Demographic Stochasticity Research Articles

Beyond mean fitness: Demographic stochasticity and resilience matter at tree species climatic edges

AbstractAimLinking local population dynamics and species distributions is crucial to predicting the impacts of climate change. Although many studies focus on the mean fitness of populations, theory shows that species distributions can be shaped by demographic stochasticity or population resilience. Here, we examine how mean fitness (measured by invasion rate), demographic stochasticity and resilience (measured by the ability to recover from disturbance) constrain populations at the edges compared with the climatic centre.LocationEurope: Spain, France, Germany, Finland and Sweden.PeriodForest inventory data used for fitting the models cover the period from 1985 to 2013.Major taxaDominant European tree species; angiosperms and gymnosperms.MethodsWe developed dynamic population models covering the entire life cycle of 25 European tree species with climatically dependent recruitment models fitted to forest inventory data. We then ran simulations using integral projection and individual‐based models to test how invasion rates, risk of stochastic extinction and ability to recover from stochastic disturbances differ between the centre and edges of the climatic niches of species.ResultsResults varied among species, but in general, demographic constraints were stronger at warm edges and for species in harsher climates. Conversely, recovery was more limiting at cold edges. In addition, we found that for several species, constraints at the edges were attributable to demographic stochasticity and capacity for recovery rather than mean fitness.Main conclusionsOur results highlight that mean fitness is not the only mechanism at play at the edges; demographic stochasticity and population capacity to recover also matter for European tree species. To understand how climate change will drive species range shifts, future studies will need to analyse the interplay between population mean growth rate and stochastic demographic processes in addition to disturbances.

Heteroclinic cycling and extinction in May–Leonard models with demographic stochasticity

May and Leonard (SIAM J Appl Math 29:243–253, 1975) introduced a three-species Lotka–Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each “cycle”, passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic Escherichia coli), in the immune system, in neural information processing models (“winnerless competition”), and in models of neural central pattern generators. Yet as May and Leonard observed “Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two.” Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard’s ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.

The stochasticity in adherence to nonpharmaceutical interventions and booster doses and the mitigation of COVID-19

Facing the more contagious COVID-19 variant, Omicron, nonpharmaceutical interventions (NPIs) were still in place and booster doses were proposed to mitigate the epidemic. However, the uncertainty and stochasticity in individuals' behaviours toward the NPIs and booster dose increase, and how this randomness affects the transmission remains poorly understood. We present a model framework to incorporate demographic stochasticity and two kinds of environmental stochasticity (notably variations in adherence to NPIs and booster dose acceptance) to analyze the effects of different forms of stochasticity on transmission. The model is calibrated using the data from December 31, 2021, to March 8, 2022, on daily reported cases and hospitalizations, cumulative cases, deaths and vaccinations for booster doses in Toronto, Canada. An approximate Bayesian computational (ABC) method is used for calibration. We observe that demographic stochasticity could dramatically worsen the outbreak with more incidence compared with the results of the corresponding deterministic model. We found that large variations in adherence to NPIs increase infections. The randomness in booster dose acceptance will not affect the number of reported cases significantly and it is acceptable in the mitigation of COVID-19. The stochasticity in adherence to NPIs needs more attention compared to booster dose hesitancy.

Understanding cellular growth strategies via optimal control.

Evolutionary prediction and control are increasingly interesting research topics that are expanding to new areas of application. Unravelling and anticipating successful adaptations to different selection pressures becomes crucial when steering rapidly evolving cancer or microbial populations towards a chosen target. Here we introduce and apply a rich theoretical framework of optimal control to understand adaptive use of traits, which in turn allows eco-evolutionarily informed population control. Using adaptive metabolism and microbial experimental evolution as a case study, we show how demographic stochasticity alone can lead to lag time evolution, which appears as an emergent property in our model. We further show that the cycle length used in serial transfer experiments has practical importance as it may cause unintentional selection for specific growth strategies and lag times. Finally, we show how frequency-dependent selection can be incorporated to the state-dependent optimal control framework allowing the modelling of complex eco-evolutionary dynamics. Our study demonstrates the utility of optimal control theory in elucidating organismal adaptations and the intrinsic decision making of cellular communities with high adaptive potential.

Biocultural aspects of species extinctions

AbstractPredicting whether a species is likely to go extinct (or not) is one of the fundamental objectives of conservation biology, and extinction risk classifications have become an essential tool for conservation policy, planning and research. This sort of prediction is feasible because the extinction processes follow a familiar pattern of population decline, range collapse and fragmentation, and, finally, extirpation of sub-populations through a combination of genetic, demographic and environmental stochasticity. Though less well understood and rarely quantified, the way in which science and society respond to population decline, extirpation and species extinction can also have a profound influence, either negative or positive, on whether a species goes extinct. For example, species that are highly sought after by collectors and hobbyists can become more desirable and valuable as they become rarer, leading to increased demand and greater incentives for illegal trade – known as the anthropogenic Allee effect. Conversely, species that are strongly linked to cultural identity are more likely to benefit from sustainable management, high public support for conservation actions and fund-raising, and, by extension, may be partially safeguarded from extinction. More generally, human responses to impending extinctions are extremely complex, are highly dependent on cultural and socioeconomic context, and have typically been far less studied than the ecological and genetic aspects of extinction. Here, we identify and discuss biocultural aspects of extinction and outline how recent advances in our ability to measure and monitor cultural trends with big data are, despite their intrinsic limitations and biases, providing new opportunities for incorporating biocultural factors into extinction risk assessment.

Probability of disease extinction and outbreak in a stochastic tuberculosis model with fast-slow progression and relapse

<abstract><p>A stochastic continuous-time Markov chain tuberculosis model with fast-slow progression and relapse is established to explore the impact of the demographic variation on TB transmission. At first, the extinction threshold and probability of the disease extinction and outbreak are obtained by applying the multitype Galton-Waston branching process for the stochastic model. In numerical simulations, the probability of the disease extinction and outbreak and expected epidemic duration of the disease are estimated. To see how demographic stochasticity affects TB dynamics, we compare dynamical behaviors of both stochastic and deterministic models, and these results show that the disease extinction in stochastic model would occur while the disease is persistent for the deterministic model. Our results suggest that minimizing the contact between the infectious and the susceptible, and detecting the latently infected as early as possible, etc., could effectively prevent the spread of tuberculosis.</p></abstract>

Improving the realism of neutral ecological models by incorporating transient dynamics with temporal changes in community size

Neutral models in ecology assume that all species are demographically equivalent, such that their abundances differ ultimately because of demographic stochasticity rather than selection. In spite of their simplicity, neutral models have been found to accurately reproduce static patterns of biodiversity for diverse communities. However, the same neutral models have been found to exhibit species abundance dynamics that are far too slow compared to reality, resulting in poor fits to temporally dynamic patterns of biodiversity. Here, we show that one of the root causes of these slow dynamics is the additional assumption that a community has reached an equilibrium with a fixed community size, with species that have a net growth rate close to zero. We removed this additional assumption by constructing and analyzing a neutral model with an expected community size that can change over time and is not necessarily at equilibrium, which thus allows the historical formation of a community to be represented explicitly. Our analysis demonstrated that for the general scenario where a small community rapidly grows in size to a carrying capacity, representing recovery from ecological disturbance or assembly of a new community, the model produced much larger changes in species abundances and much shorter species ages than a neutral model at an equilibrium with fixed community size. In addition, the species abundance distribution was biphasic with a subset of abundant species arising from a founder effect. We confirmed these new results in applications of the new model to the specific scenario of recovery of the Amazon tree community after the end-Cretaceous bolide impact, which involved periods of increasing and decreasing community size. We conclude that incorporating transient dynamics in neutral models improves realism by allowing explicit consideration of how a community is formed over realistic time-scales.

Stochastic and parameter analysis for an integrative cancer model

In previous work, we presented a model that integrates cancer cell differentiation and immunotherapy, analysing a particular therapy against cancer stem cells by cytotoxic cell vaccines. As every biological system is exposed to random fluctuations, is important to incorporate stochasticity in the models to adequate their behaviour to experimental observations. Thus, we propose a necessary upgrade to the former model incorporating fluctuations in it. On the one hand, we added multiplicative noise throughout the proposed system, and on the other, we specifically analysed the influence of demographic and multiplicative noise on the parameters of reproduction and death in cancer cells. In both cases, we studied the dynamics for different values of the parameters involved. It was observed that the final number of cancer cells decreases for different combinations of these parameters and noise intensity.

Kin networks and opportunities for reproductive cooperation and conflict among hunter-gatherers.

Little is known about the potential for reproductive conflict among hunter-gatherer populations, who are characterized by bilateral kinship ties, flexible residential mobility, and high offspring mortality. To assess the potential for reproductive conflict, we use longitudinal residence and reproductive history data for two bands of South American foragers. Using multilevel logistic regressions (N = 44 women, N = 712 person years), we examine how yearly measures of (i) camp composition, (ii) distribution of female kin and (iii) a woman's position in a female kinship network impact the likelihood of giving birth or experiencing a child's death. We compare conflict models to a demographic model that accounts for the proportion of women giving birth in a given year. Contrary to conflict models, results show that the odds of giving birth increase with the presence of highly related women. However, the odds of experiencing an offspring death are insensitive to the presence of coresident women. Network measures of closeness and centrality in the female kin network also show no significant effect on reproductive outcomes. Furthermore, chances of both births and deaths increase in years when proportionally more women are giving birth. We argue that demographic stochasticity relating to ecological conditions best predicts reproductive outcomes for women. This article is part of the theme issue 'Cooperation among women: evolutionary and cross-cultural perspectives'.

Stochasticity directs adaptive evolution toward nonequilibrium evolutionary attractors.

Stochastic processes such as genetic drift may hinder adaptation, but the effect of such stochasticity on evolution via its effect on ecological dynamics is poorly understood. Here we evaluate patterns of adaptation in a population subject to variation in demographic stochasticity. We show that stochasticity can alter population dynamics and lead to evolutionary outcomes that are not predicted by classic eco-evolutionary modeling approaches. We also show, however, that these outcomes are governed by nonequilibrium evolutionary attractors-these are maxima in lifetime reproductive success when stochasticity keeps the ecological system away from the deterministic equilibrium. These NEEAs alter the path of evolution but are not visible through the equilibrium lens that underlies much evolutionary theory. Our results reveal that considering population processes during transient periods can greatly improve our understanding of the path and pace of evolution.

The opportunity for selection: A slippery concept in ecology and evolution.

Natural selection can only occur if individuals differ in fitness. For this reason, the variance in relative fitness has been equated with the 'opportunity for selection' ( ), which has a long, albeit somewhat controversial, history. In this paper we discuss the use/misuse of and related metrics in evolutionary ecology. The opportunity is only realised if some fraction of is caused by trait variation. Thus, does not imply that selection is occurring, as sometimes erroneously assumed, because all fitness variation could be independent of phenotype. The selection intensity on any given trait cannot exceed , but this upper limit will never be reached because (a) stochastic factors always affect fitness, and (b) there might be multiple traits under selection. The expected magnitude of the stochastic component of is negatively correlated with mean fitness. Uncertainty in realised is also larger when mean fitness or population/sample size are low. Variation in across time or space thus can be dominated (or solely driven) by variation in the strength of demographic stochasticity. We illustrate these points using simulations and empirical data from a population study on great tits Parus major. Our analysis shows that the scope for fecundity selection in the great tits is substantially higher when using annual number of recruits as the fitness measure, rather than fledglings or eggs, even after adjusting for the dependence of on mean fitness. This suggests nonrandom survival of juveniles across families between life stages. Indeed, previous work on this population has shown that offspring recruitment is often nonrandom with respect to clutch size and laying date of parents, for example. We conclude that one cannot make direct inferences about selection based on fitness data alone. However, examining variation in (the opportunity for fecundity selection adjusted for mean fitness) across life stages, years or environments can offer clues as to when/where fecundity selection might be strongest, which can be useful for research planning and experimental design.

In Memoriam : Edward O. Wilson (1929-2021): It All Started with Ants.

In Memoriam : Edward O. Wilson (1929-2021): It All Started with Ants.

Association of Occupational Stress With Tinnitus Among Career Firefighters in the United States.

This study explores the relationship between occupational stress and tinnitus among firefighters, a group often exposed to two tinnitus risk factors: high stress and noise. This cross-sectional study includes 240 firefighters in the United States. Data describing demographic characteristics, occupational stress, noise exposure, and tinnitus were collected by survey. Occupational stress was measured using the short version of the Effort-Reward Imbalance Questionnaire. Forty-three percent of participants reported experiencing tinnitus within the past month. For occupational stress, higher effort (odds ratio, 1.25; 95% confidence interval, 1.05 to 1.49) and higher effort-reward ratio (odds ratio, 12.28; 95% confidence interval, 3.08 to 48.86) were associated with increased odds of tinnitus, after adjustment for demographic characteristics and noise exposure. Occupational stress may increase the likelihood of tinnitus for firefighters, an already at-risk group of workers. Health providers should incorporate stress assessment into tinnitus management programs.

Predicting point-source invasion success in the Queensland fruit fly (Bactrocera tryoni): An individual-based modelling approach

Fruit flies are a major pest worldwide for fruit producing industries. Incursions into fly free areas usually occurs via infested fruit; however, little is reported about the size of a propagule to start a new establishment. Propagule pressure is an important predictor of the probability that an invasive species will establish a breeding population. Recently, individual-based model (IBM) became a valuable modelling tool for exploring invasive species. Here, we developed a spatially-explicit individual-based model (IBM) specifically parameterized for the Queensland fruit fly (Qfly) (Bactrocera tryoni Froggatt), a major horticultural pest species in Australia and a major quarantine concern worldwide. Usually, new establishments or incursions originate from the introduction of infested fruit and larvae must progress through several stages to become sexually mature adults. For a Qfly incursion to establish a breeding population, flies must avoid predators and survive long enough to become reproductively mature, find a mate, and find ripening fruit. Additionally, their offspring must survive and successfully reproduce. The IBM model simulated release of a fixed number of flies into a heterogeneous environment of varying suitability. We conducted simulations to delineate the contributions of demographic stochasticity and Allee effects (finding a mate in a spatial environment) on establishment probability. Our model delineated several key influential factors, especially tree density, extrinsic mortality and mating range. We performed sensitivity analyses to identity which biological and ecological mechanisms strongly affect establishment probability. Integrating the model's findings with information on transport of infested fruit helps explain why Qfly incursions are common, but yet most fail to establish. Our model predicted that circa 16 and 50 flies were required for a 50% and 99% chance of establishment respectively. Additionally, our model predicted the mating distance for Qfly was 16.1 m. The mean daily dispersal distance was 30 m. We discuss how this knowledge might be used to better manage Qfly by alterations in surveillance and male annihilation technique.

Phenomenology and dynamics of competitive ecosystems beyond the niche-neutral regimes

Structure, composition, and stability of ecological populations are shaped by the inter- and intraspecies interactions within their communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, controls the structure, the diversity, and the long-term stability of ecological systems in the presence of noise and fluctuations. We address this problem using a minimal model of interacting multispecies ecological communities that incorporates competition, immigration, and demographic noise. We find that a complete phase diagram exhibits rich behavior with multiple regimes that go beyond the classical "niche" and "neutral" regimes, extending and modifying the "rare biosphere" or "niche-like" dichotomy. In particular, we observe regimes that cannot be characterized as either niche or neutral where a multimodal species abundance distribution is observed. We characterize the transitions between the different regimes and show how these arise from the underlying kinetics of the species turnover, extinction, and invasion. Our model serves as a minimal null model of noisy competitive ecological systems, against which more complex models that include factors such as mutations and environmental noise can be compared.

Toward a “modern coexistence theory” for the discrete and spatial

AbstractThe usual theoretical condition for coexistence is that each species in a community can increase when it is rare (mutual invasibility). Traditional coexistence theory implicitly assumes that the invading species is common enough that we can ignore demographic stochasticity but rare enough that it does not compete with itself, even after it has reached a stationary spatial distribution. However, short‐distance dispersal of discrete individuals leads to locally dense population clusters, and existing theory breaks down. We have an intuition that when we account for invader–invader competition, shorter‐range dispersal should reduce the invader's ability to escape competition, but exactly how does this translate into lower population growth? And how will invader discreteness affect outcomes? We need a way of partitioning the contributions to coexistence, but current modern coexistence theory (MCT) does not apply under these conditions. Here we present a computationally based partitioning method to quantify the contributions to coexistence from different mechanisms, as in MCT. We also build up an intuition for how invader clumping and discreteness will affect these contributions by analyzing a case study, a lattice‐based spatial lottery model. We first consider fluctuation‐dependent coexistence, partitioning the contributions of variable environment, variable competition, demographic stochasticity, and their correlations and interactions. Our second example examines fluctuation‐independent coexistence maintained by a fecundity–survival trade‐off, and partitions the contributions to coexistence from interspecific differences in fecundity, in mortality, and in dispersal. We find that demographic stochasticity harms an invader, but only slightly. Localized invader dispersal, on the other hand, can have a strong effect. When invaders are more clumped, they compete with each other more intensely when rare, so they too become limited by environment‐competition covariance. More invader clumping also means that variation in competition changes from helping the invader to harming it. More broadly, invader clumping is likely to weaken any coexistence mechanism that relies on the invader escaping competition from the resident, because invader clumping means that the resident is no longer the only source of competition.

Does deterministic coexistence theory matter in a finite world?

Contemporary studies of species coexistence are underpinned by deterministic models that assume that competing species have continuous (i.e., noninteger) densities, live in infinitely large landscapes, and coexist over infinite time horizons. By contrast, in nature, species are composed of discrete individuals subject to demographic stochasticity and occur in habitats of finite size where extinctions occur in finite time. One consequence of these discrepancies is that metrics of species' coexistence derived from deterministic theory may be unreliable predictors of the duration of species coexistence in nature. These coexistence metrics include invasion growth rates and niche and fitness differences, which are now commonly applied in theoretical and empirical studies of species coexistence. In this study, we tested the efficacy of deterministic coexistence metrics on the duration of species coexistence in a finite world. We introduce new theoretical and computational methods to estimate coexistence times in stochastic counterparts of classic deterministic models of competition. Importantly, we parameterized this model using experimental field data for 90 pairwise combinations of 18 species of annual plants, allowing us to derive biologically informed estimates of coexistence times for a natural system. Strikingly, we found that for species expected to deterministically coexist, community sizes containing only 10 individuals had predicted coexistence times of more than 1000 years. We also found that invasion growth rates explained 60% of the variation in intrinsic coexistence times, reinforcing their general usefulness in studies of coexistence. However, only by integrating information on both invasion growth rates and species' equilibrium population sizes could most (>99%) of the variation in species coexistence times be explained. This integration was achieved with demographically uncoupled single-species models solely determined by the invasion growth rates and equilibrium population sizes. Moreover, because of a complex relationship between niche overlap/fitness differences and equilibrium population sizes, increasing niche overlap and increasing fitness differences did not always result in decreasing coexistence times, as deterministic theory would predict. Nevertheless, our results tend to support the informed use of deterministic theory for understanding the duration of species' coexistence while highlighting the need to incorporate information on species' equilibrium population sizes in addition to invasion growth rates.

Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects

Different types of stochasticity play essential roles in shaping complex population dynamics. This paper presents a novel approach to model demographic and environmental stochasticity in a single-species model with cooperative components that are measured by component Allee effects. Our work provides rigorous mathematical proof on stochastic persistence and extinction, ergodicity (i.e., the existence of a unique stationary distribution) and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics. The theoretical and numerical results suggest that stochasticity may affect the population system in a variety of ways, specifically: (i) In the weak Allee effects case (e.g., strong cooperative efforts), the demographic stochasticity from the attack rate contributes to the expansion of the population size, while the demographic stochasticity from the handling rate and the environmental stochasticity have the opposite role, and may even lead to population extinction; (ii) In the strong Allee effects case (cooperative efforts not strong enough), both demographic and environmental stochasticity play a similar role in the survival of population, and are related to the initial population level: if the initial population level is large enough, demographic stochasticity and environmental stochasticity may be detrimental to the survival of population, otherwise if the initial population level is small enough, demographic stochasticity and environmental stochasticity may bring survival opportunities for the population that deterministically would extinct indefinitely; (iii) In the extinction case, demographic and environmental stochasticity cannot change the trend of population extinction, but they can delay or promote population extinction.

Comparison of genetic variation between rare and common congeners of Dipodomys with estimates of contemporary and historical effective population size.

Species with low effective population sizes are at greater risk of extinction because of reduced genetic diversity. Such species are more vulnerable to chance events that decrease population sizes (e.g. demographic stochasticity). Dipodomys elator, (Texas kangaroo rat) is a kangaroo rat that is classified as threatened in Texas and field surveys from the past 50 years indicate that the distribution of this species has decreased. This suggests geographic range reductions that could have caused population fluctuations, potentially impacting effective population size. Conversely, the more common and widespread D. ordii (Ord’s kangaroo rat) is thought to exhibit relative geographic and demographic stability. We assessed the genetic variation of D. elator and D. ordii samples using 3RAD, a modified restriction site associated sequencing approach. We hypothesized that D. elator would show lower levels of nucleotide diversity, observed heterozygosity, and effective population size when compared to D. ordii. We were also interested in identifying population structure within contemporary samples of D. elator and detecting genetic variation between temporal samples to understand demographic dynamics. We analyzed up to 61,000 single nucleotide polymorphisms. We found that genetic variability and effective population size in contemporary D. elator populations is lower than that of D. ordii. There is slight, if any, population structure within contemporary D. elator samples, and we found low genetic differentiation between spatial or temporal historical samples. This indicates little change in nuclear genetic diversity over 30 years. Results suggest that genetic diversity of D. elator has remained stable despite reduced population size and/or abundance, which may indicate a metapopulation-like system, whose fluctuations might counteract species extinction.

Selection on modifiers of genetic architecture under migration load.

Gene flow between populations adapting to differing local environmental conditions might be costly because individuals can disperse to habitats where their survival is low or because they can reproduce with locally maladapted individuals. The amount by which the mean relative population fitness is kept below one creates an opportunity for modifiers of the genetic architecture to spread due to selection. Prior work that separately considered modifiers changing dispersal, recombination rates, or altering dominance or epistasis, has typically focused on the direction of selection rather than its absolute magnitude. We here develop methods to determine the strength of selection on modifiers of the genetic architecture, including modifiers of the dispersal rate, in populations that have previously evolved local adaptation. We consider scenarios with up to five loci contributing to local adaptation and derive a new model for the deterministic spread of modifiers. We find that selection for modifiers of epistasis and dominance is stronger than selection for decreased recombination, and that selection for partial reductions in recombination are extremely weak, regardless of the number of loci contributing to local adaptation. The spread of modifiers that reduce dispersal depends on the number of loci, epistasis and extent of local adaptation in the ancestral population. We identify a novel effect, that modifiers of dominance are more strongly selected when they are unlinked to the locus that they modify. These findings help explain population differentiation and reproductive isolation and provide a benchmark to compare selection on modifiers under finite population sizes and demographic stochasticity.