Effects Of Environmental Stochasticity Research Articles

Unraveling the forces shaping foraging dynamics in harvester ant colonies: Recruitment efficiency and environmental variability

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

Variation in environmental stochasticity dramatically affects viability and extinction time in a predator–prey system with high prey group cohesion

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator–prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.

Effects of predator modulation and vector preference on pathogen transmission in plant populations

Biological control programs frequently rely on predators to control vector-borne pathogens by consumptive effects on vector abundance in agroecosystems. Meanwhile, the spread of vectored disease depends on the vector preference for host status (healthy or infected hosts). Yet, it is unclear how vector preferences alter the controlled effectivity of predators in pathogen transmission. Therefore, we here addressed the plant-vector-pathogen models assessing how pathogen transmission in plant was affected by variable predation rates and vector preferences for host status. Specifically, we discussed effects of predators on vector abundance and pathogen transmission under both a non-spatial model and a spatially structured metapopulation model. We showed that predators can decrease the vector abundance and inhibit pathogen prevalence, whereas vector preference contributes profoundly to the controlled effectivity of predators on the spread of vector-borne pathogens. Moreover, predation can increase oscillation amplitude of the pathogen prevalence in both plant and vector; suggesting that the inclusion of predator can amplify the effects of environmental stochasticity on pathogen dynamics. In conclusion, our results support the prediction of theoretical disease models showing predator can be a natural enemy for pathogen control, and also extend that predatory interactions interacting with vector preferences play the singularly joint effects on the spread of vector-borne pathogens.

Projected Climate and Hydroregime Variability Constrain Ephemeral Wetland-Dependent Amphibian Populations in Simulations of Southern Toads.

Amphibian populations are threatened globally by stressors, including diminishing availability of suitable wetland breeding sites, altered hydroregimes driven by changing weather patterns, and exposure to contaminants. Ecological risk assessment should encompass spatial and temporal scales that capture influential ecological processes and demographic responses. Following the PopGUIDE framework of population model development for risk assessment, we used matrix population models, in conjunction with existing hydroregime predictions, under a climate change scenario to evaluate the effects of environmental stochasticity and aquatic pesticide exposure on amphibians that are dependent on ephemeral wetlands. Using southern toads (Anaxyrus terrestris) as an example, we simulated population dynamics with breeding success dependent on hydroregime suitability. Years were defined as optimal, marginal, or insufficient for successful toad recruitment, based on the duration of their potential breeding season and rate of larval development to metamorphosis. We simulated both probabilistic and chronologically specific population projections, including variable annual fecundity, based on hydroregime suitability and reduced larval survival from carbaryl exposure. In our simulations, populations were more negatively impacted by prolonged drought, and consequently multiple sequential years of reproductive failure, than by aquatic pesticide exposure. These results highlight the necessity of reliable climate projections to accurately represent the effects of altered hydroregimes on amphibian populations. Risk assessment approaches could be improved with flexible modifications that allow inclusion of various extrinsic stressors and identification of demographic and ecological vulnerabilities when precise data are lacking.

Dynamics of Oxygen-Plankton Model with Variable Zooplankton Search Rate in Deterministic and Fluctuating Environments

It is estimated by scientists that 50–80% of the oxygen production on the planet comes from the oceans due to the photosynthetic activity of phytoplankton. Some of this production is consumed by both phytoplankton and zooplankton for cellular respiration. In this article, we have analyzed the dynamics of the oxygen-plankton model with a modified Holling type II functional response, based on the premise that zooplankton has a variable search rate, rather than constant, which is ecologically meaningful. The positivity and uniform boundedness of the studied system prove that the model is well-behaved. The feasibility conditions and stability criteria of each equilibrium point are discussed. Next, the occurrence of local bifurcations are exhibited taking each of the vital system parameters as a bifurcation parameter. Numerical simulations are illustrated to verify the analytical outcomes. Our findings show that (i) the system dynamics change abruptly for a low oxygen production rate, resulting in depletion of oxygen and plankton extinction; (ii) the proposed system has oscillatory behavior in an intermediate range of oxygen production rates; (iii) it always has a stable coexistence steady state for a high oxygen production rate, which is dissimilar to the outcome of the model of a coupled oxygen-plankton dynamics where zooplankton consumes phytoplankton with classical Holling type II functional response. Lastly, the effect of environmental stochasticity is studied numerically, corresponding to our proposed system.

Effects of environmental stochasticity on the foraging dynamics of ant colonies driven by physical interactions

Collective foraging is critical for the ecological and evolutionary success of social insect colonies. To evaluate the impact of environmental stochasticity on the collective foraging dynamics of social ants, this paper develops a collective foraging model based on stochastic differential equations, in which communication among workers mainly relies on physical interactions. By analyzing the stochastic dynamics of the constructed model, we obtain relaxation conditions for the existence of an ergodic stationary distribution. Theoretical results suggest that environmental stochasticity leads to a decrease in the effective recruitment rate and average foraging period of foragers, ultimately negatively affecting the average recruit recruitment ability of single returning forager.

Carry‐over effects of environmental stochasticity of the California Current on body condition and wing length of breeding Black‐vented Shearwaters (Puffinus opisthomelas)

Recent climatic variation has led to a change in size or mass in some species. The Black‐vented Shearwater Puffinus opisthomelas is endemic to the California Current System, a highly variable system, giving us cues as to the effects of interannual variability on predators. Here, we report the results of a comparison of biometrics measurement in the short term, 4 years, with different environmental conditions. We found that environmental variability has a direct effect on the body condition of the species, affecting not only body mass but also wing length, with shorter wings as a carry‐over effect of adverse conditions.

Dynamics induced by environmental stochasticity in a phytoplankton-zooplankton system with toxic phytoplankton.

Environmental stochasticity and toxin-producing phytoplankton (TPP) are the key factors that affect the aquatic ecosystems. To investigate the effects of environmental stochasticity and TPP on the dynamics of plankton populations, a stochastic phytoplankton-zooplankton system with two TPP is studied theoretically and numerically in this paper. Theoretically, we first prove that the system possesses a unique and global positive solution with positive initial values, and then derive some sufficient conditions guaranteeing the extinction and persistence in the mean of the system. Significantly, it is shown that the system has a stationary distribution when toxin liberation rate reaches some a critical value. Additionally, numerical analysis shows that the white noise can affect the survival of plankton populations directly. Furthermore, it has been observed that the increasing one toxin liberation rate can increase the survival chance of phytoplankton and reduce the biomass of zooplankton, but the combined effects of two liberation rates on the changes in plankton populations are stronger than that of controlling any one of the two TPP.

Cooperative and non-cooperative behaviour in the exploitation of a common renewable resource with environmental stochasticity

Classical fisheries biology aims to optimise fisheries-level outcomes, such as yield or profit, by controlling the fishing effort. This can be adjusted to allow for the effects of environmental stochasticity, or noise, in the population dynamics. However, when multiple fishing entities, which could represent countries, commercial organisations, or individual vessels, can autonomously determine their own fishing effort, the the optimal action for one fishing entity depends on the actions of others. Coupled with noise in the population dynamics, and with decisions about fishing effort made repeatedly, this becomes an iterated stochastic game. We tackle this problem using the tools of stochastic optimisation, first for the monopolist’s problem and then for the duopolist’s problem. In each case, we derive optimal policies that specify the best level of fishing effort for a given stock biomass. Under these optimal policies, we can calculate the equilibrium stock biomass, the expected long-term return from fishing and the probability of stock collapse. We also show that there is a threshold stock biomass below which it is optimal to stop fishing until the stock recovers. We then develop an agent-based model to test the effectiveness of simple strategies for responding to deviations by an opponent from a cooperative fishing level. Our results show that the economic value of the fishery to a monopolist, or to a consortium of fishing agents, is robust to a certain level of noise. However, without the means of making agreements about fishing effort, even low levels of noise make sustained cooperation between autonomous fishing agents difficult.

When do factors promoting genetic diversity also promote population persistence? A demographic perspective on Gillespie’s SAS-CFF model

Classical stochastic demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, in a 1978 Theoretical Population Biology paper, Gillespie demonstrated with his stochastic additive scale and concave fitness function (SAS-CFF) model that environmental stochasticity can promote genetic diversity. Extending the SAS-CFF to account for demography, I examine the simultaneous effects of environmental stochasticity on genetic diversity and population persistence. Explicit expressions for the per-capita growth rates of rare alleles and the population at low-density are derived. Consistent with Gillespie’s analysis, if the log-fitness function is concave and allelic responses to the environment are not perfectly correlated, then per-capita growth rates of rare alleles are positive and genetic diversity is maintained in the sense of stochastic persistence i.e. allelic frequencies tend to stay away from zero almost-surely and in probability. Alternatively, if the log-fitness function is convex, then per-capita growth rates of rare alleles are negative and an allele asymptotically fixates with probability one. If the population’s low-density, per-capita growth rate is positive, then the population persists in the sense of stochastic persistence, else it goes asymptotically extinct with probability one. In contrast to per-capita growth rates of rare alleles, the population’s per-capita growth rate is a decreasing function of the concavity of the log-fitness function. Moreover, when the log-fitness function is concave, allelic diversity increases the population’s per-capita growth rate while decreasing the per-capita growth rate of rare alleles; when the log-fitness function is convex, environmental stochasticity decreases the per-capita growth rate of rare alleles, but increases the population’s per-capita growth rate. Collectively, these results (i) highlight how mechanisms promoting population persistence may be at odds with mechanisms promoting genetic diversity, and (ii) provide conditions under which population persistence relies on existing standing genetic variation.

Comprehensive phase diagram for logistic populations in fluctuating environment.

Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular deterministic models (such as logistic growth) supports a transcritical bifurcation point between an extinction phase and an active phase. Here we provide a comprehensive analysis of the phases of that system, taking into account both the endogenous demographic noise (random birth and death events) and the effect of environmental stochasticity that causes variations in birth and death rates. Three phases are identified: in the inactive phase the mean time to extinction T is independent of the carrying capacity N and scales logarithmically with the initial population size. In the power-law phase T∼N^{q}, and in the exponential phase T∼exp(αN). All three phases and the transitions between them are studied in detail. The breakdown of the continuum approximation is identified inside the power-law phase, and the accompanying changes in decline modes are analyzed. The applicability of the emerging picture to the analysis of ecological time series and to the management of conservation efforts is briefly discussed.

Environmental stochastic effects on phytoplankton–zooplankton dynamics

In this study, we consider the environmental stochastic effects on the phytoplankton–zooplankton dynamics. The model used in our investigation is the model on interactions between algae and Daphnia with the environmental stochastic constraint. The role of environmental random constraint of the oscillations dynamics on the phytoplankton–zooplankton interactions has been studied. We estimate mathematically and numerically the threshold value of the intensity for noise generating a transition from the coexistence to the extinction. Our study has shown that environmental stochastic noise can destroy the limit cycle attractor shown in previous work on the deterministic model, and thus drive the system toward extinction of populations. We consider only the situation where the quantity of copper concentration is sufficient for the survival of the populations of the ecosystem. Depending on the copper concentration and on which populations the environmental constraints are applied, the present study reveals that stochastic environmental constraints have positive and negative effects on the life of Daphnia and algae populations. The stochastic environmental constraint provides other necessary nutrients, and we observe the extinction of the populations with the increases in the noise intensity. Both populations extinct when $$\sigma _1\ge 20$$ . One finds that when the noise is applied to the Scenedesmus populations, the Daphnia populations extinct for $$\sigma _1\ge 10$$ , while only the Scenedesmus populations survive with the increase in time. When the environmental constraint noise is applied to both populations, the Daphnia populations survive until $$\sigma _1=\sigma _2\ge 20$$ , while after this, one observes the extinction of both populations.

Permanence and extinction of a stochastic hybrid model for tumor growth

A tumor growth model perturbed by both white noise and Markov switching is formulated and explored. The threshold between permanence and extinction is obtained. Some effects of environmental stochasticity on permanence and extinction of the model are revealed.

Global Warming Can Lead to Depletion of Oxygen by Disrupting Phytoplankton Photosynthesis: A Mathematical Modelling Approach

We consider the effect of global warming on the coupled plankton-oxygen dynamics in the ocean. The net oxygen production by phytoplankton is known to depend on the water temperature and hence can be disrupted by warming. We address this issue theoretically by considering a mathematical model of the plankton-oxygen system. The model is generic and can account for a variety of biological factors. We first show that sustainable oxygen production by phytoplankton is only possible if the net production rate is above a certain critical value. This result appears to be robust to the details of model parametrization. We then show that, once the effect of zooplankton is taken into account (which consume oxygen and feed on phytoplankton), the plankton-oxygen system can only be stable if the net oxygen production rate is within a certain intermediate range (i.e., not too low and not too high). Correspondingly, we conclude that a sufficiently large increase in the water temperature is likely to push the system out of the safe range, which may result in ocean anoxia and even a global oxygen depletion. We then generalize the model by taking into account the effect of environmental stochasticity and show that, paradoxically, the probability of oxygen depletion may decrease with an increase in the rate of global warming.

Spatial distribution and optimal harvesting of an age-structured population in a fluctuating environment

We analyze a spatial age-structured model with density regulation, age specific dispersal, stochasticity in vital rates and proportional harvesting. We include two age classes, juveniles and adults, where juveniles are subject to logistic density dependence. There are environmental stochastic effects with arbitrary spatial scales on all birth and death rates, and individuals of both age classes are subject to density independent dispersal with given rates and specified distributions of dispersal distances. We show how to simulate the joint density fields of the age classes and derive results for the spatial scales of all spatial autocovariance functions for densities. A general result is that the squared scale has an additive term equal to the squared scale of the environmental noise, corresponding to the Moran effect, as well as additive terms proportional to the dispersal rate and variance of dispersal distance for the age classes and approximately inversely proportional to the strength of density regulation. We show that the optimal harvesting strategy in the deterministic case is to harvest only juveniles when their relative value (e.g. financial) is large, and otherwise only adults. With increasing environmental stochasticity there is an interval of increasing length of values of juveniles relative to adults where both age classes should be harvested. Harvesting generally tends to increase all spatial scales of the autocovariances of densities.

Macroecology of seed banks: The role of biogeography, environmental stochasticity and sampling

AbstractAimThe study of seed banks has been mainly conducted at local scales, thereby hampering our general understanding of the assembly processes of these biodiversity reservoirs. Here, we aim to document worldwide macroecological patterns of seed bank diversity and of their similarity with aboveground vegetation. Our second aim is to investigate the likely drivers of these macroecological patterns and to lay the foundation of a metacommunity theory of seed banks.LocationWorldwide.Time period1989–2005.Major taxa studiedPlants.MethodsWe compiled a worldwide dataset of 130 seed banks located in grasslands. We assessed the likely drivers of seed bank diversity and similarity with aboveground vegetation, using structural equation modelling. We then developed a time‐averaged neutral model of coupled seed bank–vegetation (S‐V) dynamics that includes the effect of environmental stochasticity, and we compared its predictions with empirical findings.ResultsWe found evidence for two weak latitudinal gradients in seed bank diversity and S‐V similarity, with larger species richness and smaller similarity closer to the tropics. We then showed that seed bank richness and S‐V similarity are correlated with the following four distinct drivers: local environmental variability, plant regional diversity, seed bank density and sampling area. Finally, we showed that the predictions of the time‐averaged neutral model are remarkably in accord with empirical observations.Main conclusionsOur results lay the foundations of a metacommunity theory for seed banks. They challenge the standard view that seed banks are principally structured by environmental variability, by highlighting the additional key roles of dispersal and stochastic sampling on seed bank diversity patterns.

Molecular analysis of genetic diversity and population structure in Everniastrum cirrhatum (Fr.) Hale (Parmeliaceae) in India

Everniastrum cirrhatum is a medicinally important lichen used in Ayurvedic and Unani systems of medicine. In the present study, DAMD and ISSR methods were used to estimate the genetic variation and population structure of E. cirrhatum collected from different geographical regions of India. Four DAMD and ten ISSR primers detected 42 and 110 polymorphic bands and accounted for 95.65 and 94.24% polymorphisms, respectively. Cumulative band data generated for DAMD and ISSR markers resulted into 94.95% polymorphism across all the accessions of E. cirrhatum. The UPGMA dendrogram showed two major clusters. The clustering pattern in the UPGMA dendrogram revealed that the groupings are largely in congruence with the geographical distribution of the accessions. Clustering patterns in STRUCTURE revealed that geographical diversity is perfectly in congruence with the genetic diversity. The clustering pattern in STRUCTURE was also supported by PCoA. Mantel test for matrix correlation showed a weak but positive correlation between genetic and geographical distance. The hierarchical analysis of molecular variance revealed that maximum percentage of variation was found within a population (57%), followed by among regions (28%) and among populations (15%). The present study provides significant insight into the genetic variability and population structure of E. cirrhatum. Understanding population structure would provide baseline information for developing its sustainable management strategies. It would also be important to conserve populations of E. cirrhatum in different localities of the Himalayan regions to prevent population decline caused by anthropogenic and environmental stochastic effects.

Stochastic population growth in spatially heterogeneous environments: the density-dependent case

This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is spread throughout n patches whose population abundances are modeled as the solutions of a system of nonlinear stochastic differential equations living on [0,infty )^n. We prove that r, the stochastic growth rate of the total population in the absence of competition, determines the long-term behaviour of the population. The parameter r can be expressed as the Lyapunov exponent of an associated linearized system of stochastic differential equations. Detailed analysis shows that if r>0, the population abundances converge polynomially fast to a unique invariant probability measure on (0,infty )^n, while when r<0, the population abundances of the patches converge almost surely to 0 exponentially fast. This generalizes and extends the results of Evans et al. (J Math Biol 66(3):423–476, 2013) and proves one of their conjectures. Compared to recent developments, our model incorporates very general density-dependent growth rates and competition terms. Furthermore, we prove that persistence is robust to small, possibly density dependent, perturbations of the growth rates, dispersal matrix and covariance matrix of the environmental noise. We also show that the stochastic growth rate depends continuously on the coefficients. Our work allows the environmental noise driving our system to be degenerate. This is relevant from a biological point of view since, for example, the environments of the different patches can be perfectly correlated. We show how one can adapt the nondegenerate results to the degenerate setting. As an example we fully analyze the two-patch case, n=2, and show that the stochastic growth rate is a decreasing function of the dispersion rate. In particular, coupling two sink patches can never yield persistence, in contrast to the results from the non-degenerate setting treated by Evans et al. which show that sometimes coupling by dispersal can make the system persistent.

Stochastic competitive exclusion leads to a cascade of species extinctions

Community ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity and niche partitioning, are based on competitive exclusion. However, this classical paradigm in ecology relies on implications derived from simple, deterministic models. Here we show how the predictions of a symmetric, deterministic model about the way extinctions proceed can be utterly different from the results derived from the same model when ecological drift (demographic stochasticity) is explicitly considered. Using analytical approximations to the steady-state conditional probabilities for assemblages with two and three species, we demonstrate that stochastic competitive exclusion leads to a cascade of extinctions, whereas the symmetric, deterministic model predicts a multiple collapse of species. To test the robustness of our results, we have studied the effect of environmental stochasticity and relaxed the species symmetry assumption. Our conclusions highlight the crucial role of stochasticity when deriving reliable theoretical predictions for species community assembly.

The effect of environmental stochasticity on species richness in neutral communities

Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to environmental variations due to the storage effect. This paper provides a systematic and comprehensive discussion of these two contradicting tendencies, using the metacommunity version of the recently proposed time-average neutral model of biodiversity which incorporates environmental stochasticity and demographic noise and allows for extinction and speciation. We show that the incorporation of demographic noise into the model is essential to its applicability, yielding realistic behavior of the system when fitness variations are relatively weak. The dependence of species richness on the strength of environmental stochasticity changes sign when the correlation time of the environmental variations increases. This transition marks the point at which the storage effect no longer succeeds in stabilizing the community.