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.     

A scenario for the hobo transposable element invasion, deduced from the structure of natural populations of Drosophila melanogaster using tandem TPE repeats

Temporal surveys of hobo transposable elements in natural populations reveal a historical pattern suggesting a recent world-wide invasion of D. melanogaster by these transposons, perhaps following a recent horizontal transfer. To clarify the dynamics of hobo elements in natural populations, and thus to provide further data for our understanding of the hobo invasion, TPE tandem repeats, observed in the polymorphic S region of the element, were used as molecular markers. The number of TPE repeats was studied in 101 current populations from around the world, and in 63 strains collected in the past. This revealed a geographical distribution which seems to have been stable since the beginning of the 1960s. This distribution is compatible with a number of hypotheses for the dynamics of hobo elements. We propose a scenario based on an invasion in two stages: first, a complete invasion by elements with three TPE repeats, followed by the beginning of a new invasion involving hobo elements with five or seven repeats.     

THE EVOLUTION OF TRANSPOSABLE ELEMENTS: CONDITIONS FOR ESTABLISHMENT IN BACTERIAL POPULATIONS

Previous theoretical studies have shown that bacterial transposons can become established in populations by infectious transfer, even if they reduce the fitness of their host cells. Conditions for the persistence of “parasitic” transposons are, however, restrictive: i) transposition must be replicative, rather than conservative; ii) the rate of transposition must be greater than the loss in host fitness caused by the transposon; and iii) cells must exchange plasmids at rates greater than the fitness cost of the transposon. I sought to test the validity of the model underlying this theory by performing experiments with laboratory populations of the bacterium Escherichia coli, the conjugative plasmid R100, and the transposons Tn3 and Tn5. A plasmid-borne transposon was introduced at low frequency into a population of bacteria carrying the same plasmid without the transposon in a habitat where the transposon offered no benefit to its host. The fate of the invading transposon was followed by tracking the various bacterial populations appearing in the cultures. Using independent estimates of the parameters of the model, predicted population changes were generated with numerical solutions of the model, and these were compared to experimental results. Plasmids transferred into new hosts as predicted by the model, and the resulting transconjugant populations either maintained a steady low density or rose slowly in abundance. Transposition appeared to play no role in population changes. Abundance of all cell types fit theoretical predictions of a system with no transposition, despite evidence that transposition was taking place. This is exactly what the model predicted. It thus appears unlikely that deleterious or neutral transposons have much impact on the genetics of bacterial populations. This is consistent with the hypothesis that most bacterial transposons are not parasitic DNA, but rather invade and persist in populations by providing a fitness advantage to cells carrying them.     

Strigolactone Hormones and Their Stereoisomers Signal through Two Related Receptor Proteins to Induce Different Physiological Responses in Arabidopsis

We speculate that multicopy transposons, carrying both fitness and unfitness genes, can provide new positive and negative selection options to intractable weed problems. Multicopy transposons rapidly disseminate through populations, appearing in approximately 100% of progeny, unlike nuclear transgenes, which appear in a proportion of segregating populations. Different unfitness transgenes and modes of propagation will be appropriate for different cases: (1) outcrossing Amaranthus spp. (that evolved resistances to major herbicides); (2) Lolium spp., important pasture grasses, yet herbicide-resistant weeds in crops; (3) rice (Oryza sativa), often infested with feral weedy rice, which interbreeds with the crop; and (4) self-compatible sorghum (Sorghum bicolor), which readily crosses with conspecific shattercane and with allotetraploid johnsongrass (Sorghum halepense). The speculated outcome of these scenarios is to generate weed populations that contain the unfitness gene and thus are easily controllable. Unfitness genes can be under chemically or environmentally inducible promoters, activated after gene dissemination, or under constitutive promoters where the gene function is utilized only at special times (e.g. sensitivity to an herbicide). The transposons can be vectored to the weeds by introgression from the crop (in rice, sorghum, and Lolium spp.) or from planted engineered weed (Amaranthus spp.) using a gene conferring the degradation of a no longer widely used herbicide, especially in tandem with an herbicide-resistant gene that kills all nonhybrids, facilitating the rapid dissemination of the multicopy transposons in a weedy population.     

Where do adaptive shifts occur during invasion? A multidisciplinary approach to unravelling cold adaptation in a tropical ant species invading the Mediterranean area

Evolution may improve the invasiveness of populations, but it often remains unclear whether key adaptation events occur after introduction into the recipient habitat (i.e. post‐introduction adaptation scenario), or before introduction within the native range (i.e. prior‐adaptation scenario) or at a primary site of invasion (i.e. bridgehead scenario). We used a multidisciplinary approach to determine which of these three scenarios underlies the invasion of the tropical ant Wasmannia auropunctata in a Mediterranean region (i.e. Israel). Species distribution models (SDM), phylogeographical analyses at a broad geographical scale and laboratory experiments on appropriate native and invasive populations indicated that Israeli populations followed an invasion scenario in which adaptation to cold occurred at the southern limit of the native range before dispersal to Israel. We discuss the usefulness of combining SDM, genetic and experimental approaches for unambiguous determination of eco‐evolutionary invasion scenarios.     

Lessepsian fish migration: genetic bottlenecks and parasitological evidence

As a rule, non‐indigenous species (NIS) populations derived from biological invasion events represent a subset of the genetic diversity of the source population. In biological invasions, host–parasite interactions play an important role, and parasitological data for NIS populations can provide useful information such as their area of origin, mechanism of invasion and prospects of success in the new habitat. When both genetic and parasitological data are available, and they suggest the same scenario, the history of an invasion can be inferred with no discrepancy, but when data cannot be reconciled an alternative model should be considered. In this study a comparison of genetic and parasitological data for the Lessepsian migrant the bluespotted cornetfish, Fistularia commersonii, in the Mediterranean Sea presents the opportunity to evaluate the compatibility of information of this nature, and to propose possible invasion scenarios consistent with evidence provided by both criteria.     

Extreme Selection Unifies Evolutionary Game Dynamics in Finite and Infinite Populations

We show that when selection is extreme—the fittest strategy always reproduces or is imitated—the unequivalence between the possible evolutionary game scenarios in finite and infinite populations resolves, in the sense that the three generic outcomes—dominance, coexistence, and mutual exclusion—emerge in well-mixed populations of any size. We consider the simplest setting of a 2-player-2-strategy symmetric game and the two most common microscopic definitions of strategy spreading—the frequency-dependent Moran process and the imitation process by pairwise comparison—both in the case allowing any intensity of selection. We show that of the seven different invasion and fixation scenarios that are generically possible in finite populations—fixation being more or less likely to occur and rapid compared to the neutral game—the three that are possible in large populations are the same three that occur for sufficiently strong selection: (1) invasion and fast fixation of one strategy; (2) mutual invasion and slow fixation of one strategy; (3) no invasion and no fixation. Moreover (and interestingly), in the limit of extreme selection 2 becomes mutual invasion and no fixation, a case not possible for finite intensity of selection that better corresponds to the deterministic case of coexistence. In the extreme selection limit, we also derive the large population deterministic limit of the two considered stochastic processes.     

Patterns of hobo elements and their effects in natural populations of Drosophila melanogaster in Japan

We studied the dynamics of hobo elements of Drosophila melanogaster in Japan with the goal of better understanding the invasion and evolution of transposons in natural populations. One hundred and twenty-six isofemale lines and 11 older stocks were tested for the presence and genetic phenotype of hobo elements. The oldest H strain, containing complete and deleted hobo elements, is Hikone-H (1957), but Hikone-R (1952) has no hobo-homologous sequences. The findings suggest that the hobo element invaded Japanese populations in the mid-1950s, at about the same time as the P element invasion in Japan. This chronology is consistent with the hypothesis of a recent worldwide hobo element invasion into D. melanogaster in the mid-1950s. In recently collected populations, H degrees strains (low hobo activity and high repression potency) are predominant, whereas H+ strains (high hobo activity and high repression potency) are predominant in the Sakishima Islands, the most southwestern islands of the Japanese archipelago. H' strains (high hobo activity and low repression potency) were first found in limited island populations. Japanese populations have not only full-size hobo elements and 1.5 kb Th elements but also characteristic deletion derivatives (1.6 and 1.8 kb XhoI fragments) that we have named Jh elements. These results are consistent with transgenic experiments with complete hobo elements, in which populations evolved to H+ or H degrees via H', and in which 1.8 kb fragments appeared. We conclude that hobo elements invaded the central region of Japan, spread to the far islands, and that the invasion is currently at an intermediate, nonequilibrium stage.     

Adaptation to P element transposon invasion in Drosophila melanogaster

Transposons evolve rapidly and can mobilize and trigger genetic instability. Piwi-interacting RNAs (piRNAs) silence these genome pathogens, but it is unclear how the piRNA pathway adapts to invasion of new transposons. In Drosophila, piRNAs are encoded by heterochromatic clusters and maternally deposited in the embryo. Paternally inherited P element transposons thus escape silencing and trigger a hybrid sterility syndrome termed P-M hybrid dysgenesis. We show that P-M hybrid dysgenesis activates both P elements and resident transposons and disrupts the piRNA biogenesis machinery. As dysgenic hybrids age, however, fertility is restored, P elements are silenced, and P element piRNAs are produced de novo. In addition, the piRNA biogenesis machinery assembles, and resident elements are silenced. Significantly, resident transposons insert into piRNA clusters, and these new insertions are transmitted to progeny, produce novel piRNAs, and are associated with reduced transposition. P element invasion thus triggers heritable changes in genome structure that appear to enhance transposon silencing.     

The diffusive spread of alleles in heterogeneous populations

The spread of genes and individuals through space in populations is relevant in many biological contexts. I study, via systems of reaction-diffusion equations, the spatial spread of advantageous alleles through structured populations. The results show that the temporally asymptotic rate of spread of an advantageous allele, a kind of invasion speed, can be approximated for a class of linear partial differential equations via a relatively simple formula, c = 2 square root of (rD), that is reminiscent of a classic formula attributed to R. A. Fisher. The parameters r and D represent an asymptotic growth rate and an average diffusion rate, respectively, and can be interpreted in terms of eigenvalues and eigenvectors that depend on the population's demographic structure. The results can be applied, under certain conditions, to a wide class of nonlinear partial differential equations that are relevant to a variety of ecological and evolutionary scenarios in population biology. I illustrate the approach for computing invasion speed with three examples that allow for heterogeneous dispersal rates among different classes of individuals within model populations.     

High mutation rate of TPE repeats: a microsatellite in the putative transposase of the hobo element in Drosophila melanogaster

The hobo transposable element contains a polymorphic microsatellite sequence located in its coding region, the TPE repeats. Previous surveys of natural populations of Drosophila melanogaster have detected at least seven different hobo transposons. These natural populations are geographically structured with regard to TPE polymorphism, and a scenario has been proposed for the invasion process. Natural populations have recently been completely invaded by hobo elements with three TPE repeats. New elements then appeared by mutation, triggering a new stage of invasion by other elements. Since TPE polymorphism appeared over a short period of time, we focused on estimating the mutation rate of these TPE repeats. We used transgenic lines harboring three TPE and/or five TPE hobo elements that had been evolving for at least 16 generations to search for a new TPE repeat polymorphism. We detected three mutants, with four, seven, and eight TPE repeats, respectively. The estimated mutation rate of the TPE repeats is therefore higher than that of neutral microsatellites in D. melanogaster (4.2 x 10-4 versus 6.5 x 10-6). The role of the transposition mechanism and the particular structure of the TPE repeats of the hobo element in this increase in the mutation rate are discussed.     

Disturbance affects short-term facilitation, but not long-term saturation, of exotic plant invasion in New Zealand forest

We investigate the spread of an exotic herb, Hieracium lepidulum, into a New Zealand Nothofagus forest with the aim of understanding how stand-development of tree populations, propagule pressure and invader persistence, affect invasion across the landscape and within communities. Using data repeatedly collected over 35 years, from 250 locations, we parametrize continuous-time Markov chain models and use these models to examine future projections of the invasion under a range of hypothetical scenarios. We found that the probability of invasion into a stand was relatively high following canopy disturbance and that local abundance of Hieracium was promoted by minor disturbances. However, model predictions extrapolated 45 years into the future show that neither the rate of landscape-level invasion, nor local population growth of Hieracium, was affected much by changing the frequency of canopy disturbance events. Instead, invasion levels were strongly affected by the ability of Hieracium to persist in the understorey following forest canopy closure, and by propagule supply from streams, forest edges and plants already established within the stand. Our results show that disturbance frequency has surprisingly little influence on the long-term trajectory of invasion, while invader persistence strongly determines invasion patterns.     

Reconstructing routes of invasion using genetic data: why,how and so what?

Detailed knowledge about the geographical pathways followed by propagules from their source to the invading populations—referred to here as routes of invasion—provides information about the history of the invasion process and the origin and genetic composition of the invading populations. The reconstruction of invasion routes is required for defining and testing different hypotheses concerning the environmental and evolutionary factors responsible for biological invasions. In practical terms, it facilitates the design of strategies for controlling or preventing invasions. Most of our knowledge about the introduction routes of invasive species is derived from historical and observational data, which are often sparse, incomplete and, sometimes, misleading. In this context, population genetics has proved a useful approach for reconstructing routes of introduction, highlighting the complexity and the often counterintuitive nature of the true story. This approach has proved particularly useful since the recent development of new model‐based methods, such as approximate Bayesian computation, making it possible to make quantitative inferences in the complex evolutionary scenarios typically encountered in invasive species. In this review, we summarize some of the fundamental aspects of routes of invasion, explain why the reconstruction of these routes is useful for addressing both practical and theoretical questions, and comment on the various reconstruction methods available. Finally, we consider the main insights obtained to date from studies of invasion routes.     

Multiple introductions,admixture and bridgehead invasion characterize the introduction history of Ambrosia artemisiifolia in Europe and Australia

Admixture between differentiated populations is considered to be a powerful mechanism stimulating the invasive success of some introduced species. It is generally facilitated through multiple introductions; however, the importance of admixture prior to introduction has rarely been considered. We assess the likelihood that the invasive Ambrosia artemisiifolia populations of Europe and Australia developed through multiple introductions or were sourced from a historical admixture zone within native North America. To do this, we combine large genomic and sampling data sets analysed with approximate Bayesian computation and random forest scenario evaluation to compare single and multiple invasion scenarios with pre‐ and postintroduction admixture simultaneously. We show the historical admixture zone within native North America originated before global invasion of this weed and could act as a potential source of introduced populations. We provide evidence supporting the hypothesis that the invasive populations established through multiple introductions from the native range into Europe and subsequent bridgehead invasion into Australia. We discuss the evolutionary mechanisms that could promote invasiveness and evolutionary potential of alien species from bridgehead invasions and admixed source populations.     

Risk map for the range expansion of Thrips palmi in Korea under climate change: Combining species distribution models with land-use change

Climate change and land-use change are the most powerful drivers for the invasion of alien species. To understand the integrated effects of these two drivers on pest invasion risk in the future, this study assessed how they impact the invasion risk of Thrips palmi Karny, which is the most serious invasive species in the Korean peninsula. The potential distribution of T. palmi was projected with a MaxEnt model for current and future climate change scenarios (RCP 4.5 and 8.5) based on occurrence records. The potential distribution extends to the north over time, except the eastern high mountainous area, for both RCPs in 2075. The MaxEnt outputs were filtered with agricultural area using data from three land-use change scenarios derived from the Shared Socio-economic Pathways (SSPs), because T. palmi populations can only be sustained in agricultural areas. The potential risk of T. palmi, based on the potential distribution probability in the future agricultural area, increased over time under all RCPs-SSPs combinations. The total area of T. palmi occurrence increased under RCPs-SSP1 and -SSP2 but decreased under RCPs-SSP3, due to agricultural areas being converted to urban areas. In conclusion, based on future climate change scenarios, T. palmi could be distributed throughout the Korean peninsula in the future. The invasion risk in agricultural areas will increase substantially; thus, intensive control measures for T. palmi are required in the future. Our research suggests that using both climate change and land-use change in pest risk mapping study can provide informative data for management strategy.     

Modeling the Manipulation of Natural Populations by the Mutagenic Chain Reaction

The use of recombinant genetic technologies for population manipulation has mostly remained an abstract idea due to the lack of a suitable means to drive novel gene constructs to high frequency in populations. Recently Gantz and Bier showed that the use of CRISPR/Cas9 technology could provide an artificial drive mechanism, the so-called mutagenic chain reaction (MCR), which could lead to rapid fixation of even a deleterious introduced allele. We establish the near equivalence of this system to other gene drive models and review the results of simple models showing that, when there is a fitness cost to the MCR allele, an internal equilibrium may exist that is usually unstable. In this case, introductions must be at a frequency above this critical point for the successful invasion of the MCR allele. We obtain estimates of fixation and invasion probabilities for the appropriate scenarios. Finally, we discuss how polymorphism in natural populations may introduce sources of natural resistance to MCR invasion. These modeling results have important implications for application of MCR in natural populations.     

Predicting impacts of lionfish (<Emphasis Type="Italic">Pterois volitans</Emphasis>) invasion in a coastal ecosystem of southern Brazil

The opportunistic feeder Pterois volitans is a voracious invader, causing large impacts in marine food-webs. We have used a Ecopath-with-Ecosim model to hypothesize an invasion by lionfish and to predict the likely impact of this potential generalist mesopredator in a subtropical food-web model. With thirty-three functional groups, the initial Ecopath model was balanced with a low biomass of lionfish (0.07 t/km²). In Ecosim, three scenarios of different vulnerability settings for the linkages between the introduced fish and its prey were tested, representing the default setting, a top-down control, and an extreme top-down control. The scenarios were tested using different assumptions on the ability of the invasive fish to change the proportions of prey consumed according to prey availability. Our model predicted that the hypothesized lionfish invasion would have a strong impact on this subtropical marine food web: (1) by reducing prey populations and, consequently, food for native predators, and; (2) by predating on key species, causing direct impacts and possibly cascading trophic effects. Reef fish were the most affected, including some groups ecologically and economically important, like lutjanids and groupers. However, some adaptations in the fishing strategy of fishermen are expected which may affect other fish groups. Stakeholders should be warned of the potential ecological and socio-economic impacts that may arise from a lionfish invasion and various strategies and policy options should be immediately developed and applied (1) to prevent the arrival and establishment of the lionfish, and; (2) to make the ecosystem more resilient to this and other possible exotic species.     

Evolution of dispersal in open advective environments

We consider a two-species competition model in a one-dimensional advective environment, where individuals are exposed to unidirectional flow. The two species follow the same population dynamics but have different random dispersal rates and are subject to a net loss of individuals from the habitat at the downstream end. In the case of non-advective environments, it is well known that lower diffusion rates are favored by selection in spatially varying but temporally constant environments, with or without net loss at the boundary. We consider several different biological scenarios that give rise to different boundary conditions, in particular hostile and “free-flow” conditions. We establish the existence of a critical advection speed for the persistence of a single species. We derive a formula for the invasion exponent and perform a linear stability analysis of the semi-trivial steady state under free-flow boundary conditions for constant and linear growth rate. For homogeneous advective environments with free-flow boundary conditions, we show that populations with higher dispersal rate will always displace populations with slower dispersal rate. In contrast, our analysis of a spatially implicit model suggest that for hostile boundary conditions, there is a unique dispersal rate that is evolutionarily stable. Nevertheless, both scenarios show that unidirectional flow can put slow dispersers at a disadvantage and higher dispersal rate can evolve.     

2BAD: an application to estimate the parental contributions during two independent admixture events

Several approaches have been developed to calculate the relative contributions of parental populations in single admixture event scenarios, including Bayesian methods. In many breeds and populations, it may be more realistic to consider multiple admixture events. However, no approach has been developed to date to estimate admixture in such cases. This report describes a program application, 2BAD (for 2-event Bayesian ADmixture), which allows the consideration of up to two independent admixture events involving two or three parental populations and a single admixed population, depending on the number of populations sampled. For each of these models, it is possible to estimate several parameters (admixture, effective sizes, etc.) using an approximate Bayesian computation approach. In addition, the program allows comparing pairs of admixture models, determining which is the most likely given data. The application was tested through simulations and was found to provide good estimates for the contribution of the populations at the two admixture events. We were also able to determine whether an admixture model was more likely than a simple split model.     

Which transposable elements are active in the human genome?

Although a large proportion (44%) of the human genome is occupied by transposons and transposon-like repetitive elements, only a small proportion (<0.05%) of these elements remain active today. Recent evidence indicates that approximately 35-40 subfamilies of Alu, L1 and SVA elements (and possibly HERV-K elements) remain actively mobile in the human genome. These active transposons are of great interest because they continue to produce genetic diversity in human populations and also cause human diseases by integrating into genes. In this review, we examine these active human transposons and explore mechanistic factors that influence their mobilization.