate when rare, E[r] , is used in MCT as a metric that measures persistence properties (like invasibility or time to extinction) of a population. Here we critique this reliance on E[r] and show that it fails to capture the effect of temporal random abundance variations on persistence properties. The problem becomes particularly severe when an increase in the amplitude of stochastic temporal environmental variations leads to an increase in E[r] , since at the same time it enhances random abundance fluctuations and the two effects are inherently intertwined. In this case, the chance of invasion and the mean extinction time of a population may even go down as E[r] increases.

Stochasticity-induced stabilization in ecology and evolution: a new synthesis.

Abstract: The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log abundances of species, with mean logarithmic growth rates when rare, E r , used as metrics for persistence. However, invasion probabilities and the times to extinction are not single-valued functions of E r and, in some cases, decrease as E r increases. Here, we present a synthesis of stochasticity-induced stabilization (SIS) phenomena based on the ratio between the expected arithmetic growth μ and its variance g . When the diffusion approximation holds, explicit formulas for invasion probabilities and persistence times are single-valued, monotonic functions of μ / g . The storage effect in the lottery model, together with other well-known examples drawn from population genetics, microbiology, and ecology (including discrete and continuous dynamics, with overlapping and non-overlapping generations), are placed together, reviewed, and explained within this new, transparent theoretical framework. We also clarify the relationships between life-history strategies and SIS, and study the dynamics of extinction when SIS fails.

Evolutionary dynamics in fluctuating environment

Abstract: This paper analyzes the effect of variations in population size and in selection on the fate of a mutant type. Using the diffusion approximation, the authors present simple analytic formulas for effective population size and effective selection, and use it to calculate the chance of ultimate fixation and the time scales.

Mean growth rate when rare is not a reliable metric for persistence of species

Abstract: The coexistence of many species within ecological communities poses a long-standing theoretical puzzle. Modern coexistence theory (MCT) and related techniques explore this phenomenon by examining the chance of a species population growing from rarity in the presence of all other species. The mean growth rate when rare, 𝔼[r], is used in MCT as a metric that measures persistence properties (like invasibility or time to extinction) of a population. Here we critique this reliance on 𝔼[r] and show that it fails to capture the effect of random abundance variations on persistence properties. The problem becomes particularly severe when an increase in the amplitude of stochastic temporal environmental variations leads to an increase in 𝔼[r], since at the same time it enhances random abundance fluctuations and the two effects are inherently intertwined. In this case, the chance of invasion and the mean extinction time of a population may even go down as 𝔼[r] increases.

Taming the diffusion approximation through a controlling-factor WKB method.

Abstract: The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. The DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied. This failure becomes severe in situations where the direction of selection switches sign. Here we employ the WKB (Wentzel-Kramers-Brillouin) large-deviations method, which requires only the logarithm of a given quantity to be smooth over its state space. Combining the WKB scheme with asymptotic matching techniques, we show how to derive the diffusion approximation in a controlled manner and how to produce better approximations, applicable for much wider regimes of parameters. We also introduce a scalable (independent of population size) WKB-based numerical technique. The method is applied to a central problem in population genetics and evolution, finding the chance of ultimate fixation in a zero-sum, two-types competition.

Invasion growth rate and its relevance to persistence: a response to Technical Comment by Ellner et al.

Abstract: Ellner et al. (2020) state that identifying the mechanisms producing positive invasion growth rates (IGR) is useful in characterising species persistence. We agree about the importance of the sign of IGR as a binary indicator of persistence, but question whether its magnitude provides much information once the sign is given.

Intraspecific variability in fluctuating environments: mechanisms of impact on species diversity.

Abstract: Recent studies have found considerable trait variations within species. The effect of such intra-specific trait variability (ITV) on the stability, coexistence and diversity of ecological communities received considerable attention and in many models it was shown to impede coexistence and decrease species diversity. Here we present a numerical study of the effect of genetically inherited ITV on species persistence and diversity in a temporally uctuating environment. Two mechanisms are identified. First, ITV buffers populations against varying environmental conditions (portfolio effect) and reduces variation in abundances. Second, the interplay between ITV and environmental variations tends to increase the mean fitness of diverse populations. The first mechanism promotes persistence and tends to increase species richness, while the second reduces the chance of a rare species population (which is usually homogeneous) to invade, thus decreasing species richness. We show that for large communities the portfolio effect is dominant, leading to ITV promoting species persistence and richness.

Stochasticity-induced stabilization in ecology and evolution: a new synthesis

Abstract: The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log-abundances of species, with mean logarithmic growth rates when rare, $\mathbb{E}[r]$, used as metrics for persistence. However, invasion probabilities and the times to extinction are not single-valued functions of $\mathbb{E}[r]$ and, in some cases, decrease as $\mathbb{E}[r]$ increases. Here, we present a synthesis of stochasticity-induced stabilization (SIS) phenomena based on the ratio between the expected arithmetic growth $\mu$ and its variance $g$. When the diffusion approximation holds, explicit formulas for invasion probabilities and persistence times are single valued, monotonic functions of $\mu/g$. The storage effect in the lottery model, together with other well-known examples drawn from population genetics, microbiology and ecology (including discrete and continuous dynamics, with overlapping and non-overlapping generations), are placed together, reviewed, and explained within this new, transparent theoretical framework. We also clarify the relationships between life-history strategies and SIS, and study the dynamics of extinction when SIS fails.

Population dynamics in stochastic environments

Abstract: Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference (master) equation, but closed-form solutions of these equations are rare. Analytical insights in fields like population genetics, ecology and evolution rely, almost exclusively, on an uncontrolled application of the diffusion approximation (DA) which assumes the smoothness of the relevant quantities over the set of integers. Here we combine asymptotic matching techniques with a first-order (controlling-factor) WKB method to obtain a theory whose range of applicability is much wider. This allows us to rederive DA from a more general theory, to identify its limitations, and to suggest alternative analytical solutions and scalable numerical techniques when it fails. We carry out our analysis for the calculation of the fixation probability in a fluctuating environment, highlighting the difference between (on average) deleterious and beneficial mutant invasion and the intricate distinction between weak and strong selection.