Models Of Frequency-dependent Selection Research Articles

Prediction of post-PCV13 pneumococcal evolution using invasive disease data enhanced by inverse-invasiveness weighting.

After introducing pneumococcal conjugate vaccines (PCVs), serotype replacement occurred in Streptococcus pneumoniae. Predicting which pneumococcal strains will become common in carriage after vaccination can enhance vaccine design, public health interventions, and understanding of pneumococcal evolution. Invasive pneumococcal isolates were collected during 1998-2018 by the Active Bacterial Core surveillance (ABCs). Carriage data from Massachusetts (MA) and Southwest United States were used to calculate weights. Using pre-vaccine data, serotype-specific inverse-invasiveness weights were defined as the ratio of the proportion of the serotype in carriage to the proportion in invasive data. Genomic data were processed under bioinformatic pipelines to define genetically similar sequence clusters (i.e., strains), and accessory genes (COGs) present in 5-95% of isolates. Weights were applied to adjust observed strain proportions and COG frequencies. The negative frequency-dependent selection (NFDS) model predicted strain proportions by calculating the post-vaccine strain composition in the weighted invasive disease population that would best match pre-vaccine COG frequencies. Inverse-invasiveness weighting increased the correlation of COG frequencies between invasive and carriage data in linear or logit scale for pre-vaccine, post-PCV7, and post-PCV13; and between different epochs in the invasive data. Weighting the invasive data significantly improved the NFDS model's accuracy in predicting strain proportions in the carriage population in the post-PCV13 epoch, with the adjusted R2 increasing from 0.254 before weighting to 0.545 after weighting. The weighting system adjusted invasive disease data to better represent the pneumococcal carriage population, allowing the NFDS mechanism to predict strain proportions in carriage in the post-PCV13 epoch. Our methods enrich the value of genomic sequences from invasive disease surveillance.IMPORTANCEStreptococcus pneumoniae, a common colonizer in the human nasopharynx, can cause invasive diseases including pneumonia, bacteremia, and meningitis mostly in children under 5 years or older adults. The PCV7 was introduced in 2000 in the United States within the pediatric population to prevent disease and reduce deaths, followed by PCV13 in 2010, PCV15 in 2022, and PCV20 in 2023. After the removal of vaccine serotypes, the prevalence of carriage remained stable as the vacated pediatric ecological niche was filled with certain non-vaccine serotypes. Predicting which pneumococcal clones, and which serotypes, will be most successful in colonization after vaccination can enhance vaccine design and public health interventions, while also improving our understanding of pneumococcal evolution. While carriage data, which are collected from the pneumococcal population that is competing to colonize and transmit, are most directly relevant to evolutionary studies, invasive disease data are often more plentiful. Previously, evolutionary models based on negative frequency-dependent selection (NFDS) on the accessory genome were shown to predict which non-vaccine strains and serotypes were most successful in colonization following the introduction of PCV7. Here, we show that an inverse-invasiveness weighting system applied to invasive disease surveillance data allows the NFDS model to predict strain proportions in the projected carriage population in the post-PCV13/pre-PCV15 and pre-PCV20 epoch. The significance of our research lies in using a sample of invasive disease surveillance data to extend the use of NFDS as an evolutionary mechanism to predict post-PCV13 population dynamics. This has shown that we can correct for biased sampling that arises from differences in virulence and can enrich the value of genomic data from disease surveillance and advance our understanding of how NFDS impacts carriage population dynamics after both PCV7 and PCV13 vaccination.

Towards a replicator dynamics model of age structured populations

We present a new modelling framework combining replicator dynamics, the standard model of frequency dependent selection, with an age-structured population model. The new framework allows for the modelling of populations consisting of competing strategies carried by individuals who change across their life cycle. Firstly the discretization of the McKendrick von Foerster model is derived. We show that the Euler–Lotka equation is satisfied when the new model reaches a steady state (i.e. stable frequencies between the age classes). This discretization consists of unit age classes where the timescale is chosen so that only a fraction of individuals play a single game round. This implies a linear dynamics and individuals not killed during the round are moved to the next age class; linearity means that the system is equivalent to a large Bernadelli–Lewis–Leslie matrix. Then we use the methodology of multipopulation games to derive two, mutually equivalent systems of equations. The first contains equations describing the evolution of the strategy frequencies in the whole population, completed by subsystems of equations describing the evolution of the age structure for each strategy. The second contains equations describing the changes of the general population’s age structure, completed with subsystems of equations describing the selection of the strategies within each age class. We then present the obtained system of replicator dynamics in the form of the mixed ODE-PDE system which is independent of the chosen timescale, and much simpler. The obtained results are illustrated by the example of the sex ratio model which shows that when different mortalities of the sexes are assumed, the sex ratio of 0.5 is obtained but that Fisher’s mechanism, driven by the reproductive value of the different sexes, is not in equilibrium.

Dominant words rise to the top by positive frequency-dependent selection

A puzzle of language is how speakers come to use the same words for particular meanings, given that there are often many competing alternatives (e.g., "sofa," "couch," "settee"), and there is seldom a necessary connection between a word and its meaning. The well-known process of random drift-roughly corresponding in this context to "say what you hear"-can cause the frequencies of alternative words to fluctuate over time, and it is even possible for one of the words to replace all others, without any form of selection being involved. However, is drift alone an adequate explanation of a shared vocabulary? Darwin thought not. Here, we apply models of neutral drift, directional selection, and positive frequency-dependent selection to explain over 417,000 word-use choices for 418 meanings in two natural populations of speakers. We find that neutral drift does not in general explain word use. Instead, some form of selection governs word choice in over 91% of the meanings we studied. In cases where one word dominates all others for a particular meaning-such as is typical of the words in the core lexicon of a language-word choice is guided by positive frequency-dependent selection-a bias that makes speakers disproportionately likely to use the words that most others use. This bias grants an increasing advantage to the common form as it becomes more popular and provides a mechanism to explain how a shared vocabulary can spontaneously self-organize and then be maintained for centuries or even millennia, despite new words continually entering the lexicon.

Estimating the predictability of evolution

Evolutionary Ecology Evolution results from expected effects, such as selection driving alleles toward fixation, and stochastic effects, such as unusual environmental variation and genetic drift. To determine the potential to predict evolutionary change, Nosil et al. examined three naturally occurring morphs of stick insects (see the Perspective by Reznick and Travis). They wanted to determine which selective parameters could be used to foresee changes, despite varying environmental conditions. One morph fit a model of negative frequency-dependent selection, likely owing to predation, but changes in other morph frequencies remained unpredictable. Thus, for specific cases, we can forecast short-term changes within populations, but evolution is more difficult to predict when it involves a balance between multiple selective factors and uncertainty in environmental conditions. Science , this issue p. [765][1]; see also p. [738][2] [1]: /lookup/doi/10.1126/science.aap9125 [2]: /lookup/doi/10.1126/science.aas9043

Natural selection and the predictability of evolution in Timema stick insects.

Predicting evolution remains difficult. We studied the evolution of cryptic body coloration and pattern in a stick insect using 25 years of field data, experiments, and genomics. We found that evolution is more difficult to predict when it involves a balance between multiple selective factors and uncertainty in environmental conditions than when it involves feedback loops that cause consistent back-and-forth fluctuations. Specifically, changes in color-morph frequencies are modestly predictable through time (r2 = 0.14) and driven by complex selective regimes and yearly fluctuations in climate. In contrast, temporal changes in pattern-morph frequencies are highly predictable due to negative frequency-dependent selection (r2 = 0.86). For both traits, however, natural selection drives evolution around a dynamic equilibrium, providing some predictability to the process.

Unmasking the delusive appearance of negative frequency-dependent selection

The existence of persistent genetic variation within natural populations presents an evolutionary problem as natural selection and genetic drift tend to erode genetic diversity. Models of balancing selection were developed to account for the high and sometimes extreme levels of polymorphism found in many natural populations. Negative frequency-dependent selection may be the most powerful selective force maintaining balanced natural polymorphisms but it is also commonly misinterpreted. The aim of this review is to clarify the processes underlying the negative frequency-dependent selection model, describe classes of natural polymorphisms that can and cannot result from these processes, and discuss observational and experimental data that can aid in accurately identifying the processes that generated or are maintain diversity in nature. Finally, I consider the importance of accurately describing the processes affecting genetic diversity within populations as it relates to research progress.

What explains rare and conspicuous colours in a snail? A test of time-series data against models of drift, migration or selection

It is intriguing that conspicuous colour morphs of a prey species may be maintained at low frequencies alongside cryptic morphs. Negative frequency-dependent selection by predators using search images (‘apostatic selection’) is often suggested without rejecting alternative explanations. Using a maximum likelihood approach we fitted predictions from models of genetic drift, migration, constant selection, heterozygote advantage or negative frequency-dependent selection to time-series data of colour frequencies in isolated populations of a marine snail (Littorina saxatilis), re-established with perturbed colour morph frequencies and followed for >20 generations. Snails of conspicuous colours (white, red, banded) are naturally rare in the study area (usually <10%) but frequencies were manipulated to levels of ~50% (one colour per population) in 8 populations at the start of the experiment in 1992. In 2013, frequencies had declined to ~15–45%. Drift alone could not explain these changes. Migration could not be rejected in any population, but required rates much higher than those recorded. Directional selection was rejected in three populations in favour of balancing selection. Heterozygote advantage and negative frequency-dependent selection could not be distinguished statistically, although overall the results favoured the latter. Populations varied idiosyncratically as mild or variable colour selection (3–11%) interacted with demographic stochasticity, and the overall conclusion was that multiple mechanisms may contribute to maintaining the polymorphisms.

Genetic architecture of resistance in Daphnia hosts against two species of host-specific parasites.

Understanding the genetic architecture of host resistance is key for understanding the evolution of host-parasite interactions. Evolutionary models often assume simple genetics based on few loci and strong epistasis. It is unknown, however, whether these assumptions apply to natural populations. Using a quantitative trait loci (QTL) approach, we explore the genetic architecture of resistance in the crustacean Daphnia magna to two of its natural parasites: the horizontally transmitted bacterium Pasteuria ramosa and the horizontally and vertically transmitted microsporidium Hamiltosporidium tvaerminnensis. These two systems have become models for studies on the evolution of host-parasite interactions. In the QTL panel used here, Daphnia's resistance to P. ramosa is controlled by a single major QTL (which explains 50% of the observed variation). Resistance to H. tvaerminnensis horizontal infections shows a signature of a quantitative trait based in multiple loci with weak epistatic interactions (together explaining 38% variation). Resistance to H. tvaerminnensis vertical infections, however, shows only one QTL (explaining 13.5% variance) that colocalizes with one of the QTLs for horizontal infections. QTLs for resistance to Pasteuria and Hamiltosporidium do not colocalize. We conclude that the genetics of resistance in D. magna are drastically different for these two parasites. Furthermore, we infer that based on these and earlier results, the mechanisms of coevolution differ strongly for the two host-parasite systems. Only the Pasteuria-Daphnia system is expected to follow the negative frequency-dependent selection (Red Queen) model. How coevolution works in the Hamiltosporidium-Daphnia system remains unclear.

Models of Frequency-Dependent Selection with Mutation from Parental Alleles

Frequency-dependent selection (FDS) remains a common heuristic explanation for the maintenance of genetic variation in natural populations. The pairwise-interaction model (PIM) is a well-studied general model of frequency-dependent selection, which assumes that a genotype's fitness is a function of within-population intergenotypic interactions. Previous theoretical work indicated that this type of model is able to sustain large numbers of alleles at a single locus when it incorporates recurrent mutation. These studies, however, have ignored the impact of the distribution of fitness effects of new mutations on the dynamics and end results of polymorphism construction. We suggest that a natural way to model mutation would be to assume mutant fitness is related to the fitness of the parental allele, i.e., the existing allele from which the mutant arose. Here we examine the numbers and distributions of fitnesses and alleles produced by construction under the PIM with mutation from parental alleles and the impacts on such measures due to different methods of generating mutant fitnesses. We find that, in comparison with previous results, generating mutants from existing alleles lowers the average number of alleles likely to be observed in a system subject to FDS, but produces polymorphisms that are highly stable and have realistic allele-frequency distributions.

Mating success of alternative male phenotypes and evidence for frequency-dependent selection in Chinook salmon, Oncorhynchus tshawytscha

As with other species, frequency-dependent selection during reproduction has long been proposed as an important mechanism in maintaining alternative male reproductive phenotypes in Pacific salmon ( Oncorhynchus spp.). Jack salmon mature one year earlier than the youngest females in a population and are much smaller than older “adult” males. We tested the hypothesis that mating success of both phenotypes is consistent with the frequency-dependent selection model. By holding male density constant and varying the frequency of adults and jacks in eight separate breeding groups, we found that adult male access to females, participation in spawning events, and adult-to-fry reproductive success increased with their decreasing frequency in a breeding group. Jacks exhibited the same pattern (increasing success with decreasing frequency), although the relationships were not as strong as for adults. Overall, jack and adult males mated with a similar number of females, but jacks sired only 20% of all offspring. Observational data suggested that adult males benefited from sperm precedence associated with their ability to court females and enter the nest first at the time of spawning. Our work provides the first experimental evidence of frequency-dependent selection during mating in the family Salmonidae.

Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection

We examine the characteristics of non-equilibrium dynamics produced by a simple well-known model of frequency-dependent selection at a single diploid locus. An examination of the parameter space of this “pairwise-interaction model” (PIM) revealed non-equilibrium dynamics for polymorphisms of 3, 4 and 5 alleles; both allele-frequency cycling and aperiodic trajectories were detected. We measured the number, cycle length and domains of attraction of the various attractors produced by the model. The domains of attraction tended to be smaller, and the cycles longer, for systems with larger number of alleles. Fitnesses that parametrized negative frequency-dependent selection were more likely to allow cycling, and these cycles also had larger domains of attraction. Aperiodic trajectories were detected only in cases with 4 or 5 alleles. The genetic cycles produced by the model do not have periods as short as those predicted in ecological models with cycling (such as predator–prey population cycles, etc.). Consequently, in a real-world system, PIM allele-frequency cycling is likely to be indistinguishable from stable equilibria when observed over short time scales.

Protection of Salmonella by ampicillin-resistant Escherichia coli in the presence of otherwise lethal drug concentrations

Microbial systems have become the preferred testing grounds for experimental work on the evolution of traits that benefit other group members. This work, based on conceptual and theoretical models of frequency-dependent selection within populations, has proven fruitful in terms of understanding the dynamics of group beneficial or 'public goods' traits within species. Here, we expand the scope of microbial work on the evolution of group-beneficial traits to the case of multi-species communities, particularly those that affect human health. We examined whether beta-lactamase-producing Escherichia coli could protect ampicillin-sensitive cohorts of other species, particularly species that could cause human disease. Both beta-lactamase-secreting E. coli and, surprisingly, those engineered to retain it, allowed for survival of a large number of ampicillin-sensitive cohorts of Salmonella enterica serovar Typhimurium, including both laboratory and clinical isolates. The Salmonella survivors, however, remained sensitive to ampicillin when re-plated onto solid medium and there was no evidence of gene transfer. Salmonella survival did not even require direct physical contact with the resistant E. coli. The observed phenomenon appears to involve increased release of beta-lactamase from the E. coli when present with S. enterica. Significantly, these findings imply that resistant E. coli, that are not themselves pathogenic, may be exploited, even when they are normally selfish with respect to other E. coli. Thus, Salmonella can gain protection against antibiotics from E. coli without gene transfer, a phenomenon not previously known. As a consequence, antibiotic-resistant E. coli can play a decisive role in the survival of a species that causes disease and may thereby interfere with successful treatment.

Optimization under frequency-dependent selection

We consider a model of frequency-dependent selection, which we refer to as the Wildcard Model. A variety of more specific models, representing quite diverse biological situations, are covered by the Wildcard Model as particular cases. Two very different particular models that are subsumed by the Wildcard Model are the game theoretically motivated two-phenotype model of Lessard [Lessard, S.,1984. Evolutionary dynamics in frequency-dependent two-phenotype models, Theor. Popul. Biol. 25, 210–234], and the model of selection on a continuous trait due to intraspecific competition of Bürger [Bürger, R., 2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50 (4), 355–396] and Schneider [Schneider, K.A., 2006. A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J. Math. Biol. 52 (4), 483–523]. Both these models have been shown in the past to have a global Lyapunov function (LF) under appropriate genetic assumptions. We show that (i) the Wildcard Model in continuous time for a single multiallelic locus, or for multiple multiallelic loci in linkage equilibrium, has a global LF, of which the Lessard and Bürger–Scheneider LF are special cases in spite of their widely different biological interpretations; (ii) the LF of the Wildcard Model can be derived from an LF previously identified for a model of density- and frequency-dependent selection due to Lotka–Volterra competition, with one locus, multiple alleles, multiple species and continuous-time dynamics [Matessi, C., Jayakar, S.D., 1981. Coevolution of species in competition: A theoretical study. Proc. Natl. Acad. Sci. USA, 78 (2, part2), 1081–1084]. We extend the LF with density and frequency dependence to the multilocus case with linkage-equilibrium dynamics. As a possible application of our results, the optimization principle we established can be used as a tool in the study of long-term evolution of various models subsumed by the Wildcard Model based on explicit short-term dynamics.

SEX RATIO VARIATION AMONG GYNODIOECIOUS POPULATIONS OF SEA BEET: CAN IT BE EXPLAINED BY NEGATIVE FREQUENCY-DEPENDENT SELECTION?

This study is devoted to assess sex ratio variation among 33 populations of the gynodioecious Beta vulgaris ssp. maritima in Brittany (France) and to explore the causes of this variation. We showed that three different CMS (cytoplasmic male sterility) cytotypes occurred in populations, but strongly differed for their frequencies and the frequency of their associated nuclear restorer alleles (which counteract the effect of CMS and restore male fertility). No correlation was found between CMS and restorer frequencies within populations, which has been previously interpreted as a result of stochasticity. However, neutral genetic variation did not indicate recent population bottlenecks in studied populations. Moreover, no significant correlation was found between female frequency or variance and current population size. Consequently, stochastic processes could not be the major cause of sex ratio variation. Alternatively, empirical estimations of the variation of females, CMS genes and nuclear restorer allele's frequencies were compared to theoretical predictions based on a frequency-dependent selection model of gynodioecy. In particular, we showed that an absence of correlation between CMS and restorer frequencies could also occur without stochasticity. The large variation of sex ratio in Beta vulgaris could thus be explained by frequency-dependent selection acting on CMS genes and restorer alleles.

The Generation and Maintenance of Genetic Variation by Frequency-Dependent Selection: Constructing Polymorphisms Under the Pairwise Interaction Model

Frequency-dependent selection remains the most commonly invoked heuristic explanation for the maintenance of genetic variation. For polymorphism to exist, new alleles must be both generated and maintained in the population. Here we use a construction approach to model frequency-dependent selection with mutation under the pairwise interaction model. The pairwise interaction model is a general model of frequency-dependent selection at the genotypic level. We find that frequency-dependent selection is able to generate a large number of alleles at a single locus. The construction process generates multiallelic polymorphisms with a wide range of allele-frequency distributions and genotypic fitness relationships. Levels of polymorphism and mean fitness are uncoupled, so constructed polymorphisms remain permanently invasible to new mutants; thus the model never settles down to an equilibrium state. Analysis of constructed fitness sets reveals signatures of heterozygote advantage and positive frequency dependence.

Stochastic fluctuations in frequency-dependent selection: A one-locus, two-allele and two-phenotype model

Stochastic fluctuations in a simple frequency-dependent selection model with one-locus, two-alleles and two-phenotypes are investigated. The steady-state statistics of allele frequencies for an interior stable phenotypic equilibrium are shown to be similar to the stochastic fluctuations in standard evolutionary game dynamics [Tao, Y., Cressman, R., 2007. Stochastic fluctuations through intrinsic noise in evolutionary game dynamics. Bull. Math. Biol. 69, 1377–1399]. On the other hand, for an interior stable phenotypic or genotypic equilibrium, our main results show that the deterministic model cannot be used to predict the expectation of phenotypic frequency. The variance of phenotypic frequency for an interior stable genotypic equilibrium is more sensitive to the expected population size than for an interior stable phenotypic equilibrium. Furthermore, the stochastic fluctuations of allele frequency and phenotypic frequency can be considered approximately independent of each other for these genotypic equilibria, but not for phenotypic.

Maximization principles for frequency-dependent selection I: the one-locus two-allele case

In this article we study the one-locus two-allele version of the pairwise-interaction model of frequency-dependent selection in discrete and continuous time. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles. We provide a systematic approach that covers all possible facets of the dynamical behavior of the model, and we illustrate our results by concrete examples. We show that the mean fitness of the population is nondecreasing if the interaction coefficients are symmetric and positive. Moreover, monotonic convergence to the set of equilibria always occurs, which is not true if we also consider negative interaction coefficients. For asymmetric interaction, we provide necessary conditions when the mean fitness is nondecreasing and sufficient conditions when it is not. Furthermore, in discrete time, we show that limit cycles cannot occur, unless some interaction coefficients are negative.

DOES FREQUENCY-DEPENDENT SELECTION WITH COMPLEX DOMINANCE INTERACTIONS ACCURATELY PREDICT ALLELIC FREQUENCIES AT THE SELF-INCOMPATIBILITY LOCUS INARABIDOPSIS HALLERI?

Frequency-dependent selection is a major force determining the evolutionary dynamics of alleles at the self-incompatibility locus (S-locus) in flowering plants. We introduce a general method using numerical simulations to test several alternative models of frequency-dependent selection on S-locus data from sporophytic systems, taking into account both genetic drift and observed patterns of dominance interactions among S-locus haplotypes (S-haplotypes). Using a molecular typing method, we estimated S-haplotype frequencies in a sample of 322 adult plants and of 245 offspring obtained from seeds sampled on 22 maternal plants, collected in a single population of Arabidopsis halleri (Brassicaceae). We found eight different S-haplotypes and characterized their dominance interactions by controlled pollinations. We then compared the likelihood of different models of frequency-dependent selection: we found that the observed haplotype frequencies and observed frequency changes in one generation best fitted a model with (1) the observed dominance interactions and (2) no pollen limitation. Overall, our population genetic models of frequency-dependent selection, including patterns of dominance interactions among S-haplotypes and genetic drift, can reliably predict polymorphism at the S-locus. We discuss how these approaches allow detecting additional processes influencing the evolutionary dynamics of the S-locus, such as purifying selection on linked loci.

Frequency-Dependent Selection and the Maintenance of Genetic Variation: Exploring the Parameter Space of the Multiallelic Pairwise Interaction Model

When individuals' fitnesses depend on the genetic composition of the population in which they are found, selection is then frequency dependent. Frequency-dependent selection (FDS) is often invoked as a heuristic explanation for the maintenance of large numbers of alleles at a locus. The pairwise interaction model is a general model of FDS via intraspecific competition at the genotypic level. Here we use a parameter-space approach to investigate the full potential for the maintenance of multiallelic equilibria under the pairwise interaction model. We find that FDS maintains full polymorphism more often than classic constant-selection models and produces more skewed equilibrium allele frequencies. Fitness sets with some degree of rare advantage maintained full polymorphism most often, but a wide variety of nonobvious fitness patterns were also found to have positive potential for polymorphism. An example is put forth suggesting possible explanations for multiallelic polymorphisms maintained despite positive FDS on individual alleles.

The coexistence of hybrid and parentalDaphnia: the role of parasites

Parasite driven time-lagged negative frequency-dependent selection of hosts has been studied in natural populations by following changes in host genotype frequencies over time. However, such dynamics have not been considered at higher taxonomic levels, for example, between parental species and their hybrids. In a field study on a Daphnia hybrid system, we observed that one Daphnia taxon first was relatively under-infected, but became over-infected after a strong increase in frequency. This finding is consistent with the idea of parasite evolution towards the most frequent host taxon. In two experiments, we investigated whether the assumptions made by a model of negative frequency-dependent selection apply to our host taxa system. First, we showed that the parasite can change the outcome of taxa competition and secondly, we confirmed that the over-infection of one host taxon observed in the field has a genetic basis. Our results indicate that the incorporation of host-parasite interactions at the species level may allow us to gain a more complete picture of forces driving dynamic taxa coexistence in Daphnia hybrid systems. More generally, we suggest that if hybrids coexist in sympatry with parental taxa, the infection patterns as observed under natural conditions may be rather temporal and unstable.