How does temporal variability affect predictions of weed population numbers?

1. Population models that are used to predict weed population dynamics or the impact of control measures on weed abundance typically ignore temporal variability in life-history parameters and control measures, and utilize mean arithmetic population growth rates to predict population abundance.
2. We demonstrate that the persistence of weeds in a stochastically varying environment depends on the geometric mean population growth rate being greater than zero, rather than the arithmetic mean population growth rate being greater than zero.
3. In a stochastically varying environment we show that temporal variability in fecundity, germination and survivorship will tend to decrease population size, relative to predictions based on arithmetic means. Conversely, variability in competitive effects and weed control will tend to increase population size, relative to predictions based on arithmetic mean values. The distinction between these two sets of parameters is that increases in the former will increase population growth rate, whereas increases in the latter will decrease it.
4. We argue that population models based on arithmetic mean population growth rates will tend to over-estimate population size. Numerical simulations indicate that this bias may be considerable.
5. Since short-term studies cannot, in general, estimate the geometric mean growth rate of a population we suggest several approaches for estimating the degree of bias in the predictions of models owing to the effects of variability. Accounting for such variability is necessary since current models for the dynamics of weed populations are based on arithmetic mean measures of population growth and hence likely to be biased.     

Expected relative fitness and the adaptive topography of fluctuating selection

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.     

Evolution of complex dynamics in spatially structured populations

Dynamics of populations depend on demographic parameters which may change during evolution. In simple ecological models given by one-dimensional difference equations, the evolution of demographic parameters generally leads to equilibrium population dynamics. Here we show that this is not true in spatially structured ecological models. Using a multi-patch metapopulation model, we study the evolutionary dynamics of phenotypes that differ both in their response to local crowding, i.e. in their competitive behaviour within a habitat, and in their rate of dispersal between habitats. Our simulation results show that evolution can favour phenotypes that have the intrinsic potential for very complex dynamics provided that the environment is spatially structured and temporally variable. These phenotypes owe their evolutionary persistence to their large dispersal rates. They typically coexist with phenotypes that have low dispersal rates and that exhibit equilibrium dynamics when alone. This coexistence is brought about through the phenomenon of evolutionary branching, during which an initially uniform population splits into the two phenotypic classes.     

The implications of rapid eco‐evolutionary processes for biological control ‐ a review

Novel environmental conditions experienced by introduced species can drive rapid evolution of diverse traits. In turn, rapid evolution, both adaptive and non‐adaptive, can influence population size, growth rate, and other important ecological characteristics of populations. In addition, spatial evolutionary processes that arise from a combination of assortative mating between highly dispersive individuals at the expanding edge of populations and altered reproductive rates of those individuals can accelerate expansion speed. Growing experimental evidence shows that the effects of rapid evolution on ecological dynamics can be quite large, and thus it can affect establishment, persistence, and the distribution of populations. We review the experimental and theoretical literature on such eco‐evolutionary feedbacks and evaluate the implications of these processes for biological control. Experiments show that evolving populations can establish at higher rates and grow larger than non‐evolving populations. However, non‐adaptive processes, such as genetic drift and inbreeding depression can also lead to reduced fitness and declines in population size. Spatial evolutionary processes can increase spread rates and change the fitness of individuals at the expansion front. These examples demonstrate the power of eco‐evolutionary dynamics and indicate that evolution is likely more important in biocontrol programs than previously realized. We discuss how this knowledge can be used to enhance efficacy of biological control.     

The impact of bottlenecks on microbial survival,adaptation, and phenotypic switching in host–pathogen interactions

Microbial pathogens and viruses can often maintain sufficient population diversity to evade a wide range of host immune responses. However, when populations experience bottlenecks, as occurs frequently during initiation of new infections, pathogens require specialized mechanisms to regenerate diversity. We address the evolution of such mechanisms, known as stochastic phenotype switches, which are prevalent in pathogenic bacteria. We analyze a model of pathogen diversification in a changing host environment that accounts for selective bottlenecks, wherein different phenotypes have distinct transmission probabilities between hosts. We show that under stringent bottlenecks, such that only one phenotype can initiate new infections, there exists a threshold stochastic switching rate below which all pathogen lineages go extinct, and above which survival is a near certainty. We determine how quickly stochastic switching rates can evolve by computing a fitness landscape for the evolutionary dynamics of switching rates, and analyzing its dependence on both the stringency of bottlenecks and the duration of within‐host growth periods. We show that increasing the stringency of bottlenecks or decreasing the period of growth results in faster adaptation of switching rates. Our model provides strong theoretical evidence that bottlenecks play a critical role in accelerating the evolutionary dynamics of pathogens.     

From nature to the laboratory: the impact of founder effects on adaptation

Most founding events entail a reduction in population size, which in turn leads to genetic drift effects that can deplete alleles. Besides reducing neutral genetic variability, founder effects can in principle shift additive genetic variance for phenotypes that underlie fitness. This could then lead to different rates of adaptation among populations that have undergone a population size bottleneck as well as an environmental change, even when these populations have a common evolutionary history. Thus, theory suggests that there should be an association between observable genetic variability for both neutral markers and phenotypes related to fitness. Here, we test this scenario by monitoring the early evolutionary dynamics of six laboratory foundations derived from founders taken from the same source natural population of Drosophila subobscura. Each foundation was in turn three‐fold replicated. During their first few generations, these six foundations showed an abrupt increase in their genetic differentiation, within and between foundations. The eighteen populations that were monitored also differed in their patterns of phenotypic adaptation according to their immediately ancestral founding sample. Differences in early genetic variability and in effective population size were found to predict differences in the rate of adaptation during the first 21 generations of laboratory evolution. We show that evolution in a novel environment is strongly contingent not only on the initial composition of a newly founded population but also on the stochastic changes that occur during the first generations of colonization. Such effects make laboratory populations poor guides to the evolutionary genetic properties of their ancestral wild populations.     

From stochastic environments to life histories and back

Environmental stochasticity is known to play an important role in life-history evolution, but most general theory assumes a constant environment. In this paper, we examine life-history evolution in a variable environment, by decomposing average individual fitness (measured by the long-run stochastic growth rate) into contributions from average vital rates and their temporal variation. We examine how generation time, demographic dispersion (measured by the dispersion of reproductive events across the lifespan), demographic resilience (measured by damping time), within-year variances in vital rates, within-year correlations between vital rates and between-year correlations in vital rates combine to determine average individual fitness of stylized life histories. In a fluctuating environment, we show that there is often a range of cohort generation times at which the fitness is at a maximum. Thus, we expect ‘optimal’ phenotypes in fluctuating environments to differ from optimal phenotypes in constant environments. We show that stochastic growth rates are strongly affected by demographic dispersion, even when deterministic growth rates are not, and that demographic dispersion also determines the response of life-history-specific average fitness to within- and between-year correlations. Serial correlations can have a strong effect on fitness, and, depending on the structure of the life history, may act to increase or decrease fitness. The approach we outline takes a useful first step in developing general life-history theory for non-constant environments.     

Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.     

QUANTITATIVE GENETICS AND POPULATION DYNAMICS

This study examines the dynamics of a competition and a host-parasite model in which the interactions are determined by quantitative characters. Both models are extensions of one-dimensional difference equations that can exhibit complicated dynamics. Compared to these basic models, the phenotypic variability given by the quantitative characters reduces the size of the density fluctuations in asexual populations. With sexual reproduction, which is described by modeling the genetics of the quantitative character explicitly with many haploid loci that determine the character additively, this reduction in fitness variance is magnified. Moreover, quantitative genetics can induce simple dynamics. For example, the sexual population can have a two-cycle when the asexual system is chaotic. This paper discusses the consequences for the evolution of sex. The higher mean growth rate implied by the lower fitness variance in sexual populations is an advantage that can overcome a twofold intrinsic growth rate of asexuals. The advantage is bigger when the asexual population contains only a subset of the phenotypes present in the sexual population, which conforms with the tangled bank theory for the evolution of sex and shows that tangled bank effects also occur in host-parasite systems. The results suggest that explicitly describing the genetics of a quantitative character leads to more flexible models than the usual assumption of normal character distributions, and therefore to a better understanding of the character's impact on population dynamics.     

Self-fertilization and the escape from pollen limitation in variable pollination environments

Seed production in many plants is pollen limited, likely because of unpredictable variation in the pollinator environment. One way for plants to escape the consequences of pollinator variability is to evolve mating systems, such as autonomous selfing, that assure reproduction without relying on pollinators. We explore this hypothesis through the construction and analysis of heuristic models of plant population dynamics in seed- or site-limited populations. Our analysis suggests several important points: the familiar rule that inbreeding depression greater than 0.5 maintains outcrossing significantly underestimates the threshold required under pollen limited conditions with prior selfing; variability in the pollination environment erodes the ability of inbreeding depression to maintain outcrossing; and variable pollination environments can result in stable intermediate rates of prior selfing. The results reflect the importance of geometric mean fitness (which in a variable environment is less than the arithmetic mean) in the face of temporal variation.     

The strength of genetic interactions scales weakly with mutational effects

Background

Genetic interactions pervade every aspect of biology, from evolutionary theory, where they determine the accessibility of evolutionary paths, to medicine, where they can contribute to complex genetic diseases. Until very recently, studies on epistatic interactions have been based on a handful of mutations, providing at best anecdotal evidence about the frequency and the typical strength of genetic interactions. In this study, we analyze a publicly available dataset that contains the growth rates of over five million double knockout mutants of the yeast Saccharomyces cerevisiae.

Results

We discuss a geometric definition of epistasis that reveals a simple and surprisingly weak scaling law for the characteristic strength of genetic interactions as a function of the effects of the mutations being combined. We then utilized this scaling to quantify the roughness of naturally occurring fitness landscapes. Finally, we show how the observed roughness differs from what is predicted by Fisher''s geometric model of epistasis, and discuss the consequences for evolutionary dynamics.

Conclusions

Although epistatic interactions between specific genes remain largely unpredictable, the statistical properties of an ensemble of interactions can display conspicuous regularities and be described by simple mathematical laws. By exploiting the amount of data produced by modern high-throughput techniques, it is now possible to thoroughly test the predictions of theoretical models of genetic interactions and to build informed computational models of evolution on realistic fitness landscapes.     

Escaping an evolutionary lobster trap: drug resistance and compensatory mutation in a fluctuating environment

The fitness landscape concept aids intuition on adaptive evolution through low fitness genotypes. Evolutionary processes become complex when environments and therefore fitnesses fluctuate. Antibiotic resistance evolution in bacteria is an important example of such dynamics. Resistance bears a cost in the drug-free environment, but compensatory mutation can lower this cost, creating a fitness valley. With the drug present, the valley becomes a hill that is easily climbed. Once a population is dominated by resistant-compensated genotypes, reversion to sensitivity is difficult: this phenomenon has been described as an evolutionary lobster trap. With increasing frequencies of drug resistance among pathogenic bacteria, it is critical to understand how this trap can be escaped. Here, we develop stochastic models to investigate these dynamics. The residual fitness cost (the cost remaining after compensatory mutation has occurred) is a key parameter. Reversion to sensitivity is favored when the time spent in the absence of the drug relative to its presence is high compared to the residual fitness cost. Population sizes are also important: in large populations, resistant-compensated mutants appear in resistant-uncompensated or sensitive-compensated genotypes without fixation of these intermediates. This stochastic tunneling effect occurs when sufficient time is allowed by the rates of environmental fluctuation.     

A life‐history perspective on the demographic drivers of structured population dynamics in changing environments

Current understanding of life‐history evolution and how demographic parameters contribute to population dynamics across species is largely based on assumptions of either constant environments or stationary environmental variation. Meanwhile, species are faced with non‐stationary environmental conditions (changing mean, variance, or both) created by climate and landscape change. To close the gap between contemporary reality and demographic theory, we develop a set of transient life table response experiments (LTREs) for decomposing realised population growth rates into contributions from specific vital rates and components of population structure. Using transient LTREs in a theoretical framework, we reveal that established concepts in population biology will require revision because of reliance on approaches that do not address the influence of unstable population structure on population growth and mean fitness. Going forward, transient LTREs will enhance understanding of demography and improve the explanatory power of models used to understand ecological and evolutionary dynamics.     

Beyond simple adaptation: Incorporating other evolutionary processes and concepts into eco-evolutionary dynamics

Studies of eco-evolutionary dynamics have integrated evolution with ecological processes at multiple scales (populations, communities and ecosystems) and with multiple interspecific interactions (antagonistic, mutualistic and competitive). However, evolution has often been conceptualised as a simple process: short-term directional adaptation that increases population growth. Here we argue that diverse other evolutionary processes, well studied in population genetics and evolutionary ecology, should also be considered to explore the full spectrum of feedback between ecological and evolutionary processes. Relevant but underappreciated processes include (1) drift and mutation, (2) disruptive selection causing lineage diversification or speciation reversal and (3) evolution driven by relative fitness differences that may decrease population growth. Because eco-evolutionary dynamics have often been studied by population and community ecologists, it will be important to incorporate a variety of concepts in population genetics and evolutionary ecology to better understand and predict eco-evolutionary dynamics in nature.     

A complete classification of Darwinian extinction in ecological interactions

The evolution of a population by individual-level natural selection can result in the population's extinction. Selection causes the spread of phenotypes with higher relative fitness, but at the same time, selection can also indirectly produce changes in the physical, biotic, or genotypical environment through population interactions (e.g., environment modification, interspecific interactions, and genomic conflict). Because fitness is environment dependent, this can cause mean fitness to decrease, resulting in extinction. I call this process "Darwinian extinction." Examples of Darwinian extinction include a variety of dynamics and modes of extinction, but the variation is constrained. I determine the complete classification of possible dynamics and modes of Darwinian extinction due to ecological interactions, using bifurcation theory and models with ecological and evolutionary changes occurring on different timescales. This classification is also extended to extinctions due to interactions within the population. The mode of extinction may be either sudden or gradual (requiring additional stochastic processes), and each mode has specific types of dynamics associated with it. Darwinian extinction is a robust and normal phenomenon, and this reasonably complete classification can help us understand more thoroughly its role in nature.     

Evolutionary game dynamics in finite populations

We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.     

EVOLUTIONARY EPIDEMIOLOGY AND THE DYNAMICS OF ADAPTATION

The mean fitness of a population, often equal to its growth rate, measures its level of adaptation to particular environmental conditions. A better understanding of the evolution of mean fitness could thus provide a natural link between evolution and demography. Yet, after the seminal work of Fisher and its renowned "fundamental theorem of natural selection," the dynamics of mean fitness has attracted little attention, and mostly from theoretical population geneticists. Here we analyze the dynamics of mean fitness in the context of host-parasite interactions. We illustrate the potential relevance of this analysis under different scenarios ranging from a simple situation in which a parasite evolves in a homogeneous host population to a more complex one with host-parasite coevolution. In each case, we contrast the effects of natural selection, recurrent mutations, and the change of the biotic environment, on the dynamics of adaptation. Decoupling these three components helps elucidate the interplay between evolutionary and ecological dynamics. In particular, it offers new perspectives on situations leading to evolutionary suicide. As mean fitness is an easily measurable quantity in microbial systems, this analysis provides new ways to track the dynamics of adaptation in experimental evolution and coevolution studies.     

Mapping the environmental fitness landscape of a synthetic gene circuit

Gene expression actualizes the organismal phenotypes encoded within the genome in an environment-dependent manner. Among all encoded phenotypes, cell population growth rate (fitness) is perhaps the most important, since it determines how well-adapted a genotype is in various environments. Traditional biological measurement techniques have revealed the connection between the environment and fitness based on the gene expression mean. Yet, recently it became clear that cells with identical genomes exposed to the same environment can differ dramatically from the population average in their gene expression and division rate (individual fitness). For cell populations with bimodal gene expression, this difference is particularly pronounced, and may involve stochastic transitions between two cellular states that form distinct sub-populations. Currently it remains unclear how a cell population's growth rate and its subpopulation fractions emerge from the molecular-level kinetics of gene networks and the division rates of single cells. To address this question we developed and quantitatively characterized an inducible, bistable synthetic gene circuit controlling the expression of a bifunctional antibiotic resistance gene in Saccharomyces cerevisiae. Following fitness and fluorescence measurements in two distinct environments (inducer alone and antibiotic alone), we applied a computational approach to predict cell population fitness and subpopulation fractions in the combination of these environments based on stochastic cellular movement in gene expression space and fitness space. We found that knowing the fitness and nongenetic (cellular) memory associated with specific gene expression states were necessary for predicting the overall fitness of cell populations in combined environments. We validated these predictions experimentally and identified environmental conditions that defined a "sweet spot" of drug resistance. These findings may provide a roadmap for connecting the molecular-level kinetics of gene networks to cell population fitness in well-defined environments, and may have important implications for phenotypic variability of drug resistance in natural settings.     

Equilibrium selection in evolutionary games with random matching of players

We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant one, where players are averse to risks. We assume that individuals play with randomly chosen opponents (they do not play against average strategies as in the standard replicator dynamics). We show that the long-run behavior of a population depends on its size and the mutation level.