Papers

Quasispecies theory describes how mutation and selection shape highly variable RNA virus populations, but most models explicitly consider neither RNA-dependent RNA polymerases nor the delays associated with their synthesis and functional activation. A recent minimal model showed that delayed polymerase availability can induce extinction by reorganizing basins of attraction, a mechanism termed {\tau}-tipping. Here, we extend this framework to a delay differential equation model in which master and mutant genomes encode distinct functional polymerases. We characterize its equilibrium and bifurcation structure, identifying master-mutant coexistence, mutant-only persistence (error catastrophe), and complete extinction governed by transcritical and saddle-node bifurcations. Although delays leave the equilibria unchanged, they reorganize their basins of attraction and can redirect populations that would otherwise persist at fixed mutation and replication parameters toward extinction, thereby extending {\tau}-tipping to systems with autonomous mutant replication. We also recover the previously studied complementation model as a limiting case in which defective genomes depend on master-derived polymerase, providing a comprehensive analysis of the bifurcation structure. Comparing the two models shows that the ability of mutant genomes to encode functional polymerases determines whether loss of the master sequence results in mutant replacement or complete population extinction. The occurrence of delay-induced extinction in both settings demonstrates the robustness of {\tau}-tipping and connects intracellular replication kinetics, complementation, and quasispecies extinction. Finally, we translate this mechanism into concrete virological predictions and propose experimental strategies to test the effects of replicase timing, RNA degradation, and functional complementation on viral persistence.

The development of large genetic biobanks with deep phenotyping and whole-exome or whole-genome sequencing is enabling an ever-deeper understanding of human evolution. Here we review recent developments in two main research directions: 1) using the increasing sample sizes to infer extremely strong evolutionary constraint and 2) leveraging biobanks' extensive phenotyping to relate the effects of natural selection on variants to their impacts on traits. In particular, there has been recent progress in gene-specific estimates of the strength of selection acting against loss-of-function mutations, as well as growing evidence supporting the importance of pleiotropic stabilizing selection on traits in shaping patterns of genetic diversity. We also discuss how these findings are, in turn, improving our understanding and interpretation of the genetic associations discovered in biobanks. Throughout, we outline open questions and promising directions for future research.

NASA planetary protection policy seeks to avoid inadvertent forward contamination of celestial bodies and backward contamination of Earth during space exploration. For Mars missions, it has historically focused on sterilization of landers and rovers. Current policy provides no framework for assessing the forward contamination risk of missions that deliberately include living organisms and must not be sterilized, such as a human crew, agriculture, or biotechnology for manufacturing and life support. We propose the PRIM (Propagation Restricted, Inert on Mars) framework to evaluate the forward-contamination risk posed by known organisms. Building on the biocontainment literature and probability-of-contamination model, PRIM bounds the ability of an organism released from a worst-case off-nominal event to sustain growth on the Martian surface at a probability under P_c <= 10^-4 using independent single-stressor propagation assays. We apply the PRIM framework to two engineered Mars biological in situ resource utilization (bio-ISRU) chassis organisms, using low water activity and carbon starvation to qualify them for low forward contamination risk even at high bioburden, and outline how to extend the assays to phototrophs and anaerobes. PRIM offers a path to flight-qualify living organisms for Mars based on laboratory assays rather than bioburden alone. This enables biological life support infrastructure for a sustained presence on Mars while keeping forward contamination risk demonstrably low.

Groups that search collectively often exploit what they find by recruiting: one member directs others to a site it has found. Recruitment raises the number of members foraging at a known site, but the return per forager may fall as that number grows, so there is an intermediate optimal recruitment rate. In addition, a site may be used by more than one group. Here we analyze a model of two groups that forage from a single site whose return declines with the total number of foragers present. The two groups interact only through this shared return. The long-run outcome is either coexistence at the foraging site or monopoly by one group, and we analyze the boundary between these two outcomes. A group's best response to its rival is not monotone: it increases its own recruitment rate with the rival's recruitment rate in an attempt to preserve a monopoly, and then its recruitment rate drops discontinuously when it is no longer optimal to preserve a monopoly. We analyze how model parameters govern this shift: a group relinquishes monopoly when the site saturates at few foragers and when the rival group is small. When the two groups have comparable size there are multiple Nash equilibria, so either group may end up with the larger share. And when two equally matched groups compete, both recruit above the rate that maximizes their common return, so that each individual ends with less than it would in a single undivided group of the same total size.

Reciprocal contacts can favor cooperation by protecting a lineage until its descendants compete as a group. An individual is chosen to reproduce from the whole population, with a probability increasing with its averaged cooperation payoff. Its offspring replaces a neighbor through contacts weighted equally in both directions. We compare a single cooperator taking over defectors with the reverse invasion, using the same distribution of introduction sites. When payoffs weakly affect reproduction, every network with at least six sites and a path visiting them all admits weights favoring cooperation at any benefit-cost ratio $b/c>1$. This holds for mutants placed uniformly or arising in newborn offspring. Unequal contacts sustain aligned domains around two protected sites, converting individual reproduction into collective competition. Cooperation cannot have an advantage when its benefit does not exceed its cost, at any positive selection strength with positive reproduction rates. Where mutants arise changes which contact patterns can use this mechanism. On a five-site path, the weak-selection threshold has the sharp lower bound seven under uniform placement; newborn introduction never favors cooperation at this order. We classify the contact patterns with at most five sites that can favor cooperation under either rule; newborn introduction requires a four- or five-site cycle. Tracing copies backward to their ancestors separates domain competition from the probability of reaching it. Exact polynomial inequalities prove sharp threshold bounds for paths and the four- and five-site cycles. The same ancestry reconstructs evolution without selection on weighted paths and cycles and fixes the slowest relaxation rate on every connected reciprocal network. Cooperation thus depends on both the collective competitors created by contacts and the route by which a new lineage enters them.

We compare eight variants of a three-variable pollution-based tourism model obtained by assigning the same discrete delay to different terms. The delay may enter three slots: the visitor factor in the deterrence term, pollution perception, or visitation-driven growth and reinvestment. We call a placement feasible when every nonnegative initial history produces a solution that exists for all future time and remains nonnegative. For every $\tau>0$, feasibility holds exactly when the visitor factor in the deterrence term is current, which occurs in four of the eight placements. In three of these four feasible placements, the positive equilibrium is locally asymptotically stable for every delay. In the fourth – the perception-lag model, with delayed pollution perception but current visitation – a conjugate pair of characteristic roots crosses the imaginary axis at a finite critical delay for every set of positive parameters. The equilibrium then loses stability and does not restabilise as the delay increases. A center-manifold reduction and numerical parameter sweep show that both supercritical and subcritical Hopf bifurcations can occur. The visitor-delayed placement, closest to earlier delayed-tourism models, can undergo a local Hopf bifurcation under additional conditions, but it does not preserve nonnegativity for all initial histories.

How cultural repertoires maintain diversity under selection is a fundamental question in cultural evolution. We address this using thirteen years of weekly popularity data for approximately 20,000 Irish traditional tunes, fitting ecological birth-process models under neutral, frequency-dependent, and per-tune selection hypotheses. We find strong evidence that tunes differ in intrinsic fitness - some are systematically more likely to be learned than others. We find that 29% of the variance in fitness can be explained by a mixture of social and melodic features. Some tunes appear to be carried along via linkage due to the tradition of playing tunes in sets, analogous to selective sweeps in genetics. By measuring changes in fitness over time and comparing this with recordings we precisely identify the mechanism by which a long-dormant tune can become fit through a popular recording. Despite the directional selection, repertoire diversity increases, driven by the continual arrival of new compositions. These results demonstrate that selection and diversity can coexist in a cultural ecosystem, and establish Irish traditional music as a quantitatively tractable system for studying the evolution of cultural variants and understanding what makes a tune stand out.

Periodic impulsive interventions arise naturally in the management of biological populations, including chemotherapy, pesticide application, and infectious-disease treatment. We develop general conditions for permanence in n-species population models subject to periodic multiplicative pulse disturbances. Our main result provides a sufficient condition for permanence in terms of weighted long-term growth rates on a Morse decomposition of the extinction set, explicitly separating the contributions of continuous population dynamics from those of the periodic pulse. To establish this result, we transform the impulsive system into an associated autonomous continuous-time dynamical system and use this correspondence to extend classical permanence theory to periodically pulsed models. We further show that the same conditions imply robust permanence under sufficiently small perturbations to the continuous dynamics, pulse period, and pulse effects. We illustrate the framework with two Lotka-Volterra models motivated by biological control: competition between chemotherapy-sensitive and chemotherapy-resistant cancer cells, and integrated control of an agricultural pest using pesticides and parasitoids. These examples demonstrate how intervention frequency and intensity interact with underlying ecological interactions to determine whether populations coexist or are excluded. Our results provide a general framework for analyzing persistence in ecological systems subject to repeated discrete disturbances.

We study feasible stable equilibria of Lotka-Volterra systems and their higher-order extensions. We complete the classification of impossible ecological interaction networks with at most four species and extend several of these impossibility results to families with arbitrarily many species. We then show that these sign-pattern obstructions are specific to the pairwise Lotka-Volterra model: arbitrary prescribed growth rates and pairwise coefficients can be supplemented by higher-order interactions so as to admit a feasible asymptotically stable equilibrium. Through the correspondence with replicator dynamics, we interpret feasible equilibria of higher-order Lotka-Volterra systems as totally mixed symmetric Nash equilibria of symmetric multiplayer games, derive bounds on their number, and study their robustness under perturbations of the payoff tensors. We conclude by showing that every impossible ecology determines a nonempty open class of symmetric two-player games with no totally mixed evolutionarily stable strategy.

One of the central challenges in evolutionary dynamics is understanding why some species combinations persist while others disappear. Although cyclic-interaction models have provided fundamental insights into biodiversity maintenance, much less is known about how hierarchical competitive interactions shape long-term community organization. Here, we investigate a hierarchical extension of the May-Leonard model, in which species interact through a directed predation chain while undergoing reproduction and mortality. Combining mean-field analysis with Monte Carlo simulations, we show that the fully coexisting state is generically unstable, causing the dynamics to evolve toward lower-dimensional coexistence states. The simulations further reveal stochastic extinctions dominating small populations with the dynamics progressively approaching the mean-field predictions as the system size increases. Rather than permitting arbitrary species combinations, the hierarchical-interaction structure dynamically constrains coexistence by selecting only specific subsets of species for long-term persistence. We show that these admissible coexistence states have a natural graph-theoretic interpretation as independent sets in the hierarchical interaction network, thereby providing general constraints on coexistence in hierarchical communities. Together, these results establish a theoretical framework linking hierarchical interactions, dynamical selection, graph topology, and biodiversity organization, extending the classical May-Leonard model beyond cyclic competition.

Continuous-time multi-type branching processes are fundamental models for expanding and migrating populations with cancer evolution being a prototypical example. Inferring model parameters, like mutation and growth rates, from time-series count data requires efficient computation of population size distributions. Existing methods are mainly based on large-time or large-number asymptotics, which rely on either restricted initial conditions or simplified interactions between cell types. Here, we introduce two numerical approximations of population size distributions for multi-type branching processes on directed graphs with arbitrary initialization. The first approach combines a saddle-point approximation with numerical integration of the probability generating function. We characterize admissibility and establish conditions for saddle-point existence and uniqueness. For directed acyclic graphs, the second approach provides a large-time small-mutation-rate alternative based on closed-form approximate Laplace transforms and efficient numerical inversion. We benchmark the accuracy and speed of both solutions in simulations, showing substantial improvement over the state-of-the-art large-number approximation and orders of magnitude speedup over Gillespie's stochastic simulation algorithm at matching accuracy. We apply our methods to analyze the relapse dynamics of an acute myeloid leukemia patient, where rapid parameter scans over a six-type patient-specific mutation tree quantify how unobserved remission burden and treatment-altered fitness can explain relapse. Our methods provide computational building blocks for future likelihood-based inference in cancer evolution and other expanding populations.

Infectious diseases may interact by competing for the same hosts or by facilitating subsequent infections. Understanding the dynamics of such multi-pathogen systems, particularly those subject to endemic seasonality and mitigation, is essential for designing robust public health interventions. We propose a three-stage modeling framework to disentangle the interplay between seasonality and behavioral feedback as a way of mitigation. First, we analyze a coupled susceptible-infectious-recovered-susceptible (SIRS) system without external forcing and show that the abrupt transition between the disease-free and endemic equilibria arises from a backward bifurcation-induced first-order phase transition. Second, we independently examine seasonality and behavioral feedback, characterizing where and when oscillatory behavior is induced near critical tipping points. Third, we demonstrate that their combination generates complex multi-annual wave patterns, with high-incidence cycles driven by seasonality and low-incidence intervals driven by behavioral feedback. By mapping stability as a function of seasonal forcing, mitigation strength, and cooperativity, we identify distinct period-doubling cascades with chaotic signatures arising from different mechanisms: the interplay between seasonality and behavior, and inter-pathogen cooperativity with the backward bifurcation it induces. We then analyze how these mechanisms interact across parameter ranges. Altogether, we show that cooperation fundamentally expands the spectrum of possible epidemic patterns, highlighting the importance of considering multi-pathogen interactions in epidemic modeling and control strategies.

We test whether the Kuramoto model quantitatively describes spatial synchronization in regional epidemic waves, using daily COVID-19 incidence for 400 German Kreise (2021–2023) and weekly ILI rates for 12 European countries (ECDC, 2021–2026). Bandpass filtering and Hilbert-transform phase extraction yield high global order parameters ($\langle r\rangle\approx0.87$ for Germany; $\langle r\rangle\approx0.97$ for Europe), yet both are dominated by a common-mode driver rather than pairwise local coupling. Removing the common mode reveals genuine short-range synchronization: an exponentially decaying residual local order with correlation length $\xi=152\pm6$~km in Germany, and a significant neighbor-vs.-non-neighbor contrast (Mann–Whitney $p=0.005$) in the European panel. We interpret this convergent pattern across two diseases and two spatial scales as a universal two-scale structure: a long-range common-mode field superimposed on shorter-range diffusive coupling. Cross-validation against a companion gauge-mediated Doi–Peliti framework shows that district-level effective screening mass $m_R$ is uncorrelated with local~$r$ (null result), the national $(m_R,r)$ phase portrait independently reproduces a previously reported hysteresis loop, and pairwise phase lags quantitatively match fractional-calculus predictions. A frequency–degree correlation provides the structural signature of explosive synchronization; excess synchronization between districts sharing the same Bundesland implicates shared school-holiday calendars and state-level policy as local coupling drivers.

Mosquito-borne diseases such as dengue, Zika, and yellow fever impose a substantial global health burden, motivating genetic control strategies that replace wild mosquito populations with disease-refractory ones. Maternal-effect dominant embryonic arrest (Medea) is a gene drive in which the offspring of a Medea-carrying mother die unless they inherit the Medea allele, producing biased inheritance capable of driving a linked refractory trait to high prevalence. We develop and analyze a continuous-time compartmental model of Medea dynamics in Aedes aegypti that tracks mosquito abundance by life stage and genotype, and that generalizes the drive mechanism to allow both imperfect Medea-killing and imperfect rescue. We characterize the biologically relevant equilibria and derive their local stability conditions, together with genotype-specific reproduction numbers and the basic reproduction number (R0) governing invasion from low frequency. Bifurcation analysis reveals bistability, and hence a release threshold that must be exceeded for Medea to take over, even though R0<1 at baseline. Imperfect killing and imperfect rescue reshape this bifurcation structure in distinct ways: killing leakage governs the invasion threshold, while rescue efficiency governs the composition of the resulting population. Sensitivity analysis identifies the fitness coefficient and killing leakage as the dominant drivers of both threshold and coverage outcomes, with mosquito demographic parameters affecting absolute abundances but not genotype proportions. Simulations of batched release programs inform efficient field deployment and show that reversing an established drive is substantially more costly than achieving forward invasion, though co-releasing both sexes accelerates reversal considerably more than it accelerates invasion.

Motivated by the pulsed control and resulting evolution of harmful biological populations, we develop and analyze an ordinary differential equation model of an n-dimensional stage-structured population undergoing periodic disturbances. The eco-evolutionary model couples both ecological dynamics through life cycle information, and evolutionary dynamics of allele frequency changes. Building off prior work in eco-evolutionary models and theory of linear systems, we show that if a resistant allele is present in the population, the population will always approach full resistance. Furthermore, we establish persistence conditions and show that these depend solely on system dynamics at full resistance. Finally, we demonstrate the utility of this model via an application to the Spotted-Winged Drosophila, an invasive species often treated periodically with insecticides. We use a parameterized model to further understand the complexities of relationships between ecological and evolutionary features of a species and its resistance evolution due to pulsed disturbances.

Tree-child networks are a useful class of binary phylogenetic networks. The Pons–Batle identity (Pons and Batle, Scientific Reports, 2021) states that the number $a_{n,k}$ of tree-child networks with $k$ reticulations on $n$ taxa satisfies \[ a_{n,k}=(n-k+1)a_{n,k-1} +\frac{n(2n+k-3)}{n-k}a_{n-1,k}. \] In this paper, we present a short combinatorial proof of this identity.

We study the population dynamics of a predator-prey system with two types in each species. Within a species, predator or prey, dynamics are described by a neutral competitive Lotka-Volterra model, i.e., birth, death and competition parameters are equal for both types. Additionally, we assume that the intra- and inter-type competition parameters are equal. The predator-prey interaction is defined by a matching-types model where predators of type $i$ exclusively interact with prey of type $i$. The individual-based model is described by a birth-death process with immigration, where immigration reflects mutations between the types of the same species. We completely describe the deterministic dynamics arising as a large population limit of this birth-death process. We find that depending on the parameters, potential equilibria are the coexistence of all four types, coexistence of a non-matching or matching pair of predators and prey, or the extinction of the predator or prey species resulting in a line of two-type equilibria. When mutations are sufficiently rare, then the predator-prey dynamics are described by successive jumps between the different deterministic equilibria on this mutational time scale. These jumps describe eco-evolutionary cycles of repeated prey or predator invasions and declines. When coexistence of all the types is possible, we show that these cycles accumulate on this time scale. Lastly, to prove that after the accumulation point the system converges to the coexistence equilibrium, we consider a slightly modified model with unequal intra- and inter-type competition parameters. This modified setting allows us to conclude that after the accumulation point all four populations remain macroscopic and converge to the coexistence equilibrium.

We introduce a fully stochastic, non-Markovian SIRS-type epidemic model that incorporates varying infectivity, waning immunity and a pulse vaccination strategy that may not confer permanent immunity. The model is constructed at the individual level, where each person is characterized by random infectivity and susceptibility functions, and vaccination campaigns occur at the jump times of a Poisson random measure with arbitrary intensity. We rigorously derive the epidemic dynamics as the large-population limit of an interacting stochastic particle system, leading to a system of nonlinear Volterra-type integral equations governing the average susceptibility and total force of infection. We establish a functional law of large numbers(FLLN) for the empirical processes and provide explicit expressions for the limiting compartmental proportions. The long-term behavior of the system is analyzed: we prove that the infection-free solution is globally asymptotically stable when the basic reproduction number falls below a critical threshold, and that the disease persists when this threshold is exceeded. The threshold is given by the harmonic mean of the maximal susceptibility across individuals and generalizes previous results by incorporating vaccination and memory effects. Our framework provides a probabilistically grounded extension of classical deterministic pulse vaccination models and offers new insights into the control of epidemics through scheduled immunization policies.

Chronic wasting disease (CWD) is a fatal prion disease affecting deer, elk, moose, reindeer, muntjac, and other cervids. Because free-ranging cervid populations face environmental variability and randomness, deterministic models may miss important dynamics like stochastic fade-out. We develop a stochastic Susceptible-Infectious-Environmental model using differential equations with reflection to ensure the susceptible class remains non-negative. We examine how environmental variability influences cervid populations as CWD pressure and control measures increase. For the deterministic model, we derive the basic reproduction number as the sum of direct and environmental contributions, showing the endemic phase arises at R0=1. For the stochastic system, we establish local well-posedness, positivity, and the disease-free law. The top Lyapunov exponent for invasion remains unaffected by reflection. We evaluate CWD mitigation using a deep reinforcement learning agent trained with Proximal Policy Optimization in a hybrid action space, comparing hunting, decontamination, and combined strategies. In the deterministic case, hunting alone can control the disease but reduces the population by about 58%, while decontamination requires sustained effort. The combined policy more than doubles the cervid population and nearly eliminates infection and contamination. In the stochastic case, the policy contains the disease in about 80% of runs, with 10% experiencing large outbreaks; effectiveness decreases as noise increases. Across all scenarios, the agent consistently emphasizes environmental decontamination, the key control method.

Species Distribution Modelling (SDM) is essential for understanding how environmental conditions shape biodiversity, particularly for destructive pests such as the Desert Locust (Schistocerca gregaria), whose breeding dynamics are tightly coupled to rapidly evolving environmental conditions. Maxent has become the dominant method for presence-only data, but its reliance on a linear combination of hand chosen feature transforms limits its ability to capture the nonlinear, temporal relationships common in ecological monitoring, where covariates such as precipitation, soil moisture, and vegetation indices evolve meaningfully over time. Standard implementations flatten time-series covariates into independent features, discarding sequential structure that carries critical signal. We introduce RNN Maxent, an extension of the Maxent framework that replaces the fixed feature dictionary with a neural network, specifically a Gated Recurrent Unit (GRU), trained end to end via backpropagation. The approach preserves Maxent's presence only statistical foundations, background normalization, and probability calibration, differing only in that the nonlinearity is learned from data rather than fixed in advance. We apply RNN Maxent to map suitable habitat for the Desert Locust using 50 day environmental time series derived from ERA5 Land, MODIS, and Sentinel 3, maintaining a 7 day gap between covariates and presence records to yield forecasting behavior. Compared against standard Maxent, RNN Maxent improves performance across metrics (ROC AUC 0.862 std 0.036 vs. 0.792; F1 0.671 std 0.056 vs. 0.590).

Large-language models (LLMs) are rapidly becoming part of human culture, reshaping how information is produced, transmitted, and used. Here we propose that their diffusion can be understood through a viral analogy, with LLM use spreading through populations, becoming embedded in cognitive and cultural practices. We model transitions among uncoupled, coupled, and persistently dependent users, and show that the interplay between social transmission, recovery, and collective reinforcement can generate tipping points and technological lock-in. A central consequence is the possibility of runaway dynamics: once a critical threshold is crossed, small increases in adoption can trigger rapid population-level shifts toward persistent dependence, with abrupt losses in cognitive competence. The same framework, however, identifies conditions for cognitive immunization, based on reducing transmission and facilitating reversibility. Our results highlight how LLM adoption may involve nonlinear collective transitions with important consequences for cognitive autonomy.

Agent-based models (ABMs) provide a natural framework for representing cell-level rules and spatial heterogeneity in bacterial infections, but their computational cost limits their use for macroscopic tissue-scale simulations and broad parameter exploration. We derive a deterministic coarse-grained description for a class of bacterial-infection ABMs in which immune cells and extracellular bacteria diffuse, immune cells ingest nearby bacteria, and intracellular bacterial loads evolve through prescribed birth and clearance processes. The first coarse-grained model is a semidiscrete reaction–diffusion system that retains a discrete internal state for each immune-cell bacterial load while representing cell and bacterial populations by continuum concentration fields. The key technical step is the derivation of state-dependent effective ingestion rates from the microscopic ABM parameters: these rates are obtained by solving an auxiliary diffusion problem around a single bacterium and computing the flux of immune cells into the interaction region. We then take a continuum limit in the internal state variable, yielding a state-structured reaction–diffusion system in which intracellular dynamics appear as advection and diffusion in state space. Numerical comparisons with ensemble-averaged ABM simulations show close agreement in biologically motivated parameter regimes. The resulting framework preserves the rule-based structure of the ABM while producing PDE models that are substantially more tractable for large-scale simulation and parameter studies.

The structure of the genotype-phenotype map plays a central role in determining how populations move through fitness landscapes, yet less is known about how this structure interacts with environmental constraints and fitness trade-offs. Here, we study evolution on a tunable multilayer genotype-phenotype map in which binary genotypes are transformed through successive feed-forward layers before being evaluated by phenotype-level fitness functions. We explicitly model the phenotype to fitness transformation in order to compare an emergent trade-off fitness with a no-trade-off control. We explore different map architecture as models of more and less complex genotype-phenotype relationships by tuning the genotype length and number of layers. We find that ruggedness and navigability have a complex, architecture-dependent relationship. Landscapes with few local maxima can still have low navigability for wide and shallow maps, and navigability is high even at mean values of ruggedness for wide and deep maps. Trade-offs increase navigability in wide and shallow maps, while their effect is muted in other architectures. The effect of trade-offs on epistasis depends on evolutionary history. While trade-offs change which mutational neighborhoods are sampled by evolution, the background degree of epistatic interactions is set by map architecture. Finally, we use our framework to investigate micro-evolution of high-fitness populations and show that temporal covariance in allele-frequency changes can arise from the internal structure of a rugged genotype-phenotype map, producing signatures that resemble short-term alternating selection.

Bayesian phylogenetic and phylodynamic analyses can be very time-consuming, owing to the combination of complex models that are used to estimate key parameters from increasingly large genomic data sets and their associated metadata. The use of high-performance computer hardware can – to a certain extent – alleviate the computational burden and markedly decrease the time to results. Still, even converging to the posterior can be a lengthy endeavour, with the burn-in aspect of such analyses potentially taking days or even weeks for large data sets. One of the key aspects that hampers performance in Bayesian phylogenetic inference is the efficiency with which tree topology proposals explore tree space. We here propose a novel adaptive tree transition kernel, which we call `subTreeLeap' (STL), which involves modifying the phylogeny by walking along patristic distance paths in the tree according to an adaptable radius parameter. STL is a general proposal, which can be used with contemporaneous or time-calibrated sequence data, being particularly suited to the latter due to respecting temporal precedence constraints. We carefully assess its impact on convergence and statistical mixing of the exploration of posterior tree space, by comparison to replicate “golden runs” obtained from lengthy analyses of empirical data under standard tree transition kernels. We find that STL successfully explores the same posterior tree space as standard kernels, but often does so in a more efficient manner. We discuss limitations as well as future potential improvements to STL that could substantially increase the speed at which Bayesian phylogenetic inferences are obtained.

Species area curves, which describe the number of species present as a function of area, have long been used to understand biodiversity and inform conservation efforts. While understanding the number of species is important, it leaves out information about the population sizes of each species. In this work, we examine the relationship between the effective number of species from different diversity indices, like Simpson's index and the Shannon index, and area. These effective number of species are also referred to as Hill numbers. Using a spatial and neutral model that has previously been used to understand species area curves, we show through a combination of theory and simulations that the relationship between the effective number of species and area is linear when the area is sufficiently large and resembles a power law for smaller areas.

We study a trait-structured population model incorporating mutation, selection and density-dependent regulation on a countably infinite trait space. The underlying stochastic process is a continuous-time Markov chain in which individuals reproduce at a trait-independent rate, offspring traits are determined by a mutation kernel on $\mathbb Z$, mortality depends on trait, and births are progressively suppressed as the population approaches a fixed population ceiling. Using results for density-dependent Markov population processes with countably many types, we derive a deterministic approximation in the form of an infinite system of nonlinear differential equations. We establish existence and positive invariance of solutions, and investigate the equilibrium structure of the deterministic system. A fundamental distinction emerges between bounded and confining mortality profiles. When mortality remains bounded, mutation may continually transport mass through the trait space and a stationary trait distribution need not exist. In contrast, when mortality increases without bound as the absolute value of the trait index becomes large, the operator $L=D^{-1}P$, where $P$ and $D$ govern mutation and mortality, is compact. By combining compactness with Kreĭn-Rutman theory for compact positive operators on Banach lattices, we show that $L$ has an algebraically simple principal eigenvalue with a strictly positive eigenvector, and we derive a threshold condition for the existence of a non-zero equilibrium. In this regime the equilibrium is unique, and its trait distribution is determined by the principal eigenvector of $L$. Numerical experiments support the theoretical results and illustrate the contrasting behaviours associated with bounded and confining mortality profiles.

A central challenge in movement ecology is to describe ecologically meaningful residence sites from raw tracking data due to heterogeneous sampling frequency and uncertain site boundaries. Here, we develop a greedy nearest-neighbor clustering approach with local reassignment and polygon-based site construction that generates timestamped sequences of site visits for each tracked individual, and apply it to nine years of GPS data from two sympatric raven species in the Dead Sea region—the Fan-tailed Raven (Corvus rhipidurus) and the Brown-necked Raven (C. ruficollis). Using the resulting visitation sequences, we quantify recursion patterns using the non-Markovian individual mobility model (IMM), which captures the balance between novel-site discovery $\beta$ and preferential return $\alpha$. The inferred dynamics are consistent with IMM predictions and reveal clear interspecific differences: Brown-necked Ravens continue to discover new sites at a higher rate (lower $\beta$), whereas Fan-tailed Ravens show a steeper concentration of visits among top-ranked sites. Entropy analyses further separate the species, with Brown-necked Ravens exhibiting higher site entropy and higher conditional entropy of site-to-site transitions. Together, these results provide a robust framework for describing interspecific differences in movement strategies that can be used to infer memory from GPS data and suggest distinct space-use strategies in two closely related sympatric species.

Like pairwise distances, quartets can be highly redundant and correlated on a phylogenetic tree, and their number grows on the order of n^4 rather than n^2. I explore BME-like weights for reweighting quartet scores before summing them to score a full tree. Three weights are considered on an unrooted binary tree: w_ext(q)=2^(-I_ext(q)), w_int(q)=2^(-I_int(q)), and w_tot(q)=2^(-I_tot(q))=w_ext(q)w_int(q), where the exponents count specified internal nodes in the minimal connecting subtree of a quartet. Exact tree-shape counts, total quartet-weight sums, and internal-edge crossing sums are calculated for all unlabeled unrooted binary tree shapes on 6-10 taxa. For w_ext, the total quartet weight is tree-shape-invariant and the edge-crossing sum depends only on split size. For any n-leaf tree, we prove sum_q w_ext(q)=(n-2)(n-3)/8, and the sum over quartets crossing an internal edge with split a|b equals (a-1)(b-1)/4. Exact tree-shape-specific normalizers are also derived for w_int and w_tot. A degree-corrected hard-polytomy extension is given for multifurcating trees, and a conditional consistency result shows that these positive weights preserve consistency when the underlying quartet estimates are themselves consistent for the true induced quartet states. These results provide a mathematical foundation for evaluating and applying BME-like quartet weights to reduce redundancy with the particular aim of improving statistical efficiency with finite data.

Ecological interactions are often mediated by feedbacks between organisms and their resource environments. Yet, how resource supply dynamics dictate collective dynamical phases of an ecosystem remains unclear. Here, we analyse a generalised consumer–resource model with non-reciprocal interactions to demonstrate that self-renewing versus externally-supplied resources yield fundamentally different dynamical phase diagrams. As interactions become increasingly non-reciprocal, ecosystems relying on self-renewing resources transition from stable dynamics to chaos and ultimately to infeasibility. By contrast, ecosystems with externally-supplied resources remain stable over a broader parameter range and transition to infeasibility without experiencing an intervening chaotic phase. Using the cavity method, we derive a unified stability condition applicable to a broad class of resource supply functions, explaining why externally-supplied resources can expand the stable region. We show that stability hinges crucially on the susceptibility of resources to perturbations, which depends strongly on their supply. Further, we show that external resource supply suppresses chaos in the unstable region by drastically reducing the susceptibility of resources closest to extinction. Our findings demonstrate that resource dynamics fundamentally reshape the accessible dynamical behaviours of an ecosystem, with implications for interpreting microbial community experiments.

By analyzing a stochastic Lotka-Volterra (LV) equation, we show that the underlying logic behind the diversity-stability debate in ecology can be framed as a dimensionality-induced critical phase transition, that is, a transition separating the regime dominated by statistical averaging and a systemic tipping point. This phase transition framework unifies the opposing ecological predictions in the diversity-stability debate and sets an intrinsic diversity ceiling for stochastic ecological communities.