Many anthropogenic stressors broadly inflict mortality or reduce fecundity, including habitat destruction, pollution, climate change, invasive species, and multispecies harvesting. Here, we show-in four analytical models of interspecies competition-that broadly inflicted stressors disproportionately cause competitive exclusions within groups of ecologically similar species. As a result, we predict that ecosystems become progressively -that is, they have progressively less functional redundancy-as broadly inflicted stressors become progressively more intense. This may negatively affect the temporal stability of ecosystem functions, but it also buffers ecosystem productivity against stress by favoring species less sensitive to the stressors. Our main result follows from the weak limiting similarity principle: species with more similar ecological niches compete more strongly, and their coexistence can be upset by smaller perturbations. We show that stressors can cause indirect competitive exclusions at much lower stressor intensity than needed to directly cause species extinction, consistent with the finding of empirical studies that species interactions are often the proximal drivers of local extinctions. The excluded species are more sensitive to the stressor relative to their ecologically similar competitors. Moreover, broadly inflicted stressors may cause hydra effects-where higher stressor intensity results in higher abundance for a species with lower sensitivity to the stressor than its competitors. Correlations between stressor impacts and ecological niches reduce the potential for indirect competitive exclusions, but they consequently also reduce the buffering effect of ecosystem thinning on ecosystem productivity. Our findings suggest that ecosystems experiencing stress may continue to provision ecosystem services but lose functional redundancy and stability.

Second-order statistics such as the variance and autocorrelation can be useful indicators of the stability of randomly perturbed systems, in some cases providing early warning of an impending, dramatic change in the system's dynamics. One specific application area of interest is the surveillance of infectious diseases. In the context of disease (re-)emergence, a goal could be to have an indicator that is informative of whether the system is approaching the epidemic threshold, a point beyond which a major outbreak becomes possible. Prior work in this area has provided some proof of this principle but has not analytically treated the effect of imperfect observation on the behavior of indicators. This work provides expected values for several moments of the number of reported cases, where reported cases follow a binomial or negative binomial distribution with a mean based on the number of deaths in a birth-death-immigration process over some reporting interval. The normalized second factorial moment and the decay time of the number of reported cases are two indicators that are insensitive to the reporting probability. Simulation is used to show how this insensitivity could be used to distinguish a trend of increased reporting from a trend of increased transmission. The simulation study also illustrates both the high variance of estimates and the possibility of reducing the variance by averaging over an ensemble of estimates from multiple time series.

Ecological theory predicts that the presence of temporal autocorrelation in environments can considerably affect population extinction risk. However, empirical estimates of autocorrelation values in animal populations have not decoupled intrinsic growth and density feedback processes from environmental autocorrelation. In this study we first discuss how the autocorrelation present in environmental covariates can be reduced through nonlinear interactions or by interactions with multiple limiting resources. We then estimated the degree of environmental autocorrelation present in the Global Population Dynamics Database using a robust, model-based approach. Our empirical results indicate that time series of animal populations are affected by low levels of environmental autocorrelation, a result consistent with predictions from our theoretical models. Claims supporting the importance of autocorrelated environments have been largely based on indirect empirical measures and theoretical models seldom anchored in realistic assumptions. It is likely that a more nuanced understanding of the effects of autocorrelated environments is necessary to reconcile our conclusions with previous theory. We anticipate that our findings and other recent results will lead to improvements in understanding how to incorporate fluctuating environments into population risk assessments.

Does society benefit from private measures to mitigate infectious disease risks? Since mitigation reduces both peak prevalence and the number of people who fall ill, the answer might appear to be yes. But mitigation also prolongs epidemics and therefore the time susceptible people engage in activities to avoid infection. These avoidance activities come at a cost-in lost production or consumption, for example. Whether private mitigation yields net social benefits depends on the social weight given to the costs of illness and illness avoidance, now and into the future. We show that, for a large class of infectious diseases, private risk mitigation is socially beneficial. However, in cases where society discounts the future at either very low or very high rates relative to private individuals, or where it places a low weight on the private cost of illness, the social cost of illness under proportionate mixing (doing nothing) may be lower than the social cost of illness under preferential mixing (avoiding infectious individuals). That is, under some circumstances, society would prefer shorter, more intense epidemics without avoidance costs over longer, less intense epidemics with avoidance costs. A sobering (although not surprising) implication of this is that poorer societies should be expected to promote less private disease-risk mitigation than richer societies.

Measles was successfully eradicated in the Pan-American Health Region in 2002. However, maintenance of elimination in parts of Africa, Europe, the USA, and other regions is proving difficult, despite apparently high vaccine coverage. This may be due to the different age structure in developed and developing populations, as well as to differences in the duration of maternal immunity. We explore the interaction between maternal immunity and age structure and quantify the resulting immunity gap between vaccine coverage and population immunity; we use this immunity gap as a novel metric of vaccine program success as it highlights the difference between actual and estimated immunity. We find that, for some combinations of maternal immunity and age structure, the accepted herd immunity threshold is not maintainable with a single-dose vaccine strategy for any combination of target age and coverage. In all cases, the herd immunity threshold is more difficult to maintain in a population with developing age structure. True population immunity is always improved if the target age at vaccination is chosen for the specific combination of maternal immunity and age structure.

Classical life-history theory predicts that acute, immunizing pathogens should maximize between-host transmission. When such pathogens induce violent epidemic outbreaks, however, a pathogen's short-term advantage at invasion may come at the expense of its ability to persist in the population over the long term. Here, we seek to understand how the classical and invasion-persistence trade-offs interact to shape pathogen life-history evolution as a function of the size and structure of the host population. We develop an individual-based infection model at three distinct levels of organization: within an individual host, among hosts within a local population, and among local populations within a metapopulation. We find a continuum of evolutionarily stable pathogen strategies. At one end of the spectrum-in large well-mixed populations-pathogens evolve to greater acuteness to maximize between-host transmission: the classical trade-off theory applies in this regime. At the other end of the spectrum-when the host population is broken into many small patches-selection favors less acute pathogens, which persist longer within a patch and thereby achieve enhanced between-patch transmission: the invasion-persistence tradeoff dominates in this regime. Between these extremes, we explore the effects of the size and structure of the host population in determining pathogen strategy. In general, pathogen strategies respond to evolutionary pressures arising at both scales.

Mosquito-borne diseases contribute significantly to the global disease burden. High-profile elimination campaigns are currently underway for many parasites, e.g., spp., the causal agent of malaria. Sustaining momentum near the end of elimination programs is often difficult to achieve and consequently quantitative tools that enable monitoring the effectiveness of elimination activities after the initial reduction of cases has occurred are needed. Documenting progress in vector-borne disease elimination is a potentially important application for the theory of critical transitions. Non-parametric approaches that are independent of model-fitting would advance infectious disease forecasting significantly. In this paper, we consider compartmental Ross-McDonald models that are slowly forced through a critical transition through gradually deployed control measures. We derive expressions for the behavior of candidate indicators, including the autocorrelation coefficient, variance, and coefficient of variation in the number of human cases during the approach to elimination. We conducted a simulation study to test the performance of each summary statistic as an early warning system of mosquito-borne disease elimination. Variance and coefficient of variation were highly predictive of elimination but autocorrelation performed poorly as an indicator in some control contexts. Our results suggest that tipping points (bifurcations) in mosquito-borne infectious disease systems may be foreshadowed by characteristic temporal patterns of disease prevalence.

Lifetime reproductive output (LRO) determines per-generation growth rates, establishes criteria for population growth or decline, and is an important component of fitness. Empirical measurements of LRO reveal high variance among individuals. This variance may result from genuine heterogeneity in individual properties, or from individual stochasticity, the outcome of probabilistic demographic events during the life cycle. To evaluate the extent of individual stochasticity requires the calculation of the statistics of LRO from a demographic model. Mean LRO is routinely calculated (as the net reproductive rate), but the calculation of variances has only recently received attention. Here, we present a complete, exact, analytical, closed-form solution for all the moments of LRO, for age- and stage-classified populations. Previous studies have relied on simulation, iterative solutions, or closed-form analytical solutions that capture only part of the sources of variance. We also present the sensitivity and elasticity of all of the statistics of LRO to parameters defining survival, stage transitions, and (st)age-specific fertility. Selection can operate on variance in LRO only if the variance results from genetic heterogeneity. The potential opportunity for selection is quantified by Crow's index , the ratio of the variance to the square of the mean. But variance due to individual stochasticity is only an opportunity for selection. In a comparison of a range of age-classified models for human populations, we find that proportional increases in mortality have very small effects on the mean and variance of LRO, but large positive effects on . Proportional increases in fertility increase both the mean and variance of LRO, but reduce . For a size-classified tree population, the elasticity of both mean and variance of LRO to stage-specific mortality are negative; the elasticities to stage-specific fertility are positive.

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.

The ongoing pandemic disease COVID‑19 has caused worldwide social and financial disruption. As many countries are engaged in designing vaccines, the harmful second and third waves of COVID‑19 have already appeared in many countries. To investigate changes in transmission rates and the effect of social distancing in the USA, we formulate a system of ordinary differential equations using data of confirmed cases and deaths in these states: California, Texas, Florida, Georgia, Illinois, Louisiana, Michigan, and Missouri. Our models and their parameter estimations show social distancing can reduce the transmission of COVID‑19 by 60% to 90%. Thus, obeying the movement restriction rules is crucial in reducing the magnitude of the outbreak waves. This study also estimates the percentage of people who were not social distancing ranges between 10% and 18% in these states. Our analysis shows the management restrictions taken by these states do not slow the disease progression enough to contain the outbreak.

Dispersal is a fundamental biological process that results in the redistribution of organisms due to the interplay between the mode of dispersal, the range of scales over which movement occurs, and the scale of spatial heterogeneity, in which patchiness may occur across a broad range of scales. Despite the diversity of dispersal mechanisms and dispersal length scales in nature, we posit that a fundamental scaling relationship should exist between dispersal and spatial heterogeneity. We present both a conceptual model and mathematical formalization of this expected relationship between the scale of dispersal and the scale of patchiness, which predicts that the magnitude of dispersal (number of individuals) among patches should be maximized when the scale of spatial heterogeneity (defined in terms of patch size and isolation) is neither too fine nor too coarse relative to the gap-crossing abilities of a species. We call this the "dispersal scaling hypothesis" (DSH). We demonstrate congruence in the functional form of this relationship under fundamentally different dispersal assumptions, using well-documented isotropic dispersal kernels and empirically derived dispersal parameters from diverse species, in order to explore the generality of this finding. The DSH generates testable hypotheses as to when and under what landscape scenarios dispersal is most likely to be successful. This provides insights into what management scenarios might be necessary to either restore landscape connectivity, as in certain conservation applications, or disrupt connectivity, as when attempting to manage landscapes to impede the spread of an invasive species, pest, or pathogen.

Analyses of transient dynamics are critical to understanding infectious disease transmission and persistence. Identifying and predicting transients across scales, from within-host to community-level patterns, plays an important role in combating ongoing epidemics and mitigating the risk of future outbreaks. Moreover, greater emphases on non-asymptotic processes will enable timely evaluations of wildlife and human diseases and lead to improved surveillance efforts, preventive responses, and intervention strategies. Here, we explore the contributions of transient analyses in recent models spanning the fields of epidemiology, movement ecology, and parasitology. In addition to their roles in predicting epidemic patterns and endemic outbreaks, we explore transients in the contexts of pathogen transmission, resistance, and avoidance at various scales of the ecological hierarchy. Examples illustrate how (i) transient movement dynamics at the individual host level can modify opportunities for transmission events over time; (ii) within-host energetic processes often lead to transient dynamics in immunity, pathogen load, and transmission potential; (iii) transient connectivity between discrete populations in response to environmental factors and outbreak dynamics can affect disease spread across spatial networks; and (iv) increasing species richness in a community can provide transient protection to individuals against infection. Ultimately, we suggest that transient analyses offer deeper insights and raise new, interdisciplinary questions for disease research, consequently broadening the applications of dynamical models for outbreak preparedness and management.

Phenology is a fundamental determinant of species distributions, abundances, and interactions. In host-parasite interactions, host phenology can affect parasite fitness due to the temporal constraints it imposes on host contact rates. However, it remains unclear how parasite transmission is shaped by the wide range of phenological patterns observed in nature. We develop a mathematical model of the Lyme disease system to study the consequences of differential tick developmental-stage phenology for the transmission of . Incorporating seasonal tick activity can increase fitness compared to continuous tick activity but can also prevent transmission completely. fitness is greatest when the activity period of the infectious nymphal stage slightly precedes the larval activity period. Surprisingly, is eradicated if the larval activity period begins long after the end of nymphal activity due to a feedback with mouse population dynamics. These results highlight the importance of phenology, a common driver of species interactions, for the fitness of a parasite.

Bark beetle outbreaks and forest fires have imposed severe ecological damage and caused billions of dollars in lost resources in recent decades. The impact of such combined disturbances is projected to become more severe, especially as climate change takes its toll on forest ecosystems in the coming years. Here, we investigate the impact of multiple disturbances in a demographically heterogeneous tree population, using an age-structured difference equation model of bark beetle outbreaks and forest fires. We identify two dynamical regimes for beetle and fire dynamics. The model predicts that fire helps dampen beetle outbreaks not only by removing host trees but also by altering the demographic structure of forest stands. We show that a stand thinning protocol, which reduces the population size of the largest few juvenile classes by a small percentage, is able to significantly reduce beetle-induced tree mortality. Our research demonstrates one approach to capturing compound disturbances in a mathematical model.

History matters when individual prior conditions contain important information about the fate of individuals. We present a general framework for demographic models which incorporates the effects of history on population dynamics. The framework incorporates prior condition into the -state variable and includes an algorithm for constructing the population projection matrix from information on current state dynamics as a function of prior condition. Three biologically motivated classes of prior condition are included: prior stages, linear functions of current and prior stages, and equivalence classes of prior stages. Taking advantage of the matrix formulation of the model, we show how to calculate sensitivity and elasticity of any demographic outcome. Prior condition effects are a source of inter-individual variation in vital rates, i.e., individual heterogeneity. As an example, we construct and analyze a second-order model of , a long-lived herb. We present population growth rate, the stable population distribution, the reproductive value vector, and the elasticity of to changes in the second-order transition rates. We quantify the contribution of prior conditions to the total heterogeneity in the stable population of using the entropy of the stable distribution.

A tension between cooperation and conflict characterizes the behavioral dynamics of many social species. The foraging benefits of group living include increased efficiency and reduced need for vigilance, but social foraging can also encourage theft of captured prey from conspecifics. The payoffs of stealing prey from others (scrounging) versus capturing prey (producing) may depend not only on the frequency of each foraging strategy in the group but also on an individual's ability to steal. By observing the foraging behavior of juvenile coho salmon (), we found that, within a group, relatively smaller coho acted primarily as producers and took longer to handle prey, and were therefore more likely to be targeted by scroungers than relatively larger coho. Further, our observations suggest that the frequency of scrounging may be higher when groups contained individuals of different sizes. Based on these observations, we developed a model of phenotype-limited producer-scrounger dynamics, in which rates of stealing were structured by the relative size of producers and scroungers within the foraging group. Model simulations show that when the success of stealing is positively related to body size, relatively large predators should tend to be scroungers while smaller predators should be producers. Contrary to previous models, we also found that, under certain conditions, producer and scrounger strategies could coexist for both large and small phenotypes. Large scroungers tended to receive the highest payoff, suggesting that producer-scrounger dynamics may result in an uneven distribution of benefits among group members that-under the right conditions-could entrench social positions of dominance.

Anticipating infectious disease emergence and documenting progress in disease elimination are important applications for the theory of critical transitions. A key problem is the development of theory relating the dynamical processes of transmission to observable phenomena. In this paper, we consider compartmental susceptible-infectious-susceptible (SIS) and susceptible-infectious-recovered (SIR) models that are slowly forced through a critical transition. We derive expressions for the behavior of several candidate indicators, including the autocorrelation coefficient, variance, coefficient of variation, and power spectra of SIS and SIR epidemics during the approach to emergence or elimination. We validated these expressions using individual-based simulations. We further showed that moving-window estimates of these quantities may be used for anticipating critical transitions in infectious disease systems. Although leading indicators of elimination were highly predictive, we found the approach to emergence to be much more difficult to detect. It is hoped that these results, which show the anticipation of critical transitions in infectious disease systems to be theoretically possible, may be used to guide the construction of online algorithms for processing surveillance data.

Ecological theory about the dynamics of interacting populations is mainly based on unstructured models that account for species abundances only. In turn, these models constitute the basis for our understanding of the functioning of ecological communities and ecosystems and their responses to environmental change, natural disturbances and human impacts. Structured models that take into account differences between individuals in age, stage or size have been shown to sometimes make predictions that run counter to the predictions of unstructured analogues. It is however unclear which biological mechanisms that are accounted for in the structured models give rise to these contrasting predictions. Focusing on two particular rules-of-thumb that generally hold in unstructured consumer-resource models, one relating to the relationship between mortality and equilibrium density of the consumer and the other relating to the stability of the equilibrium, I investigate the necessary conditions under which accounting for juvenile-adult stage structure can lead to qualitatively different model predictions. In particular, juvenile-adult stage structure is shown to overturn the two rules-of-thumb in case the model also accounts for the energetic requirements for basic metabolic maintenance. Given the fundamental nature of both juvenile-adult stage structure as well as metabolic maintenance requirements, these results call into question the generality of the predictions derived from unstructured models.

Simple temporal models that ignore the spatial nature of interactions and track only changes in mean quantities, such as global densities, are typically used under the unrealistic assumption that individuals are well mixed. These so-called mean-field models are often considered overly simplified, given the ample evidence for distributed interactions and spatial heterogeneity over broad ranges of scales. Here, we present one reason why such simple population models may work even when mass-action assumptions do not hold: spatial structure is present but it relates to global densities in a special way. With an individual-based predator-prey model that is spatial and stochastic, and whose mean-field counterpart is the classic Lotka-Volterra model, we show that the global densities and densities of pairs (or spatial covariances) establish a at the stationary state and also in their transient approach to this state. This relationship implies that the dynamics of global densities can be written simply as a function of those densities alone without invoking pairs (or higher order moments). The exponents of the bi-power law for the predation rate exhibit a remarkable robustness to changes in model parameters. Evidence is presented for a connection of our findings to the existence of a critical phase transition in the dynamics of the spatial system. We discuss the application of similar modified mean-field equations to other ecological systems for which similar transitions have been described, both in models and empirical data. The online version of this article (doi:10.1007/s12080-011-0116-2) contains supplementary material, which is available to authorized users.

Ecological stability is a fundamental aspect of food web dynamics. In this study, we explore the factors influencing stability in complex ecological networks, characterizing it through biomass oscillations and species persistence. Using an Extended Niche model, we generate diverse food web structures and investigate the effects of intraspecific consumer interference, network size, connectance, and diet specialism on stability. Our findings reveal that intraspecific consumer interference plays a pivotal role in shaping stability. Higher interference results in stable dynamics, reducing oscillations and extinctions. Additionally, differences emerge between food webs comprised of invertebrate consumers and those of ectotherm vertebrates, with the latter showing higher oscillations. Network size and connectance also influence stability, where larger and more connected webs tend to exhibit reduced oscillations. Overall, our study sheds light on the complex interplay of factors affecting ecological stability in food webs. Understanding these dynamics is crucial for biodiversity conservation and ecosystem management.