Papers

Colony demographic models often treat worker deaths as independent events, but shared environmental exposure may synchronize mortality within species. Using a 15-month field dataset of 18 Australian ant species and 106 cohorts, we quantified intra-specific mortality synchrony with the intra-class correlation coefficient (ICC) and tested body size and temperature as candidate correlates. Synchrony was widespread: credible intervals excluded zero in 9 of 18 species, and the assemblage mean ICC was 0.21 +/- 0.09, indicating that about 21% of daily mortality variance reflected shared within-species exposure. Body size did not buffer synchrony. Worker mass was unrelated to ICC (Spearman rho = +0.10, p = 0.69; WLS beta = +0.05, p = 0.35), decoupling how long workers live from when they die together. Temperature showed a suggestive lagged association: maximum temperature preceded mortality pulses by 1-7 days in 13 of 15 analyzable species, with mean peak r = 0.16, but no species survived Bonferroni correction. A sensitivity analysis using mean correlation across lags 1-7 days instead of the peak removed the assemblage-level signal (mean r = -0.03, p = 0.93), and ICC was unrelated to temperature-coupling strength (Spearman rho = -0.004, p = 0.99). Mortality synchrony is therefore widespread, size-independent, and only partly thermal. Species-specific thermal tolerance, rather than body mass, is a more promising candidate for explaining variation in synchronized mortality.

SARS-CoV-2 possesses a furin cleavage site (FCS) insertion in its spike protein, that is not found in other sarbecoviruses, and is responsible for its transmissibility in humans. The origin of the FCS insertion is unclear, and has been a point of debate regarding whether it arose naturally, or represents an artificial insertion. The FCS is destabilizing to spike protein, and as a consequence a compensatory mutation, D614G, rapidly emerged during the early pandemic and swept to fixation. Using a range of empirically determined parameters, a waiting time calculation can be used to determine the time interval between the appearance of the FCS and generation of the compensating D614G mutation. The waiting time is estimated to range from 37 to 65 days. Given the earliest detection of D614G on 1 January 2020, the latest dates for the appearance of the FCS range from October 28 to November 25 2019. This timeline is consistent with dates generated from phylogenetic considerations for the emergence of SARS-CoV-2 in late 2019, indicating that FCS appearance and virus emergence correspond. The waiting time approach enables discrimination between various scenarios of SARS-CoV-2 emergence, in particular cryptic circulation of a FCS-containing progenitor in the human population prior to late 2019 is unlikely, while prolonged circulation of a FCS-containing progenitor in bats appears inconsistent with absence of the compensatory mutation.

Competitive interactions can maintain diversity, yet coexistence is often fragile in well-mixed populations, where stochastic fluctuations can lead to extinction. This is the case in non-transitive systems, such as rock-paper-scissors dynamics, where no single type dominates globally. While spatial structure can stabilize these systems by providing refuges in space, it remains unclear whether analogous mechanisms can operate in time in well-mixed environments. Here, we develop a population-genetic framework showing that dormancy can act as a temporal refuge, preserving lineages and preventing collapse to fixation under interaction-driven fluctuations. We introduce a discrete-time Wright-Fisher model that combines generalized seed-banks with frequency-dependent interactions, allowing individuals to inherit their type from potential parents sampled across multiple past generations. This construction provides a tractable framework in which dormancy stores and later reintroduces lost types. In the case of either weak or moderate selection, we prove a multidimensional diffusion limit for the resulting type-frequency process and use it to analyze complex selective interactions. In non-transitive systems, dormancy stabilizes trajectories that would otherwise collapse through stochastic extinction, extends fixation times, and sustains coexistence. These effects cannot be explained solely by an increase in effective population size. Our results show that dormancy introduces temporal memory that qualitatively alters competitive dynamics, stabilizing otherwise fragile systems and enabling long-term coexistence.

This paper provides a complete characterization of the sign of the propagation speed in the symmetric two-species Lotka-Volterra competition-diffusion model under strong competition. The system admits a unique bistable travelling front and the sign of its speed determines which of the two species invades the other. We prove that for every strong competition intensity greater than $1$ and every diffusion ratio $d\neq1$, the travelling front propagates so as to expand the territory occupied by the faster-diffusing species. The front has a zero speed exactly when $d=1$. We also establish the smooth dependence of the wave speed and the travelling front on the model parameters. The main step in the sign characterization is to prove that a monotone standing front cannot exist when the diffusion rates are different. Combined with continuity of the wave speed with respect to the parameters, the species-exchange symmetry of the system, and an explicit travelling front at a particular parameter value, we obtain the sign of the propagation speed throughout the entire parameter region. This establishes the “Unity is not strength” theorem, which was previously known only in restricted parameter regimes.

Classical mathematical oncology employs deterministic mean-field models predicting that sufficiently high chemotherapy doses drive tumor density to zero. We show that this apparent cure is an artifact of neglecting demographic fluctuations. We construct a nonequilibrium stochastic PK-PD field theory combining a two-compartment pharmacokinetic model with a stochastic tumor-immune sector in the Doi-Peliti formalism, then map it to coupled multiplicative Langevin equations via the Martin-Siggia-Rose/Janssen-De Dominicis approach. In immune-depleted sanctuary sites, the dynamics reduce to a time-dependent Feller diffusion whose Fokker-Planck equation yields an analytical survival functional: demographic noise implies a strictly nonzero relapse probability for tumor micro-clusters under high-dose chemotherapy. Standard bolus administration acts as a nonselective annihilation process, driving immune fields into an absorbing state and creating a spatially immune-depleted vacuum that enables fluctuation-induced relapse – Stochastic Pharmacokinetic Escape. We derive quantitative conditions under which metronomic dosing and adjuvant immunotherapy suppress this stochastic window of vulnerability. A model-agnostic analysis of 1461 longitudinal patient records shows that the majority of evaluable lesions exhibit a nadir followed by measurable regrowth rather than monotonic elimination; fitting the model's drift functional to these trajectories reproduces this pattern quantitatively, and a direct test of the predicted demographic-noise scaling law reveals size-dependent noise largest at the smallest observed tumor volumes, consistent with the proposed mechanism.

Growth is a fundamental process in living systems. Although the stress-deformation response of growing materials is often described as either purely elastic or purely viscous, many biological tissues, from biofilms to tumors, exhibit both elastic and viscous behavior. Here, we show that this viscoelastic response can crucially control the mechanics of proliferating matter when the growth rate becomes comparable to the rate of stress relaxation. Focusing first on the prototypical case of a growing elastic beam, we find that the dynamics are governed by a single dimensionless parameter, $g \tau$, where $g$ is the growth rate and $\tau$ is the viscoelastic relaxation time. While the limits $g \tau \to 0$ and $g \tau \to \infty$ recover purely viscous and purely elastic behavior, respectively, the intermediate regime is not merely a smooth crossover between them. Instead, qualitatively new dynamics emerge at $g \tau \sim 1$, including rapid transitions between metastable states that occur in neither limiting regime. We then develop a general, growth-compatible theoretical framework in which unconstrained growth is intrinsically stress-free, extending the analysis to other prototypical geometries and enabling simulations of more realistic growing biological materials. Within this framework, sharp mechanical transitions arise when stress generated by exponential growth accumulates faster than it can be dissipated by viscoelastic relaxation.

The concept of valuing evolutionary history has a long tradition and was formalized by several research groups in the early 1990s, each aiming to capture the products of evolution more comprehensively than species richness alone. Preserving the "Tree of Life" has since become a central, if sometimes contested, goal in conservation biology. Faith's phylogenetic diversity (PD), defined as the sum of the edge lengths of a rooted tree connecting a set of focal entities, is the most widely used metric in this context and underpins an extensive methodological framework. This framework includes widely used species-specific indices such as EDGE, as well as approaches that quantify expected species-specific contributions to PD such as EDGE2. This chapter focuses on the development of this framework of phylogeny-based conservation metrics. We review the development of species-specific indices, highlighting their strengths and limitations, and trace their progression from simple formulations to game-theoretic approaches and more abstract generalizations. We also discuss how these indices are applied in conservation practice, with particular emphasis on the EDGE framework. We further discuss the relationship between the edge lengths of a phylogeny and the evolutionary features they are intended to represent. Finally, we highlight recent advances in the field and identify areas for future research.

This work investigates the class of SIR/SEIR models and their extension to an ODE-based SVEIR system, whose parameters are calibrated and validated using real influenza outbreak data. The theoretical part establishes existence and uniqueness of solutions for the SVEIR model via the Picard-Lindelof theorem and analyzes invariance of the admissible region. To describe spatiotemporal infection spread in an urban setting, a diffusion-chemotaxis extension of the SIR framework is formulated as a PDE system; an additional term is introduced to represent fear/avoidance effects in the system dynamics. A numerical workflow is proposed, including grid discretization, Neumann boundary conditions enforced by mirror extension, a semi-implicit IMEX time-stepping scheme, and sparse linear solves; computational correctness is monitored, in particular, by checking conservation of the total population.

Solitary animals face a tradeoff when detecting threats: faster detection means accepting more false alarms. We show that groups can manage this tradeoff better by treating an undisturbed neighbor as evidence against a threat, becoming both faster and more accurate than lone individuals. Modeling each animal as a noisy evidence-accumulator that flees when its belief crosses a threshold, we find that a neighbor's flight signals danger while its stillness signals safety. A naive responder reacts only to flights and inflates false alarms as the group grows; a Bayesian responder weighs both, approximated by a single social discounting rate that interpolates between these limits. This yields closed-form expressions for group performance, including cascade branching ratios that stay strongly subcritical in safety and turn supercritical under threat, so the rate at which an animal discounts a threat while its neighbors stay still can be inferred from behavior alone, and it sets a ceiling on how many neighbors an animal can attend before discounting alone can no longer hold its false-alarm rate. Wild sulphur molly shoals under bird attack are best described by discounting rates well above what individually Bayesian updating supplies over any neighborhood they could plausibly attend, and the same model, at the inferred value, predicts a false-alarm rate that stays constant as shoals grow.

Extinction is inevitable; every species eventually dies out, impacting the ecosystem it is part of. Over the past few decades, extensive research stemming from the stability-diversity debate has addressed how species diversity contributes to the stability of large ecosystems. However, conventional stability criteria often rely on deterministic frameworks, overlooking the intrinsic population fluctuations that allow any species to go extinct by chance. In this paper, we incorporate demographic stochasticity into large complex ecosystems with a rule-based model. We demonstrate that such demographic fluctuations rapidly prune the low-abundance species from the ecological community, thereby securing higher systemic stability. By developing a bottom-up theory to characterise the statistics of extinction dynamics, we discover that the fraction of surviving species exhibits an anomalous heavy-tailed decay over time, revealing the emergence of remnant communities with robust metastability. Our results highlight that when demographic fluctuations are accounted for, ecosystems self-stabilise by reducing their diversity even when they are predicted to be chaotic in the deterministic limit.

What decides whether people do things together or separately? Many activities cannot be carried out alone, and an individual must rank them against the private tasks competing for the same time. We address this within the priority-queue description of human activity by letting each agent choose the priority of a shared task rather than drawing it from a fixed distribution: the value of the joint activity, discounted by the estimated risk that the partner will not take part. Participation becomes strategic, and the model acquires a phase transition. A coupled phase, in which joint activity is sustained, is separated from an absorbing solitary phase by a saddle-node bifurcation that we obtain in closed form. The transition is discontinuous and the solitary phase is absorbing, so collapse is irreversible unless an agent persists unilaterally for of order one memory time, a cost we also compute. The heavy-tailed interevent statistics that motivate queueing models of human dynamics survive only in a narrow window at the transition, and there the exponent is fixed by the fraction of time spent coupled rather than by queue length: the universality classes of the non-strategic model do not survive the introduction of choice. On a network, attention divides as $1/(k+a)$ and fixes a critical degree beyond which no coupled state exists, so the solitary phase percolates according to the Molloy–Reed criterion with the second moment truncated at that degree — formally an attack on hubs, with no attacker. For group activities the critical degree falls as the $(m-1)$th root, implying a maximum group size. The transition organises two quantities already measured in communication records: a finite capacity for keeping ties active, and the decay of ties whose rhythm is interrupted.

In social insects, mortality risk comprises distinct components that may not share the same predictors: lifespan duration, senescence trajectory, and thermal vulnerability. We tested these three axes in 18 Australian ant species using paired field-laboratory survival assays (2,363 cohort-day observations; 1,148 workers). Body size predicted duration (Cox HR = 0.67, p = 0.002), while colony size (p = 0.60) and the size x temperature interaction (p = 0.72) showed no detectable moderating effect. A weak but significant size x foraging-rate interaction was detected (LRT p = 0.014), suggesting that intrinsic physiology remains the most parsimonious explanation for the main size-longevity pattern, although ecological context may contribute. Senescence trajectory was associated with circadian niche rather than size: it was steepest in matinal species (Kruskal-Wallis p = 0.009; matinal vs. crepuscular p = 0.002) and was uncorrelated with body mass (Spearman p = 0.32). Thermal hazard plateaued above 20 degrees C (Delta AIC = -38; p < 0.001), with elevated thermal sensitivity in Rhytidoponera (Ectatomminae) above the plateau (5% per degree C, p = 0.015). Circadian regime and lineage identity, not body size, therefore emerge as the most climate-relevant axes, although they are strongly collinear (Cramer's V = 0.85). These results show that body size captures only one dimension of mortality risk and that size-based vulnerability indices may misrank taxa when senescence and thermal sensitivity are decoupled from body size.

Multi-strain epidemiological systems frequently exhibit self-sustained oscillations, yet severe algebraic complexity has long obstructed a complete analytical characterization of these dynamics. Seeking to bypass these barriers, we have identified a broad, analytically tractable class of two-strain models featuring asymmetric cross-immunity that precludes secondary infections for a single strain. This targeted structural simplification allows us to derive explicit expressions for coexistence equilibria and map their stability. We show that the relative transmission advantage of secondary infections fundamentally governs the onset of robust limit-cycle oscillations, extending previous narrow-borderline results. Crucially, numerical simulations reveal a rich macroscopic landscape where small-amplitude local oscillations coexist with large-amplitude, recurrent outbreak cycles. The structural robustness of these phenomena is confirmed by incorporating effects such as waning immunity and isolation and extending the framework beyond the analytically tractable class. These findings provide a clear mechanistic explanation for multi-strain epidemic cycles and offer a highly tractable baseline for future theoretical developments.

Environmental sharing changes the value of diversification even when the marginal statistics experienced by each lineage remain unchanged. A minimal model of cell division couples this effect to the inheritance of a conserved protective reserve. Each mother partitions its reserve between two daughters, and each fixed partition policy generates a random demographic operator whose top Lyapunov exponent determines long-term growth. Weak environmental sharing favors symmetric inheritance, whereas sufficiently shared innovation selects a separated asymmetric branch near {\alpha \simeq 0.2}. The transition therefore occurs by a finite branch crossing rather than by a continuous departure from equal partition. The asymmetric phase persists when the protection law or reserve turnover is changed, although its boundary depends on protection nonlinearity and reserve memory. Because shared and private environmental innovations have identical marginal statistics, the mean reproductive operator is independent of the shared-innovation fraction. A dominant-mode second-order approximation then separates the asymmetric advantage into a mean-operator growth cost of specialization and a reduction of sensitivity to collective fluctuations. This approximation predicts the finite asymmetric branch selected by the full random-operator dynamics, while the full operator product determines the numerical crossing. Environmental sharing can therefore drive symmetry breaking in the inheritance of a conserved protective resource when the loss of diversification between lineages increases the value of diversification generated at division.

Highly pathogenic avian influenza (HPAI) outbreaks require rapid control during active transmission and evidence-based decisions on the safe restocking of depopulated farms. We developed a stochastic spatial SEIR-based metapopulation model for a synthetic HPAI outbreak on the fictional Jolly Island. Farms were classified as `Broiler-2', `organic duck', or `Other' production systems. The model incorporated local, environmental, movement-mediated, and distance-dependent transmission, together with reactive and preventive culling, production-specific confinement, and capacity-based restocking. The simulated epidemic was geographically concentrated and differed substantially among production classes. Preventive culling reduced mean cumulative burden from 16,362.7 to 13,631.9 infectious-farm-days, with an overall reduction of 16.7%. Earlier confinement substantially reduced epidemic magnitude, while stronger environmental transmission increased the epidemic peak. Restocking risk declined as the epidemic approached resolution. Under the model assumptions, 24 May 2026 was the first candidate date satisfying the predefined rebound-probability threshold of 0.20. For restocking on 15 March 2026, none of the tested restocking fractions met this criterion. Capacity-based restocking reduced cumulative burden by 8.45% and rebound probability from 0.780 to 0.533, compared with restocking relative to the baseline population. These findings demonstrate the value of integrating epidemic control and post-outbreak recovery within a single modelling framework. Timely confinement, targeted preventive culling, and phased capacity-based restocking may reduce both epidemic burden and resurgence risk, although operational decisions should also incorporate surveillance, biosecurity, economic considerations, and regulatory requirements.

Microbial populations generally evolve in fluctuating environments under time-varying conditions. These are often described by binary switching models, sometimes seen as coarse-grained feast-famine cycles, in which resource availability switches abruptly between abundant and scarce conditions. However, experimental studies suggest that feast-famine environments actually exhibit more complex temporal dynamics. Here, we study how two strains, one growing slightly slower than the other, compete for the same resources in fluctuating environments comprising a finite number of intermediate states, each having its own carrying capacity. Environmental switching between these states and their carrying capacities represents gradual changes in nutrient availability. This class of multi-state stochastic switching models can be interpreted as a coarse-grained description of feast–famine cycles and allows us to investigate strain competition under the gradual recovery and depletion of resources. By computational and analytical means, we characterise the population dynamics in these multi-state fluctuating environments. In particular, we study how the switching rates and distribution of carrying capacities affect the population-size statistics, fixation probability, and mean fixation time. By comparing these results with their counterparts in binary environments, we clarify how the frequency and amplitude of environmental fluctuations influence population dynamics in coarse-grained feast-famine cycles.

Scaling relations linking species size, abundance, and resource availability are among the most robust empirical regularities in ecology. However, a mechanistic explanation for how these community-level laws emerge from ecological processes remains elusive. Here, we address this gap by developing a minimal spatially explicit dynamical framework for forest communities that incorporates seed dispersal, growth limited by local light availability, local competition, and global resource constraints grounded in metabolic scaling principles. By deriving an analytical solution for the tree-size distribution, we show that its stationary state exhibits two distinct power-law regimes whose exponents are controlled by the relative strength of resource and spatial competition. The crossover between these regimes is set by the interplay between seed injection and local resource availability, establishing an explicit link between the scaling exponent of the size distribution and forest condition. Finally, we show that boundary disturbances can break the ecological balance between competing species and induce effects that propagate deeply into the forest bulk, far beyond the single-plant dispersal range. Together, these results provide a unifying dynamical perspective on forest scaling laws with potential applications to a broad range of biological communities.

Wastewater contains rich biological signals that can be used to monitor population health, track infectious diseases, and detect emerging outbreaks. Pathogens and other biomarkers in sewage provide a unique, noninvasive view of disease prevalence at the community level. However, extracting these signals requires extensive field sampling, laboratory analysis, and expert interpretation. Consequently, wastewater-based epidemiology (WBE) datasets are scarce, geographically fragmented, and rarely released as open data. Even when available, existing datasets typically cover short time periods and limited geographic regions, restricting their usefulness for method development, benchmarking, and large-scale modeling. To address this gap, we present an application of an existing patterns-of-life simulation framework for generating synthetic infectious disease and wastewater pathogen datasets for wastewater-based epidemiology. Our approach extends a patterns-of-life simulation framework by using it as a model of human mobility and behavior while incorporating disease transmission and pathogen shedding dynamics. The resulting framework generates high-resolution spatial and temporal datasets capturing infection dynamics, mobility behavior, and wastewater-associated pathogen signals. We release a fully simulated dataset containing check-in records, social network links, infection states, pathogen loads, and ground-truth disease transmission information. These data support controlled experimentation for outbreak detection, source localization, resource allocation, surveillance strategy design, mobility-aware wastewater analysis, and targeted public health interventions. We provide datasets for Fulton County and demonstrate that the framework generalizes to other regions by generating data for any city with available OpenStreetMap information.

A subcritical age-structured branching population dies out almost surely. Conditioned on survival, it converges to its Yaglom limit, a quasi-stationary equilibrium that we take as the operating point for control. We model preventive removal (culling) as an age-dependent actuator that raises the mortality rate and leaves the offspring law untouched, and we show that its authority over this equilibrium is bounded for structural reasons. Two facts drive the result. First, the input is matched to the killing rate but unmatched with respect to the Foster–Lyapunov drift, so the transmission barrier $\Lbar$ set by reproduction alone is invariant under such actuation. Second, and this does not follow from invariance alone,} the supremum of the reachable decay rates is $\Lbar+\nu^\star$, where $\nu^\star\le0$ is the Malthusian parameter of the lineage conditioned never to die childless; the gap $|\nu^\star|$ is given in closed form and vanishes exactly when no individual has two or more offspring. Consequently no removal law of this class reaches the barrier, and along the admissibility boundary the achievable decay rate is governed by the shape of the actuator rather than by its size. We illustrate these results on a model calibrated to the 2001 Cumbrian foot-and-mouth outbreak.

Here, we present an overview of how archaeogenomic data can be used to investigate past mobilities and how it can be integrated with archaeological research to reconstruct models of human mobility at different scales. We first seek to explain the importance of a clear terminological and theoretical approach to mobility, discussing terms such as migration, admixture, ancestry, and replacement. We then describe the theoretical principles and state-of-the-art tools for inferring past mobility from ancient DNA data, including exploratory approaches and formal modeling, and the relevance of using diverse lines of evidence including allele-frequency patterns, haplotype-sharing, genetic relatedness, and uniparental markers. We further discuss the power and limitations of these methods for inferring different modes of mobility, such as large-scale and long-distance mobility, which we refer to as migration, and also small-scale and short-distance movements, which we argue constituted the bulk of past human mobility and may have had the major share in shaping cultural landscapes. We also describe inference of sex-biased mobility events. Finally, we present examples of joint analyses of genomic data with archaeological, bioarchaeological and historical evidence, demonstrating the potential of interdisciplinary analyses in building comprehensive models of past mobilities. We finish by calling for further integration across fields.

Evolutionary dynamics in finite structured populations are commonly modeled by the Moran Birth-death process. A key quantity is the fixation probability of a single invader attempting to take over a population of residents. A recent work introduced a new neighborhood-aware phenotype called a replacer. A replacer never wastes their reproductive turn by always replacing an individual of the other type (if available). In this work, we study the evolutionary stability of resident replacers who are invaded by mutant replacers. We find that residents are strongly protected against such invasions, and we quantify the strength of this effect by showing three types of results. First, we show that on well-mixed populations of size $N$, the invader fixation probability is exponentially small in $N$, even when the invader has a fixed relative reproductive rate $r>1$, and the same holds for all high-degree graphs. Second, we study bounded-degree graphs. We prove that on cycles, the fixation probability of an advantageous invader decreases only by a constant factor. However, we also present graphs with maximum degree 4, where the invader fixation probability is exponentially small in $N$ whenever $r\le1.9$. Thus, high degrees are sufficient for evolutionary stability, whereas with low degrees the evolutionary stability depends on specific features of the underlying spatial structure. Third, we prove general bounds for arbitrary graphs. Namely, we show that for any graph $G$ the invader fixation probability drops below the natural baseline given by the standard Moran process with oblivious individuals on a well-mixed population, both for $r\approx 1$ and for $r\ge 2$. Together, our results establish that the evolutionary dynamics of replacers is better characterized by the phrase “survival of the first” rather than the classic “survival of the fittest”.

Many local search methods for problems in artificial intelligence can be viewed as an uphill climb on a corresponding discrete fitness landscapes. Finding even local peaks in these fitness landscapes is computationally intractable in theory, but often works in practice. So what features of fitness landscapes allow for efficient local search? Since any fitness landscapes can be represented by a (hyper)graph of valued constraints, I re-frame this as a question of parameterized complexity: what structural parameter of a valued constraint graph guarantees that a strict local search will find a local peak in the corresponding fitness landscape efficiently? Given a valued constrain graph of vertex cover number k, I prove that greedy local search will find the a local fitness peak in at most $2^{2k}\cdot(n - k + 1)$ steps and random uphill local search will find a local fitness peak in an expected number of at most $2^k\cdot n(n - k)$ steps. I also show that these results are asymptotically good for strict local search because there are valued constraint graphs of vertex cover number $k$ where every ascent from some initial assignment has a length of $\frac{9}{128} \cdot 2^k \cdot (n - k)$ or greater. This suggests vertex cover number as a good structural parameter for the complexity of local search.

Direct reciprocity is a mechanism for evolution of cooperation based on repeated interactions between the same individuals. Direct reciprocity can help natural selection to favor cooperators over defectors, but whether or not cooperation prevails depends on the details of the evolutionary dynamics. We describe simple processes of evolution that have the astonishing ability of driving direct reciprocity to maximum payoff in all social dilemmas which we study. The basic process is based on mutation and pairwise comparison. Mutation samples strategies near the boundary of the strategy space. Pairwise comparison includes a parameter for intensity of selection. For large population sizes, intermediate to high mutation rates and intermediate to strong intensities of selection, we find that the process leads to communities of strategies that reach maximum payoff in Prisoner's Dilemma, Snowdrift, Stag Hunt and Harmony games. Maximum payoff in all four games is consistently achieved if players have access to memory-2 strategies. Memory-1 strategies have the capacity to resolve all four social dilemmas, but they are usually defeated by a “Hold-trap” in Snowdrift games.

Generalized dissimilarity models (GDMs) have emerged as a valuable tool for formal statistical analysis of biodiversity. In particular, beta diversity, measured using dissimilarity measures, e.g., the Bray-Curtis dissimilarity in our case, provides a statistical summary of the difference in species composition between sites. It also provides novel data for spatial and spatio-temporal modeling as it resides over the product space of one space-time pair and a second space-time pair. In earlier work we developed the spatial generalized dissimilarity mixed model (spGDMM) to remedy some of the stochastic issues concerned with the foundational GDM in the literature. Here, we extend that work to include dynamics. We find much richer modeling opportunities as we consider beta diversity with regard to change in time as well as space. We illustrate with a dataset from the Cape Floristic Region (CFR) in South Africa.

Parameter identification from observations of dynamical systems is a fundamental problem in population biology. Mechanistic models of ecological systems rely on optimization methods that require accurate initial guesses to guarantee convergence. In ecological applications, datasets contain observation noise and are collected at sparse time points. This sparsity creates irregular likelihoods that cause standard optimization methods to struggle, while the ordinary differential equation solvers can become stiff or unstable in certain regions of the parameter space. These instabilities cause long running times or runtime errors. Here we present a computational framework for parameter identification that addresses these numerical instabilities by employing Natural Gradient Ascent, and we apply it to the classical Lotka-Volterra predator-prey model. We exploit the non-dimensionalization of the ordinary differential equations to treat scaling factors as nuisance parameters, reducing the dimensionality of the optimization problem. To prevent the solver step from becoming small, we implement an adaptive solver that switches between two independent second-order equations derived from the two components of the model. This approach allows Natural Gradient Ascent to converge in fewer iterations and with more stability than standard gradient ascent or BFGS methods. This framework provides a reliable method for parameter estimation in ecology when data is limited. The method can be generalized to other dynamical systems as long as the different components of the system do not become numerically problematic at the same time.

We investigate the emergence of traveling front solutions in a spatial SIRS epidemic model with diffusion acting on the infected population. The model exhibits a natural slow-fast structure due to the presence of a small parameter governing the loss of immunity, which induces a separation of scales in the dynamics. Using a traveling wave reduction, the PDE system is transformed into a singularly perturbed system of ODEs, which we analyze within the framework of Geometric Singular Perturbation Theory. In the singular limits, we study the fast excursions governed by the layer problem, and the slow evolution close to the critical manifold. In particular, we identify an entry-exit mechanism tracking the transitions between slow and fast regimes, and derive a quantitative characterization of the entry-exit dynamics. Numerical simulations of the full system confirm the validity of the proposed geometric picture. The traveling front is shown to consist of a concatenation of local, fast, and slow segments, in agreement with the theoretical analysis.

Several statistical methods of phylogenetic network inference and testing for non-tree-like relationships are based on assessing genomic data through quartet Concordance Factors, the frequencies of 4-taxon topological relationships on gene trees. While such an approach obviates making several undesirable modeling assumptions, it also results in non-identifiability issues for network roots and for small cycles. In this work, an algorithm and accompanying Macaulay2 implementation are provided for computing $n$-tet Concordance Factors on any phylogenetic network. We employ this algorithm on quintet Concordance Factors, summarizing 5-taxon gene trees, to explore identifiability of level-1 networks under the Network Multispecies Coalescent model. We show some additional network features become identifiable that are not through quartets. As identifiability is a necessary prerequisite to inference by any method, this lays a foundation for future inference work.