arXiv subjects

William F. Fagan

Publications and source records attributed to William F. Fagan.

11 recordsLinked to original sources

arXiv2026

Range residency determines how movement persistence shapes encounter rates

Encounters between individuals link movement behavior to population-level processes such as predation and disease transmission. For many animal species, movement can be modeled as a multiscale stochastic process, dominated by directional persistence at short time scales and range residency at long time scales. Their separate effects on encounters are well understood: range residency can raise or lower encounter rates depending on home-range overlap, whereas moving with higher directional persistence systematically increases them. However, how directional persistence and range residency jointly determine encounters remains unknown. We present an analytical encounter theory for movement models that combine both features. In this framework, we derive a threshold in home-range overlap above which directional persistence diminishes, rather than enhances, encounters. At shorter time scales, attraction toward the home-range center displaces individual locations, altering encounter rates even when range residency is not measurable in movement tracks. Movement models fitted to short tracks can therefore describe trajectories accurately yet under- or overestimate the encounters derived from those trajectories, depending on home range spatial configuration. Encounter rates are a more demanding target for inference than movement parameters themselves.

q-bio.PE↗

arXiv2026

The Influence of Exclusion Zones on the Coexistence of Predator and Prey with an Allee Effect

We propose a reaction--diffusion model of predator--prey interaction in which the predators occupy only a subset of the prey's territory, leaving a predator-free exclusion zone. Ecological examples include marine protected areas where it is illegal to fish, or buffer zones left between the territories of rival predators. The prey are subject to a strong Allee effect, so excessive predation may lead to the extinction of both species. The exclusion zone mitigates this problem by providing the prey with a refuge in which to proliferate without predation. Thus, paradoxically, a smaller predator territory may be able to support a more substantial population than a larger one. Using a topological degree argument, we show in any dimensions that, provided the exclusion zone is large enough, the system possesses spatially heterogeneous coexistence equilibria with positive populations of both species. This result is global in the sense that it does not rely on local bifurcations from semi-trivial stationary states. We also show that as the predator domain becomes asymptotically small, the total predator population does not vanish, and in some cases may actually be maximized in this limit of shrinking predation area. Conversely, we show that as the predator domain becomes large, it may exhibit thresholding behavior, passing suddenly from a regime with coexistence solutions to one in which extinction becomes unavoidable, highlighting the need for careful analysis in the management of predator--prey systems.

math.AP↗

arXiv2026

How animal movement influences wildlife-vehicle collision risk: a mathematical framework for range-resident species

Wildlife-vehicle collisions (WVC) threaten both biodiversity and human safety worldwide. Despite empirical efforts to characterize the major determinants of WVC risk and optimize mitigation strategies, we still lack a theoretical framework linking traffic, landscape, and individual movement features to collision risk. Here, we introduce such a framework by leveraging recent advances in movement ecology and reaction-diffusion stochastic processes with partially absorbing boundaries. Focusing on range-resident terrestrial mammals -- responsible for most fatal WVCs -- we model interactions with a single linear road and derive exact expressions for key survival statistics, including mean collision time and road-induced lifespan reduction. These quantities are expressed in terms of measurable parameters, such as traffic intensity or road width, and movement parameters that can be robustly estimated from relocation data, such as home-range crossing times, home-range sizes, or distance between home-range center and road. Therefore, our work provides an effective theoretical framework integrating movement and road ecology, laying the foundation for data-driven, evidence-based strategies to mitigate WVCs and promote safer, more sustainable transportation networks.

q-bio.PE↗

arXiv2026

A predator-prey model with age-structured role reversal

We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an "ontogenetic niche shift," in which a species' functional role changes as it grows. This structure adds complexity to our model but increases its biological relevance. The time evolution of the age-structured predator population is motivated by the Kermack-McKendrick Renewal Equation (KMRE). Unlike KMRE, the predator population's birth and death rate functions depend on the prey population's size. We establish the existence, uniqueness, and positivity of the solutions to the proposed model's initial value problem. The dynamical properties of the proposed model are investigated via Latin Hypercube Sampling in the 15-dimensional space of its parameters. Our Linear Discriminant Analysis suggests that the most influential parameters are the maturation age of the predator and the rate of consumption of juvenile predators by the prey. We carry out a detailed study of the long-term behavior of the proposed model as a function of these two parameters. In addition, we reduce the proposed age-structured model to ordinary and delayed differential equation (ODE and DDE) models. The comparison of the long-term behavior of the ODE, DDE, and the age-structured models with matching parameter settings shows that the age structure promotes the instability of the Coexistence Equilibrium and the emergence of the Coexistence Periodic Attractor.

q-bio.PE↗

arXiv2026

Drivers of periodicity in population dynamic models of long-lived, large mammals

Population cycles are important components of many natural systems. Most studied in short-lived and small-bodied species, cycles frequently appear to be driven by density-dependent feedbacks. However, compelling evidence of cycles -- often more qualitative than quantitative -- also exists in large mammals. Among ungulates, both density-dependent vital rates and 'cohort effects' (lasting impacts of birth conditions on fecundity and survival) exist, but the implications of such feedbacks for oscillatory population dynamics have not been explored. Here, we present a synthetic model of ungulate population dynamics, parameterized for barren-ground caribou (Rangifer tarandus groenlandicus) and motivated by extensive Indigenous knowledge suggesting decades-long fluctuations in abundance. Caribou herds are theorized to be subject to both cohort effects and density dependence, and we linked these endogenous factors with environmental stochasticity to understand cycling. Using wavelet analysis, we characterized periodic phenomena and performed sensitivity analyses to clarify the drivers and characteristics of population cycles. We found that cohort effects, predominantly those impacting survival, can produce long-period oscillatory behavior across a wide range of environments and demographic structures. Our modeling framework is generalizable to other long-lived, large-bodied species with complex demography, and collectively, these efforts broaden the scope of inquiry into proximal drivers of population cycling.

q-bio.PE↗

arXiv2025

Ergodicity shapes inference in biological reactions driven by a latent trajectory

Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random intervals, when an underlying, often unobserved and therefore latent, dynamical system occupies a set of reactive states within its phase space. We show how the ergodicity of this latent dynamical system, i.e. existence of a well-behaved limiting stationary distribution, constrains the statistics of the reaction counts. This formulation makes explicit the conditions under which the counting process approaches a limiting Poisson process, a subject of debate in the application of counting processes to different fields. We show that the overdispersal relative to this limit encodes properties of the latent trajectory through its hitting times. These results set bounds on how information about a latent process can be inferred from a local detector, which we explore for two biophysical scenarios. First, in estimating an animal's activity level by how often it crosses a detector, we show how the mean count can fail to give any information on movement parameters, which are encoded in higher order moments. Second, we show how the variance of the inter-reaction time sets a fundamental limit on how precisely the size of a population of trajectories can be inferred by a detector, vastly generalizing the Berg-Purcell limit for chemosensation. Overall, we develop a flexible theoretical framework to quantify inter-event time distributions in reaction-diffusion systems that clarifies existing debates in the literature and explicitly shows which properties of latent processes can be inferred from observed reactions.

cond-mat.stat-mech↗

arXiv2024

Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size

Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape heterogeneity influences individual movement. We relax this assumption and introduce a reaction-advection-diffusion equation that describes population dynamics when individuals exhibit space-dependent movement bias toward preferred regions. Our model incorporates two types of these preferred regions: a high-quality habitat patch, termed `habitat', which is included to model avoidance of degraded habitats like deforested regions; and a preferred location, such as a chemoattractant source or a watering hole, that we allow to be asymmetrically located with respect to habitat edges. In this scenario, the critical habitat size depends on both the relative position of the preferred location and the movement bias intensities. When preferred locations are near habitat edges, the critical habitat size can decrease when diffusion increases, a phenomenon called the drift paradox. Also, ecological traps arise when the habitat overcrowds due to excessive attractiveness or the preferred location is near a low-quality region. Our results highlight the importance of species-specific movement behavior and habitat preference as drivers of population dynamics in fragmented landscapes and, therefore, in the design of protected areas.

q-bio.PE↗

arXiv2019

How range residency and long-range perception change encounter rates

Encounter rates link movement strategies to intra- and inter-specific interactions, and therefore translate individual movement behavior into higher-level ecological processes. Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range, and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. Here, we explore how these empirically supported behaviors change pairwise encounter rates. Specifically, we derive novel analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range. We compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived. For both models, we further explore how the interplay between the scale of perception and home range size affects encounter rates. We find that neglecting realistic movement and perceptual behaviors can systematically bias encounter rate predictions.

q-bio.PE↗

arXiv2014

A niche remedy for the dynamical problems of neutral theory

We demonstrate how niche theory and Hubbell's original formulation of neutral theory can be blended together into a general framework modeling the combined effects of selection, drift, speciation, and dispersal on community dynamics. This framework connects many seemingly unrelated ecological population models, and allows for quantitative predictions to be made about the impact of niche stabilizing and destabilizing forces on population extinction times and abundance distributions. In particular, the existence of niche stabilizing forces in our blended framework can simultaneously resolve two major problems with the dynamics of neutral theory, namely predictions of species lifetimes that are too short and species ages that are too long.

q-bio.PE↗

arXiv2011

A Multivariate Moran Process with Lotka-Volterra Phenomenology

For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This correspondence, on the one hand, allows us to infer the phenomenology of our Moran process based on much simpler Lokta-Volterra phenomenology, and on the other, allows us to study Lotka-Volterra dynamics within the finite populations of a Moran process. Applications to community ecology, population genetics, and evolutionary game theory are discussed.

q-bio.PE↗

arXiv2010

A sampling theory for asymmetric communities

We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community dynamics, while an analogous extension of Hubbell's metacommunity dynamics is deferred to an appendix. We find that mass-effects may facilitate coexistence in asymmetric local communities and generate unimodal species abundance distributions indistinguishable from those of symmetric communities. Multiple modes, however, only arise from asymmetric processes and provide a strong indication of non-neutral dynamics. Although the exact stationary distributions of fully asymmetric communities must be calculated numerically, we derive approximate sampling distributions for the general case and for nearly neutral communities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability. In the latter case, our approximate distributions are fully normalized, and novel asymptotic expansions of the required hypergeometric functions are provided to make evaluations tractable for large communities. Employing these results in a Bayesian analysis may provide a novel statistical test to assess the consistency of species abundance data with the neutral hypothesis.

q-bio.PE↗