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We study the optimal sustainable harvesting of a population that lives in a random environment. The novelty of our setting is that we maximize the asymptotic harvesting yield, both in an expected value and almost sure sense, for a large class of harvesting strategies and unstructured population models. We prove under relatively weak assumptions that there exists a unique optimal harvesting strategy characterized by an optimal threshold below which the population is maintained at all times by utilizing a local time push-type policy. We also discuss, through Abelian limits, how our results are related to the optimal harvesting strategies when one maximizes the expected cumulative present value of the harvesting yield and establish a simple connection and ordering between the values and optimal boundaries. Finally, we explicitly characterize the optimal harvesting strategies in two different cases, one of which is the celebrated stochastic Verhulst Pearl logistic model of population growth.

The application of genetic relationships among individuals, characterized by a genetic relationship matrix (GRM), has far-reaching effects in human genetics. However, the current standard to calculate the GRM generally does not take advantage of linkage information and does not reflect the underlying genealogical history of the study sample. Here, we propose a coalescent-informed framework to infer the expected relatedness between pairs of individuals given an ancestral recombination graph (ARG) of the sample. Through extensive simulations we show that the eGRM is an unbiased estimate of latent pairwise genome-wide relatedness and is robust when computed using genealogies inferred from incomplete genetic data. As a result, the eGRM better captures the structure of a population than the canonical GRM, even when using the same genetic information. More importantly, our framework allows a principled approach to estimate the eGRM at different time depths of the ARG, thereby revealing the time-varying nature of population structure in a sample. When applied to genotyping data from a population sample from Northern and Eastern Finland, we find that clustering analysis using the eGRM reveals population structure driven by subpopulations that would not be apparent using the canonical GRM, and that temporally the population model is consistent with recent divergence and expansion. Taken together, our proposed eGRM provides a robust tree-centric estimate of relatedness with wide application to genetic studies.

Population and community ecology traditionally has a very strong theoretical foundation with well-known dynamical models, such as the logistic and its variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are being confronted with data via fitting to empirical time series for purposes of projections or for estimating model parameters of interest. However, using statistical models to fit theoretical models to data is far from trivial, especially for time series data where subsequent measurements are not independent. This raises the question of whether statistical inferences using pure observation error models, such as simple (non-)linear regressions, are biased, and whether more elaborate process error models or state-space models have to be used to address this complexity.In order to help empiricists, especially researchers working with experimental laboratory populations in micro- and mesocosms, make informed decisions about the statistical formalism to use, we here compare different error structures one could use when fitting classical deterministic ODE models to empirical data. We consider a large range of biological scenarios and theoretical models, from single species to community dynamics and trophic interactions. In order to compare the performance of different error structure models, we use both realistically simulated data and empirical data from microcosms in a Bayesian framework.We find that many model parameters can be estimated precisely with an appropriate choice of error structure using pure observation error or state-space models, if observation errors are not too high. However, Allee effect models are typically hard to identify and state-space models should be preferred when model complexity increases.Our work shows that, at least in the context of low environmental stochasticity and high quality observations, deterministic models can be used to describe stochastic population dynamics that include process variability and observation error. We discuss when more complex state-space model formulations may be required for obtaining accurate parameter estimates. Finally, we provide a comprehensive tutorial for fitting these models in R.Open researchCode for stochastic individual-based simulations is available fromhttps://doi.org/10.5281/zenodo.5500442. A tutorial for fitting ODE models to time series data in R is presented in the Supplementary Information and is also available onlinehttps://github.com/benjamin-rosenbaum/fittingdeterministic population models. Data (Fronhofer et al., 2020) will be provided via GitHub and Zenodo.

We develop a food web population dynamical based on an experimental pest biocontrol setup consisting of thrips and aphids (pests) being consumed by two agentsMacrolophus pygmaeusandOrius laevigatus, and withO. laevigatusbeing an intraguild predator ofM. pygmaeus. By means of numerical simulations, we show that pest biocontrol disruption can be avoided depending on initial population densities of pests and agents, despite the intraguild predation (IGP) ofO. laevigatusuponM. pygmaeus. This possible avoidance of pest biocontrol disruption is in accordance with the referred experimental setup and moreover, the proposed model corroborates the importance of initial densities of pests and agents in the determination of the failure or success of pest biocontrol found in this and other biocontrol experimental setups.

With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a strong influence on epidemic propagation, were always neglected in previous studies. In this paper, we mainly propose two models from the individual and population perspectives. In the first individual model, we introduce the individual protection degree that effectively suppresses the epidemic level as a stochastic variable to the SIRS model. In the alternative population model, an open Markov queueing network is constructed to investigate the individual number of each epidemic state, and we present an evolving population network via the migration of people. Besides, stochastic methods are applied to analyze both models. In various simulations, the infected probability, the number of individuals in each state and its limited distribution are demonstrated.

Human actions led to the worldwide decline of marine mammal populations in the 18th–19th centuries. Global adoption of protective legislation during the 20th century has recently allowed many marine mammal populations to recover. This positive trend is particularly true of pinnipeds (e.g., seals and sea lions), whose recovering populations are increasingly in conflict with fisheries. Fisheries organisations have called for managed culls of sea lion populations to reduce competition for target fish species as well as damage to catch and fishing gear through operational interactions. However, despite widespread perceptions that sea lion populations are generally increasing, to-date, culls have often been considered or implemented without quantitative evidence of their impacts on seal lion population viability. This knowledge gap is particularly concerning given the expected increase in extreme climate conditions, such as extreme El Niño events, which together with culls could push sea lion populations in some parts of the world into the extinction vortex. Here, I develop stochastic matrix population models of the South American sea lion (Otaria flavescens) parameterised through a combination of species-specific field data and phylogenetic imputation using data from related species in the COMADRE animal matrix database. Using these models, I project the impact of (1) three cull scenarios with different intensity and temporal frequency targeting adult females, (2) extreme El Niño events whose frequency is modelled using a Markovian transition matrix, and (3) the interaction of culls and extreme climate events on population dynamics. I focus on the Chilean population of O. flavescens, where recent increases in sea lion numbers have triggered widespread conflict with small-scale fisheries, and where sea lion populations will increasingly be affected by extreme El Niño conditions. I find that sea lion populations decline below minimum viable population sizes within 16–28 years under all scenarios involving culls and extreme climate events. This research explicitly incorporates parameter uncertainty into population projections—in so doing, it illustrates the need for future research to collect stage-specific, annual population data to reduce uncertainty regarding marine mammal vital rates.

We consider incomplete observations of stochastic processes governing the spread of infectious diseases through finite populations by way of contact. We propose a flexible semiparametric modelling framework with at least three advantages. First, it enables researchers to study the structure of a population contact network and its impact on the spread of infectious diseases. Second, it can accommodate short- and long-tailed degree distributions and detect potential superspreaders, who represent an important public health concern. Third, it addresses the important issue of incomplete data. Starting from first principles, we show when the incomplete-data generating process is ignorable for the purpose of Bayesian inference for the parameters of the population model. We demonstrate the semiparametric modelling framework by simulations and an application to the partially observed MERS epidemic in South Korea in 2015. We conclude with an extended discussion of open questions and directions for future research.

1. The social environment in which individuals live affects their fitness and in turn population dynamics as a whole. Birds with facultative cooperative breeding can live in social groups with dominants, subordinate helpers that assist with the breeding of others, and subordinate non-helpers. Helping behaviour benefits dominants through increased reproductive rates and reduced extrinsic mortality, such that cooperative breeding might have evolved in response to unpredictable, harsh conditions affecting reproduction and/or survival of the dominants. Additionally, there may be different costs and benefits to both helpers and non-helpers, depending on the time-scale. For example, early-life costs might be compensated by later-life benefits. These differential effects are rarely analysed in the same study. 2. We examined whether helping behaviour affects population persistence in a stochastic environment and whether there are direct fitness consequences of different life-history tactics adopted by helpers and non-helpers. 3. We parameterised a matrix population model describing the population dynamics of female Seychelles warblers Acrocephalus sechellensis, birds that display facultative cooperative breeding. The stochastic density-dependent model is defined by a (st)age structure that includes life-history differences between helpers and non-helpers and thus can estimate the demographic mechanisms of direct benefits of helping behaviour. 4. We found that population dynamics are strongly influenced by stochastic variation in the reproductive rates of the dominants, that helping behaviour promotes population persistence and that there are only early-life differences in the direct fitness of helpers and non-helpers. 5. Through a matrix population model, we captured multiple demographic rates simultaneously and analysed their relative importance in determining population dynamics of these cooperative breeders. Disentangling early-life versus lifetime effects of individual tactics sheds new light on the costs and benefits of helping behaviour. For example, the finding that helpers and non-helpers have similar lifetime reproductive outputs and that differences in reproductive values between the two life-history tactics arise only in early life suggests that overall, helpers and non-helpers have a similar balance of costs and benefits when analysing direct benefits. We recommend analysing the consequence of different life-history tactics, during both early life and over the lifetime, as analyses of these different time frames may produce conflicting results.

The familial structure of a population and the relatedness of its individuals are determined by its demography. There is, however, no general method to infer kinship directly from the life-cycle of a structured population. Yet this question is central to fields such as ecology, evolution and conservation, especially in contexts where there is a strong interdependence between familial structure and population dynamics. Here, we give a general formula to compute, from any matrix population model, the expected number of arbitrary kin (sisters, nieces, cousins, etc) of a focal individual ego, structured by the class of ego and of its kin. Central to our approach are classic but little-used tools known as genealogical matrices. Our method can be used to obtain both individual-based and population-wide metrics of kinship, as we illustrate. It also makes it possible to analyze the sensitivity of the kinship structure to the traits implemented in the model.

Epidemic modeling has been a key tool for understanding the impact of global viral outbreaks for over two decades. Recent developments of the COVID-19 pandemic have accelerated research using compartmental models, like SI, SIR, SEIR, with their appropriate modifications. However, there is a large body of recent research consolidated on homogeneous population mixing models, which are known to offer reduced tractability, and render conclusions hard to quantify. As such, based on our recent work, introducing the heterogeneous geo-spatial mobility population model (GPM), we adapt a modified SIR-V (susceptible-infected-recovered-vaccinated) epidemic model which embodies the idea of patient relapse from R back to S, vaccination of R and S patients (reducing their infectiousness), thus altering the infectiousness of V patients (from λn to λr). Simulation results spanning over a period of t = 2000 days (6 years, the period « 2020-2025) compare the impact of an epidemic outbreak with variable vaccination strategies, starting after 1 year (as is the case of COVID-19). The infected proportion in the remaining 5-year period is analyzed using vaccination rates from rv = 0 (no vaccination) to rv = 1. While rv < 0.4 is less effective during the earlier stages, all strategies with rv > 0.4 show a similar downward convergence reducing the number of infected by more than half, compared to no vaccination. Given the complexity of epidemic processes, we conclude that higher vaccination rates yield similar results, but a minimal rv = 0.4 (40% of population over five years) should be targeted.

Population genetic studies in non-model systems increasingly use next-generation sequencing to obtain more loci, but such methods also generate more missing data that may affect downstream analyses. Here we focus on the principal component analysis (PCA) which has been widely used to explore and visualize population structure with mean-imputed missing data. We simulated data of different population models with various total missingness (1%, 10%, 20%) introduced either randomly or biased among individuals or populations. We found that individuals biased with missing data would be dragged away from their real population clusters to the origin of PCA plots, making them indistinguishable from true admixed individuals and potentially leading to misinterpreted population structure. We also generated empirical data of the big brown bat (Eptesicus fuscus) using restriction site-associated DNA sequencing (RADseq). We filtered three data sets with 19.12%, 9.87%, and 1.35% total missingness, all showing nonrandom missing data with biased individuals dragged towards the PCA origin, consistent with results from simulations. We highlight the importance of considering missing data effects on PCA in non-model systems where nonrandom missing data are common due to varying sample quality. To help detect missing data effects, we suggest to (1) plot PCA with a colour gradient showing per sample missingness, (2) interpret samples close to the PCA origin with extra caution, (3) explore filtering parameters with and without the missingness-biased samples, and (4) use complementary analyses (e.g., model-based methods) to cross-validate PCA results and help interpret population structure.

In survey planning, sometimes, there arises situation to use cluster sampling because of nature of spatial relationship between elements of population or physical feature of land over which elements are dispersed or unavailability of reliable list of elements. At the same time, there requires technique and strategy for ensuring precision of the sample in representing the parent population. Although several theoretical cum practical works have been done in cluster sampling, stratified sampling and stratified cluster sampling, so far, the problem of stratified cluster sampling for a study variable based on an auxiliary variable, which is required in practice, has never been approached. For the first time, this paper deals with the problem of optimum stratification of population of clusters in cluster sampling with clusters of equal size of a characteristic y under study based on highly correlated concomitant variable x for allocation proportional to stratum cluster totals under a super population model. Equations giving optimum strata boundaries (OSB) for dividing population, in which sampling unit of the population is a cluster, are obtained by minimising sampling variance of the estimator of population mean. As the equations are implicit in nature, a few methods of finding approximately optimum strata boundaries (AOSB) are deduced from the equations giving OSB. In deriving the equations, mathematical tools of calculus and algebra are used in addition to statistical methods of finding conditional expectation of variance. All the proposed methods of stratification are empirically examined by illustrating in live data, population of villages in Lunglei and Serchhip districts of Mizoram State, India, and found to perform efficiently in stratifying the population. The proposed methods may provide practically feasible solution in planning socio-economic survey.

The concept of source-sink dynamics as a potentially important component of metapopulation dynamics was introduced in the 1980s. The objective of the present review was to review the considerable body of work that has been developed, to consider its theoretical implications as well as to understand how source-sink dynamics may manifest under field conditions in the specific case of nontarget arthropods in the agricultural environment. Our review concludes that metapopulation dynamics based on field observations are often far more complex than existing theoretical source-sink models would indicate, because they are dependent on numerous population processes and influencing factors. The difficulty in identifying and measuring these factors likely explains why empirical studies assessing source-sink dynamics are scarce. Furthermore, we highlight the importance of considering the spatial and temporal heterogeneity of agricultural landscapes when assessing the population dynamics of nontarget arthropods in the context of the risk from the use of plant protection products. A need is identified to further develop and thoroughly validate predictive population models, which can incorporate all factors relevant to a specific system. Once reliable predictive models for a number of representative nontarget arthropod species are available, they could provide a meaningful tool for refined risk evaluations (higher tier level risk assessment), addressing specific concerns identified at the initial evaluation stages (lower tier level risk assessment). Environ Toxicol Chem 2021;40:2667-2679. © 2021 ERM, FMC, Syngenta, Bayer AG, BASF SE, Corteva agriscience. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

Coalescent methods are proven and powerful tools for population genetics, phylogenetics, epidemiology, and other fields. A promising avenue for the analysis of large genomic alignments, which are increasingly common, are coalescent hidden Markov model (coalHMM) methods, but these methods have lacked general usability and flexibility. We introduce a novel method for automatically learning a coalHMM and inferring the posterior distributions of evolutionary parameters using black-box variational inference, with the transition rates between local genealogies derived empirically by simulation. This derivation enables our method to work directly with three or four taxa and through a divide-and-conquer approach with more taxa. Using a simulated data set resembling a human-chimp-gorilla scenario, we show that our method has comparable or better accuracy to previous coalHMM methods. Both species divergence times and population sizes were accurately inferred. The method also infers local genealogies and we report on their accuracy. Furthermore, we illustrate how to scale the method to larger data sets through a divide-and-conquer approach. This accuracy means our method is useful now, and by deriving transition rates by simulation it is flexible enough to enable future implementations of all kinds of population models.

Mechanistic, individual-based simulation models have been used for >25 years to overcome well-known limitations of “habitat suitability” models. InSTREAM 7 is the latest of our individual-based models for predicting the effects of flow and temperature regimes on stream salmonid populations. Unlike PHABSIM (or other methods based on habitat “quality,” e.g., as net rate of energy intake), inSTREAM mechanistically represents specific effects of flow and temperature on all life stages, and how those effects combine into testable predictions of population measures such as abundance, relative abundance of multiple trout species, and persistence. InSTREAM 7 is the first version to also represent the daily light cycle (dawn, day, dusk, and night) and how feeding, predation risk, and individual behavior vary among light phases. An example assessment illustrates the importance of inSTREAM's multiple mechanisms: predicted trout population response to flow and temperature regimes depended on the effects of sub-lethal temperatures on feeding behavior and effects of temperature on egg survival and development, as well as how depth and velocity affected growth and predation risk. While its input data requirements are comparable to PHABSIM's, inSTREAM provides a more comprehensive framework for thinking about and predicting specific, well-known effects of flow and temperature. It has also proven useful for designing and evaluating restoration projects and for prioritizing alternative management actions. InSTREAM 7 is free, open-source, completely updated with recent literature, and implemented in the popular NetLogo software platform that makes customization easy.

Processes that change with density are inherent in all populations, yet quantifying density dependence with empirical data remains a challenge. This is especially true for animals recruiting in patchy landscapes because heterogeneity in habitat quality in combination with habitat choice can obscure patterns expected from density dependence. Mosquitoes (Diptera: Culicidae) typically experience strong density dependence when larvae compete for food, however, effects vary across species and contexts. If populations experience intense intraspecific density-dependent mortality then overcompensation can occur, where the number of survivors declines at high densities producing complex endogenous dynamics. To seek generalizations about density dependence in a widespread species of Arctic mosquito, Aedes nigripes, we combined a laboratory experiment, field observations, and modeling approaches. We evaluated alternative formulations of discrete population models and compared best-performing models from our lab study to larval densities from ponds in western Greenland. Survivorship curves from the lab were the best fit by a Hassell model with compensating density dependence (equivalent to a Beverton-Holt model) where peak recruitment ranged from 8 to 80 mosquitoes per liter depending on resource supply. In contrast, our field data did not show a signal of strong density dependence, suggesting that other processes such as predation may lower realized densities in nature, and that expected patterns may be obscured because larval abundance covaries with resources (cryptic density dependence). Our study emphasizes the importance of covariation between the environment, habitat choice, and density dependence in understanding population dynamics across landscapes, and demonstrates the value of pairing lab and field studies.

The Southern Ocean has been disproportionately affected by climate change and is therefore an ideal place to study the influence of changing environmental conditions on ecosystems. Changes in the demography of predator populations are indicators of broader shifts in food web structure, but long‐term data are required to study these effects. Southern elephant seals (Mirounga leonina) from Macquarie Island have consistently decreased in population size while all other major populations across the Southern Ocean have recently stabilized or are increasing. Two long‐term mark‐recapture studies (1956–1967 and 1993–2009) have monitored this population, which provides an opportunity to investigate demographic performance over a range of climatic conditions. Using a 9‐state matrix population model, we estimated climate influences on female survival by incorporating two major climatic indices into our model: The Southern Annular Mode (SAM) and the Southern Oscillation Index (SOI). Our best model included a 1 year lagged effect of SAM and an unlagged SOI as covariates. A positive relationship with SAM1 (lagged) related the previous year's SAM with juvenile survival, potentially due to changes in local prey availability surrounding Macquarie Island. The unlagged SOI had a negative effect on both juvenile and adult seals, indicating that sea ice dynamics and access to foraging grounds on the East Antarctic continental shelf could explain the different contributions of ENSO events on the survival of females in this population., This research investigated the influence of large‐scale climate modes (SAM and SOI) on female southern elephant seal survival (φ) by creating demographic models from historic capture‐mark‐recapture data. Map of the Southern Ocean from Tasmania (top) to East Antarctica and the Ross Sea (bottom) with Macquarie Island location marked by a small circle. Surrounding Antarctica, the Polar Front (blue line), 60th parallel south, (gray circle) and winter sea ice extent (white) are overlaid. Top right: Vegetation map of Macquarie Island (adapted from the Australian Antarctic Data Centre map no. 13106) and stylized illustration of a female southern elephant seal, Mirounga leonina (artwork by: Sophia Volzke).

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α = 1.6455.

In this work, an ecological population model with the Allee effect is studied, and the dispersal rate in a one-dimensional patch is estimated. The population is observed to grow in accordance with the logistic-type map with the Allee effect, and the dynamics of the population growth is observed to be controlled by the growth rate and the threshold of the Allee effect. The spread of the species in a one-dimensional patch structure can be described by using the discrete diffusion equation, and the time evolution is continuous. In discrete space and continuous-time dynamics, the expansion velocity of the population is observed to depend strongly on the Allee threshold and the dispersal rate. Without the Allee effect, the invasion velocity increases as a function of the dispersal rate whereas, with the Allee effect, the invasion velocity depends on the dispersal rate, Allee threshold, and growth rate. Three regions are observed in the plane of the dispersal rate and growth rate: namely, the pinning state, the invading state, and the absorbing state.

While ecologists know that models require assumptions, the consequences of their violation become vague as model complexity increases. Integrated population models (IPMs) combine several datasets to inform a population model and to estimate survival and reproduction parameters jointly with higher precision than is possible using independent models. However, accuracy actually depends on an adequate fit of the model to datasets. We first investigated bias of parameters obtained from integrated population models when specific assumptions are violated. For instance, a model may assume that all females reproduce although there are non-breeding females in the population. Our second goal was to identify which diagnostic tests are sensitive to detect violations of the assumptions of IPMs. We simulated data mimicking a short- and a long-lived species under five scenarios in which a specific assumption is violated. For each simulated scenario, we fitted an IPM that violates the assumption (simple IPM) and an IPM that does not violate each specific assumption. We estimated bias and uncertainty of parameters and performed seven diagnostic tests to assess the fit of the models to the data. Our results show that the simple IPM was quite robust to violation of many assumptions and only resulted in small bias of the parameter estimates. Yet, the applied diagnostic tests were not sensitive to detect such small bias. The violation of some assumptions such as the absence of immigrants resulted in larger bias to which diagnostic tests were more sensitive. The parameters informed by the least amount of data were the most biased in all scenarios. We provide guidelines to identify misspecified models and to diagnose the assumption being violated. Simple models should often be sufficient to describe simple population dynamics, and when data are abundant, complex models accounting for specific processes will be able to shed light on specific biological questions. &nbsp

This study performs approbation of trend CMSY model on the example of Black sea sprat fishing unit, localized in Russian waters. Data sources has been reduced to the level of data limited modeling for indicator and trend models approach. CMSY population model results were compared with previously performed estimations by more powerful cohort model - XSA. CMSY results shows no significant deviations from the XSA results. Forecast scenarios and conclusions based on CMSY model fitting leads to the same statements with previously published results by XSA. CMSY model shows next results: stock biomass in 2019 B2019 = 63,9 ths. t, fishing mortality – F2019 = 0,29. Stock biomass in 2019 was significant below the target reference point BMSY = 105 ths. t and higher then limit reference point Blim = 52,7 ths. t. Some uncertain overexploitation in 2019 was underlined, F2019/FMSY = 1,12. Investigation of forecast scenarios with different total allowed catch levels indicates that there are no features for increasing the catch capacity in short-term projection. CMSY model fitting have passed the necessary stability tests and confirm previously founded results. In summary of this study, we can recommend to use CMSY model for stock assessment procedure in terms of data-limited information background.

Background Available evidence suggests that cognitive impairment (CI), which leads to deficits in episodic memory, executive functions, visual attention, and language, is associated with difficulties in the capacity to perform activities of daily living. Hence any forecast of the future prevalence of functional disability should account for the likely impact of cognitive impairment on the onset of functional disability. Thus, this research aims to address this gap in literature by projecting the number of older adults in China with functional disability and cognitive impairment while accounting for the impact of cognitive impairment on the onset of functional disability. Methods We developed and validated a dynamic multi-state population model which simulates the population of China and tracks the transition of Chinese older adults (65 years and older) from 2010 to 2060, to and from six health states—(i) active older adults without cognitive impairment, (ii) active older adults with cognitive impairment, (iii) older adults with 1 to 2 ADL limitations, (iv) older adults with cognitive impairment and 1 to 2 ADL limitations, (v) older adults with 3 or more ADL limitations, and (vi) older adults with cognitive impairment and 3 or more ADL limitations. Results From 2015 to 2060, the number of older adults 65 years and older in China is projected to increase, of which the number with impairment (herein referred to as individuals with cognitive impairment and/or activity of daily living limitations) is projected to increase more than fourfold from 17·9 million (17·8–18·0) million in 2015 to 96·2 (95·3–97·1) million by 2060. Among the older adults with impairment, those with ADL limitations only is projected to increase from 3·7 million (3·6–3·7 million) in 2015 to 23·9 million (23·4–24·6 million) by 2060, with an estimated annual increase of 12·2% (12·1–12·3); while that for cognitive impairment only is estimated to increase from 11·4 million (11·3–11·5 million) in 2015 to 47·8 million (47·5–48·2 million) by 2060—this representing an annual growth of 7·07% (7·05–7·09). Conclusion Our findings suggest there will be an increase in demand for intermediate and long-term care services among the older adults with functional disability and cognitive impairment.

The dynamical behaviors of a stochastic heroin population model with standard incidence rates between distinct patches are investigated in this paper. We firstly derive the fitness of a global positive solution. Then, under some moderate conditions, we show that the heroin population model always admits a stationary Markov process in the long run. More precisely, the coexistence of the drug users and the susceptible is studied by constructing multiple proper functions when the intensities of the white noises are under control, and the spectral radius of the irreducible matrix is greater than one ( R 0 > 1 ). For the elimination of the drug users, if the intensities of the white noises are large, then the elimination of drug users in a heroin population would exponentially decrease with probability one. Especially, when the spectral radius of the irreducible matrix is less than one ( R 0 1 ), the elimination of drug users who are not in treatment also follows the exponential decline with probability one. As a consequence, two examples and their corresponding numerical simulations are demonstrated to present the validity and feasibility of the theoretical results.

A considerable amount of analytical work has been done in recent years to understand extinction in finite discrete population systems in the presence of demographic noise. This has been made possible by advances in employing the WKB method for solving a wide variety of stochastic single population systems. Previous works have focussed on extinction in logistic/Verhulst-type models with a single stable fixed point, Allee-type models which has an additional unstable nonzero fixed point and switching behaviour of bistable finite population systems. However, the mean extinction time in bistable systems with an absorbing state hasn’t received much focus in these studies. In this work, we study the mean extinction time (MTE) in a phenomenological single population model exhibiting bistability using the WKB method. The quasi-stationary distribution (QSD) is derived in the limit of a large parameter, N, of the model, and by matching the QSD in different regimes of stability, an analytical expression for the mean extinction time has been derived. The MTE is exponentially large in N but shows a significant reduction in the extinction time due to the presence of bistable fixed points as compared to models that have only single stable states such as the Verhulst model. It is demonstrated that the analytical results compare well with that derived from direct numerical calculations.

In this paper, we study a three-stage tick population model with three development delays. Using the total delay τ as the bifurcation parameter, we conduct local and global Hopf bifurcation analysis. Especially, we examine the onset and termination of Hopf bifurcations of periodic solutions from the unique positive equilibrium. We locate all of the stability switches for the equilibrium and demonstrate that the global Hopf bifurcation branches are bounded. This result implies the system undergoes oscillatory behavior only with bounded delays. The key step in the proof is the exclusion of 2τ-periodic solutions due to the negative Lozinskiĭ measure of the corresponding compound matrix. Numerical simulations are provided to show the complicated patterns of the tick population when the development delays are altered by the temperature and other environmental factors.

This paper is concerned with the existence and global stability of forced waves for reaction diffusion equations with density-dependent diffusion in a shifting environment, which arises from population dynamics. Our argument is based on the introduction of suitable families of upper and lower solutions and on a comparison result through Holmgren's method. Our analysis yields, for any wave speed c > 0 , the density-dependent dispersal population models with shifting habitats admit forced traveling waves. To overcome the difficulties caused by peculiar structure of forced waves and degeneracy, we develop a novel weighted estimate technique to prove the global and exponential stability of these waves. Different from the spatial homogenous case Huang et al. 2018 [24] , the weight function is introduced near the positive equilibrium r ( + ∞ ) instead of the zero equilibrium.

How neuronal variability impacts neuronal codes is a central question in systems neuroscience, often with complex and model dependent answers. Most population models are parametric, with a tacitly assumed structure of neuronal tuning and population-wide variability. While these models provide key insights, they purposely divorce any mechanistic relationship between trial average and trial variable neuronal activity. By contrast, circuit based models produce activity with response statistics that are reflection of the underlying circuit structure, and thus any relations between trial averaged and trial variable activity are emergent rather than assumed. In this work, we study information transfer in networks of spatially ordered spiking neuron models with strong excitatory and inhibitory interactions, capable of producing rich population-wide neuronal variability. Motivated by work in the visual system we embed a columnar stimulus orientation map in the network and measure the population estimation of an orientated input. We show that the spatial structure of feedforward and recurrent connectivity are critical determinants for population code performance. In particular, when network wiring supports stable firing rate activity then with a sufficiently large number of decoded neurons all available stimulus information is transmitted. However, if the inhibitory projections place network activity in a pattern forming regime then the population-wide dynamics compromise information flow. In total, network connectivity determines both the stimulus tuning as well as internally generated population-wide fluctuations and thereby dictates population code performance in complicated ways where modeling efforts provide essential understanding.

This research was aimed to describe the application of differential equations of the population growth model in the City of Mataram, which is an exponential and logistic models for estimating the population of the City of Mataram in 2024. The research method used in this research is descriptive research with a qualitative approach carried out by observation and analyze the subject. The subject of this research was data on the population of the City of Mataram from 2006 to 2019. Meanwhile, to determine the accuracy and validity of the research data, the triangulation of sources was used. The data used comes from the Dispendukcapil and BPS the City of Mataram. The research result, it shows that the exponential model has an accuracy rate of 99,6%, which is very accurate, while for estimating with a logistic model each criterion is very accurate but the confidence level is 97,9%. Estimation results also show that population growth in the city of Mataram in the future will slowdown in its growth every 2 years, with an average decrease of 0.5%.

The Yangtze finless porpoise (Neophocaena asiaeorientalis asiaeorientalis), a critically endangered species, is the only cetacean species in the Yangtze River following the functional extinction of baiji (Lipotes vexillifer). To inform conservation actions, two important questions need to be addressed: what is the threshold value of survival rate, and what is the threshold value of population size? We calculate the instantaneous rate of population increase ( r¯ ) for the Yangtze finless porpoise for various combinations of the calf and the non-calf survival rates. We also test the probability of extinction for different minimum carrying capacities for 100 and 500 years using a stable population model. The threshold value of the non-calf survival rate is never lower than 0.869, but current estimates from field data have been far below this threshold. Our model based on extinction probability and carrying capacity suggests that the threshold for the population size to persist 100 years required 113 animals, and 472 animals are required to persist 500 years. Therefore, we recommend establishing an ex situ reserve network to guarantee the minimum 100-year carrying capacity. To ensure the long-term population viability, we suggest establishing two in situ reserve zones in two lakes and their surrounding reserves to meet a minimum 500-year carrying capacity. In addition, measures to avoid further habitat fragmentation should be priority.

A key goal of ecological research is to obtain reliable estimates of population demographic rates, abundance and trends. However, a common challenge when studying wildlife populations is imperfect detection or breeding observation, which results in unknown survival status and reproductive output for some individuals. It is important to account for undetected individuals in population models because they contribute to population abundance and dynamics, and can have implications for population management. Promisingly, recent methodological advances provide us with the tools to integrate data from multiple independent sources to gain insights into the unobserved component of populations. We use data from five reintroduced populations of a threatened New Zealand bird, the hihi (Notiomystis cincta), to develop an integrated population modelling framework that allows missing values for survival status, sex and reproductive output to be modelled. Our approach combines parallel matrices of encounter and reproduction histories from marked individuals, as well as counts of unmarked recruits detected at the start of each breeding season. Integrating these multiple data types enabled us to simultaneously model survival and reproduction of detected individuals, undetected individuals and unknown (never detected) individuals to derive parameter estimates and projections based on all available data, thereby improving our understanding of population dynamics and enabling full propagation of uncertainty. The methods presented will be especially useful for management programmes for populations that are intensively monitored but where individuals are still imperfectly detected, as will be the case for most threatened wild populations.

In Focus: Jaatinen, K., Westerbom, M., Norkko, A., Mustonen, O., & Koons, D. N. (2021). Detrimental impacts of climate change may be exacerbated by density-dependent population regulation in blue mussels. Journal of Animal Ecology, 90, 562-573, https://doi.org/10.1111/1365-2656.13377. Conservation strategies for threatened species are increasingly dependent on forecasts of population responses to climate change. For such forecasts to be accurate, they must account for multiple sources of uncertainty, including those associated with projections of future climate scenarios and those associated with the models used to describe population dynamics. While many population forecasts incorporate parameter uncertainty in abiotic effects and process variance related to unexplained temporal variation, most forecasts overlook the importance of evaluating uncertainty in the structure of the population model itself. By accounting for structural uncertainties in a model of population growth for blue mussels, Jaatinen et al. (2021) demonstrated that density-dependent processes are likely to exacerbate adverse effects of climate change and reduce population viability of this keystone species. These findings highlight the importance of incorporating structural unknowns in population forecasts and the value of approaches that account for multiple sources of climate and model uncertainties. Forecasts that capture a range of possible population trajectories under climate change will help ensure efficient allocation of limited conservation resources.

1. Relevance of breeding season fecundity as a driver of population dynamics has been highlighted by many studies. Despite that, knowledge about how brood type specific (i.e. first, second or replacement) fecundity affects demography of multiple- brooded species is limited. In fact, estimation of brood type specific fecundity is often challenging due to imperfect detection of nesting attempts. 2. We examined the demographic contribution and the feedback on population density of different components of fecundity, along with other vital rates, in a facultative multiple- brooded migratory bird. 3. We used a novel formulation of a fecundity model that allows incorporating re-productive data for which information on the type of brood was unknown in some cases, and embedded it into an integrated population model (IPM) to obtain con-sensual estimates of all demographic rates, including brood type specific fecundities, reproductive success probabilities and proportion of breeding pairs that performed a second or replacement brood. We then conducted transient life table response experiments on IPM estimates to account for non-stationary environments. We applied the model to two 20-year datasets collected in a Swiss and a German local population of wrynecks Jynx torquilla. 4. Brood type specific fecundities and temporal patterns of brood type specific probabilities of success, number of successful and unsuccessful first broods, probability of starting a second or a replacement brood and proportion of pairs that performed a second or a replacement brood differed between the two populations. However, changes in immigration rate and apparent survival were the dominant contributors to temporal variation and large sequential changes in realized population growth rates in both populations. In the Swiss population we also found that second brood fecundity declined when population size increased. 5. Our study provides insight into the reproductive processes that affect population dynamics and mediate density-dependent fecundity in a migratory bird. In addition, the analytical approach proposed can be used in other studies of multiple- brooded species to maximize the use of available fecundity data through the estimation of unknown brood types, thus favouring a better understanding of the demographic contribution of brood type specific fecundity.

In the classical Lotka-Volterra population models, the interacting species affect each other's growth rate. We propose an alternative model, in which the species affect each other through the limitation coefficients, rather then through the growth rates. This appears to be more realistic: the presence of foxes is not likely to diminish the fertility of rabbits, but will contribute to limiting rabbit's population. Both the cases of predation and of competition are considered, as well as competition in case of periodic coefficients. Our model becomes linear when one switches to the reciprocals of the variables. In another direction we use a similar idea to derive a multiplicity result for a class of periodic equations., Comment: 12 pages, 2 figures

Managers and researchers have identified a reproducing population of grass carp (Ctenopharyngodon idella) in the western basin of Lake Erie, generating concern over the potential threat to ecosystem function in the Great Lakes Basin. Capture histories indicate that grass carp may be present at low levels in other areas of Lake Erie, necessitating a large scale, multi-jurisdictional response. As a result, a group of experts and decision makers began a structured decision making exercise to collaboratively address the threat and identify potential response actions. To aid this process, we developed a spatially-explicit periodic matrix population model to project grass carp abundance, and probabilistically evaluate specific management actions. We evaluated four potential management response actions ranging from no action, diffuse removal efforts, and concentrated removal efforts with and without a barrier on the Sandusky River to reduce spawning success. Based on our current knowledge, concentrated removal including a barrier on the Sandusky River provides the most likely path to achieving and maintaining a management target of no more than 10 fish/ha. Our understanding of grass carp ecology in Lake Erie is growing. This model and parameter development methods were designed to flexibly accommodate new information as our understanding of grass carp ecology evolves, or management objectives change. Ultimately, this modeling framework and use of Bayesian methods could facilitate management response efforts for other invasive species occurring over large scales and multiple jurisdictions.

Sundarbans is the largest mangrove wetland ecosystem of the world with rich biodiversity suffering from deteriorated water quality due to excessive fertilization that leads to an uncontrolled increase in phytoplankton. Such eutrophication also changes the community structure and increases the harmful algal blooms (HABs). In this work, we propose an interacting population model for phytoplankton–zooplankton system in which the density of zooplankton is influenced by non-toxic phytoplankton (NTP) and toxin-producing phytoplankton (TPP) followed by Holling type II and Monod–Haldane (MH)-type functional response. The growth of zooplankton species is assumed to reduce due to toxic chemicals released by TPP population. The mathematical model of the proposed system includes the competition terms between TPP and NTP. System dynamics is studied in both cases, i.e., system with diffusion and without diffusion. For the non-diffusive system, we have investigated the condition for boundedness along with the existing criteria of all feasible equilibrium point. Stability analysis of the model system is carried out in detail for each equilibrium point. Forward and backward bifurcation diagrams are obtained for the temporal system in order to understand the behavior of different parameters that control the system dynamics. Theoretically, stability criteria and Turing instability of diffusive system are derived. In this study, we have taken a case of Sundarban mangrove wetland which is suffering from algal blooms due to the presence of toxic Dinoflagellates and Cyanophyceae. Our numerical investigation shows that the lower value of intraspecific interference of zooplankton promotes the complex spatiotemporal dynamics for the population of non-toxic, toxic phytoplankton and zooplankton. The higher value of inter-specific competition coefficient of NTP leads to reduction in zooplankton density that may cause bad health of the wetland system. This investigation renders the importance of diffusion in algal blooms by the occurrence of different Turing patterns and the role of time delay in destabilization of stationary points through the creation of limit cycles. We observed that the increasing value of diffusion coefficient of zooplankton and time allows the algal blooms to settle down from spot-strip mixture to spot patterns.

Eco-evolutionary models commonly assume that traits are normally distributed in a population, and that the trait bounds do not influence the adaptation of traits. However, recent empirical evidence suggests that at least some traits are not normally distributed, and there is theoretical support for the view that trait bounds can be fundamental to trait adaptation. These attributes suggest that a beta distribution, which can accommodate unbounded (i.e. normal), singly bounded (i.e. gamma) or doubly bounded (beta) trait distributions, may be an appropriate alternative assumption for eco-evolutionary models. We develop an evolutionary model that represents how the mean values of a population’s traits change. Implementation of the model requires assumptions to be made regarding the relative fitness of the individuals in the population, and how their traits are distributed within natural bounds. We compare the numerical results of “population” models that evolve a plant population and the means of its two traits using our eco-evolutionary equations with those of “phenotype” models that evolve 10,000 phenotypes, each defined by a pair of trait values, of a plant population. The phenotype models do not assume any particular trait distribution or fitness, and allow phenotypes to wax and wane according to their ability to compete with other phenotypes in the population for a finite resource. Comparison of the trait distributions obtained by solving 3 coupled population odes with those obtained by solving 10,000 coupled phenotype odes reveals very good agreement between the approaches for each of four mortality functions. Further, it supports the ubiquity of the beta distribution in describing evolutionary processes in populations. An advantage of the simple population model is that it provides insights into why particular results are obtained, which augments the predictive power of the modelling, suggesting that in fact a simplified, abstracted modelling approach is sometimes preferable to the detailed, complicated alternative.

Training in Population Ecology asks for scalable applications capable of embarking students on a trip from basic concepts to the projection of populations under the various effects of density dependence and stochasticity. Demography_Lab is an educational tool for teaching Population Ecology aspiring to cover such a wide range of objectives. The application uses stochastic models to evaluate the future of populations. Demography_Lab may accommodate a wide range of life cycles and can construct models for populations with and without an age or stage structure. Difference equations are used for unstructured populations and matrix models for structured populations. Both types of models operate in discrete time. Models can be very simple, constructed with very limited demographic information or parameter‐rich, with a complex density‐dependence structure and detailed effects of the different sources of stochasticity. Demography_Lab allows for deterministic projections, asymptotic analysis, the extraction of confidence intervals for demographic parameters, and stochastic projections. Stochastic population growth is evaluated using up to three sources of stochasticity: environmental and demographic stochasticity and sampling error in obtaining the projection matrix. The user has full control on the effect of stochasticity on vital rates. The effect of the three sources of stochasticity may be evaluated independently for each vital rate. The user has also full control on density dependence. It may be included as a ceiling population size controlling the number of individuals in the population or it may be evaluated independently for each vital rate. Sensitivity analysis can be done for the asymptotic population growth rate or for the probability of extinction. Elasticity of the probability of extinction may be evaluated in response to changes in vital rates, and in response to changes in the intensity of density dependence and environmental stochasticity., Demography_Lab is an educational application to evaluate the growth of populations. The application uses stochastic unstructured and matrix models and allows for the independent implementation of environmental and demographic stochasticity and sampling error. A large variety of life cycles may be accommodated.

Mechanistic population models are gaining considerable interest in ecological risk assessment. The dynamic energy budget approach for toxicity (debtox) and the general unified threshold model for survival (guts) is a well-established theoretical framework that describes sub-lethal and lethal effects of a chemical stressor, respectively. However, there have been limited applications of these models for mixtures of chemicals, especially to predict long-term effects on populations. Here, we used DEBtox and GUTS in an Individual-Based Model (IBM) framework to predict both single and combined effects of copper and zinc on Daphnia magna populations. The model was calibrated based on standard chronic toxicity test results with the single substances. A mixture toxicity implementation based on the general independent action model for mixtures was developed and validated with data from a population experiment with copper and zinc mixtures. Population-level effects of exposure to individual metals were accurately predicted by DEB-IBM. The DEB-IBM framework also allowed to identify the potential mechanisms underlying these observations. Under independent action the DEB-IBM was able to predict the population dynamics observed in populations exposed to the single metals and their mixtures (R2 > 65% in all treatments). Our modelling shows that it is possible to extrapolate from single-substance effects at the individual level to mixture toxicity effects at the population level, without the need for mixture toxicity data at the individual level from standard mixture toxicity tests. The application of such modelling techniques can increase the ecological realism in risk assessment. This article is protected by copyright. All rights reserved.

This paper analytically investigates a nonlocal system of reaction-diffusion-advection equations modeling the competition of two phytoplankton species for a limiting nutrient and light in a water column, where dead phytoplankton species can get recycled back into the system as a resource for growth. The threshold dynamics of the single population model is first established. Then the utilization of abstract persistence theory enables us to show that two species population system admits a coexistence steady state and the system is uniformly persistent if the trivial steady state and two global attractors on the boundary are all weak repellers.

For a stage-structured population model in periodic discrete habitat, with periodic initial values it reduces to a system of two differential equations with time delay. Assuming the birth rate is of unimodal type, we obtain the influence of time delay on the local and global dynamics. In particular, large delay leads to population vanishing. As delay decreases, we found three critical values of delay for the emergence of different dynamics, by appealing to a combination of monotone dynamical system theory, Hopf bifurcation theory and the fluctuation method. Numerical simulations are also performed to illustrate the results.

The Human Immunodeficiency Virus (HIV) epidemic in Khartoum constitutes the most serious health problem in the region and one that we do not fully understand. Recent approaches aiming to understand the situation have attempted to model the Human Immunodeficiency Virus (HIV) epidemic using deterministic compartmental models. Our work has reviewed the formal mathematical work on deterministic models of this nature and considers the relevance of the modelling approach to the HIV in Khartoum. This model is built on SIR and population models. Evaluation of the basic reproduction number, R0, will be carried out using the SIR model for an optimal value of α and γ where α and γ are the inflow and the outflow of infectious individuals per infectious capita respectively (R0 = α γ ). The population will be divided into compartments, in- and out-flows from compartments leading to a corresponding differential equation. A numerical solver in MATLAB is then used to compute the solutions. Our model will be fitted to the data from Khartoum state, which is the capital of the Sudan and it has very good data related to HIV. Our results demonstrated that Khartoum was endemic for HIV when the epidemic began in the year 2002 until the year 2005 (R0 is 1.02). The value of R0 decreases and remains stable for ten years from the year 2006-2016 (R0 is 0.98). The most affected Sudanese population in Khartoum with AIDS was the male (Teenager) 10 - 19 age group. Also the treatment (ART) is recommended for everyone who had HIV.

A general nonlinear model describing the evolution of size-structured populations influenced by coagulation and vertical effects is presented. The nonlinear population dynamics occur in a multi-region setting in which the transfer, coagulation, and vital rates of an individual depend on a vector describing conditions in the environment. The model for these dynamics consists of a system of two-dimensional nonlinear-nonlocal hyperbolic partial differential equations coupled with a system of one-dimensional nonlocal differential equations parametrized by a vertical location coordinate $$${z}$$$ describing the environmental time-dynamics. A finite difference approximation approach is employed to study the wellposedness of the model and convergence of the scheme to the unique weak solution is established. Several examples are presented to illustrate the generality of the model and to motivate applications.

We consider a methodology for organizing hybrid computing structures to simulate abrupt changes in controlled natural processes and analyzing phases of extreme environmental phenomena. Systems of differential equations with the dynamically redefinable right-hand side at special moments (events) are used. The truth conditions for transitions are obtained from computing other equations for additional characteristics of the state of a generation. Threshold states in process modeling are the result of the inclusion of trigger functions. Their values on the right-hand side are specifically different from the neutral value only in narrow ranges of the space of changing characteristics of a hybrid system and depend on the initial conditions. The restricted limits of functions and their domain of values rest on the core of the threshold effects for the simulated biosystem, which are observed under special conditions. The method allows us to implement actual qualitative changes in management scenarios as bifurcations of the appearance (reduction) of equilibrium states or the boundary crisis of a complex attractor consisting of intervals scattered in a limited area. Computational scenarios for different population processes are investigated. The collapse of fish stocks is described in the model by the examples of cod in the North Atlantic and sturgeon in the Caspian Sea. The rapid outbreak of their abundance is modeled according to observations on the pulsation of the population size of pests of relict evergreen forests. The threshold scenario of the outbreak of insects in the scenario ends spontaneously due to the local exhaustion of forest resources with a sharp transition to fluctuations of the pest, which are ordinary for the environment. The methodology of organizing the structure for the population model is summarized to predict a wide range of extreme processes related to rapid changes in controlled biological systems and the spread of unwanted biological invasions.

The academic community has seen a tremendous growth in number of authors and publications in recent times. Most previous studies of the academic community, whether on individual activity, productivity and influence, or collaboration patterns and their implications, have been based on a flat and static view of the system. However, the academic community resembles a dynamic growing population, with entry and exit of authors. In this paper, we study this systemic inflation by proposing a population model for academia. We use a generalized branching process as an overarching framework, which enables us to describe the research community from an evolutionary and structural perspective. Further, the observed patterns allow us to shed light on researchers’ life-cycle encompassing their arrival, academic life expectancy , activity, productivity and offspring distribution in the community. In our study, we used data from DBLP for a case study in the computer science community, although our methodology can be adopted in a systematic manner to any other research domain with sufficient publication records. We believe that the results can help academics and policy makers alike to better understand and evaluate the development and evolution of their respective academic communities.

Understanding biotic interactions and abiotic forces that govern population regulation is crucial for predicting stability from both theoretical and applied perspectives. In recent years, social information has been proposed to profoundly affect the dynamics of populations and facilitate the coexistence of interacting species. However, we have limited knowledge about how social information use influences cyclic and non-cyclic fluctuations of populations and if any population-level effects can be expected in species where individuals do not form social groups. In this study, I built individual-based models in a factorial design to investigate how predator avoidance behaviour and associated inadvertent social information (ISI) use alters the predictions of classical predator–prey population models in non-grouping (e.g., randomly moving) animals. Simulation results showed that ISI use in prey stabilized population dynamics by disrupting high-amplitude cyclic fluctuations in both predator and prey populations. Moreover, it also decreased the strength of the negative feedback of second-order dependence between predator and prey. I propose that if social cues are commonly used sources of information in animals regardless of the level of social organization, then similar social information-mediated effects on trophic interactions and population dynamics may be prevalent in natural communities.

Understanding how events throughout the annual cycle are linked is important for predicting variation in individual fitness, but whether and how carry-over effects scale up to influence population dynamics is poorly understood. Using 38 years of demographic data from Algonquin Provincial Park, Ontario, and a full annual cycle integrated population model, we examined the influence of environmental conditions and density on the population growth rate of Canada jays (Perisoreus canadensis), a resident boreal passerine that relies on perishable cached food for over-winter survival and late-winter breeding. Our results demonstrate that fall environmental variables, most notably the number of freeze-thaw events, carried over to influence late-winter fecundity, which, in turn, was the main vital rate driving population growth. These results are consistent with the hypothesis that warmer and more variable fall conditions accelerate the degradation of perishable stored food that is relied upon for successful reproduction. Future warming during the fall and winter may compromise the viability of cached food that requires consistent subzero temperatures for effective preservation, potentially exacerbating climate-driven carry-over effects that impact long-term population dynamics.

Background: Spatial population models are important to inform understanding of historical demographic development patterns and to project possible future changes, especially for use in anticipating environmental interactions. Objective: We document, calibrate, and evaluate a high-resolution gravity-based population downscaling model for each US state and interpret its historical urban and rural spatial population change patterns. Methods: We estimate two free parameters that govern the spatial population change pattern using the historical population grids of each state. We interpret the resulting parameters in light of the spatial development pattern they represent. We evaluate the model by comparing the resulting total population grid of each state in 2010 against its census-based grid. We also analyze the temporal stability of parameters across the 1990–2000 and 2000–2010 decades. Results: Our analysis indicates varying levels of performance across states and population types. While our results suggest a consolidated change pattern in urban population across states, rural population change patterns are diverse. We find urban parameters are more stable. Conclusions: The model’s adaptability, performance, and interpretability indicate its potential for depicting historical state-level spatial population changes. It assigns these changes to different representative categories to assist interpretation. Contribution: We document and evaluate a gravitational model as well as investigate historical state-level spatial population changes. This research facilitates future work creating projections of the spatial distribution of population at the subnational level, especially those according to the Shared Socioeconomic Pathways (SSPs), widely used scenarios for climate change research.

1. How environmental conditions affect the life history of individuals and how these effects shape population and community dynamics on ecological and evolutionary time-scales is a central question in many eco-evolutionary studies.2. Physiologically structured population models (PSPMs) allow to address this question theoretically as PSPMs are built on a function-based life-history model, which explicitly describes how life history depends on individual traits and environmental factors. PSPMs furthermore explicitly account for population feedback on these environmental factors, which translates into density-dependent effects on life history.3. PSPManalysis is an R package that allows to simulate ecological dynamics of PSPMs, compute their ecological steady states as a function of model parameters and detect bifurcation points in the computed curves where dynamics change drastically. It furthermore allows for analysing evolutionary dynamics and evolutionary singular states of PSPMs based on Adaptive Dynamics theory. The package only requires a relatively straightforward specification of the life-history functions as input.4. Compared to dynamic simulations alone, PSPManalysis uses methods from bifurcation analysis to gain a more complete and comprehensive understanding of model behaviour which is much less dependent on particular parameter values or initial model conditions. Given the central role of the individual life history in many studies, there is substantial scope for using PSPManalysis in fields as diverse as ecology, ecotoxicology, conservation biology and evolutionary biology.

Cooperation significantly impacts a species’ population dynamics as individuals choose others to associate with based upon fitness opportunities. Models of these dynamics typically assume that individuals can freely move between groups. Such an assumption works well for facultative co-operators (e.g. flocking birds, schooling fish, and swarming locusts) but less so for obligate co-operators (e.g. canids, cetaceans, and primates). With obligate co-operators, the fitness consequences from associations are stronger compared to facultative co-operators. Consequently, individuals within a group should be more discerning and selective over their associations, rejecting new members and even removing current members. Incorporating such aspects into population models may better reflect obligately cooperative species. In this paper, we create and analyze a model of the population dynamics of obligate co-operators. In our model, a behavioral game determines within-group population dynamics that then spill over into between-group dynamics. Our analysis shows that group number increases when population dynamics are stable, but additional groups lead to unstable population dynamics and an eventual collapse of group numbers. Using a more general analysis, we identify a fundamental mismatch between the stability of the behavioral dynamics and the stability of the population dynamics. When one is stable, the other is not. Our results suggest that group turnover may be inherent to the population dynamics of obligate co-operators. The instability arises from a non-chaotic deterministic process, and such dynamics should be predictable and testable.

The spatial distribution of resources for diffusive populations can have a strong effect on population abundance. We investigate the optimal allocation of resources for a diffusive population. Population dynamics are represented by a parabolic partial differential equation with density-dependent growth and resources are represented through their space- and time-varying influence on the growth function. We consider both local and integral constraints on resource allocation. The goal is to maximize the abundance of the population while minimizing the cost of resource allocation. After characterizing the optimal control in terms of the population solution and the adjoint functions, we illustrate several scenarios numerically. The effects of initial and boundary conditions are important for the optimal allocation of resources.