How long a newly emerging trait will stay in a population is a fundamental but rarely asked question in cultural evolution. To tackle this question, the distribution and mean of the time to extinction of a discrete cultural trait are derived for models with overlapping generations, in which trait transmission occurs from multiple role models to a single newborn and may fail with a certain probability

The reproductive number R (or R0, the initial reproductive number in an immune-naïve population) has long been successfully used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic

Coevolutionary negative frequency-dependent selection has been hypothesized to maintain genetic variation in host and parasites. Despite the extensive literature pertaining to host-parasite coevolution, the temporal dynamics of genetic variation have not been examined in a matching-alleles model (MAM) with a finite population size relative to the expectation under neutral genetic drift alone. The dynamics

The multispecies coalescent process models the genealogical relationships of genes sampled from several species, enabling useful predictions about phenomena such as the discordance between a gene tree and the species phylogeny due to incomplete lineage sorting. Conversely, knowledge of large collections of gene trees can inform us about several aspects of the species phylogeny, such as its topology

Cooperation significantly impacts a species’ population dynamics as individuals choose others to associate with based upon fitness opportunities. Models of these dynamics typically assume that individuals can freely move between groups. Such an assumption works well for facultative co-operators (e.g. flocking birds, schooling fish, and swarming locusts) but less so for obligate co-operators (e.g. canids

In the evolutionary biology literature, it is generally assumed that for deterministic frequency-independent haploid selection models, no polymorphic equilibrium can be stable in the absence of variation-generating mechanisms such as mutation. However, mathematical analyses that corroborate this claim are scarce and almost always depend upon additional assumptions. Using ideas from game theory, we

A recent theoretical, deterministic model of the effects of phenotypic robustness on adaptive evolutionary dynamics showed that a certain level of phenotypic robustness (critical robustness) is a required condition for adaptation to occur and to be maintained during evolution in most real organismal systems. We built an individual-based heuristic model to verify the soundness of these theoretical results

We consider a game theoretical model of kleptoparasitic interaction between two individuals, the Owner and the Intruder. The Owner is in possession of a resource and must decide whether to defend the resource against the Intruder or flee. If the Owner defends, the Intruder must decide whether to fight with the Owner or flee. The outcome of the fight depends on the hunger of the individuals, the hungrier

Sexual selection and divergent selection are among the major driving forces of reproductive isolation, which could eventually result in speciation. A magic trait is defined such that a single trait is subject to both divergent selection and mate choice through phenotype-based assortative mating. We are here interested in the evolutionary behavior of alleles at a genetic locus responsible for a magic

During a range expansion, deleterious mutations can “surf” on the colonization front. The resultant decrease in fitness is known as expansion load. An Allee effect is known to reduce the loss of genetic diversity of expanding populations, by changing the nature of the expansion from “pulled” to “pushed”. We study the impact of an Allee effect on the formation of an expansion load with a new model,

Resistance to insecticide is considered nowadays one of the major threats to insect control, as its occurrence reduces drastically the efficiency of chemical control campaigns, and may also perturb the application of other control methods, like biological and genetic control. In order to account for the emergence and spread of such phenomenon as an effect of exposition to larvicide and/or adulticide

The order Hymenoptera includes most of the eusocial species on the planet. Correlated is the fact that many of the social species within the order are haplodiploid and use complementary sex determination (CSD) to determine the sex of offspring. CSD is the mechanism by why single sex alleles within an organism result in male development (haploid) and mismatched sex alleles develop into females (diploids)

Although the Reduction Principle for rates of mutation, migration, and recombination has been proved for large populations under constant selection, the fate of modifiers of these evolutionary forces under frequency-dependent or fluctuating selection is, in general, less well understood. Here we study modifiers of transmission, which include modifiers of mutation and oblique cultural transmission,

This paper considers predator–prey systems in which the predator moves between two patches. One patch is a source, where the predator and prey can persist, while the other is a sink where the predator cannot survive. Our aim is to show whether or not the dispersal is beneficial to the predator’s total abundance at equilibrium. Using dynamical systems theory, we demonstrate conditions under which a

The stationary sampling distribution of a neutral decoupled Moran or Wright–Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this distribution as a starting point we derive results for maximum likelihood estimates of scaled mutation rates from site frequency data under three model assumptions: a twelve-parameter

The Kingman coalescent process is a classical model of gene genealogies in population genetics. It generates Yule-distributed, binary ranked tree topologies – also called histories – with a finite number of n leaves, together with n−1 exponentially distributed time lengths: one for each layer of the history. Using a discrete approach, we study the lengths of the external branches of Yule distributed

A diffusion approximation for a randomized 2 × 2-matrix game in a large finite population is ascertained in the case of random payoffs whose expected values, variances and covariances are of order given by the inverse of the population size N. Applying the approximation to a Randomized Prisoner’s Dilemma (RPD) with independent payoffs for cooperation and defection in random pairwise interactions, conditions

The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death process, started at a random time in the past, and conditioned to have n sampled individuals at the present. The genealogy of individuals sampled at the present time

Missov and Lenart (2013) derived closed-form solutions to the life expectancy and remaining life expectancy at age x when the mortality is governed by a Gompertz-Makeham hazard, which is a parametric model commonly applied to human mortality data at adult and old ages. However, the closed-form expressions provided by these authors are not correct. We provide, therefore, valid and correct expressions

Long-term evolution of quantitative traits is classically and usefully described as the directional change in phenotype due to the recurrent fixation of new mutations. A formal justification for such continual evolution ultimately relies on the "invasion implies substitution"-principle. Here, whenever a mutant allele causing a small phenotypic change can successfully invade a population, the ancestral

A plausible biocontrol strategy for the eradication of invasive species involves augmenting wild populations with genetically modified supermales. Supermales contain double YY chromosomes. When they are augmented into a wild population, destabilization and eventual extinction occurs over time due to a strongly skewed gender ratio towards males. Here, we employ a mathematical model that considers an

Territorial behaviour is an important part of the lives of many animals. Once a territory has been acquired, an animal may spend its entire life on it, and may have to repeatedly defend it from conspecifics. Some species make great investments in the defence of a territory, and this defence can be costly, in terms of time, energy and risk of injury. Time costs in particular have rarely been explicitly

For many diseases, the basic reproduction number (R0) is a threshold parameter for disease extinction or survival in isolated populations. However no human population is fully isolated from other human or animal populations. We use compartmental models to derive simple rules for the basic reproduction number in populations where an endemic disease is sustained by a combination of local transmission

Only 6% of known species have a conservation status. Methods that assess conservation statuses are often based on individual counts and are thus too laborious to be generalized to all species. Population genomics methods that infer past variations in population size are easy to use but limited to the relatively distant past. Here we propose a population genomics approach that tests for recent population

Most natural environments vary stochastically and are temporally autocorrelated. Previous theory investigating the effects of environmental autocorrelation on evolution mostly assumed that total fitness resulted from a single selection episode. Yet organisms are likely to experience selection repeatedly along their life, in response to possibly different environmental states. We model the evolution

Populations whose mating pairs have levels of similarity in phenotypes or genotypes that differ systematically from the level expected under random mating are described as experiencing assortative mating. Excess similarity in mating pairs is termed positive assortative mating, and excess dissimilarity is negative assortative mating. In humans, empirical studies suggest that mating pairs from various

The year 2020 marks the 50th anniversary of Theoretical Population Biology. This special issue examines the past and continuing contributions of the journal. We identify some of the most important developments that have taken place in the pages of TPB, connecting them to current research and to the numerous forms of significance achieved by theory in population biology.

Trade-offs between dispersal and reproduction are known to be important drivers of population dynamics, but their direct influence on the spreading speed of a population is not well understood. Using integrodifference equations, we develop a model that incorporates a dispersal–reproduction trade-off which allows for a variety of different shaped trade-off curves. We show there is a unique reproductive-dispersal

In this article, we propose a Wright-Fisher model with two types of individuals: the inefficient individuals, those who need more resources to reproduce and can have a higher growth rate, and the efficient individuals. In this model, the total amount of resource N is fixed, and the population size varies randomly depending on the number of efficient individuals. We show that, as N increases, the frequency

Tree shape statistics are important for investigating evolutionary mechanisms mediating phylogenetic trees. As a step towards bridging shape statistics between rooted and unrooted trees, we present a comparison study on two subtree statistics known as numbers of cherries and pitchforks for the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. Based on recursive

We address the effect of population structure on key properties of the Ewens sampling formula. We use our previously-introduced inductive method for determining exact allele frequency spectrum (AFS) probabilities under the infinite-allele model of mutation and population structure for samples of arbitrary size. Fundamental to the sampling distribution is the novel-allele probability, the probability

Because demographic realism complicates analysis, mathematical modelers either ignore demography or make simplifying assumptions (e.g., births and deaths equal). But human populations differ demographically, perhaps most notably in their mortality schedules. We developed an age-stratified population model with births, deaths, aging and mixing between age groups. The model includes types I and II mortality

Whole genome epistasis models with interactions between different loci can be approximated by genomic relationship models based on Hadamard powers of the additive genomic relationship. We illustrate that the quality of this approximation reduces when the degree of interaction d increases. Moreover, considering relationship models defined as weighted sum of interactions of different degree, we investigate

Individuals differ in their life courses, but how this diversity is generated, how it has evolved and how it is maintained is less understood. However, this understanding is crucial to comprehend evolutionary and ecological population dynamics. In structured populations, individual life courses represent sequences of stages that end in death. These life course trajectories or sequences can be described

We derive statistical tools to analyze the patterns of genetic variability produced by models related to seed banks; in particular the Kingman coalescent, its time-changed counterpart describing so-called weak seed banks, the strong seed bank coalescent, and the two-island structured coalescent. As (strong) seed banks stratify a population, we expect them to produce a signal comparable to population

Mosquitoes cause more human suffering than any other organism. It is estimated that over one million people worldwide die from mosquito-borne diseases every year. With the continuous efforts of many researchers, Wolbachia gets more and more attention due to its characteristics of maternal transmission in mosquito population and it may cause cytoplasmic incompatibility (CI) which makes healthy females

This paper analyzes source-sink systems with asymmetric dispersal between two patches. Complete analysis on the models demonstrates a mechanism by which the dispersal asymmetry can lead to either an increased total size of the species population in two patches, a decreased total size with persistence in the patches, or even extinction in both patches. For a large growth rate of the species in the source

In this paper we develop a general framework for how the genetic composition of a structured population with strong migration between its subunits, evolves over time. The dynamics is described in terms of a vector-valued Markov process of allele, genotype or haplotype frequencies that varies on two time scales. The more rapid changes are random fluctuations in terms of a multivariate autoregressive

For a panmictic population of constant size evolving under neutrality, Kingman's coalescent describes the genealogy of a population sample in equilibrium. However, for genealogical trees under selection, not even expectations for most basic quantities like height and length of the resulting random tree are known. Here, we give an analytic expression for the distribution of the total tree length of

Genome sequencing has revealed that prophages, viral sequences integrated in a bacterial chromosome, are abundant, accounting for as much as 20% of the bacterial genome. These sequences can confer fitness benefits to the bacterial host, but may also instigate cell death through induction. Several recent investigations have revealed that the distribution of prophage lengths is bimodal, with a clear

Non-random mating has a significant impact on the evolution of organisms. Here, I developed a modelling framework for discrete traits (with any number of phenotypes) to explore different models connecting the non-random mating causes (mate competition and/or mate choice) and their consequences (sexual selection and/or assortative mating). I derived the formulaefor the maximum likelihood estimates of

Tick-borne pathogens pose a considerable disease burden in Europe and North America, where increasing numbers of human cases and the emergence of new tick-borne pathogens has renewed interest in resolving the mechanisms underpinning their geographical distribution and abundance. For Borrelia burgdorferi and tick-borne encephalitis (TBE) virus, transmission of infection from one generation of ticks

A simple competition model with time varying periodic coefficients, in which two species use different reproduction strategies, is explored in this paper. The two species considered comprise a native species which reproduces once a year over a short time period and an invasive species which is capable of reproducing throughout the entire year. A monotonicity property of the model is instrumental for

We investigate a new approach for identifying the contribution of horizontal transmission between groups to cross-cultural similarity. This method can be applied to datasets that record the presence or absence of artefacts, or attributes thereof, in archaeological and ethnographic assemblages, from which popularity spectra can be constructed. Based on analytical and simulation models, we show that

The Trivers-Willard hypothesis (TWH) states that parents in good condition preferentially produce the sex with a higher variation in reproductive success, whereas parents in bad condition favour the opposite sex. Theorists distinguish two variants of the TWH: (a) a biased sex-ratio at birth and (b) biased parental investment after birth. It has been argued before that the conditions stated by Trivers

The dynamics of evolution is intimately shaped by epistasis - interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary

Fluctuating environmental conditions have consequences for the evolution of life histories because they cause fitness variance. This variance can favor risk-spreading strategies, often known as bet-hedging strategies, in which growth or reproduction is spread over time or space, with some costs, but greater certainty of success. An important example is seed dormancy in annual plants, in which some

We consider the problem of estimating the elapsed time since the most recent common ancestor of a finite random sample drawn from a population which has evolved through a Bienaymé-Galton-Watson branching process. More specifically, we are interested in the diffusion limit appropriate to a supercritical process in the near-critical limit evolving over a large number of time steps. Our approach differs

Fluctuations in population size may have negative consequences (e.g., an increased risk of extinction or the occurrence of repeated outbreaks), and many management strategies are aimed at avoiding them by either only restocking or only harvesting the population. Two of these strategies are adaptive limiter control (ALC) and adaptive threshold harvesting (ATH). With ALC the population is controlled

An early question in evolutionary theory asked why frequency distributions of taxonomic group sizes exhibit "hollow curves" so frequently. An answer to this question was provided by G. Udny Yule's seminal contribution introducing a discrete model for those distributions. But Yule observed that the fit of his model to observed distributions was sometimes imperfect, in particular for the class of reptiles