Mutation Rate Evolution in Replicator Dynamics

The mutation rate of an organism is itself evolvable. In stable environments, if faithful replication is costless, theory predicts that mutation rates will evolve to zero. However, positive mutation rates can evolve in novel or fluctuating environments, as analytical and empirical studies have shown. Previous work on this question has focused on environments that fluctuate independently of the evolving population. Here we consider fluctuations that arise from frequency-dependent selection in the evolving population itself. We investigate how the dynamics of competing traits can induce selective pressure on the rates of mutation between these traits. To address this question, we introduce a theoretical framework combining replicator dynamics and adaptive dynamics. We suppose that changes in mutation rates are rare, compared to changes in the traits under direct selection, so that the expected evolutionary trajectories of mutation rates can be obtained from analysis of pairwise competition between strains of different rates. Depending on the nature of frequency-dependent trait dynamics, we demonstrate three possible outcomes of this competition. First, if trait frequencies are at a mutation–selection equilibrium, lower mutation rates can displace higher ones. Second, if trait dynamics converge to a heteroclinic cycle—arising, for example, from “rock-paper-scissors” interactions—mutator strains succeed against non-mutators. Third, in cases where selection alone maintains all traits at positive frequencies, zero and nonzero mutation rates can coexist indefinitely. Our second result suggests that relatively high mutation rates may be observed for traits subject to cyclical frequency-dependent dynamics.     

Dynamic-persistence of cooperation in public good games when group size is dynamic

The evolution of cooperation is possible with a simple model of a population of agents that can move between groups. The agents play public good games within their group. The relative fitness of individuals within the whole population affects their number of offspring. Groups of cooperators evolve but over time are invaded by defectors which eventually results in the group's extinction. However, for small levels of migration and mutation, high levels of cooperation evolve at the population level. Thus, evolution of cooperation based on individual fitness without kin selection, indirect or direct reciprocity is possible. We provide an analysis of the parameters that affect cooperation, and describe the dynamics and distribution of population sizes over time.     

Can natural selection favour altruism between species?

Darwin suggested that the discovery of altruism between species would annihilate his theory of natural selection. However, it has not been formally shown whether between‐species altruism can evolve by natural selection, or why this could never happen. Here, we develop a spatial population genetic model of two interacting species, showing that indiscriminate between species helping can be favoured by natural selection. We then ask if this helping behaviour constitutes altruism between species, using a linear‐regression analysis to separate the total action of natural selection into its direct and indirect (kin selected) components. We show that our model can be interpreted in two ways, as either altruism within species, or altruism between species. This ambiguity arises depending on whether or not we treat genes in the other species as predictors of an individual's fitness, which is equivalent to treating these individuals as agents (actors or recipients). Our formal analysis, which focuses upon evolutionary dynamics rather than agents and their agendas, cannot resolve which is the better approach. Nonetheless, because a within‐species altruism interpretation is always possible, our analysis supports Darwin's suggestion that natural selection does not favour traits that provide benefits exclusively to individuals of other species.     

Inertia: the discrepancy between individual and common good in dispersal and prospecting behaviour

The group selection debate of the 1960s made it clear that evolution does not necessarily increase population performance. Individuals can be selected to have traits that diminish a common good and make population persistence difficult. At the extreme, the discrepancy between levels of selection is predicted to make traits evolve towards values at which a population can no longer persist (evolutionary suicide). Dispersal and prospecting are prime examples of traits that have a strong influence on population persistence under environmental and demographic stochasticity. Theory predicts that an ‘optimal’ dispersal strategy from a population point of view can differ considerably from that produced by individual‐level selection. Because dispersal is frequently risky or otherwise costly, individuals are often predicted to disperse less than would be ideal for population performance (persistence or size). We define this discrepancy as ‘inertia’ and examine current knowledge of its occurrence and effects on population dynamics in nature. We argue that inertia is potentially widespread but that a framework is currently lacking for predicting precisely the extent to which it has a real influence on population persistence. The opposite of inertia, ‘hypermobility’ (more dispersal by individuals than would maximize population performance) remains a possibility: it is known that highest dispersal rates do not lead to best expected population performance, and examples of such high dispersal evolving exist at least in the theoretical literature. We also show, by considering prospecting behaviour, that similar issues arise in species with advanced cognitive and learning abilities. Individual prospecting strategies and the information acquired during dispersal are known to influence the decisions and therefore the fate of individuals and, as a corollary, populations. Again, the willingness of individuals to sample environments might evolve to levels that are not optimal for populations. This conflict can take intriguing forms. For example, better cognitive abilities of individuals may not always lead to better population‐level performance. Simulation studies have found that ‘blind’ dispersal can lead to better connected metapopulations than cognitively more advanced habitat choice rules: the latter can lead to too many individuals sticking to nearby safe habitat. The study of the mismatch between individual and population fitness should not be a mere intellectual exercise. Population managers typically need to take a population‐level view of performance, which may necessitate human intervention if it differs from what is selected for. We conclude that our knowledge of inertia and hypermobility would advance faster if theoretical studies—without much additional effort—quantified the population consequences of the evolving traits and compared this with hypothetical (not selectively favoured) dispersal rules, and if empirical studies were similarly conducted with the differing levels of selection in mind.     

Selective feedback between dispersal distance and the stability of mutualism

The evolution and maintenance of mutually beneficial interactions has been one of the oldest problems for evolutionary theory. For cooperation to be stable, mechanisms such as spatial population structure must exist that prevent non‐cooperative individuals from invading cooperative groups. Selection for certain traits like increased dispersal can erode that structure. Here, I used a spatially explicit individual based dual lattice computer simulation to investigate how the evolution of dispersal interacts with the evolution of mutualism and how this interaction affects the stability of mutualism in the face of non‐mutualists. I ran simulations manipulating the self‐structuring phenotype, dispersal distance, over a range of environmental conditions, as well as letting both dispersal and mutualism evolve independently, with and without a cost of dispersal. I found that environmental productivity is negatively correlated with the stability of mutualism, and that the stability of mutualism relied on the ability of mutualists to evolve shorter dispersal distances than non‐mutualists. The inclusion of a dispersal cost essentially fixed the upper limit of dispersal, and therefore limits the ability of non‐mutualists to evolve higher average dispersal than mutualists, but as costs are relaxed, the differences are recovered. These results show how selection on seemingly unrelated traits can align suites of traits into holistic life history strategies.     

Consumer-resource dynamics: quantity, quality, and allocation

Background

The dominant paradigm for modeling the complexities of interacting populations and food webs is a system of coupled ordinary differential equations in which the state of each species, population, or functional trophic group is represented by an aggregated numbers-density or biomass-density variable. Here, using the metaphysiological approach to model consumer-resource interactions, we formulate a two-state paradigm that represents each population or group in a food web in terms of both its quantity and quality.

Methodology and Principal Findings

The formulation includes an allocation function controlling the relative proportion of extracted resources to increasing quantity versus elevating quality. Since lower quality individuals senesce more rapidly than higher quality individuals, an optimal allocation proportion exists and we derive an expression for how this proportion depends on population parameters that determine the senescence rate, the per-capita mortality rate, and the effects of these rates on the dynamics of the quality variable. We demonstrate that oscillations do not arise in our model from quantity-quality interactions alone, but require consumer-resource interactions across trophic levels that can be stabilized through judicious resource allocation strategies. Analysis and simulations provide compelling arguments for the necessity of populations to evolve quality-related dynamics in the form of maternal effects, storage or other appropriate structures. They also indicate that resource allocation switching between investments in abundance versus quality provide a powerful mechanism for promoting the stability of consumer-resource interactions in seasonally forcing environments.

Conclusions/Significance

Our simulations show that physiological inefficiencies associated with this switching can be favored by selection due to the diminished exposure of inefficient consumers to strong oscillations associated with the well-known paradox of enrichment. Also our results demonstrate how allocation switching can explain observed growth patterns in experimental microbial cultures and discuss how our formulation can address questions that cannot be answered using the quantity-only paradigms that currently predominate.     

Individual differences, density dependence and offspring birth traits in a population of red deer

Variation between individuals is an essential component of natural selection and evolutionary change, but it is only recently that the consequences of persistent differences between individuals on population dynamics have been considered. In particular, few authors have addressed whether interactions exist between individual quality and environmental variation. In part, this is due to the difficulties of collecting sufficient data, but also the challenge of defining individual quality. Using a long-established study population of red deer, Cervus elaphus, inhabiting the North Block of the Isle of Rum, and three quality measures, this paper investigates how differences in maternal quality affect variation in birth body mass and date, as population density varies, and how this differs depending on the sex of the offspring and the maternal quality measure used. Significant interactions between maternal quality, measured as a hind's total contribution to population growth, and population density are reported for birth mass, but only for male calves. Analyses using dominance or age at primiparity to define maternal quality showed no significant interactions with population density, highlighting the difficulties of defining a consistent measure of individual quality.     

Co-evolutionary Dynamics of Collective Action with Signaling for a Quorum

Collective signaling for a quorum is found in a wide range of organisms that face collective action problems whose successful solution requires the participation of some quorum of the individuals present. These range from humans, to social insects, to bacteria. The mechanisms involved, the quorum required, and the size of the group may vary. Here we address the general question of the evolution of collective signaling at a high level of abstraction. We investigate the evolutionary dynamics of a population engaging in a signaling N-person game theoretic model. Parameter settings allow for loners and cheaters, and for costly or costless signals. We find a rich dynamics, showing how natural selection, operating on a population of individuals endowed with the simplest strategies, is able to evolve a costly signaling system that allows individuals to respond appropriately to different states of Nature. Signaling robustly promotes cooperative collective action, in particular when coordinated action is most needed and difficult to achieve. Two different signaling systems may emerge depending on Nature’s most prevalent states.     

Travel costs, oviposition behaviour and the dynamics of insect–plant systems

Insect attack can have major consequences for plant population dynamics. We used individually based simulation models to ask how insect oviposition behaviour influences persistence and potential stability of an herbivore–plant system. We emphasised effects on system dynamics of herbivore travel costs and of two kinds of behaviour that might evolve to mitigate travel costs: insect clutch size behaviour (whether eggs are laid singly or in groups) and female aggregation behaviour (whether females prefer or avoid plants already bearing eggs). Travel costs that increase as plant populations drop lead to inverse density dependence of plant reproduction under herbivore attack. Female clutch size and aggregation behaviours also strongly affect system dynamics. When females lay eggs in large clutches or aggregate their clutches, herbivore damage varies strongly among plants, providing probabilistic refuges that permit plant reproduction and persistence. However, the population dynamics depend strongly on whether insect behaviour is fixed or responds adaptively to plant population size: when (and only when) females increase clutch size or aggregation as plants become rare, refuges from herbivory weaken at high plant density, creating inverse density dependence in plant reproduction. Both herbivore travel costs themselves, and also insect behaviour that might evolve in response to travel costs, can thus create plant density dependence—a basic requirement for regulation of plant populations by their insect herbivores.     

Evolutionary dynamics of escape from biomedical intervention

Viruses, bacteria, eukaryotic parasites, cancer cells, agricultural pests and other inconvenient animates have an unfortunate tendency to escape from selection pressures that are meant to control them. Chemotherapy, anti-viral drugs or antibiotics fail because their targets do not hold still, but evolve resistance. A major problem in developing vaccines is that microbes evolve and escape from immune responses. The fundamental question is the following: if a genetically diverse population of replicating organisms is challenged with a selection pressure that has the potential to eradicate it, what is the probability that this population will produce escape mutants? Here, we use multi-type branching processes to describe the accumulation of mutants in independent lineages. We calculate escape dynamics for arbitrary mutation networks and fitness landscapes. Our theory shows how to estimate the probability of success or failure of biomedical intervention, such as drug treatment and vaccination, against rapidly evolving organisms.     

Adaptation to larval crowding in Drosophila ananassae leads to the evolution of population stability

Density-dependent selection is expected to lead to population stability, especially if r and K tradeoff. Yet, there is no empirical evidence of adaptation to crowding leading to the evolution of stability. We show that populations of Drosophila ananassae selected for adaptation to larval crowding have higher K and lower r, and evolve greater stability than controls. We also show that increased population growth rates at high density can enhance stability, even in the absence of a decrease in r, by ensuring that the crowding adapted populations do not fall to very low sizes. We discuss our results in the context of traits known to have diverged between the selected and control populations, and compare our results with previous work on the evolution of stability in D. melanogaster. Overall, our results suggest that density-dependent selection may be an important factor promoting the evolution of relatively stable dynamics in natural populations.     

Evolutionary Convergence to Ideal Free Dispersal Strategies and Coexistence

We study a two species competition model in which the species have the same population dynamics but different dispersal strategies and show how these dispersal strategies evolve. We introduce a general dispersal strategy which can result in the ideal free distributions of both competing species at equilibrium and generalize the result of Averill et al. (2011). We further investigate the convergent stability of this ideal free dispersal strategy by varying random dispersal rates, advection rates, or both of these two parameters simultaneously. For monotone resource functions, our analysis reveals that among two similar dispersal strategies, selection generally prefers the strategy which is closer to the ideal free dispersal strategy. For nonmonotone resource functions, our findings suggest that there may exist some dispersal strategies which are not ideal free, but could be locally evolutionarily stable and/or convergent stable, and allow for the coexistence of more than one species.     

Opposite responses to selection and where to find them

We generally expect traits to evolve in the same direction as selection. However, many organisms possess traits that appear to be costly for individuals, while plant and animal breeding experiments reveal that selection may lead to no response or even negative responses to selection. We formalize both of these instances as cases of “opposite responses to selection.” Using quantitative genetic models for the response to selection, we outline when opposite responses to selection should be expected. These typically occur when social selection opposes direct selection, when individuals interact with others less related to them than a random member of the population, and if the genetic covariance between direct and indirect effects is negative. We discuss the likelihood of each of these occurring in nature and therefore summarize how frequent opposite responses to selection are likely to be. This links several evolutionary phenomena within a single framework.     

Cooperation driven by mutations in multi-person Prisoner's Dilemma

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoner's Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that time-scale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterized by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterized by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size. For some parameter values, we find more than one stable fixed point, corresponding to different structures of the initial population.     

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.     

Evolutionary dynamics of two related malignant plasma cell lines

Cancer is the consequence of sequential acquisition of mutations within somatic cells. Mutations alter the relative reproductive fitness of cells, enabling the population to evolve in time as a consequence of selection. Cancer therapy itself can select for or against specific subclones. Given the large population of tumor cells, subclones inevitably emerge and their fate will depend on the evolutionary dynamics that define the interactions between such clones. Using a combination of in vitro studies and mathematical modeling, we describe the dynamic behavior of two cell lines isolated from the same patient at different time points of disease progression and show how the two clones relate to one another. We provide evidence that the two clones coexisted at the time of initial presentation. The dominant clone presented with biopsy proven cardiac AL amyloidosis. Initial therapy selected for the second clone that expanded leading to a change in the diagnosis to multiple myeloma. The evolutionary dynamics relating the two cell lines are discussed and a hypothesis is generated in regard to the mechanism of one of the phenotypic characteristics that is shared by these two cell lines.     

Severe drought and calf survival in elephants

Climate change in Africa is expected to lead to a higher occurrence of severe droughts in semi-arid and arid ecosystems. Understanding how animal populations react to such events is thus crucial for addressing future challenges for wildlife management and conservation. We explored how gender, age, mother's experience and family group characteristics determined calf survival in an elephant population during a severe drought in Tanzania in 1993. Young males were particularly sensitive to the drought and calf loss was higher among young mothers than among more experienced mothers. We also report high variability in calf mortality between different family groups, with family groups that remained in the National Park suffering heavy calf loss, compared with the ones that left the Park. This study highlights how severe droughts can dramatically affect early survival of large herbivores and suggests that extreme climatic events might act as a selection force on vertebrate populations, allowing only individuals with the appropriate behaviour and/or knowledge to survive.     

The evolution of an 'intelligent' dispersal strategy: biased, correlated random walks in patchy landscapes

Theoretical work exploring dispersal evolution focuses on the emigration rate of individuals and typically assumes that movement occurs either at random to any other patch or to one of the nearest‐neighbour patches. There is a lack of work exploring the process by which individuals move between patches, and how this process evolves. This is of concern because any organism that can exert control over dispersal direction can potentially evolve efficiencies in locating patches, and the process by which individuals find new patches will potentially have major effects on metapopulation dynamics and gene flow. Here, we take an initial step towards filling this knowledge gap. To do this we constructed a continuous space population model, in which individuals each carry heritable trait values that specify the characteristics of the biased correlated random walk they use to disperse from their natal patch. We explore how the evolution of the random walk depends upon the cost of dispersal, the density of patches in the landscape, and the emigration rate. The clearest result is that highly correlated walks always evolved (individuals tended to disperse in relatively straight lines from their natal patch), reflecting the efficiency of straight‐line movement. In our models, more costly dispersal resulted in walks with higher correlation between successive steps. However, the exact walk that evolved also depended upon the density of suitable habitat patches, with low density habitat evolving more biased walks (individuals which orient towards suitable habitat at quite large distances from that habitat). Thus, low density habitat will tend to develop individuals which disperse efficiently between adjacent habitat patches but which only rarely disperse to more distant patches; a result that has clear implications for metapopulation theory. Hence, an understanding of the movement behaviour of dispersing individuals is critical for robust long‐term predictions of population dynamics in fragmented landscapes.     

Dispersal of introduced house sparrows Passer domesticus: an experiment

An important issue concerning the introduction of non-indigenous organisms into local populations is the potential of the introduced individuals to spread and interfere both demographically and genetically with the local population. Accordingly, the potential of spatial dispersal among introduced individuals compared with local individuals is a key parameter to understand the spatial and temporal dynamics of populations after an introduction event. In addition, if the variance in dispersal rate and distance is linked to individual characteristics, this may further affect the population dynamics. We conducted a large-scale experiment where we introduced 123 house sparrows from a distant population into 18 local populations without changing population density or sex ratio. Introduced individuals dispersed more frequently and over longer distances than residents. Furthermore, females had higher probability of dispersal than males. In females, there was also a positive relationship between the wing length and the probability of dispersal and dispersal distance. These results suggest that the distribution and frequency of introduced individuals may be predicted by their sex ratio as well as their phenotypic characteristics.