Bacteria can be selected to help beneficial plasmids spread

A recent commentary raised concerns about aspects of the model and assumptions used in a previous study which demonstrated that selection can favor chromosomal alleles that confer higher plasmid donation rates. Here, the authors of that previous study respond to the concerns raised.

In our original work [1], we demonstrated experimentally that selection can favor chromosomal alleles that confer higher plasmid donation rates, given the plasmid is beneficial and the recipient has an elevated chance of carrying the donor allele (i.e., preferential donation to kin). Our experiments demonstrated this effect via 2 mechanisms of preferential donation: biased conjugation rates and structured populations. We interpreted these results through the lens of kin selection theory (benefits via horizontal gene transfer to kin), supported by simulations and an analytical fitness function model. These results hold importance by outlining that the evolution of plasmid transfer rates (a key aspect of the antibiotic resistance crisis) is not necessarily the sole product of selection on the plasmid itself and forms part of a broader series of papers from our labs investigating the sociomicrobiology of plasmids [2–4].A new commentary raises concerns over our fitness function model, flagging issues with both the structure of the model and assumptions made in our analysis [5]. We stand by the general conclusions of our work but accept that our fitness function and stated analysis assumptions could be better formulated. Our initial fitness function is heuristic in the sense it was designed to capture general processes acting on the fitness of individuals, dependent on the plasmid and donor allele status—without explicitly modeling the myriad demographic events of dispersal, reproduction, conjugation, and death that result in selective shifts across a metapopulation of cells. Specifically, we captured the “force of infection” faced by an uninfected cell as the product of average plasmid prevalence and average donor allele prevalence in the local patch (p_jq_j; see commentary for notation details). We agree with the authors that this force of infection is better phrased as the average of the product ((1/N)∑p_ij q_ij), in part because this avoids the potential pathology under limit conditions described by the authors, but also because this approach better highlights that the particular social trait in question is an “other only” cooperative trait [6], illustrated by commentary equation [2], where transmission to self and transmission to others are separated. This separation has the important consequence of highlighting that unlike many microbial social traits where benefits accrue to a group (including self), a cooperative plasmid donor trait can only benefit other cells that lack the plasmid. Given established costs of donation (e.g., see figure S2 in our original article), this defines our “donor” behavior as an altruistic trait, which can, therefore, only be favored by selection given nonrandom interactions among individuals (e.g., [7]).Our experimental results outline 2 mechanisms of nonrandom interactions: preferential donation to kin and population structure. Each of these mechanisms will generate positive covariances between focal individual q_ij and non-self-recipient q_j donor allele states (cov(q_j, q_ij) > 0). The pathway via preferential donation to kin (order-of-magnitude differences according to our analyses and more recent measurements among lineages coexisting within natural populations [8]) will also likely generate positive covariances between donor and recipient abilities (cov(s_ij, q_ij) > 0). In contrast, to arrive at the result that selection always works against plasmid donor alleles (equation [4]), the commentary makes the assumption that both of the above covariances are zero. We suggest that the additional analyses begun by the authors are an exciting starting point to better map selection on donor alleles, under a broader array of defined assumptions on cell–cell and gene–gene structure, ideally informed by data on structures found in natural bacterial populations.     

Unpredictable selection in a structured population leads to local genetic differentiation in evolved reaction norms

Unpredictability during development of the optimum phenotype under future selection leads to a compromise reaction norm with a slope that is shallower than the slope of the optimum reaction norm. Unpredictability of selection can lead to an evolved curved reaction norm when genetic variation for curvature is available even if the optimum reaction norm is linear. This requires asymmetry in the frequency distribution of the habitats of selection; at small population size, stochasticity in the number of individuals per selection habitat is sufficient to generate such asymmetry. Unpredictability of selection in structured populations leads to local genetic differentiation of reaction norms. The mean habitat of a subpopulation is defined as the subpopulation's focal habitat. The evolved mean reaction norm of each subpopulation is anchored at the optimum genotypic value in its focal habitat. Linear reaction norms are parallel if the conditional distribution of adults around the focal habitats is the same for each subpopulation. Adult migration and absence of zygote dispersal represents the ultimate structured population, each habitat playing the role of focal habitat. Absence of zygote dispersal requires that the flow of individuals through the habitats is used instead of the habitats’ frequencies in the prediction of the evolved reaction norm. Adult migration in absence of zygote dispersal leads to an evolved pattern of locally differentiated reaction norms with optimum genotypic value anchored in the focal habitat and, for linear reaction norms, parallel slopes.     

Increased coupling between subpopulations in a spatially structured environment can lead to population outbreaks

Destruction and fragmentation of habitats is widely considered as a major threat to biological diversity. A theoretical framework aimed at understanding and predicting species responses to these destructive processes is still lacking, however. In this paper, the species dynamics in a spatially structured, two-habitat, patchy environment is considered subject to changes in individual migration intensity, i.e. coupling between the habitats. The subpopulation dynamics inside each habitat is assumed to be bistable but with different parameter values. By using space-discrete/continuous metapopulation dynamic models and computer simulations, we show that there can be two principally different regimes of metapopulation dynamics. With increasing intensity in the interplay between subpopulations, the total abundance can either gradually decrease or experience a sudden burst-like increase. This result is shown to be robust to the choice of mathematical models (discrete or continuous). Particularly, both the "self-excitation" and "self-inhibition" regimes of the metapopulation system are robust to variation in habitat size; however, when one of the habitats is much smaller than the other, the "self-excitation" regime can give way to the "self-inhibition" regime and vice versa.     

On harvesting a structured ungulate population

Variation in demographic rates within a spatially structured population could have important consequences for management decisions, harvesting strategies and offtake rates. Although there is a growing body of evidence suggesting that demographic rates vary within populations over a range of spatial scales, there has been little research investigating the consequences of this variation for population management. In this paper, data on the dynamics of two female red deer sub-populations on Rum are analysed, and evidence is presented for differences between the fecundity and mortality rates of the two sub-populations. A simple harvesting model is developed to represent the dynamics of the two sub-populations, including density-independent migration between sub-populations and spatially correlated environmental variability. The highest monetary yield in the model is obtained by harvesting the more resilient sub-population at a higher rate. Surprisingly the losses involved in harvesting both sub-populations at the same rate are insignificant. However, if migration were density-dependent, the size of one sub-population would be more relevant to harvesting policy for the other sub-population. The results of this empirical study are compared to theoretical work on spatially structured populations; it is shown that when a species has complex age- and sex-structured population dynamics, previous theoretical results may not hold.     

Adaptive evolution in a spatially structured asexual population

We study the process of adaptation in a spatially structured asexual haploid population. The model assumes a local competition for replication, where each organism interacts only with its nearest neighbors. We observe that the substitution rate of beneficial mutations is smaller for a spatially structured population than that seen for populations without structure. The difference between structured and unstructured populations increases as the adaptive mutation rate increases. Furthermore, the substitution rate decreases as the number of neighbors for local competition is reduced. We have also studied the impact of structure on the distribution of adaptive mutations that fix during adaptation.     

Hitchhiking effect of a beneficial mutation spreading in a subdivided population

A central problem in population genetics is to detect and analyze positive natural selection by which beneficial mutations are driven to fixation. The hitchhiking effect of a rapidly spreading beneficial mutation, which results in local removal of standing genetic variation, allows such an analysis using DNA sequence polymorphism. However, the current mathematical theory that predicts the pattern of genetic hitchhiking relies on the assumption that a beneficial mutation increases to a high frequency in a single random-mating population, which is certainly violated in reality. Individuals in natural populations are distributed over a geographic space. The spread of a beneficial allele can be delayed by limited migration of individuals over the space and its hitchhiking effect can also be affected. To study this effect of geographic structure on genetic hitchhiking, we analyze a simple model of directional selection in a subdivided population. In contrast to previous studies on hitchhiking in subdivided populations, we mainly investigate the range of sufficiently high migration rates that would homogenize genetic variation at neutral loci. We provide a heuristic mathematical analysis that describes how the genealogical structure at a neutral locus linked to the locus under selection is expected to change in a population divided into two demes. Our results indicate that the overall strength of genetic hitchhiking--the degree to which expected heterozygosity decreases--is diminished by population subdivision, mainly because opportunity for the breakdown of hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection. Furthermore, the amount of genetic variation after a selective sweep is expected to be unequal over demes: a greater reduction in expected heterozygosity occurs in the subpopulation from which the beneficial mutation originates than in its neighboring subpopulations. This raises a possibility of detecting a "hidden" geographic structure of population by carefully analyzing the pattern of a selective sweep.     

Reproductive isolation with a learned trait in a structured population

Assortative mating displays and/or preferences can be affected by learning across a wide range of animal taxa, but the specifics of how this learning affects speciation with gene flow are not well understood. We use population genetic models with trait learning to investigate how the identity of the tutor affects the divergence of a self‐referent phenotype‐matching trait. We find that oblique learning (learning from unrelated individual of the previous generation) and maternal learning mask sexual selection and therefore do not allow the maintenance of divergence. In contrast, by enhancing positive frequency‐dependent sexual selection, paternal learning can maintain more divergence than genetic inheritance, but leads to the loss of polymorphism more easily. Furthermore, paternal learning inhibits the invasion of a novel self‐referent phenotype‐matching trait, especially in a large population.     

Dynamics of a physiologically structured population in a time-varying environment

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.     

Q(ST) in a hierarchically structured population

Under some circumstances, selection and drift can be disentangled with comparisons of the Q(ST) of a quantitative trait and the F(ST) of putatively neutral loci. Most previous comparisons of F(ST) and Q(ST) are carried out at a single spatial scale. We derive a hierarchical Q(ST) appropriate for study across varying levels of spatial structure.     

Variance and covariance of homozygosity in a structured population

The variance of homozygosity for a K-allele model with n partially isolated subpopulations is derived numerically using identity coefficients. The variance of homozygosity within a subpopulation is shown to depend strongly upon the migration rates between subpopulations but is not strongly influenced by the number of alleles possible at a locus. The variance of homozygosity within a subpopulation, given the value of expected homozygosity, is approximately equal to the value of the variance of homozygosity given by Stewart's formula for a single population. If the population is presumed to be panmictic, but is actually subdivided, and the gametes are sampled at random from the total population, the apparent variance of homozygosity depends on the number of alleles possible. With small migration rates and K large, the apparent variance of homozygosity is much smaller than in a single population with the same expected homozygosity. However, when K is small, the variance of homozygosity is approximately given by Stewart's formula. The transient behavior of the variance of homozygosity shows that a large number of generations may be required to approach equilibrium values.     

The maintenance of sexual reproduction in a structured population

We present the results of a computer simulation model in which a sexual population produces an asexual mutant. We estimate the probability that the new asexual lineage will go extinct. We find that whenever the asexual lineage does not go extinct the sexual population is out-competed, and only asexual individuals remain after a sufficiently long period of time has elapsed. We call this type of outcome an asexual takeover. Our results suggest that, given repeated mutations to asexuality, asexual takeover is likely in an unstructured environment. However, if the environment is subdivided into demes that are connected by migration, then asexual takeover becomes less likely. The probability of asexual takeover declines towards zero as the number of demes increases and as the rate of migration decreases. The reason for this is that asexuality leads to a greater loss of fitness due to mutation and genetic drift, in comparison to what occurs under sexual reproduction. Population subdivision slows the spread of asexual lineages, which allows more time for the genetic degeneration caused by asexuality to take place.     

Complex transition to cooperative behavior in a structured population model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior.     

Travelling wave dynamics and self-organization in a spatio-temporally structured population

We analyse spatial population dynamics showing that periodic or period-like chaotic dynamics produce self-organization structures, such as travelling waves. We suggest that self-organized patterns are associated with spatial synchrony patterns that often depend on geographical distance between subpopulations. The population dynamics also show statistical spatial autocorrelation patterns. We contrast our theoretical simulations with empirical data on annual damages in young sapling stands caused by voles. We conclude, on the basis of the periodicity, synchrony, and spatial autocorrelation patterns, and our simulation results, that vole dynamics represent travelling waves in population dynamics. We suggest that because such synchrony patterns are frequently observed in natural populations, spatial self-organization may be more common in population dynamics than reported in the literature.     

Factors influencing the optimum sex ratio in a structured population

W. D. Hamilton (1967, Science 156, 477-488) calculated the optimum sex-ratio strategy for a population subdivided into local mating groups. He made three important assumptions: that the females founding each group responded precisely to the number of them initiating the group; that ail broods within a group matured synchronously; and that males were incapable of dispersing between groups. We have examined the effects of relaxing each of these assumptions and obtained the following results: (1) When broods mature asynchronously the optimum sex ratio is considerably more female biased than the Hamiltonian prediction. (2) Increasing male dispersal always decreases the optimum female bias to the sex ratio, but it is of particular interest that when moderate levels of dispersal are coupled with asynchrony of brood maturation then the optimum strategy is relatively insensitive to changes in foundress number. (3) When females cannot precisely determine the number of other foundresses initiating the group then the optimum strategy is almost exactly the strategy appropriate to a group of average size. These effects can be most easily understood in terms of local parental control (LPC) of the sex ratio. Through LPC a founding female can alter the mating success of her sons by altering the sex ratio of her brood. Asynchrony in the maturation of broods within a group increases the control that a founding female has over the mating success of her sons, whereas male dispersal reduces it. We have shown that the role of LPC and the role of inbreeding, which favors a female-biased sex ratio in haploidiploid species, are independent and that their effects can be combined into a single general formula r = (1-(r2/z2) E(alpha z/alpha r]/(1 + I). The concept of LPC can also be used to interpret two factors which have been proposed to select for the Hamiltonian sex ratios: local mate competition is LPC acting through sons; and sib mating is LPC acting through daughters.     

The spread and persistence of infectious diseases in structured populations

A basic assumption of many epidemic models is that populations are composed of a homogeneous group of randomly mixing individuals. This is not a realistic assumption. Most actual populations are divided into a number of subpopulations, within which there may be relatively random mixing, but among which there is nonrandom mixing. As a consequence of the structuring of the population, there are several sources of heterogeneity within populations that can affect the course of an infection through the population. Two of these sources of heterogeneity are differences in contact number between subpopulations, and differences in the patterns of contact among subpopulations. A model for the spread of a disease in such a population is described. The model considers two levels of interaction: interactions between individuals within a subpopulation because of geographic proximity, and interactions between individuals of the same or different subpopulations because of attendance at common social functions. Because of this structure, it is possible to analyze with the model both heterogeneity in contact number and variation in the patterns of contact. A stability analysis of the model is presented which shows that there is a unique threshold for disease maintenance. Below the threshold the disease goes extinct, and the equilibrium is globally asymptotically stable. Above the threshold, the extinction equilibrium is unstable, and there is a unique endemic equilibrium. The analysis presents a sufficient condition for disease maintenance, which determines critical subpopulation sizes above which the disease cannot go extinct. The condition is a simple inequality relating the removal rate of infectives to the infection rate of susceptibles. In addition, bounds on the actual threshold and the effect of symmetry in the interaction matrix on the threshold are presented.     

Disease spread in age structured populations with maternal age effects

Fundamental ecological processes, such as extrinsic mortality, determine population age structure. This influences disease spread when individuals of different ages differ in susceptibility or when maternal age determines offspring susceptibility. We show that Daphnia magna offspring born to young mothers are more susceptible than those born to older mothers, and consider this alongside previous observations that susceptibility declines with age in this system. We used a susceptible‐infected compartmental model to investigate how age‐specific susceptibility and maternal age effects on offspring susceptibility interact with demographic factors affecting disease spread. Our results show a scenario where an increase in extrinsic mortality drives an increase in transmission potential. Thus, we identify a realistic context in which age effects and maternal effects produce conditions favouring disease transmission.