Elm woodlands provide important ecological functions in sandy dryland ecosystems, but their regeneration and population dynamics are affected by environmental stress and biotic interactions. Understanding how symmetric and asymmetric forms of intraspecific competition and facilitation influence elm populations can improve theoretical understanding of woodland dynamics under stress. In this study, we developed a hybrid agent-based and system-dynamics model to examine how interaction symmetry and environmental stress affect final population abundance, age structure, and spatial organization of elm populations. The results showed that completely asymmetric competition produced a significantly larger final population than completely symmetric competition (P < 0.01). This outcome reflected size-biased resource capture by larger individuals in the model, but it was also accompanied by a more seedling-dominated age structure, indicating that higher final abundance did not necessarily correspond to greater demographic balance. Facilitation had stress-dependent effects. Under low stress, differences between symmetric and asymmetric facilitation were small, whereas under moderate and high stress, completely symmetric facilitation produced significantly larger final populations than completely asymmetric facilitation (P < 0.05 and P < 0.01, respectively). Symmetric facilitation was also associated with a less strongly truncated age structure under higher stress, suggesting that broadly distributed stress buffering helped maintain juvenile and mature-stage representation in the simulated population. Spatial point-pattern analysis showed that elm populations were generally clustered, but the effects of facilitation on clustering depended on competition mode and stress level. Overall, the results indicate that competition and facilitation jointly shape simulated elm population outcomes through size-biased resource capture, stress buffering, and local spatial interactions. The ABM-SD framework provides a theoretical tool for comparing alternative interaction mechanisms in sparse elm woodlands, although the results should be interpreted as scenario comparisons rather than site-specific predictions.
Species dispersal plays a critical role in shaping the spatial structure of communities and ultimately determines species distributions. In this study, we incorporated spatial factors and constructed a mathematical model of spatial community dynamics using a three-species food web to explore how different dispersal patterns influence species coexistence in a landscape of habitat loss and habitat fragmentation. We further examined how variation in colonization rates under different dispersal strategies affects species within the food web. The results show that: (1) In landscapes experiencing habitat fragmentation and habitat loss, increasing dispersal range enlarges the coexistence region of species; (2) Coexistence is maximized at intermediate dispersal rates and declines when dispersal is either too weak or too strong; (3) Changes in dispersal patterns can either promote or inhibit coexistence, depending on the direction and magnitude of the changes; (4) when all species adopt global dispersal, habitat loss exerts a progressively negative effect on each species, whereas habitat fragmentation has no impact. This study provides theoretical insights into the role of dispersal in shaping species distributions and offers a foundation for future research on species dispersal dynamics.
Climate change has created new and evolving environmental conditions, impacting all species, including hosts and parasitoids. In that context, we present integrodifference equation (IDE) models of host–parasitoid systems to model population dynamics in the context of climate-driven shifts in habitats. In this paper, we describe and analyze two IDE models of host–parasitoid systems to determine criteria for coexistence of the host and parasitoid. Specifically, we determine the critical habitat speed, beyond which the parasitoid cannot survive. By comparing the results from two IDE models, we investigate the impacts of assumptions that reduce the system to a single-species model. We also compare critical speeds predicted by a spatially-implicit difference-equation model with critical speeds determined from numerical simulations of the IDE system. The spatially-implicit model uses approximations for the dominant eigenvalue of an integral operator. The classic methods to approximate the dominant eigenvalue for IDE systems do not perform well for asymmetric kernels, including those that are present in shifting-habitat IDE models. Therefore, we compare several methods for approximating dominant eigenvalues that have not previously been compared in two-species IDE moving-habitat models. Ultimately, geometric symmetrization and iterated geometric symmetrization approximations give the best estimates of the parasitoid critical speed, which extends the superiority of these approximations into the two-species context.
This article develops stochastic models of different ecological mechanisms of natural selection that explicitly account for the interdependence of individual fates in case of ecological competition. Competition as a zero-sum game makes the fates of individuals interdependent. Competition for a limited resource and competition to escape predators are shown to have markedly different statistical properties. The effect of selection depends not only on individual phenotypes, but also on the strength of competition. This is illustrated with simulations comparing five different selection mechanisms with and without competition. It is shown how the rate of genetic change, the probability of fixation of a mutant allele, mean fixation time, etc. depend on the strength of competition, fitness ratio between individuals with different competitive abilities, initial allele fraction, population size, and Mendelian dominance. The effect of competition is reduced when mobility is limited so that individuals can compete with conspecifics only within a limited distance. This is regarded as imperfect interdependence. A lower limit for the effect of competition under imperfect interdependence is estimated. The statistical effects of different forms of ecological competition is a previously neglected area of study where many traditional models ignore the interdependence of fates.
Population growth models are essential tools for predicting population demographic trends and assessing population viability over time. Population growth models are often parameterized using demographic data that account for imperfect detection; however, historical datasets—collected prior to the widespread incorporation of imperfect detection—may still yield valuable insights into long-term population dynamics. Here, we used a deterministic age structured model and a stochastic individual based model, which were both parameterized with age-specific vital rates, to estimate population growth in a woodland salamander (Plethodon metcalfi). To parameterize our model, we used long-term historical demographic data collected by Hairston (1983) to estimate population growth. Our objectives were to evaluate differences between the population growth models and assess whether historical demographic data can produce realistic estimates of population dynamics. We found that the individual based model predicted a declining population size, whereas the age structured model predicted an increasing population size. However, sensitivity analyses revealed that minimal changes to survival or fecundity were sufficient to produce stable populations in both models, reflecting observations of these populations in the wild. Therefore, our results suggest that historical data can be informative even in the absence of detection-corrected estimates in cryptic species. We also found that both models were capable of predicting age distributions similar to those observed in nature. Together, these results emphasize the importance of model selection and utility of historical datasets in forecasting population resilience under variable environmental conditions.
Foraging site constancy, or repeated return to the same foraging location, is a foraging strategy used by many species to decrease uncertainty and risks. It is often unclear, however, exactly how organisms identify the foraging site. Here we are interested in the context where the actual harvesting of food is first preceded by a separate exploration period. In this context, foraging consists of three distinct steps: (1) exploration of the landscape (site-generation), (2) selection of a foraging site (site-selection), and (3) exploitation (harvesting) through repeated trips between the foraging site and "home base". This type of foraging has received scant attention in the modelling literature, leading to two main knowledge gaps. First, there is very little known about how organisms implement steps (1) and (2). Second, it is not known how the choice of implementation method affects the outcomes of step (3). Typical outcomes include the foragers’ rate of energy return, and the distribution of foragers on the landscape. We investigate these two gaps, using an agent-based model with bumble bees as our model organism foraging in a patchy resource landscape of crop, wildflower, and empty cells. We tested two different site-generation methods (random and circular foray exploration behaviour) and four different site-selection methods (random and optimizing based on distance from the nest, local wildflower density, or net rate of energy return) on a variety of outcomes from the site-constant harvesting step. We find that site-selection method has a high impact on crop pollination services as well as the percent of crop resources collected, while site-generation method has a high impact on the percent of time spent harvesting and the total trip time. We also find that some of the patterns we identify can be used to infer how a given real organism is identifying a foraging site. Our results underscore the importance of explicitly considering exploratory behaviour to better understand the ecological consequences of foraging dynamics.
We develop a spatially explicit age-structured model to study the invasion dynamics of plant species, integrating habitat quality, demographic structure, and seed dispersal. Our approach incorporates continuous age structuring and explicitly derives a habitat-quality-dependent invasion threshold, 𝒯_0(q) , which determines whether a species can establish ( 𝒯_0(q)> 1 ) or extinct ( 𝒯_0(q)≤ 1 ). This threshold encapsulates three fundamental components of biological invasions: (i) biotic factors, (ii) abiotic conditions, and (iii) dispersal capacity. Our model is applied to the invasion of black cherry (Prunus serotina) in France, using empirical data to simulate spatio-temporal invasion dynamics.
Synchronous oscillations of spatially disjunct populations are widely observed in ecology. Even in the absence of spatially synchronized exogenous forces, metapopulations may synchronize via dispersal. For many species, most dispersal is local, but rare long-distance dispersal events also occur. While even small amounts of long-range dispersal are known to be important for processes like invasion and spatial spread rates, their potential influence on population synchrony is often overlooked, since local dispersal on its own can be strongly synchronizing. In this work, we investigate the effect of random, rare, long-range dispersal on the spatial synchrony of a metapopulation and find profound effects not only on synchrony but also on properties of the resulting spatial patterns. While controlling for the overall amount of emigration from each local subpopulation, we vary the fraction of dispersal that occurs locally (to nearest neighbors) versus globally (to random locations, irrespective of distance). Using a metric that measures the instantaneous level of global synchrony, we show that this form of long-range dispersal significantly favors the spatially synchronous state and homogenizes the population by decreasing the size of clusters of subpopulations that are out of phase with the rest of the metapopulation. Moreover, the addition of non-local dispersal significantly decreases the equilibration time of the metapopulation.
While the mechanisms that govern disease emergence and spread among hosts are increasingly well-described, the mechanisms that promote parasite diversity within-hosts, affecting host outcomes and spillover potential, have been comparatively understudied. Furthermore, while attention has been paid to the effects of increasing temperatures on disease systems, the effects of environmental variability have been left underexplored, despite rising climatic variability. To investigate the impacts of environmental variability on parasite co-occurrence within-hosts, we analysed a model of within-host population dynamics wherein two parasites indirectly compete through the host’s immune response. We simulated the model under constant, demographically stochastic, environmentally stochastic, and demographically and environmentally stochastic conditions, and analysed the viability and longevity of non-equilibrium parasite co-occurrence. We found that environmental stochasticity increased the viability and longevity of parasite co-occurrence, suggesting that thermal variability arising from climatic change and as a physiological trait may promote parasite diversity within ectotherms and help explain bats’ propensity to support diverse communities of parasites. Further, we found that under certain conditions, the transmissibility of co-occurring parasites can surpass the transmissibility of single parasites, suggesting that thermal variability may increase the transmissibility of co-occurring parasites.
Many macroscopic organisms enter tightly linked symbioses with microbial communities. Although experimental work has demonstrated the importance of these symbioses, a theoretical understanding of stable, multi-scale coexistence remains underdeveloped. Here, we explored how the competition-colonization tradeoff, a classic coexistence mechanism, operates when bacterial species compete for a dynamic biological host. Specifically, we introduce a model where corals are colonized by fast-growing mutualists and slow-growing pathogens. Vital rates of the host coral influenced coexistence outcomes between bacterial types. Notably, pathogen-induced host death expanded the region of parameter space where coexistence was stable for all three species, and mutualistic bacteria enabled coexistence in systems that would have otherwise collapsed. In an explicitly spatial model, dispersal limitation favored the mutualist over the pathogen when the mutualist increased the host colonization rate. These findings provide new insights into the interplay between microbial interactions and macroscopic processes. Our work illustrates how host-microbe interactions can shape ecosystem stability, providing a theoretical framework applicable to a wide range of symbiotic systems.
The decline of honey bee (Apis mellifera) populations poses a growing threat to global biodiversity and food security. Among the factors contributing to this phenomenon is nosemosis, a parasitic disease that affects the longevity and behavior of adult bees. This study proposes a comprehensive mathematical model to describe the spread of nosemosis within honey bee colonies, simultaneously incorporating the effects of agrochemical exposure, pharmacological treatments, and hygienic measures applied inside the hive. The model enables an integrated analysis of infection dynamics and control strategies, both at the individual colony level and across interconnected colonies represented by a complex network. Through theoretical analysis and numerical simulations, we identify equilibrium points, stability conditions, and optimal intervention policies that minimize the impact of the disease and the costs associated with its management. The results demonstrate that a balanced combination of hygienic practices and pharmacological treatments can significantly reduce disease prevalence, even under moderate agrochemical exposure. This work provides a quantitative tool for designing practical sanitary control strategies in apiculture, allowing the evaluation of management measures under diverse environmental scenarios. Overall, the findings contribute to the development of sustainable beekeeping practices aimed at preserving hive health and the resilience of pollinator ecosystems.
Ecological networks tend to contain many weak and only a few strong links. Furthermore, link strengths are often patterned within a network in ways that enhance system stability considerably, increasing the ability of the system to return to equilibrium after a perturbation. However, little attention has been given to the relation between the skewed “many weak and few strong links” distribution and the stabilising effect of patterning. Here, we focus on the stabilising effect of a hierarchical patterning in bryozoan competition networks and demonstrate that this stabilising effect critically depends on a skewed distribution of link strengths. We first show that, in line with many other ecological networks, the empirically derived link strengths in these competition networks were characterised by a high level of skewness, with many weak and few strong links. Then, we analysed the relationship between the link strength distributions, hierarchy and stability by comparing theoretical competition matrices with different distributions of link strengths. We found that the full stabilising effect of hierarchy only appeared when we used skewed link strengths produced by a gamma distribution, but not in matrices built with uniform or half-normal distributions. This has important methodological implications, since theoretical studies often assume normal or uniform distributions to investigate ecological stability, and therefore might overlook stabilising mechanisms. These implications are relevant for theory on the relation between structure and stability of ecological networks in general, since skewed link strengths are also a common feature of food webs and mutualistic systems.
Based on an example of a four dimensional ecological community composed of three ant species and a group of phorid flies, a simplified dynamic model is proposed and analyzed qualitatively. The model contains an intransitive triplet of ant species coupled with a predator/prey pair, where the prey is one of the ants in the intransitive competition, thus coupling a 3D oscillator with a 2D oscillator. Relaxing basic symmetries, a chaotic attractor emerges in which two distinct unstable modalities are recognizable, identifiable with the two biological processes involved. The unstable manifolds of each of the instabilities are of distinct dimensionalities, a characteristic known as hetero-chaos. It is suggested that the qualitative arrangement may be common as a modality within large ecological systems, thus proposing hetero-chaos as possibly common in ecosystems that have chaotic behavior.
New advents in technology have improved our ability to study and track host-associated organisms. Often, these organisms experience vastly different spatial and temporal scales than their hosts. However, host-associated organisms are not independent of their hosts nor are hosts independent of their host-associated organisms. Rather, processes at the host and host-associated organism scales interact to alter outcomes for both the host and its symbionts. Often, host-associated organisms are described in terms of metapopulations, wherein individual hosts act as habitat patches for their symbionts. When hosts themselves also exist in patchy environments, the result is metapopulation structure at two distinct scales. In this paper, we develop a model to explore how the incorporation of multiscale metapopulation dynamics impacts metapopulation predictions at both the host and symbiont scales. While related to several disease models, our system differs in its inclusion of full colonization and extinction dynamics at both scales, and its emphasis on how the interaction between colonization and extinction at these two scales impacts the host and its host-associated organisms, including pathogens as well as symbionts that are beneficial to the host. Overall, our multiscale metapopulation model predicts rich dynamics that often deviate from the dynamics of metapopulation models built for either the host or its host-associated organisms independently.
We employ an n-player coordination game to model mutualism emergence and abandonment. We illustrate our findings focusing on the host–host interactions among plants in plant-mycorrhizal fungi (MF) mutualisms. The coordination game payoff structure captures the insight that mutualistic strategies lead to robust advantages for plants only after such “biological markets” reach a certain scale. The game gives rise to three types of Nash equilibria, which correspond to the states derived in studies of the ancestral reconstruction of the mycorrhizal symbiosis in seed plants. We show that these Nash equilibria correspond to steady states of a dynamical system describing the underlying evolutionary process. We then employ methods from large deviation theory on discrete-time Markov processes to study stochastic evolutionary dynamics. We provide a sharp analytical characterization of the stochastic steady states and of the transition dynamics across Nash equilibria and employ simulations to illustrate these results in special cases. We find that the mutualism is abandoned and re-established several times through evolutionary time, but the mutualism can persist the majority of time. Changes that reduce the benefit-to-cost ratio associated with the symbiosis increase the likelihood of its abandonment. While the mutualism establishment and abandonment could result from direct transitions across the mutualistic and non-mutualistic states, it is far more likely for such transitions to occur indirectly through intermediate partially mutualistic states. The MF-plant mutualism might be (partially or fully) abandoned by plants even if it provides overall superior fitness.
Insect behavior is influenced by the presence of defense chemicals in herbaceous plants. In particular, which plants insect herbivores choose as host plants is influenced by the composition of volatile chemicals emitted by plants including chemical defense compounds. If plants grow in vicinity to each other, their chemical plumes may overlap, and the effectiveness of allocating resources to the defense of a focal plant may depend on the defense strategies employed by neighboring plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants, where cooperators are plants investing in defense, and defectors are plants that do not. The optimal resource allocation problem is solved using a stochastic dynamic programming model, and the neighborhood effect is incorporated using a spatial game theory algorithm. We incorporate an individual-based model for an herbivore population and allow herbivores to move between herbaceous plants growing in seasonal environments. Our model predicts under which conditions natural selection may select for the entire population to consist of only cooperators, only defectors (pure stable strategies), or a mixture of both (mixed stable strategy). We show that our model offers a theoretical explanation for the neighborhood effect seen in empirical studies.
Movement across fragmented landscapes has profound implications for biodiversity and ecosystem function. In this study, we develop and analyse a discrete-time metapopulation model that captures the effects of landscape heterogeneity and incorporates both density-dependent and costly dispersal. Each region’s population dynamics are modelled using bounded population maps, while dispersal proportions are described by nonlinear functions. Our framework extends traditional metapopulation models, which typically focus on constant and/or costless dispersal, by providing a more ecologically realistic basis for understanding persistence in fragmented environments. We begin by detailing the modelling framework, then state sufficient conditions for the local and global stability of the extinction equilibrium and the existence of a positive equilibrium, while also identifying a region where such an equilibrium lies. We further provide a condition for uniform strong persistence in terms of both the total and minimum population sizes. Through an extensive numerical study, within a source-sink context, we explore some of the model’s qualitative dynamics. In particular, we show that introducing density-dependent dispersal can stabilise systems that are otherwise oscillatory under passive dispersal or destabilise systems that are otherwise stable. We demonstrate that connecting sources to sinks or multiple sources via density-dependent dispersal can result in a reduction of the long-term average population size. We finally conduct bifurcation analyses to explore parameter sensitivity, revealing the complex dynamics our model can capture. This includes transitions between extinction and convergence to positive equilibria, as well as the emergence of periodic behaviour, chaotic-type dynamics, and bubbling effects, depending on the interplay between density-dependent dispersal and intrinsic growth rates. Throughout, we discuss the implications of these findings for pest management and conservation, emphasising the need for nuanced, context-dependent strategies that account for the nonlinear effects of dispersal on metapopulation dynamics.
Shallow lakes are ecosystems up to 3 m’ depth and provide a number of ecosystem services such as the habitat of migratory birds, but are also vulnerable to environmental changes such as temperature warming. In shallow lakes, floating macrophytes have greater exposure to the atmosphere than submerged macrophytes, therefore, under global change (increased atmospheric CO2 and temperatures), floating macrophytes have an advantage and can be more competitive than submerged macrophytes. Since a universal model that is easily tractable and more integrated with data was not available, I developed a model of submerged macrophyte interacting with floating (SMIF), which is a modification of an existing model Scheffer et al. (2003) and incorporation of sub-models (Driever et al. 2005; Peeters et al. 2013). My main goal is to use the developed model to gain insights into the temporal growth dynamics of submerged and floating macrophytes. First, I calibrated the developed model using data at a site in Netherlands. Then I examined the sensitivity of the model to high temperature and low nitrogen levels. The modeling results showed that (1) the model is capable of adequately predicting temporal patterns of biomass for floating and submerged macrophytes and (2) the maximum growth and turnover rates are the most sensitive parameters for biomass of floating and submerged macrophyte. The developed model agreed well with the experimental data for various geographical regions—this indicates that the model can capture species differences. SMIF can be incorporated into land systems models that are often used to examine how climate affects lake ecosystems.
Pollinators, particularly honeybees (Apis mellifera), are indispensable for global food security and ecosystem stability. However, pesticide exposure has emerged as a critical stressor threatening colony survival, with complex ecological and population-level consequences that remain poorly quantified. This study introduces a novel mathematical framework to rigorously analyze the nonlinear dynamics of honeybee colonies under pesticide-induced stress. Our dynamical systems model, based on nonlinear ordinary differential equations, integrates multiple ecological mechanisms often overlooked in previous studies, including logistic growth, social inhibition, and the beekeeping principle known as Farrar’s rule. By conducting an extensive equilibrium, stability, and bifurcation analysis, we identify previously unrecognized threshold effects that dictate colony persistence or collapse. A key theoretical finding is that if pesticide-induced mortality inside the hive surpasses the intrinsic population growth rate, extinction is inevitable. Additionally, we reveal a counterintuitive ecological feedback: hive overcrowding, in combination with pesticide exposure, reduces the foraging workforce, exacerbating colony decline in a way not previously described. These insights provide critical quantitative benchmarks for sustainable pesticide regulation and pollinator conservation. Our study not only advances theoretical ecology by elucidating complex stability transitions in pollinator populations but also delivers practical implications for agroecosystem management. By establishing explicit thresholds for intervention, our findings underscore the urgent need to rethink pesticide policies and conservation strategies to safeguard pollinators and global food systems.
How individuals use space and, thus, the rate and the nature of their interactions with others are shaped by their environment. Exogenous changes that alter aggregation patterns, such as resource pulses, can therefore have a significant impact on seemingly unrelated processes like disease spread. White-tailed deer (Odocoileus virginianus) aggregate in oak forests during mast events, and chronic wasting disease (CWD) transmission patterns vary with deer density, so we hypothesize a link between the masting cycle and CWD dynamics. We investigate various possible effects of masting on deer, including shifts to more frequency-dependent CWD transmission due to aggregation, as well as elevated fecundity and decreased mortality of deer in response to the resource pulse, using a simplified compartment model of CWD spread. When masting affects epidemiological parameters, including the strength of frequency dependence in CWD transmission, disease spread during masting events significantly reduces the size of deer populations but, paradoxically, without any change in the proportion of the population in the CWD-diseased state. In contrast, demographic parameters were found in principle to be capable of altering both population size and disease incidence, though the observed effects were very small. While our quantitative findings should be validated using more detailed models of CWD transmission before they are taken as specific predictions about this system, our fundamental qualitative result appears to be quite general. That is, our conclusion that epidemiological rates only influence population size, but demographic rates may affect both population size and disease incidence, can be derived not only from the model we studied but also from classical epidemiological models as well. Our work extends the understanding of the far-reaching impacts of resource pulses through ecological communities by highlighting the vastly different consequences of the same resource pulse acting in different ways.
