Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with stochastic noise terms that characterize population fluctuations. The effects of the stochastic population fluctuations on diversity and total population sizes on evolutionary time scales are studied. In one model, species can make either predator-prey, mutualistic, or competitive interactions, while the other model allows only predator-prey interactions. When the noise in the population dynamics is strong enough, both models show intermittent behavior and their power spectral densities show approximate $1/f$ fluctuations. In the noiseless limit, the two models have different power spectral densities. For the predator-prey model, $1/f^2$ fluctuations appears, indicating random-walk like behavior, while the other model still shows $1/f$ noise. These results indicate that stochastic population fluctuations may significantly affect long-time evolutionary dynamics.
Despite great interest in techniques for stabilizing the dynamics of biological populations and metapopulations, very few practicable methods have been developed. We propose an easily implementable method, Adaptive Limiter Control (ALC), for reducing extinction frequencies and the magnitude of fluctuation in population sizes and demonstrate its efficacy in stabilizing laboratory populations and metapopulations of Drosophila melanogaster. Metapopulation stability was attained through a combination of reduced size fluctuations and synchrony at the subpopulation level. Simulations indicated that …
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species, while migrants have no correlation with the resident species. It is found that the dynamics of community assembly with mutations are quite different from the case with migrations. In contrast to mutation models, which show intermittent dynamics of quasi-steady states interrupted by sudden reorganizations of the community, migration models show smooth and gradu…
Biological populations are subject to fluctuating environmental conditions. Different adaptive strategies can allow them to cope with these fluctuations: specialization to one particular environmental condition, adoption of a generalist phenotype that compromise between conditions, or population-wise diversification (bet-hedging). Which strategy provides the largest selective advantage in the long run depends on the range of accessible phenotypes and the statistics of the environmental fluctuations. Here, we analyze this problem in a simple mathematical model of population growth. First, we re…
Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. While these inequalities have been derived before for age controlled models with negligible mother-daughter correlations, we show that they also hold for a broad class of size-controlled models. We discuss the implications of this result for the interpretation o…
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the …
Previously, we developed a population model incorporating the Allee effect and periodic environmental fluctuations, in which organisms alternate between nomadic and colonial behaviours. This switching strategy is regulated by biological clocks and the abundance of environmental resources, and can lead to population persistence despite both behaviours being individually losing. In the present study, we consider stochastic noise models in place of the original periodic ones, thereby allowing a wider range of environmental fluctuations to be modelled. The theoretical framework is generalized to a…
Gene expression is a biochemical process, where stochastic binding and un-binding events naturally generate fluctuations and cell-to-cell variability in gene dynamics. These fluctuations typically have destructive consequences for proper biological dynamics and function (e.g., loss of timing and synchrony in biological oscillators). Here, we show that gene expression noise counter-intuitively accelerates the evolution of a biological oscillator and, thus, can impart a benefit to living organisms. We used computer simulations to evolve two mechanistic models of a biological oscillator at differ…
Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet-hedging, to increase their probability of survival under stressful environmental fluctutation. In this context, the concept of preadaptation refers to a common type of bet-hedging protection strategy in which a relatively small number of individuals in a population stochastically switch their phenotypes to a `dormant' metabolic state in which they increase their probability of survival against potential environmental shocks. Hence, if an environmental shock took place at…
In a genetic algorithm, fluctuations of the entropy of a genome over time are interpreted as fluctuations of the information that the genome's organism is storing about its environment, being this reflected in more complex organisms. The computation of this entropy presents technical problems due to the small population sizes used in practice. In this work we propose and test an alternative way of measuring the entropy variation in a population by means of algorithmic information theory, where the entropy variation between two generational steps is the Kolmogorov complexity of the first step c…
In order to increase their robustness against environmental fluctuations, many biological populations have developed bet-hedging mechanisms in which the population `bets' against the presence of prolonged favorable environmental conditions by having a few individual behaving as if they sensed a threatening or stressful environment. As a result, the population (as a whole) increases its chances of surviving environmental fluctuations in the long term, while sacrificing short-term performance. In this paper, we propose a theoretical framework, based on Markov jump linear systems, to model and ev…
Climate-mediated changes in the spatiotemporal distribution of thermal stress can destabilize animal populations and promote extinction risk. Using quantile, spectral, and wavelet analyses of temperature projections from the latest generation of earth system models, we show that significant regional differences are expected to arise in the way that temperatures will increase over time. When integrated into empirically-parameterized mathematical models that simulate the dynamical and cumulative effects of thermal stress on the performance of 38 global ectotherm species, the projected spatiotemp…
Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to re…
The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially-extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and non-orthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, …
Biological organisms have to cope with stochastic variations in both the external environment and the internal population dynamics. Theoretical studies and laboratory experiments suggest that population diversification could be an effective bet-hedging strategy for adaptation to varying environments. Here we show that bet-hedging can also be effective against demographic fluctuations that pose a trade-off between growth and survival for populations even in a constant environment. A species can maximize its overall abundance in the long term by diversifying into coexisting subpopulations of bot…
System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case, it is useful to resort to simplified models relying on effective stochastic equations. A natural consideration is to assume that there is a noisy contribution from the environment, such that the parameters which characterize it are not constant but instead fluctuate around their characteristic values. From this perspective, we propose a stochastic generalizat…
We consider a general class of Markovian models describing the growth in a randomly fluctuating environment of a clonal biological population having several phenotypes related by stochastic switching. Phenotypes differ e.g. by the level of gene expression for a population of bacteria. The time-averaged growth rate of the population, $Λ$, is self-averaging in the limit of infinite times; it may be understood as the fitness of the population in a context of Darwinian evolution. The observation time $T$ being however typically finite, the growth rate fluctuates. For $T$ finite but large, we obtai…
