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 histories

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.

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

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

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

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

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

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

Classical stochastic demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, in a 1978 Theoretical Population Biology paper, Gillespie demonstrated with his stochastic additive scale and concave fitness function (SAS-CFF) model that environmental stochasticity can promote genetic diversity. Extending the SAS-CFF to

Predator interference is a form of competition between predator individuals over access to their prey. There is broad empirical evidence for interference to exist in different strengths in various types of ecological communities. At the same time, parasites are increasingly recognized to alter food web structure and dynamics. In order to investigate the eco-epidemiological interplay between interference

There are many mechanisms that hosts can evolve to defend against parasites, two of which are resistance and tolerance. These defences often have different evolutionary behaviours, and it is important to consider how each individual mechanism may respond to changes in environment. In particular, host defence through tolerance is predicted to be unlikely to lead to variation, despite many observations

There is growing theoretical evidence that spatial structure can affect the ecological and evolutionary outcomes of host-parasite interactions. Locally restricted interactions have been shown in particular to affect host resistance and tolerance. In this study we investigate the evolution of several types of host disease resistance strategies, alone or in combination, in spatially structured populations

The outcome of natural selection depends on the demographic processes of birth, death, and development. Here, we derive conditions for protected polymorphism in a population characterized by age- or stage-dependent demography with two sexes. We do so using a novel two-sex matrix population model including basic Mendelian genetics (one locus, two alleles, random mating). Selection may operate on survival

Quantitative fishery harvest strategies in many countries throughout the world are based on maximum sustainable yield (MSY) reference points (RPs); in particular, the fishing mortality rate that produces MSY (i.e. Fmsy) and the population biomass (Bmsy) that results from fishing at Fmsy. There is often great interest in the sensitivity of MSY RPs to their inputs and underlying assumptions. We perturb

We study the evolution of the population genealogy in the classic neutral Moran Model of finite size n∈N and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise to a process on a state space consisting of n-sized binary increasing trees. We derive a number of properties of this process, and show that they are in agreement

Indirect effects, both density- and trait-mediated, have been known to act in tandem with direct effects in the interactions of numerous species. They have been shown to affect populations embedded in competitive and mutualistic networks alike. In this work, we introduce a four-dimensional system of ordinary differential equations and investigate the interplay between direct density-effects and density-

The number of clines (i.e., polymorphic equilibria) maintained by a step-environment in a unidimensional pocket at a single diallelic locus is investigated. The monoecious population is locally panmictic; its density is uniform. Migration and viability selection are both weak; the former is homogeneous and symmetric; the latter is directional and usually specified by a unimodal function f(p) of the

Size inequality has been considered a key feature of plant population structure with impacts on ecosystem functions. In forest ecosystems, studies examining the relationship between tree size inequality and stand productivity have produced mixed outcomes. These studies found positive, neutral or negative relationships and discussed how this could be influenced by competition for light between trees