Theoretical Population Biology

Understanding how mutations evolve on Y chromosomes is central to explaining the origin, diversity and persistence of sex chromosomes. Mutations occurring on the Y chromosome in sexual populations experience selective dynamics that differ markedly from those on autosomes, due to a reduced effective population size and the presence of large non-recombining regions containing alleles maintained in a permanently heterozygous state. These specific features alter gene transmission in the Y chromosome population compared to autosomes, even within the same pedigree. Here, we provide a two-sex diploid Wright-Fisher model that explicitly incorporates both sex chromosomes and autosomes within a unified population framework, in order to capture the influence of these specificities on the fate of mutations, not only considering fixation probabilities but also segregation times. We use diffusion approximations and provide analytical and numerical tools to compute these quantities across a wide range of parameters and selection regimes. We recover classical results on fixation probabilities in various scenarios, including purely beneficial, deleterious or overdominant mutations, and extend them in the light of mean segregation time, a key but often overlooked determinant of evolutionary outcomes over finite timescales. In particular, our analyses show that overdominant mutations are overall more likely to fix in observable time windows on the Y chromosome than on autosomes. Individual-based simulations corroborate our approximations and highlight parameter regimes where the theoretical approach is particularly useful, especially for parameter values inducing long segregation times or small fixation probabilities, for which simulations are impractical. Our results provide a comprehensive and tractable framework for clarifying how chromosome-specific features shape evolutionary dynamics beyond fixation probabilities alone.

We study one of the simplest scenarios of polygenic selection that can be imagined: a subdivided population of diploid individuals expressing an additive trait under spatially homogeneous stabilizing selection. We are interested in the amounts of variation that can be maintained at mutation-selection-migration-drift equilibrium, at individual loci and at the level of the trait, within and among subpopulations. We derive analytical approximations for variance components and summary statistics such as FST and QST under the assumptions of the infinite-island model and compare these with individual-based simulations. We find that: (i) There is a critical migration threshold (which depends on effect sizes of trait loci) below which population structure strongly inflates genic variance in the subdivided population to levels well above those in a panmictic population. Variation within each subpopulation is maximized close to the critical migration rate. (ii) The genetic basis of trait variation across subpopulations is most similar close to this migration threshold and (counter-intuitively) decreases for higher migration rates. This has consequences for the portability of Genome-Wide Association Studies (GWAS) between subpopulations, i.e, the extent to which loci with large contributions to variance in one subpopulation explain variance in other subpopulations. (iii) An analytical mean-field approach based on the single-locus diffusion approximation, together with effective migration and selection parameters (to account for associations between loci), very accurately predicts various quantities.

Alleles with opposing effects on fitness characters are said to exhibit selectional antagonistic pleiotropy (broadly construed so that effects are not necessarily confined to the same individual). A number of theoretical investigations considered the case where a pair of alleles at a locus influences two fitness components and derived the conditions giving rise to stable polymorphism under various assumptions about the mode of trait-interaction. Strikingly, many of these analyses concluded that the potential for maintaining polymorphism is strongly constrained by the joint influence of two factors: (1) the prevalence of weak selection coefficients over coefficients of large magnitude, and (2) the absence of beneficial dominance reversals (where the deleterious effects of each allele are partially or completely masked in the heterozygous genotype). Consequently, the conclusion that selective polymorphism is unlikely to be maintained by intralocus mechanisms of antagonistic pleiotropy has achieved widespread acceptance. Here we argue that such conclusions do not apply to any of the following models of antagonism: (i) additive trait-interaction, (ii) multiplicative trait-interaction, (iii) bivoltine selection, (iv) soft selection, (v) hard selection, and (vi) sexual antagonism. We demonstrate that the parameter space giving rise to stable allelic variation is quite large throughout, and moreover, the plenitude of suitable parameters neither depends on the strength of selection nor requires dominance reversal. Dominance coefficients associated with stringent conditions for stable polymorphism are shown to be atypical as compared to all feasible parameters, and best regarded as an outcome of adherence to a special relation: dominance with a constant magnitude and direction, which includes the case of additive allelic effects at a locus. Properties of single-locus equilibria (heterozygosity, allele frequency differentiation) are investigated, as well as the contribution of dominance schemes to the genetic variance in fitness characters in populations at multilocus linkage equilibrium. Author summaryAllelic variants at a locus with opposing effects on multiple fitness components (antagonistic fitness pleiotropy) have long been appreciated as a possible source of balancing selection. The prevalence of polymorphism owing to this form of natural selection, however, has been doubted on theoretical grounds due to the fact that standard assumptions of genetic models (namely, constant magnitudes for the dominance coefficients) are hardly conducive to the maintenance of polymorphism. The major exception to this conclusion lies with schemes that exhibit dominance reversal (where the direction of dominance for antagonistic alleles flips across fitness components). Here we conduct a geometric analysis of the space of polymorphism-promoting dominance parameters and conclude that the conditions for maintaining balanced alleles is unrestrictive, with non-reversals playing an underappreciated role.

Article summaryGene interactions are common, yet additive genetic models often predict short-term evolution and breeding response. This study argues that additivity can arise because populations sample only a small neighbourhood of a curved fitness landscape. In additive channels, genetic variation is small enough that local curvature contributes little to heritable fitness differences. The study defines an additivity index ([A]g) that compares variance from the local slope of log-fitness with variance from curvature, and links this ratio to expected prediction accuracy under Gaussian assumptions. A selection-inheritance framework shows when additive channels persist and when populations leave them. It yields testable predictions.

Evolving populations, especially in the strong-selection-weak-mutation limit, can be modelled as adaptive walks on fitness landscapes, moving in fitness-increasing mutational steps until reaching a fitness peak--a local optimum. Simulations of such adaptive walks--on a multi-peaked empirical landscape of the folA gene and on landscapes generated by the Rough Mount Fuji (RMF) model-- have shown that some landscapes are highly navigable, meaning that the highest x% of peaks are reached by >> x% of adaptive walks. This prompts the question of how adaptive walks can be so successful despite the local, myopic rules behind each adaptive step. Here, we investigate this question using simulations and mathematical approximations of random adaptive walks on a simplified RMF landscape. The landscape has a low-to-intermediate fitness region, whose size reconciles a low peak density with a high peak number. Despite the high number of peaks, walkers are likely to exit this region without terminating at a peak because the probability of a peak transition at each step is low and a fitness gradient guides walkers to the high-fitness region in few steps. Thus, three features are sufficient to explain why adaptive walks in the simplified RMF landscape are likely to reach a small fraction of top-ranking peaks: a low-to-intermediate fitness region with a high number of peaks, a low peak-transition probability, and which is crossed in few steps. We find that these three features are also present in the empirical folA landscape, suggesting that similar principles may apply.

Additive fitness landscapes--also called Mount Fuji landscapes--are the simplest and most widely used models of sequence-function relationships. As such, they play essential roles across multiple areas of biology, including evolutionary theory, quantitative genetics, gene regulation, and protein science. One of the most basic properties of any fitness landscape is its genotypic density--the number of sequences near a given fitness value. Understanding this density is especially important near fitness peaks, as it quantifies the supply of high-fitness genotypes. Here I study the genotypic density of additive landscapes near fitness peaks. Although this density is well known to be approximately Gaussian near the middle of the fitness range, its behavior near maximal fitness has not been reported. I begin by deriving a saddle-point approximation that accurately describes the genotypic density of additive landscapes over virtually the entire fitness range. I then show that the log density follows a power law near maximal fitness, with an exponent determined by how much the best allele at each position outperforms its nearest competitor. This power-law behavior holds over a substantial fraction of fitness values, besting the Gaussian approximation on both simulated and empirical landscapes across roughly a quarter to a third of the fitness range. Under certain conditions this behavior also extends to globally epistatic landscapes (defined as nonlinear functions over one or more additive traits), though with a reduced range of validity. These findings advance our understanding of one of the most fundamental models of sequence-function relationships. In particular, they reveal that the uppermost reaches of Mount Fuji landscapes, rather than being sharply peaked, are actually quite stubby.

We describe an approach for analyzing biological networks using rows of the Krylov subspace of the adjacency matrix. Specifically, we explore the scenario where the Krylov subspace matrix is computed via power iteration using a non-random and potentially non-uniform initial vector that captures a specific biological state or perturbation. In this case, the rows the Krylov subspace matrix (i.e., Krylov trajectories) carry important functional information about the network nodes in the biological context represented by the initial vector. We demonstrate the utility of this approach for community detection and perturbation analysis using the C. Elegans neural network.

At the fundamental conceptual level, two alternatives have traditionally been considered for how mutations arise and how evolution happens: 1) random mutation and natural selection, and 2) Lamarckism. Recently, the theory of Interaction-based Evolution (IBE) has been proposed, according to which mutations are neither random nor Lamarckian, but are influenced by information accumulating internally in the genome over generations. Based on the estimation-of-distribution algorithms framework, we present a simulation model that demonstrates nonrandom, non-Lamarckian mutation concretely while capturing indirectly several aspects of IBE: selection, recombination, and nonrandom, non-Lamarckian mutation interact in a complementary fashion; evolution is driven by the interaction of parsimony and fit; and random bits do not directly encode improvement but enable generalization by the manner in which they connect with the rest of the evolutionary process. Connections are drawn to Darwins observations that changed conditions increase the rate of production of heritable variation; to the causes of bell-shaped distributions of traits and how these distributions respond to selection; and to computational learning theory, where analogizing evolution to learning in accord with IBE casts individuals as examples and places the learned hypothesis at the population level. The model highlights the importance of incorporating internal integration of information through heritable change in both evolutionary theory and evolutionary computation.

Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.

Shenhar et al. (2026) report 50% "intrinsic" lifespan heritability after calibrating a one-component correlated-frailty survival model to Scandinavian twin lifespans. Their framework is mathematically coherent, but the intrinsic component is not identified if heritable, mortality-relevant extrinsic susceptibility is omitted at calibration. We show that one-component calibration absorbs omitted familial extrinsic structure into the intrinsic frailty scale parameter{sigma}{theta} , and that this variance absorption is visible through separate diagnostics (1) Variance absorption. Under misspecification,{sigma}{theta} is inflated by +22.1% (95% CI: 21.5-22.7%), corresponding to +49% inflation in [Formula]. Falconer h2 is downstream of calibration and inherits a +9.2 pp bias (95% CI: 8.7-9.7). The{sigma}{theta} inflation is model-general: +22% (GM), +18% (MGG), +14% (SR); any dependence summary that is strictly increasing in{sigma}{theta} inherits this inflation, so Falconer h2 is one affected downstream quantity among many (Corollary B3). (2) Structural fingerprint. In the joint twin survival surface S(t1, t2), misspecification produces systematic dependence errors (ISE 48x that of the recovery model). Conditional twin dependence is inflated at all ages, peaking at age 80 ({Delta}r = 0.048). (3) Specificity. The bias requires an omitted component that is both heritable and mortality-relevant. Three negative controls, a boundary check ({rho} = 0), and a two-component recovery refit ({sigma}{theta} restored to within -3.2%) establish specificity. ACE decomposition yields C {approx} 0 throughout: the omitted extrinsic component loads onto A (because it is shared 1.0/0.5 in MZ/DZ), so switching summary statistics does not restore identification. (4) Sensitivity and falsifiability. Over an empirically anchored regime ({sigma}{gamma} [isin] [0.30, 0.65],{rho} [isin] [0.20, 0.50]), Falconer bias ranges from +2.8 to +18.9 pp (mean 9 pp). If{rho} is sufficiently negative, the bias reverses sign in all three model families (Corollary B4). A full-likelihood robustness check shows that this upward pull is partly structural and partly estimator-specific: in the same misspecified one-component model, ML still inflates{sigma}{theta} (+3%), whereas matching only rMZ inflates it much more (+21%). These results do not resolve true intrinsic heritability but establish that Shenhars 50% estimate carries a structured, model-general upward bias originating in the fitted latent variance{sigma}{theta} .

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity--thoracic and wing flexion--reveals that distributed elasticity is moderate-risk but high-reward morphological feature. Well-tuned distributions expand the resonance band over fourfold whereas poorly-tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have adaptive value, and motivate broader work identifying distributions across species.

Animal-associated bacteria (microbiomes) can have important effects on host phenotypes and fitness. Microbiomes can also vary across individuals in ways that depend on host genotype and environment. Temperature is an especially important environmental factor that can affect the microbiome in a way that depends on host genotype and affects organismal fitness. Thermal stress, in particular, can have dramatic effects on animal microbiomes, including dysbiosis and immune dysregulation. However, most previous work on extreme temperature effects has focused on heat stress. To investigate how low temperatures affect the microbiome of a warm-adapted animal, we characterized the bacterial communities associated with house fly (Musca domestica) males raised at cool (18{degrees}C) and warm (29{degrees}C) temperatures. We sampled two distinct genotypes in these experimental flies, each of which is associated with a particular thermal environment (warm or cool). We contrasted our experimental results with the microbiomes we characterized in wild house flies from two collection sites with different large animals present. We found that temperature has a much stronger effect on the house fly microbiome than the host genotype in our experimental flies. Consistent with the strong environmental effects in our experiment, we found that wild house fly microbiomes differed between the two collection sites. Despite these environmental effects on the house fly microbiome, we did not detect evidence for dysbiosis associated with either cool or warm temperatures. We therefore conclude that the environment has more of an effect on the house fly microbiome than host genotype, but dysbiosis does not occur within the temperature range we considered.

Biological diversity driven by endosymbiosis arises from the intertwined evolution of microbes and their hosts. Each partner affects the fitness and therefore the evolution of the other. Here, we tested a further question: does the history of symbiosis affect evolution even after the partnership is dissolved? We analyzed phenotypic data from experimentally evolved strains of Dictyostelium discoideum hosts, each of which had had its symbiont removed, to study how their traits evolved. We found that host trait evolution was affected by the prior history of infection, specifically by which of three Paraburkolderia bacterial symbionts had been removed. Thus, symbionts affect not only current evolution but also generate path dependence that affects the subsequent evolutionary trajectories even after the symbionts are lost. Impact statementThe evolution of partner dependence in host-microbial symbioses has fundamentally shaped biological diversity and ecosystem function. To examine variation in symbiont dependence in the social amoeba, we compared how different strains of Dictyostelium discoideum respond evolutionarily after the loss of their bacterial symbionts. We analyzed phenotypic data from experimentally evolved strains and found that the absence of different symbiont species leads to distinct changes in the subsequent evolution of key traits like cell proliferation, slug migration, and spore production. This research expands our current understanding of microbial symbiosis by revealing that symbiont species may impact the evolution of their hosts even after the symbiont is gone. Data summaryWe used phenotypic traits data from our previous experimental-evolution dataset from the open-access repository Dryad (https://doi.org/10.5061/dryad.kkwh70s97). Scripts for the statistical analyses are available in a GitHub repository (https://github.com/jahanisrat/SymbiontLoss). The accompanying R project includes code to reproduce the graphs in the results section.

The Allee effect is a phenomenon where individual fitness is reduced in small populations, for example because of mate-finding difficulties or increased predation. Allee effects matter in conservation biology because they can drive small populations to extinction. The severity of Allee effects can depend on traits such as mate-search rate and defense against predators. Many natural populations exhibit considerable intraspecific trait variation (ITV) in such traits, but most studies so far assume these traits to be constant. Thus the impact of ITV on populations with Allee effect is largely unknown. Here we create two individual-based stochastic models that simulate a small population experiencing either a mate-finding Allee effect or a predator-driven Allee effect. We analyze how ITV, trait inheritance, and mutation affect the proportion of surviving populations. Under the mate-finding Allee effect, higher ITV hindered population survival and increased Allee thresholds. This can be explained by Jensens inequality and the negative curvature of the mate-finding function. Under the predator-driven Allee effect, ITV effects were weak, but higher mutation standard deviations were beneficial, likely because they provided more substrate for selection to act on. We thus recommend to take into account ITV when dealing with threatened populations with an Allee effect.

Across many complex traits, genetic variants with larger effect sizes tend to occur at lower frequencies, which is often interpreted as a signature of stabilizing selection. In statistical genetics, the so-called -model captures this relationship by assuming that effect size variance is inversely proportional to heterozygosity raised to a power 0 [<=] [<=] 1. Although empirically useful, the -model is phenomenological rather than mechanistic and lacks a direct population-genetic interpretation. In this paper, we derive an alternative to the -model based on evolutionary theory. Our approach yields a linear mixed model in which the frequency dependence of effect size emerges naturally as a function of interpretable evolutionary quantities describing mutational variance, selection intensity, and coupling between the focal and selected traits. These quantities enter through two identifiable variance components that can be estimated by restricted maximum likelihood (REML). The resulting framework links a fitness-landscape model to standard mixed-model methodology, enabling both inference on evolutionary parameters and downstream prediction by best linear unbiased prediction (BLUP). In forward simulations, the model accurately recovers the focal-trait variance and generally improves genetic prediction relative to conventional -model baselines.

Recent progress in mathematical kinship modelling has allowed one to predict the probable numbers of kin for a typical population member. In the models, kin may be structured by age and sex, both in static or time-variant demographies. Knowing the probable numbers of kin in different stages - such as parity, health status, or geographic location - however, remains an open challenge in Kinship Demography. Knowing how population structure delimits kin to distinct stages is an advance - for instance, the probability of having one sister at home and one sister away has different social implications from the probability of having two sisters. We present a novel analytical framework, grounded in branching process theory, that provides kin-number distributions jointly structured by age and stage. Using recursive compositions of probability generating functions (PGFs), we derive the joint age, stage, and age x stage kin-number distributions. All marginal distributions over either dimension naturally emerge. Simple extensions of the PGF approach additionally yield: the joint distribution of an individuals own stage and their kins stage; the probable numbers of kin deaths, both in total and by generation number; and the probabilities of being kinless and/or orphaned. We demonstrate the framework through novel results in an application using UK parity-specific fertility and mortality data. HighlightsO_LIA new method calculates probability generating functions for the number of kin structured by age and stage C_LIO_LIThe model allows predicting the probable numbers of kin organised by age and stage C_LIO_LIRecursive nesting of probability generating functions in branching processes is used C_LIO_LIAn application is presented highlighting the novel results C_LI

In many systems, mutations can have background-dependent fitness effects due to genetic interactions between loci within a genome (intragenomic epistasis). In some cases, such as when species are coevolving, genetic interactions between loci can span across species; this is described as intergenomic epistasis. It is known that intragenomic epistasis can make adaptation more repeatable by constraining accessible mutational paths. Here, we investigate whether intergenomic epistasis leads to the same pattern of increased repeatability and how repeatability is influenced by the interplay of intra- and intergenomic epistasis. For this, we model a two-species system in which the fitness of a species depends on the combination of genotypes that are present in both species. We implement this system using an NKC model, which allows us to construct coevolutionary fitness landscapes on which we simulate adaptation by means of mutations in both species. To quantify the repeatability of adaptation, we track the realised endpoints of adaptive walks and record the distribution of fitnesses of the focal and partner species at these evolutionary endpoints. We find that intergenomic epistasis creates highly repeatable patterns of adaptation that depend on the underlying shape of the coevolutionary landscapes. The patterns of repeatability deviate from expectations based on intragenomic epistasis due to fitness trade-offs between species, which can lead to cycling and large co-evolutionary fitness loads.

Genetic surveillance is increasingly used to track malaria transmission, yet genomic metrics can respond nonlinearly to changes in transmission intensity and depend on the diversity already present in the parasite population. Here, we present a stochastic agent-based model of hu-man-mosquito transmission that integrates SEIS-like epidemiological dynamics with within-host Plasmodium falciparum haplotype dynamics. By varying the maximum mosquito biting rate and the initial parasite diversity, we examine how transmission intensity and standing diversity jointly shape mixed infections, recombination, and long-term population structure across a continuous transmission gradient. Our study revealed a sequential pattern in which increasing biting intensity first increases infection prevalence and multiplicity of infection, then expands opportunities for outcrossing, and only thereafter increases effective recombination and recombinant haplotype generation. These responses are strongest in low- to intermediate transmission and tend to plateau at higher transmission levels. Initial population diversity constrains the amount of diversity that can be maintained and the magnitude of recombination output, while temporal trajectories show that haplotype evenness can pass through transient non-equilibrium phases before stabilizing. Together, these results show that the structure of the parasite population is shaped not by trans-mission intensity alone but by its interaction with standing genetic diversity. Furthermore, this study works to clarify when and how genomic metrics reliably reflect transmission conditions across heterogeneous malaria settings.

We introduce a mechanistic, nonlocal tumour-growth model designed specifically to capture explosive dynamics that are not adequately explained by standard logistic reaction-diffusion descriptions. The motivation is empirical: the universal scaling law reported in [1] provides compelling cross-sectional evidence of superlinear tumour activity versus tumour burden, but as a phenomenological relationship it does not by itself supply a dynamical mechanism, nor does it rigorously describe how explosive growth emerges, how fast it develops, or how spatial interactions and tissue boundaries influence it. Our model addresses this gap by incorporating nonlocal proliferative feedback--cells respond to a spatially aggregated neighbourhood signal--and a singular, Kawarada-type acceleration that produces "quenching": tumour density stays bounded while the proliferative drive becomes unbounded as the aggregated signal approaches a critical threshold. This offers a concrete mechanistic route to explosive escalation consistent with physical boundedness. We analyse the model under no-flux (Neumann) boundary conditions, appropriate for reflecting tissue interfaces. In the spatially homogeneous setting we prove finite-time onset of the explosive regime and obtain explicit rates for how rapidly it is approached. For spatially heterogeneous perturbations we derive a transparent spectral stability theory showing how the interaction kernel selects spatial scales and how the singular acceleration tightens stability margins as the explosive threshold is approached. These results provide interpretable links between nonlocal interaction structure, boundary effects, and the emergence of rapid growth. Finally, to connect mechanism to data in the spirit of [1], we embed the model in a Bayesian inference framework that treats the interaction kernel and the acceleration strength as unknown and learned from tumour-growth observations. This enables uncertainty-aware estimation of explosive onset times, escalation rates, and stability margins, while positioning the scaling law of [1] as an observable signature that our mechanistic model can explain and quantify rather than merely fit.

AO_SCPLOWBSTRACTC_SCPLOWA new Bayesian measure of phylogenetic information content is introduced based on geodesic distances in treespace. The measure is based on the relative variance of phylogenetic trees sampled from the posterior distribution compared to the prior distribution. This ratio is expected to equal 1 if there is no information in the data about phylogeny and 0 if there is complete information. Trees can be scaled to have the same mean tree length to avoid dominance by edge length information and focus on topological information. The method scales well, requiring only that a valid sample can be obtained from both prior and posterior distributions. We show how dissonance (information conflict) among data sets can also be estimated. Both simulated and empirical examples are provided to illustrate that the new approach produces sensible and intuitive results.