Stochastic Population Dynamics Model Research Articles

Small populations of Palaeolithic humans in Cyprus hunted endemic megafauna to extinction.

The hypothesized main drivers of megafauna extinctions in the late Quaternary have wavered between over-exploitation by humans and environmental change, with recent investigations demonstrating more nuanced synergies between these drivers depending on taxon, spatial scale, and region. However, most studies still rely on comparing archaeologically based chronologies of timing of initial human arrival into naïve ecosystems and palaeontologically inferred dates of megafauna extinctions. Conclusions arising from comparing chronologies also depend on the reliability of dated evidence, dating uncertainties, and correcting for the low probability of preservation (Signor-Lipps effect). While some models have been developed to test the susceptibility of megafauna to theoretical offtake rates, none has explicitly linked human energetic needs, prey choice, and hunting efficiency to examine the plausibility of human-driven extinctions. Using the island of Cyprus in the terminal Pleistocene as an ideal test case because of its late human settlement (~14.2-13.2 ka), small area (~11 000 km2), and low megafauna diversity (2 species), we developed stochastic models of megafauna population dynamics, with offtake dictated by human energetic requirements, prey choice, and hunting-efficiency functions to test whether the human population at the end of the Pleistocene could have caused the extinction of dwarf hippopotamus (Phanourios minor) and dwarf elephants (Palaeoloxodon cypriotes). Our models reveal not only that the estimated human population sizes (n = 3000-7000) in Late Pleistocene Cyprus could have easily driven both species to extinction within < 1000 years, the model predictions match the observed, Signor-Lipps-corrected chronological sequence of megafauna extinctions inferred from the palaeontological record (P. minor at ~12-11.1 ka, followed by P. cypriotes at ~10.3-9.1 ka).

A stochastic model of predator-prey population dynamics

We present results of an analysis for a randomized three-dimensional predator-prey model representing the dynamics of wolf-deer interactions.

Stochastic Modeling in Immunology Based On a Stage-Dependent Framework with Non-Markov Constraints for Individual Cell and Pathogen Dynamics

We present a systematic approach to modelling the responses of the immune system to virus infections. Two continuous-discrete stochastic models arising in mathematical immunology are developed and computationally implemented. The variables of the models are integer random variables that denote the quantity of individuals (cells and viral particles), and sets of unique types of individuals that take into account the current state and history of stay of individuals in some stages of their development. The distribution laws of the durations of the mentioned stages are different from exponential or geometric. A probabilistic description of a one-stage stochastic model of population dynamics is presented. A stochastic model of the development of HIV-1 infection in the lymph node in the initial period after infection of a healthy person is formulated. A computational algorithm based on the Monte Carlo method is given. Each of the stochastic models is complemented by a deterministic analogue in the form of integral and delay differential equations. The results of numerical simulation are presented.

Stability and control in a stochastic model of malaria population dynamics

This article proves a stability theorem for the disease-free equilibrium of a stochastic differential equations model of malaria disease dynamics. The theorem is formulated in terms of an invariant which is similar to the basic reproduction number of a related deterministic model. Compared to the deterministic model, stability of the disease-free equilibrium holds more generally for the stochastic model. The optimal control theory is applied to the stochastic model, revealing some important new insights. Theoretical results are illustrated by way of simulations.

An exploratory assessment of the Bering-Chukchi-Beaufort Seas stock of bowhead whales using a stochastic population dynamics model

The stochastic population dynamics model used by Aboriginal Whaling Management Procedure developers is revised to correct weaknesses related to uncertainty parameterisation and replacement yield estimation. Two variants of this model, along with the standard deterministic version, are used to assess the Bering-Chukchi-Beaufort Seas stock of bowhead whales. The variants differ with respect to the magnitude and complexity of the stochastic variation they introduce into natural mortality and birth/calf survival processes. An allowable catch statistic, E (Q0), is defined for appropriate use with stochastic model assessments. Using the same assessment methods, likelihood and priors as IWC (1999a), 5th percentiles of E (Q0) were found to be 117, 106 and 91 for the deterministic, simpler stochastic and extreme stochastic models, respectively. Bayes factor results show that there is no evidence suggesting that either stochastic model should be favoured over any simpler alternative, and the deterministic model yielded the best fit overall. The E (Q0) estimates confirm and strengthen past IWC Scientific Committee inference that under current bowhead subsistence hunting levels the stock should continue to increase towards stabilisation above its maximum sustainable yield level.

Establishing new populations in water-secure locations may benefit species persistence more than interventions in water-stressed locations

The effects of climate and land-use change, coupled with limited management resources, mean that managers are increasingly faced with decisions to invest in some locations at the expense of others. Given their potentially controversial nature, such decisions require predictions of likely outcomes under different management strategies and potential future climates. We develop an approach to prioritise management interventions across multiple locations in highly variable and uncertain environments, using a stochastic model of population dynamics structured to include the (dynamic) effects of environmental conditions on key vital rates. We demonstrate this approach with a case study on the endangered Australian freshwater fish, the Macquarie perch (Macquaria australasica), assessing the effectiveness of seven management interventions under five scenarios of deterministic climate change. All management interventions were predicted to improve Macquarie perch population outcomes (increased abundances, reduced risk of quasi-extinction), with the risk of declines lowest when management included augmented gene flow and enforcement of fishing regulations. The lowest levels of risk occurred in locations with stable environmental conditions, which suggests that reintroducing Macquarie perch to large, regulated rivers with suitable access to spawning habitat may be more beneficial than investment in small, unregulated streams where populations were unlikely to persist under any scenario. Population reintroductions provide opportunities to shift populations from water-stressed to water-secure locations where required (e.g. to preserve unique genetic diversity). This finding likely applies to many aquatic species, and highlights a potential need to supplement threat mitigation in water-stressed locations with efforts to establish new populations in water-secure locations.

A bifurcation threshold for contact-induced language change

One proposed mechanism of language change concerns the role played by second-language (L2) learners in situations of language contact. If sufficiently many L2 speakers are present in a speech community in relation to the number of first-language (L1) speakers, then those features which present a difficulty in L2 acquisition may be prone to disappearing from the language. This paper presents a mathematical account of such contact situations based on a stochastic model of learning and nonlinear population dynamics. The equilibria of a deterministic reduction of the model, describing a mixed population of L1 and L2 speakers, are fully characterized. Whether or not the language changes in response to the introduction of L2 learners turns out to depend on three factors: the overall proportion of L2 learners in the population, the strength of the difficulty speakers face in acquiring the language as an L2, and the language-internal utilities of the competing linguistic variants. These factors are related by a mathematical formula describing a phase transition from retention of the L2-difficult feature to its loss from both speaker populations. This supplies predictions that can be tested against empirical data. Here, the model is evaluated with the help of two case studies, morphological levelling in Afrikaans and the erosion of null subjects in Afro-Peruvian Spanish; the model is found to be broadly in agreement with the historical development in both cases.

Reservoir ecological operation by quantifying outflow disturbance to aquatic community dynamics

Reservoir operation causes spatiotemporal variations in outflow, which influence the dynamics of downstream aquatic communities. However, empirical evidence of community responses to hydrological alteration remains limited for dam-regulated rivers. This study focused on quantifying the streamflow disturbance to multi-population dynamics in downstream of the China’s Danjiangkou Reservoir. First, the stochastic population dynamics model (PDM) was used to simulate aquatic community dynamics. Then, the flow–ecology relationship was established to identify community response to reservoir outflow. Third, two novel ecological indicators, stable time (ST) and coefficient of variation at stable time (CVST), were proposed to evaluate the resilience and resistance of multi-population systems, respectively. Finally, the reservoir operating rule curves were optimized by considering tradeoffs between socioeconomic and ecological objectives. The coevolution processes of multi-population systems (fish, phytoplankton, zooplankton, zoobenthos, and macrophytes) were simulated by stochastic PDMs. The population densities of stable states showed continuous downward trends with increasing degree of hydrological alteration for multi-population systems, and aquatic community systems could be destroyed when alteration reached its acceptable maximum. The greater the degree of hydrological alteration, the longer the recovery time from an unstable to a stable state, and the weaker resistance for each population system. The resilience and resistance of downstream multi-population systems were enhanced by optimizing reservoir outflow. The optimization results illustrated that the performances of the multiple objectives of water supply, hydropower generation, and ST were improved by 2.37%, 2.40%, and 2.67%, respectively, whereas the performance of CVST was the same as the conventional operation. The flow–ecology relationship provided an approach to quantify the impacts of reservoir outflow on an aquatic community, which is helpful in guiding ecological flow strategies.

Fine-scale estimation of key life-history parameters of malaria vectors: implications for next-generation vector control technologies

BackgroundMosquito control has the potential to significantly reduce malaria burden on a region, but to influence public health policy must also show cost-effectiveness. Gaps in our knowledge of mosquito population dynamics mean that mathematical modelling of vector control interventions have typically made simplifying assumptions about key aspects of mosquito ecology. Often, these assumptions can distort the predicted efficacy of vector control, particularly next-generation tools such as gene drive, which are highly sensitive to local mosquito dynamics.MethodsWe developed a discrete-time stochastic mathematical model of mosquito population dynamics to explore the fine-scale behaviour of egg-laying and larval density dependence on parameter estimation. The model was fitted to longitudinal mosquito population count data using particle Markov chain Monte Carlo methods.ResultsBy modelling fine-scale behaviour of egg-laying under varying density dependence scenarios we refine our life history parameter estimates, and in particular we see how model assumptions affect population growth rate (Rm), a crucial determinate of vector control efficacy.ConclusionsSubsequent application of these new parameter estimates to gene drive models show how the understanding and implementation of fine-scale processes, when deriving parameter estimates, may have a profound influence on successful vector control. The consequences of this may be of crucial interest when devising future public health policy.Graphical abstract

Elucidating host-microbe interactions in vivo by studying population dynamics using neutral genetic tags.

Host-microbe interactions are highly dynamic in space and time, in particular in the case of infections. Pathogen population sizes, microbial phenotypes and the nature of the host responses often change dramatically over time. These features pose particular challenges when deciphering the underlying mechanisms of these interactions experimentally, as traditional microbiological and immunological methods mostly provide snapshots of population sizes or sparse time series. Recent approaches - combining experiments using neutral genetic tags with stochastic population dynamic models - allow more precise quantification of biologically relevant parameters that govern the interaction between microbe and host cell populations. This is accomplished by exploiting the patterns of change of tag composition in the microbe or host cell population under study. These models can be used to predict the effects of immunodeficiencies or therapies (e.g. antibiotic treatment) on populations and thereby generate hypotheses and refine experimental designs. In this review, we present tools to study population dynamics in vivo using genetic tags, explain examples for their implementation and briefly discuss future applications.

A Machine Learning Assisted Development of a Model for the Populations of Convective and Stratiform Clouds

AbstractTraditional parameterizations of the interaction between convection and the environment have relied on an assumption that the slowly varying large‐scale environment is in statistical equilibrium with a large number of small and short‐lived convective clouds. They fail to capture nonequilibrium transitions such as the diurnal cycle and the formation of mesoscale convective systems as well as observed precipitation statistics and extremes. Informed by analysis of radar observations, cloud‐permitting model simulation, theory, and machine learning, this work presents a new stochastic cloud population dynamics model for characterizing the interactions between convective and stratiform clouds, with the goal of informing the representation of these interactions in global climate models. Fifteen wet seasons of precipitating cloud observations by a C‐band radar at Darwin, Australia are fed into a machine learning algorithm to obtain transition functions that close a set of coupled equations relating large‐scale forcing, mass flux, the convective cell size distribution, and the stratiform area. Under realistic large‐scale forcing, the derived transition functions show that, on the one hand, interactions with stratiform clouds act to dampen the variability in the size and number of convective cells and therefore in the convective mass flux. On the other, for a given convective area fraction, a larger number of smaller cells is more favorable for the growth of stratiform area than a smaller number of larger cells. The combination of these two factors gives rise to solutions with a few convective cells embedded in a large stratiform area, reminiscent of mesoscale convective systems.

Persistence and extinction in a stochastic nonautonomous logistic model of population dynamics

Persistence and extinction in a stochastic nonautonomous logistic model of population dynamics

Crossing a fitness valley as a metastable transition in a stochastic population model

We consider a stochastic model of population dynamics where each individual is characterised by a trait in $\{0,1,\ldots,L\}$ and has a natural reproduction rate, a logistic death rate due to age or competition and a probability of mutation towards neighbouring traits at each reproduction event. We choose parameters such that the induced fitness landscape exhibits a valley: mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fitness. We focus on the limit of large population and rare mutations at several speeds. In particular, when the mutation rate is low enough, metastability occurs: the exit time of the valley is an exponentially distributed random variable.

Fine-scale modelling finds that breeding site fragmentation can reduce mosquito population persistence

Fine-scale geographic variation in the transmission intensity of mosquito-borne diseases is primarily caused by variation in the density of female adult mosquitoes. Therefore, an understanding of fine-scale mosquito population dynamics is critical to understanding spatial heterogeneity in disease transmission and persistence at those scales. However, mathematical models of dengue and malaria transmission, which consider the dynamics of mosquito larvae, generally do not account for the fragmented structure of larval breeding sites. Here, we develop a stochastic metapopulation model of mosquito population dynamics and explore the impact of accounting for breeding site fragmentation when modelling fine-scale mosquito population dynamics. We find that, when mosquito population densities are low, fragmentation can lead to a reduction in population size, with population persistence dependent on mosquito dispersal and features of the underlying landscape. We conclude that using non-spatial models to represent fine-scale mosquito population dynamics may substantially underestimate the stochastic volatility of those populations.

Stochastic Modeling of Compartmental Systems with Pipes

An approach to the construction of a stochastic model of population dynamics distributed over a compartmental system with pipes is proposed. Population dynamics is described in terms of a multidimensional random process of birth and death, supplemented by taking into account point distributions reflecting different types of particles. In this model, the belonging of a particle to a certain type is determined by the time of its transition between compartments. The duration of particle transitions through the pipes are not random, but are set as parameters of the environment in which the population develops. Graph theory is used for formalization and compact representation of the model. On the basis of the Monte Carlo method the algorithm of numerical simulation of population dynamics is constructed. The results of computational experiments for a system consisting of five compartments are presented.

Colonization and extinction rates estimated from temporal dynamics of ecological communities: The islandrpackage

AbstractThe temporal dynamics of ecological communities are inherently complex, as dispersal processes, interspecific biotic interactions and environmental fluctuations interact to shape species assemblages. We developed anrpackage,island—a community ecology tool to analyse temporal patterns and explore potential drivers of community dynamics.Therpackageislandis inspired by the simplicity of the Theory of Island Biogeography. Our package includes a suite of functions to easily confront models of increasing complexity to community data from the simplest stochastic model underlying Island Biogeography Theory to more elaborate models that include species responses to environmental variables and imperfect detectability, obtained at regular or irregular sampling times, using maximum‐likelihood andAIC‐based model selection.Models implemented inislandshould be regarded as simple approximations of true temporal community dynamics. In this sense, we call themeffective modelswhich we use to estimateeffective parameters. These models are simple, but dynamic, as opposed to purely statistical. We illustrate the concept of dynamiceffective modelsby using an immigration–birth–death stochastic model of population dynamics. We generated simulated community data to demonstrate the correspondence between the underlying true model parameters values and our effective parameter estimates.We present three examples showcasing the uses of our package: detectability estimation and model selection, influence of environmental covariates on community dynamics and estimation of co‐occurrence networks. Three detailed vignettes with a full set of examples accompany therPackageislandavailable onCRAN.

Landscape-level field data reveal broad-scale effects of a fatal, transmissible cancer on population ecology of the Tasmanian devil

In order to project and plan for the future of threatened species, conservationists require good quality estimates of basic population parameters, such as population sex ratios and breeding rates. These data can be difficult to obtain in many threatened species where pervasive threats perturb population dynamics. For Tasmanian devils, previous studies at several sites across Tasmania revealed demographic consequences of the fatal and transmissible devil facial tumour disease (DFTD). In the current analysis, we take advantage of broad-scale survey data across the state, since 2003, to examine the differences between DFTD-present and DFTD-absent populations at the landscape level. Consistent with expectations based on previous studies, we found that devils trapped in DFTD-present sites were significantly younger (based on tooth-wear age estimates) than those in DFTD-absent sites. Interestingly, we also found that females in DFTD-present sites were more likely to show evidence of breeding than females in DFTD-absent sites. This difference could not be attributed to differences in age or body condition. Devil populations are declining, so increased female breeding rate is unlikely to be successfully compensating for decreased lifespan as a result of DFTD at the population level. These data can be used to inform stochastic and evolutionary models of population dynamics for devils, and inform the assessment of conservation strategies for the species in the presence of disease.

An efficient moments-based inference method for within-host bacterial infection dynamics.

Over the last ten years, isogenic tagging (IT) has revolutionised the study of bacterial infection dynamics in laboratory animal models. However, quantitative analysis of IT data has been hindered by the piecemeal development of relevant statistical models. The most promising approach relies on stochastic Markovian models of bacterial population dynamics within and among organs. Here we present an efficient numerical method to fit such stochastic dynamic models to in vivo experimental IT data. A common approach to statistical inference with stochastic dynamic models relies on producing large numbers of simulations, but this remains a slow and inefficient method for all but simple problems, especially when tracking bacteria in multiple locations simultaneously. Instead, we derive and solve the systems of ordinary differential equations for the two lower-order moments of the stochastic variables (mean, variance and covariance). For any given model structure, and assuming linear dynamic rates, we demonstrate how the model parameters can be efficiently and accurately estimated by divergence minimisation. We then apply our method to an experimental dataset and compare the estimates and goodness-of-fit to those obtained by maximum likelihood estimation. While both sets of parameter estimates had overlapping confidence regions, the new method produced lower values for the division and death rates of bacteria: these improved the goodness-of-fit at the second time point at the expense of that of the first time point. This flexible framework can easily be applied to a range of experimental systems. Its computational efficiency paves the way for model comparison and optimal experimental design.

A stochastic analysis of the spatially extended May–Leonard model

Numerical studies of the May–Leonard model for cyclically competing species exhibit spontaneous spatial structures in the form of spirals. It is desirable to obtain a simple coarse-grained evolution equation describing spatio-temporal pattern formation in such spatially extended stochastic population dynamics models. Extending earlier work on the corresponding deterministic system, we derive the complex Ginzburg–Landau equation as the effective representation of the fully stochastic dynamics of this paradigmatic model for cyclic dominance near its Hopf bifurcation, and for small fluctuations in the three-species coexistence regime. The internal stochastic reaction noise is accounted for through the Doi–Peliti coherent-state path integral formalism, and subsequent mapping to three coupled non-linear Langevin equations. This analysis provides constraints on the model parameters that allow time scale separation and in consequence a further reduction to just two coarse-grained slow degrees of freedom.

Simulated bat populations erode when exposed to climate change projections for western North America.

Recent research has demonstrated that temperature and precipitation conditions correlate with successful reproduction in some insectivorous bat species that live in arid and semiarid regions, and that hot and dry conditions correlate with reduced lactation and reproductive output by females of some species. However, the potential long-term impacts of climate-induced reproductive declines on bat populations in western North America are not well understood. We combined results from long-term field monitoring and experiments in our study area with information on vital rates to develop stochastic age-structured population dynamics models and analyzed how simulated fringed myotis (Myotis thysanodes) populations changed under projected future climate conditions in our study area near Boulder, Colorado (Boulder Models) and throughout western North America (General Models). Each simulation consisted of an initial population of 2,000 females and an approximately stable age distribution at the beginning of the simulation. We allowed each population to be influenced by the mean annual temperature and annual precipitation for our study area and a generalized range-wide model projected through year 2086, for each of four carbon emission scenarios (representative concentration pathways RCP2.6, RCP4.5, RCP6.0, RCP8.5). Each population simulation was repeated 10,000 times. Of the 8 Boulder Model simulations, 1 increased (+29.10%), 3 stayed approximately stable (+2.45%, +0.05%, -0.03%), and 4 simulations decreased substantially (-44.10%, -44.70%, -44.95%, -78.85%). All General Model simulations for western North America decreased by >90% (-93.75%, -96.70%, -96.70%, -98.75%). These results suggest that a changing climate in western North America has the potential to quickly erode some forest bat populations including species of conservation concern, such as fringed myotis.