Population dynamics, demographic stochasticity, and the evolution of cooperation

A basic evolutionary problem posed by the Iterated Prisoner’s Dilemma game is to understand when the paradigmatic cooperative strategy Tit-for-Tat can invade a population of pure defectors. Deterministically, this is impossible. We consider the role of demographic stochasticity by embedding the Iterated Prisoner’s Dilemma into a population dynamic framework. Tit-for-Tat can invade a population of defectors when their dynamics exhibit short episodes of high population densities with subsequent crashes and long low density periods with strong genetic drift. Such dynamics tend to have reddened power spectra and temporal distributions of population size that are asymmetric and skewed toward low densities. The results indicate that ecological dynamics are important for evolutionary shifts between adaptive peaks.

Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.

Metapopulation extinction caused by mutation accumulation

Theory suggests that the risk of extinction by mutation accumulation can be comparable to that by environmental stochasticity for an isolated population smaller than a few thousand individuals. Here we show that metapopulation structure, habitat loss or fragmentation, and environmental stochasticity can be expected to greatly accelerate the accumulation of mildly deleterious mutations, lowering the genetic effective size to such a degree that even large metapopulations may be at risk of extinction. Because of mutation accumulation, viable metapopulations may need to be far larger and better connected than would be required under just stochastic demography.

Estimating risks in declining populations with poor data

Census data on endangered species are often sparse, error-ridden, and confined to only a segment of the population. Estimating trends and extinction risks using this type of data presents numerous difficulties. In particular, the estimate of the variation in year-to-year transitions in population size (the “process error” caused by stochasticity in survivorship and fecundities) is confounded by the addition of high sampling error variation. In addition, the year-to-year variability in the segment of the population that is sampled may be quite different from the population variability that one is trying to estimate. The combined effect of severe sampling error and age- or stage-specific counts leads to severe biases in estimates of population-level parameters. I present an estimation method that circumvents the problem of age- or stage-specific counts and is markedly robust to severe sampling error. This method allows the estimation of environmental variation and population trends for extinction-risk analyses using corrupted census counts—a common type of data for endangered species that has hitherto been relatively unusable for these analyses.

Evolution of genome–phenome diversity under environmental stress

The genomic era revolutionized evolutionary biology. The enigma of genotypic-phenotypic diversity and biodiversity evolution of genes, genomes, phenomes, and biomes, reviewed here, was central in the research program of the Institute of Evolution, University of Haifa, since 1975. We explored the following questions. (i) How much of the genomic and phenomic diversity in nature is adaptive and processed by natural selection? (ii) What is the origin and evolution of adaptation and speciation processes under spatiotemporal variables and stressful macrogeographic and microgeographic environments? We advanced ecological genetics into ecological genomics and analyzed globally ecological, demographic, and life history variables in 1,200 diverse species across life, thousands of populations, and tens of thousands of individuals tested mostly for allozyme and partly for DNA diversity. Likewise, we tested thermal, chemical, climatic, and biotic stresses in several model organisms. Recently, we introduced genetic maps and quantitative trait loci to elucidate the genetic basis of adaptation and speciation. The genome–phenome holistic model was deciphered by the global regressive, progressive, and convergent evolution of subterranean mammals. Our results indicate abundant genotypic and phenotypic diversity in nature. The organization and evolution of molecular and organismal diversity in nature at global, regional, and local scales are nonrandom and structured; display regularities across life; and are positively correlated with, and partly predictable by, abiotic and biotic environmental heterogeneity and stress. Biodiversity evolution, even in small isolated populations, is primarily driven by natural selection, including diversifying, balancing, cyclical, and purifying selective regimes, interacting with, but ultimately overriding, the effects of mutation, migration, and stochasticity.