Nutrients and flow shape the cyclic dominance games between Escherichia coli strains

Evolutionary game theory has provided various models to explain the coexistence of competing strategies, one of which is the rock-paper-scissors (RPS) game. A system of three Escherichia coli strains-a toxin-producer, a resistant and a sensitive-has become a classic experimental model for studying RPS games. Previous experimental and theoretical studies, however, often ignored the influence of ecological factors such as nutrients and toxin dynamics on the evolutionary game dynamics. In this work, we combine experiments and modelling to study how these factors affect competition dynamics. Using three-dimensional printed mini-bioreactors, we tracked the frequency of the three strains in different culturing media and under different flow regimes. Although our experimental system fulfilled the requirements of cyclic dominance, we did not observe clear cycles or long-term coexistence between strains. We found that both nutrients and flow rates strongly impacted population dynamics. In our simulations, we explicitly modelled the release, removal and diffusion of toxin. We showed that the amount of toxin that is retained in the system is a simple indicator that can predict competition outcomes across broad parameter space. Moreover, our simulation results suggest that high rates of toxin diffusion might have prevented cyclic patterns from emerging in our experimental system. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Simulating the effects of long-distance dispersal and landscape heterogeneity on the eco-evolutionary outcomes of range expansion in an invasive riverine fish, Tench (Tinca tinca)

Predicting how quickly populations expand their range and whether they will retain genetic diversity when they are introduced to new regions or track environmental conditions suited to their survival is an important applied and theoretical challenge. The literature suggests that long-distance dispersal, landscape heterogeneity and the evolution of dispersal influence populations' expansion rates and genetic diversity. We used individual-based spatially explicit simulations to examine these relationships for Tench (Tinca tinca), an invasive fish expanding its geographical range in eastern North America since the 1990s. Simulated populations varied greatly in expansion rates (1.1-28.6 patches year^-1 ) and genetic diversity metrics, including changes in observed heterozygosity (-19 to +0.8%) and effective number of alleles (-0.32 to -0.01). Populations with greater dispersal distances expanded faster than those with smaller dispersal distances but exhibited considerable variation in expansion rate among local populations, implying less predictable expansions. However, they tended to retain genetic diversity as they expanded, suggesting more predictable evolutionary trajectories. In contrast, populations with smaller dispersal distances spread predictably more slowly but exhibited more variability among local populations in genetic diversity losses. Consistent with empirical data, populations spreading in a longer, narrower dispersal corridor lost more neutral genetic variation to the stochastic fixation of alleles. Given the unprecedented pace of anthropogenic environmental change and the increasing need to manage range-expanding populations, our results have conservation ramifications as they imply that the evolutionary trajectories of populations characterised by shorter dispersal distances spreading in narrower landscapes are more variable and, therefore, less predictable.

The collective effect of finite-sized inhomogeneities on the spatial spread of populations in two dimensions

The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here, we study the influence of finite-sized individual inhomogeneities and their collective effect on front speed if randomly placed in a two-dimensional habitat. We use an individual-based model to investigate the front dynamics for a region in which dispersal or growth of individuals is reduced to zero (obstacles) or increased above the background (hotspots), respectively. In a regime where front dynamics is determined by a local front speed only, a principle of least time can be employed to predict front speed and shape. The resulting analytical solutions motivate an event-based algorithm illustrating the effects of several obstacles or hotspots. We finally apply the principle of least time to large heterogeneous environments by solving the Eikonal equation numerically. Obstacles lead to a slow-down that is dominated by the number density and width of obstacles, but not by their precise shape. Hotspots result in a speed-up, which we characterize as function of hotspot strength and density. Our findings emphasize the importance of taking the dimensionality of the environment into account.

Evolutionary simulations clarify and reconcile biodiversity-disturbance models

There is significant geographic variation in species richness. However, the nature of the underlying relationships, such as that between species richness and environmental stability, remains unclear. The stability-time hypothesis suggests that environmental instability reduces species richness by suppressing speciation and increasing extinction risk. By contrast, the patch-mosaic hypothesis suggests that small-scale environmental instability can increase species richness by providing a steady supply of non-equilibrium environments. Although these hypotheses are often applied to different time scales, their core mechanisms are in conflict. Reconciling these apparently competing hypotheses is key to understanding how environmental conditions shape the distribution of biodiversity. Here, we use REvoSim, an individual-based, eco-evolutionary system, to model the evolution of sessile organisms in environments with varying magnitudes and scales of environmental instability. We demonstrate that when environments have substantial permanent heterogeneity, a high level of localized environmental instability reduces biodiversity, whereas in environments lacking permanent heterogeneity, high levels of localized instability increase biodiversity. By contrast, broad-scale environmental instability, acting on the same time scale, invariably reduces biodiversity. Our results provide a new view of the biodiversity–disturbance relationship that reconciles contrasting hypotheses within a single model and implies constraints on the environmental conditions under which those hypotheses apply. These constraints can inform attempts to conserve adaptive potential in different environments during the current biodiversity crisis.

Evolutionary Hysteresis and Ratchets in the Evolution of Periodical Cicadas

It has been previously hypothesized that the perfectly synchronized mass emergence of periodical cicadas (Magicicada spp.) evolved as a result of a switch from size-based to age-based emergence. In the former case, cicada nymphs emerge immediately (at the first opportunity) on reaching maturity, whereas in the latter case, nymphs wait in order to emerge at a specific age. Here we use an individual-based model to simulate the cicada life cycle and to study the evolution of periodicity. We find that if age-based emergence evolves in a constant abiotic environment, it typically results in a population that is protoperiodic, and synchronous emergence of the whole population is not achieved. However, perfect periodicity and synchronous emergence can be attained, if the abiotic environment changes back and forth between favorable and unfavorable conditions (hysteresis). Furthermore, once age-based emergence evolves, generally it can only be invaded by other age-based emergence strategies with longer cycle lengths (evolutionary ratchet). Together, these mechanisms promote the evolution of long periodic life cycles and synchronous emergence in the Magicicada. We discuss how our results connect to previous theories and recent phylogenetic studies on Magicicada evolution.

Understanding policing as a mechanism of cheater control in cooperating bacteria

Policing occurs in insect, animal and human societies, where it evolved as a mechanism maintaining cooperation. Recently, it has been suggested that policing might even be relevant in enforcing cooperation in much simpler organisms such as bacteria. Here, we used individual-based modelling to develop an evolutionary concept for policing in bacteria and identify the conditions under which it can be adaptive. We modelled interactions between cooperators, producing a beneficial public good, cheaters, exploiting the public good without contributing to it, and public good-producing policers that secrete a toxin to selectively target cheaters. We found that toxin-mediated policing is favoured when (a) toxins are potent and durable, (b) toxins are cheap to produce, (c) cell and public good diffusion is intermediate, and (d) toxins diffuse farther than the public good. Although our simulations identify the parameter space where toxin-mediated policing can evolve, we further found that policing decays when the genetic linkage between public good and toxin production breaks. This is because policing is itself a public good, offering protection to toxin-resistant mutants that still produce public goods, yet no longer invest in toxins. Our work thus highlights that not only specific environmental conditions are required for toxin-mediated policing to evolve, but also strong genetic linkage between the expression of public goods, toxins and toxin resistance is essential for this mechanism to remain evolutionarily stable in the long run.

Unpacking Conditional Neutrality: Genomic Signatures of Selection on Conditionally Beneficial and Conditionally Deleterious Mutations

It is common to look for signatures of local adaptation in genomes by identifying loci with extreme levels of allele frequency divergence among populations. This approach to finding genes associated with local adaptation often assumes antagonistic pleiotropy, wherein alternative alleles are strongly favored in alternative environments. Conditional neutrality has been proposed as an alternative to antagonistic pleiotropy, but conditionally neutral polymorphisms are transient, and it is unclear how much outlier signal would be maintained under different forms of conditional neutrality. Here, we use individual-based simulations and a simple analytical heuristic to show that a pattern that mimics local adaptation at the phenotypic level, where each genotype has the highest fitness in its home environment, can be produced by the accumulation of mutations that are neutral in their home environment and deleterious in nonlocal environments. Because conditionally deleterious mutations likely arise at a rate many times higher than conditionally beneficial mutations, they can have a significant cumulative effect on fitness even when individual effect sizes are small. We show that conditionally deleterious mutations driving nonlocal maladaptation may be undetectable by even the most powerful genome scans, as differences in allele frequency between populations are typically small. We also explore the evolutionary effects of conditionally beneficial mutations and find that they can maintain significant signals of local adaptation, and they would be more readily detectable than conditionally deleterious mutations using conventional genome scan approaches. We discuss implications for interpreting outcomes of transplant experiments and genome scans that are used to study the genetic basis of local adaptation.

neogen: A tool to predict genetic effective population size (Ne ) for species with generational overlap and to assist empirical Ne study design

Molecular genetic estimates of population effective size (N_e ) lose accuracy and precision when insufficient numbers of samples or loci are used. Ideally, researchers would like to forecast the necessary power when planning their project. neogen (genetic N_e for Overlapping Generations) enables estimates of precision and accuracy in advance of empirical investigation and allows exploration of the power available in different user-specified age-structured sampling schemes. neogen provides a population simulation and genetic power analysis framework that simulates the demographics, genetic composition, and N_e , from species-specific life history, mortality, population size, and genetic priors. neogen guides the user to establish a tractable sampling regime and to determine the numbers of samples and microsatellite or SNP loci required for accurate and precise genetic N_e estimates when sampling a natural population. neogen is useful at multiple stages of a study's life cycle: when budgeting, as sampling and locus development progresses, and for corroboration when empirical N_e estimates are available. The underlying model is applicable to a wide variety of iteroparous species with overlapping generations (e.g., mammals, birds, reptiles, long-lived fishes). In this paper, we describe the neogen model, detail the workflow for the point-and-click software, and explain the graphical results. We demonstrate the use of neogen with empirical Australian east coast zebra shark (Stegostoma fasciatum) data. For researchers wishing to make accurate and precise genetic N_e estimates for overlapping generations species, neogen facilitates planning for sample and locus acquisition, and with existing empirical genetic N_e estimates neogen can corroborate population demographic and life history properties.

An Individual-Based Diploid Model Predicts Limited Conditions Under Which Stochastic Gene Expression Becomes Advantageous

Recent studies suggest the existence of a stochasticity in gene expression (SGE) in many organisms, and its non-negligible effect on their phenotype and fitness. To date, however, how SGE affects the key parameters of population genetics are not well understood. SGE can increase the phenotypic variation and act as a load for individuals, if they are at the adaptive optimum in a stable environment. On the other hand, part of the phenotypic variation caused by SGE might become advantageous if individuals at the adaptive optimum become genetically less-adaptive, for example due to an environmental change. Furthermore, SGE of unimportant genes might have little or no fitness consequences. Thus, SGE can be advantageous, disadvantageous, or selectively neutral depending on its context. In addition, there might be a genetic basis that regulates magnitude of SGE, which is often referred to as “modifier genes,” but little is known about the conditions under which such an SGE-modifier gene evolves. In the present study, we conducted individual-based computer simulations to examine these conditions in a diploid model. In the simulations, we considered a single locus that determines organismal fitness for simplicity, and that SGE on the locus creates fitness variation in a stochastic manner. We also considered another locus that modifies the magnitude of SGE. Our results suggested that SGE was always deleterious in stable environments and increased the fixation probability of deleterious mutations in this model. Even under frequently changing environmental conditions, only very strong natural selection made SGE adaptive. These results suggest that the evolution of SGE-modifier genes requires strict balance among the strength of natural selection, magnitude of SGE, and frequency of environmental changes. However, the degree of dominance affected the condition under which SGE becomes advantageous, indicating a better opportunity for the evolution of SGE in different genetic models.

Fishing for nutrients in heterogeneous landscapes: modelling plant growth trade-offs in monocultures and mixed communities

The problem of how best to find and exploit essential resources, the quality and locations of which are unknown, is common throughout biology. For plants, the need to grow an efficient root system so as to acquire patchily distributed soil nutrients is typically complicated by competition between plants, and by the costs of maintaining the root system. Simple mechanistic models for root growth can help elucidate these complications, and here we argue that these models can be usefully informed by models initially developed for foraging fish larvae. Both plant and fish need to efficiently search a spatio-temporally variable environment using simple algorithms involving only local information, and both must perform this task against a backdrop of intra- and inter-specific competition and background mortality. Here we develop these parallels by using simple stochastic models describing the growth and efficiency of four contrasting idealized root growth strategies. We show that plants which grow identically in isolation in homogeneous substrates will typically perform very differently when grown in monocultures, in heterogeneous nutrient landscapes and in mixed-species competition. In particular, our simulations show a consistent result that plants which trade-off rapid growth in favour of a more efficient and durable root system perform better, both on average and in terms of the best performing individuals, than more rapidly growing ephemeral root systems. Moreover, when such slower growing but more efficient plants are grown in competition, the overall community productivity can exceed that of the constituent monocultures. These findings help to disentangle many of the context-dependent behaviours seen in the experimental literature, and may form a basis for future studies at the level of complex population dynamics and life history evolution.

How mechanisms of habitat preference evolve and promote divergence with gene flow

Habitat preference may promote adaptive divergence and speciation, yet the conditions under which this is likely are insufficiently explored. We use individual-based simulations to study the evolution and consequence of habitat preference during divergence with gene flow, considering four different underlying genetically based behavioural mechanisms: natal habitat imprinting, phenotype-dependent, competition-dependent and direct genetic habitat preference. We find that the evolution of habitat preference generally requires initially high dispersal, is facilitated by asymmetry in population sizes between habitats, and is hindered by an increasing number of underlying genetic loci. Moreover, the probability of habitat preference to emerge and promote divergence differs greatly among the underlying mechanisms. Natal habitat imprinting evolves most easily and can allow full divergence in parameter ranges where no divergence is possible in the absence of habitat preference. The reason is that imprinting represents a one-allele mechanism of assortative mating linking dispersal behaviour very effectively to local selection. At the other extreme, direct genetic habitat preference, a two-allele mechanism, evolves under restricted conditions only, and even then facilitates divergence weakly. Overall, our results indicate that habitat preference can be a strong reproductive barrier promoting divergence with gene flow, but that this is highly contingent on the underlying preference mechanism.

Evolution of mate choice and the so-called magic traits in ecological speciation

Non-random mating provides multiple evolutionary benefits and can result in speciation. Biological organisms are characterised by a myriad of different traits, many of which can serve as mating cues. We consider multiple mechanisms of non-random mating simultaneously within a unified modelling framework in an attempt to understand better which are more likely to evolve in natural populations going through the process of local adaptation and ecological speciation. We show that certain traits that are under direct natural selection are more likely to be co-opted as mating cues, leading to the appearance of magic traits (i.e. phenotypic traits involved in both local adaptation and mating decisions). Multiple mechanisms of non-random mating can interact so that trait co-evolution enables the evolution of non-random mating mechanisms that would not evolve alone. The presence of magic traits may suggest that ecological selection was acting during the origin of new species.