Stage-structured Population Model Research Articles

A general subpopulation model for the Animal Landscape and Man Simulation System (ALMaSS)

ALMaSS (the Animal Landscape and Man Simulation System) is a well-established modelling system known for its detailed agent-based animal models. However, for certain species, such as aphids, extremely high population sizes and limited detailed individual behaviour information make agent-based approaches either computationally expensive or unfeasible. Additionally, when these species are modelled as a prey base for other species, such as aphids for ladybirds, an efficient and accurate modelling approach is required. To address these challenges, we introduce a subpopulation-based model framework that effectively handles high population densities, while reducing computational complexity. This framework divides the landscape into a non-overlapping grid and population dynamics are managed within each grid using a flexible stage-structured population model. Grids are interconnected through short- and long-distance dispersal mechanisms, allowing for realistic movement and interactions. Parallel programming is employed to enhance performance, enabling faster simulation runs. We demonstrate the application of this model framework with a hypothetical species (not a species in the real world) and showcase its use in modelling aphid populations. This foundational subpopulation model could be used to model species with large population sizes within the ALMaSS framework and can be integrated into other simulation systems.

Existence and uniqueness result for reaction-diffusion model of diffusive population dynamics

The present work investigates a convolution type nonlinear integrodifferential equation with diffusion. This type of equations represents not only pure mathematical interest, but also is widely used in various applications, especially in wide range of problems on population dynamics arising in biology. The existence of a parametric family of travelling wave solutions as well as the uniqueness of the solution in certain class of bounded continuous functions on R \mathbb {R} is proved. The study investigates also some important properties as well as asymptotic behaviour of constructed solutions. These results are then used to derive a new uniform estimate for the deviation between successive iterations, which provides us with a strong tool to control the number of iterations on our way of computing the desired numerical approximation of the exact solution. Finally, we apply our theoretical results to two well-known population problems modelled by delayed reaction-diffusion equation: Diffusion model for spatial-temporal spread of epidemics and stage structured population model.

Hopf-bifurcation analysis of a stage-structured population model of cell differentiation

A cell differentiation model with maturity structure in progenitor cells is described by a system of nonlinear ODEs coupled to a PDE. The work mainly discusses Hopf-bifurcation for the model when the maturation rate of progenitor cells only depends on the number of mature cells, and is a continuation of the previous work (Doumic et al., 2011). Using the methods of characteristics and a change in variable, the system can be transformed into one of state-dependent delay differential equations and then into constant delay differential equations. A qualitative analysis of the solutions is performed, which includes well-posedness, non-negativity, uniform boundedness and linearized stability. Furthermore, we conduct Hopf-bifurcation analysis by taking the maturation level of progenitor as the bifurcation parameter, which means that the levels of stem and mature cells may vary with persistent oscillations. A numerical analysis stresses the role of some important parameters on the stability and Hopf-bifurcation.

Well-Posedness of a Nonlocal Stage-Structured Population Model with Free Boundary

Well-Posedness of a Nonlocal Stage-Structured Population Model with Free Boundary

Spatial and temporal heterogeneity alter the cost of plasticity in Pristionchus pacificus.

Phenotypic plasticity, the ability of a single genotype to produce distinct phenotypes under different environmental conditions, has become a leading concept in ecology and evolutionary biology, with the most extreme examples being the formation of alternative phenotypes (polyphenisms). However, several aspects associated with phenotypic plasticity remain controversial, such as the existence of associated costs. While already predicted by some of the pioneers of plasticity research, i.e. Schmalhausen and Bradshaw, experimental and theoretical approaches have provided limited support for the costs of plasticity. In experimental studies, one common restriction is the measurement of all relevant parameters over long time periods. Similarly, theoretical studies rarely use modelling approaches that incorporate specific experimentally-derived fitness parameters. Therefore, the existence of the costs of plasticity remains disputed. Here, we provide an integrative approach to understand the cost of adaptive plasticity and its ecological ramifications, by combining laboratory data from the nematode plasticity model system Pristionchus pacificus with a stage-structured population model. Taking advantage of measurements of two isogenic strains grown on two distinct diets, we illustrate how spatial and temporal heterogeneity with regard to the distribution of resources on a metapopulation can alter the outcome of the competition and alleviate the realized cost of plasticity.

Population Dynamics of a Declining White-Tailed Deer Population in the Southern Appalachian Region of the United States

Although generally abundant, white-tailed deer (Odocoileus virginianus) populations in the southeastern United States have recently experienced several localized declines attributed to reduced fawn recruitment following the establishment of coyotes (Canis latrans). The Southern Appalachians is a mountainous region suggested to be experiencing white-tailed deer declines, as harvest numbers and hunter success rates have substantially decreased in northern Georgia since 1979. Low fawn survival (16%) was also recently documented in the Chattahoochee National Forest (CNF) in northern Georgia, necessitating further examination. We radio-collared 14 yearling and 45 adult female white-tailed deer along with 71 fawns during 2018–2020 in the CNF to estimate field-based vital rates (i.e., survival and fecundity) and parameterize stage-structured population models. We projected population growth rates (λ) over 10 years to evaluate the current rate of decline and various other management scenarios. Our results indicated that the observed population would decline by an average of 4.0% annually (λ = 0.960) under current conditions. Only scenarios including antlerless harvest restrictions in addition to improved fawn survival resulted in positive growth (λ = 1.019, 1.085), suggesting these measures are likely necessary for population recovery in the region. This approach can be applied by wildlife managers to inform site-specific management strategies.

Integrating human behavior into structured population models

Human behavior shapes modern ecosystems but is difficult to parse into parameters for ecological models. We used Bayesian models of human behavior, a stage-structured population model, and a novel mortality integration approach to ask how human decisions affect animal population dynamics and conservation outcomes in the context of recreational fishing. Walleye (Sander vitreus) are a broadcast-spawning freshwater fish with large, slow-maturing females and small, fast-maturing males. We observed that simpler and less restrictive fishing regulations outperformed more complex and stricter regulations at conserving equilibrium adult female abundance and overall population abundance while still facilitating large harvests. This outcome was possible because angler behavior within the least restrictive regulation concentrated harvest on juveniles and adult males. Our findings indicate that, counter to intuitive expectations, moderate regulations can acheive conservation objectives when we account for the interaction of regulatory policy, human behavior, and animal life history. We suggest that integrating models of human behavior with models of animal life history and population dynamics will provide essential insights for conservation in ecosystems increasingly shaped by human decisions.

Models for the practitioner: Predicting the efficient biocontrol of Tuta absoluta under different management scenarios

Tuta absoluta (Meyrick) (Lepidoptera: Gelechiidae) is one of the most destructive pests of solanaceous crops. One possible biological control strategy is the augmentative release of parasitoids. However, parasitoid intervention efficacy is highly sensitive to the release timing and intensity. Virus-based biopesticides are additional control means since they are highly selective and can be combined with natural enemies. We developed a stage-structured population model, validated with results from a semi-field experiment, to investigate and predict the population dynamics of the pest T. absoluta and one of its parasitoids, Necremnus tutae Ribes & Bernardo (Hymenoptera: Eulophidae). The aim of the study was to assess the best release parameters of N. tutae to control the pest in four different management scenarios: without any other control method, with a biopesticide (PhopGV, Baculoviridae), with the natural presence of the parasitoid, and when combining the natural presence of the parasitoid with a biopesticide. Moreover, in each scenario, two growing seasons of different lengths were compared. To achieve the same control level, 3–45% fewer parasitoids are necessary in a long growing season than in a shorter one. Biopesticide applications reduce the number of required parasitoids by 66% and 78%, whereas the natural presence of parasitoids reduces it by 11% and 17% for short and long growing seasons, respectively. On average, with biopesticide application, the parasitoid intervention can be delayed by a month and remains efficient. These findings highlight the importance of mathematical models in applied pest management drawing precise predictions crucial for efficient control.

Estimated effectiveness of treatments against salmon lice in marine salmonid farming

We here estimate the effectiveness of ten types of salmon lice treatments currently used in the salmonid industry by analysing daily and cage-wise data from 90 full production cycles from farms spread along the Norwegian coast. The calculations are based on a stage-structured population model for salmon lice and accounts for the structure of the data, including the uncertainties that arise from the weekly counting of lice on a subset of the fish. Results suggest that the most commonly used treatment methods in the data set, i.e. thermal, mechanical and freshwater treatments, kill 70–80% of the lice in average, but with high variability. Feed treatments with emamectin benzoate are also commonly used, but are only estimated to kill around 35% of the lice in average. Bath treatments with hydrogen peroxide are estimated to kill around 74% and pyrethroids 50% of the lice in average. The other medicinal treatments were infrequently used in the data set and the estimates are therefore more uncertain. Of note is that the recently licenced bath treatment with imidacloprid is estimated to kill more than 99% of sessile and 98% of pre-adult and adult lice in average. The estimated effects of hydrogen peroxide, pyrethroids and azamethiphos, here based on data from 2017–2020, are lower than estimates from a previous analysis of production data from 2011–2014, possibly because of resistance development. In contrast, there is no indication of reduced effects of thermal, mechanical or freshwater treatments compared to previous analyses of production data from 2013–2018. These results allow comparing the effectiveness of the different treatment methods in a consistent and comprehensive way, hence enabling fish farmers and authorities to better balance the expected benefits of the treatments in terms of lice control against the economic costs, fish welfare and risk of resistance development.

Coexistence and Replacement of Two Different Maturation Strategies Adopted by a Stage-Structured Population

Maturation strategies play a key role in the survival and development of populations. In response to changes in the external environment and human interventions, populations adopt appropriate maturation strategies. Different maturation strategies can lead to different birth and mortality rates. In this paper, we develop and analyze a stage-structured population model with two maturation strategies to obtain conditions for the coexistence of two maturation strategies and conditions for competitive exclusion. Our results also show that equality of fitness—represented by basic reproductive numbers being greater than 1 under different maturation strategies—promotes the coexistence of the two strategies. The reason why a strategy is replaced by another one is that the population adopting this strategy has weak fitness, which is measured by the basic reproductive number.

Dynamic analysis of a stage-structured forest population model with non-smooth continuous threshold harvesting

In this article, we develop a delayed tree population model with non-smooth continuous threshold harvesting. By carefully addressing the main difficulty caused by the nonlinear term and the time delay together, the existence and number of the positive equilibrium points are classified. Taking full use of the domain-decomposition method and Hopf bifurcation theory, the stability of the model, including local and global asymptotic stability of the equilibria, bistability and stability switches occurring at the positive equilibrium, is analyzed relatively completely. This is followed by an investigation of the influence of the maturation delay of trees on the optimal harvesting. Numerical analysis illustrates that the model gives rise to chaotic-like oscillations through period doubling with the increase of the maturation delay or the harvesting rate and undergoes long transients and regime shifts. Even, the maturation delay can induce multi-types of tristability.

Modeling the effects of spatially explicit patterns of climate and fire on future populations of a fire-dependent plant

Many plant species are likely to face population decline or even extinction in the coming century, especially those with a limited distribution and inadequate dispersal relative to the projected rates of climate change. The obligate seeding California endemic, Ceanothus perplexans is especially at risk, and depending on how climate change interacts with altered fire regimes in Southern California, certain populations are likely to be more at risk than others. To identify which areas within the species’ range might need conservation intervention, we modeled population dynamics of C. perplexans under various climate and fire regime change scenarios, focusing on spatially explicit patterns in fire frequency. We used a species distribution model to predict the initial range and potential future habitat, while adapting a density-dependent, stage-structured population model to simulate population dynamics. As a fire-adapted obligate seeder, simulated fire events caused C. perplexans seeds to germinate, but also killed all adults in the population. Our simulations showed that the total population would likely decline under any combination of climate change and fire scenario, with the species faring best at an intermediate fire return interval of around 30–50 years. Nevertheless, while the total population declines least with a 30–50 year fire return interval, the effect of individual subpopulations varies depending on spatially explicit patterns in fire simulations. Though climate change is a greater threat to most subpopulations, increased fire frequencies particularly threatened populations in the northwest of the species’ range closest to human development. Subpopulations in the mountainous southern end of the range are likely to face the sharpest declines regardless of fire. Through a combination of species distribution modeling, fire modeling, and spatially explicit demographic simulations, we can better prepare for targeted conservation management of vulnerable species affected by global change.

Experimental and theoretical support for costs of plasticity and phenotype in a nematode cannibalistic trait.

Developmental plasticity is the ability of a genotype to express multiple phenotypes under different environmental conditions and has been shown to facilitate the evolution of novel traits. However, while the associated cost of plasticity, i.e., the loss in fitness due to the ability to express plasticity in response to environmental change, and the cost of phenotype, i.e., the loss of fitness due to expressing a fixed phenotype across environments, have been theoretically predicted, empirically such costs remain poorly documented and little understood. Here, we use a plasticity model system, hermaphroditic nematode Pristionchus pacificus, to experimentally measure these costs in wild isolates under controlled laboratory conditions. P. pacificus can develop either a bacterial feeding or predatory mouth morph in response to different external stimuli, with natural variation of mouth-morph ratios between strains. We first demonstrated the cost of phenotype by analyzing fecundity and developmental speed in relation to mouth morphs across the P. pacificus phylogenetic tree. Then, we exposed P. pacificus strains to two distinct microbial diets that induce strain-specific mouth-form ratios. Our results indicate that the plastic strain does shoulder a cost of plasticity, i.e., the diet-induced predatory mouth morph is associated with reduced fecundity and slower developmental speed. In contrast, the non-plastic strain suffers from the cost of phenotype since its phenotype does not change to match the unfavorable bacterial diet but shows increased fitness and higher developmental speed on the favorable diet. Furthermore, using a stage-structured population model based on empirically derived life history parameters, we show how population structure can alleviate the cost of plasticity in P. pacificus. The results of the model illustrate the extent to which the costs associated with plasticity and its effect on competition depend on ecological factors. This study provides support for costs of plasticity and phenotype based on empirical and modeling approaches.

Demographic Analysis of Shortfin Mako Shark (Isurus oxyrinchus) in the South Pacific Ocean.

The shortfin mako shark (Isurus oxyrinchus) demonstrates low productivity and is thus relatively sensitive to fishing. Natural mortality (M) and fishing mortality (F) data are critical to determine their population dynamics. However, catch and fishing effort data are unavailable for this species in the South Pacific Ocean, making stock assessments difficult. Demographic quantitative methods aid in analyzing species with limited data availability. We used a two-sex stage-structured matrix population model to examine the demographic stock status of mako sharks. However, data-limited models to determine fishery management strategies have limitations. We performed Monte Carlo simulations to evaluate the effects of uncertainty on the estimated mako shark population growth rate. Under unfished conditions, the simulations demonstrated that the mako sharks showed a higher finite population growth rate in the 2-year reproductive cycle compared to the 3-year reproductive cycle. Protecting immature mako sharks led to a higher population growth rate than protecting mature mako sharks. According to the sex-specific data, protecting immature male and female sharks led to a higher population growth rate than protecting mature male and female sharks. In conclusion, sex-specific management measures can facilitate the sustainable mako shark conservation and management.

About Stability of Nonlinear Stochastic Differential Equations with State-Dependent Delay

A nonlinear stage-structured population model with a state-dependent delay under stochastic perturbations is investigated. Delay-independent and delay-dependent conditions of stability in probability for two equilibria of the considered system are obtained via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The model under consideration is not the aim of the work and was chosen only to demonstrate the proposed research method, which can be used for the study of other types of nonlinear systems with a state-dependent delay.

Can predators stabilize host-parasite interactions? Changes in aquatic predator identity alter amphibian responses and parasite abundance across life stages.

The role of parasites can change depending on the food web community. Predators, for instance, can amplify or dilute parasite effects on their hosts. Likewise, exposure to parasites or predators at one life stage can have long-term consequences on individual performance and survival, which can influence population and disease dynamics. To understand how predators affect amphibian parasite infections across life stages, we manipulated exposure of northern leopard frog (Rana pipiens) tadpoles to three predators (crayfish [Orconectes rusticus], bluegill [Lepomis macrochirus], or mosquitofish [Gambusia affinis]) and to trematode parasites (Echinostoma spp.) in mesocosms and followed juveniles in outdoor terrestrial enclosures through overwintering. Parasites and predators both had strong impacts on metamorphosis with bluegill and parasites individually reducing metamorph survival. However, when fish were present, the negative effects of parasites on survival was not apparent, likely because fish altered community composition via increased algal food resources. Bluegill also reduced snail abundance, which could explain reduced abundance of parasites in surviving metamorphs. Bluegill and parasite exposure increased mass at metamorphosis, which increased metamorph jumping, swimming, and feeding performance, suggesting that larger frogs would experience better terrestrial survival. Effects on size at metamorphosis persisted in the terrestrial environment but did not influence overwintering survival. Based on our results, we constructed stage-structured population models to evaluate the lethal and sublethal effects of bluegill and parasites on population dynamics. Our models suggested that positive effects of bluegill and parasites on body size may have greater effects on population growth than the direct effects of mortality. This study illustrates how predators can alter the outcome of parasitic infections and highlights the need for long-term experiments that investigate how changes in host-parasite systems alter population dynamics. We show that some predators reduce parasite effects and have indirect positive effects on surviving individuals potentially increasing host population persistence.

Properties in Stage-Structured Population Models with Deterministic and Stochastic Resource Growth

Modelling population dynamics in ecological systems reveals properties that are difficult to find by empirical means, such as the probability that a population will go extinct when it is exposed to harvesting. To study these properties, we use an aquatic ecological system containing one fish species and an underlying resource as our models. In particular, we study a class of stage-structured population systems with and without starvation. In these models, we study the resilience, the recovery potential, and the probability of extinction and show how these properties are affected by different harvesting rates, both in a deterministic and stochastic setting. In the stochastic setting, we develop methods for deriving estimates of these properties. We estimate the expected outcome of emergent population properties in our models, as well as measures of dispersion. In particular, two different approaches for estimating the probability of extinction are developed. We also construct a method to determine the recovery potential of a species that is introduced in a virgin environment.

Evolution of reproductive strategies in incipient multicellularity.

Multicellular organisms potentially show a large degree of diversity in reproductive strategies, producing offspring with varying sizes and compositions compared to their unicellular ancestors. In reality, only a few of these reproductive strategies are prevalent. To understand why this could be the case, we develop a stage-structured population model to probe the evolutionary growth advantages of reproductive strategies in incipient multicellular organisms. The performance of reproductive strategies is evaluated by the growth rates of the corresponding populations. We identify the optimal reproductive strategy, leading to the largest growth rate for a population. Considering the effects of organism size and cellular interaction, we found that distinct reproductive strategies could perform uniquely or equally well under different conditions. If a single reproductive strategy is optimal, it is binary splitting, dividing into two parts. Our results show that organism size and cellular interaction can play crucial roles in shaping reproductive strategies in nascent multicellularity. Our model sheds light on understanding the mechanism driving the evolution of reproductive strategies in incipient multicellularity. Beyond multicellularity, our results imply that a crucial factor in the evolution of unicellular species’ reproductive strategies is organism size.

The First Population Simulation for the Zalophus japonicus (Otariidae: Sea Lions) on Dokdo, Korea

The Japanese sea lion (Z. japonicus) has been regarded as an extinct species since the last report on Dokdo in 1951. Not much ecological information on the Z. japonicus on Dokdo (hereafter Dokdo sea lion) is currently available. Using a discrete time stage-structured population model, we reconstructed the Dokdo sea lion population to explore the effect of human hunting pressure on them. This study provides the first estimate for the Dokdo sea lion population from 1900 to 1951. The reconstructed capture numbers of the Dokdo sea lion and the parameters estimated in this study were well matched with the recorded numbers and ecological parameters reported previously for the Californian sea lion. Based on the reconstructed population, their number rapidly declined after hunting started and it took less than 10 years for a 70% decline of the initial population, which would be considered to be an extinction risk. Since some caveats exist in this study, some caution about our results is necessary. However, this study demonstrates how rapidly human over-hunting can cause the extermination of a large local population. This study will be helpful to raise people’s awareness about endangered marine animals such as local finless porpoises in Korea.

Stability, bifurcations and hydra effects in a stage-structured population model with threshold harvesting

In this paper, we investigate the dynamics of a discrete-time stage-structured population model where juveniles and adults may be subject to threshold harvesting. This management policy allows the harvesting of the target population only if its size exceeds a predetermined threshold. It is commonly used for maintaining biomass, obtaining a higher yield, and preventing population collapse. We focus on the response of the structured populations to harvesting and study how they can be affected by considering different thresholds for each age class. We find all possible equilibria of the system and analyze their stability; we show that harvesting does not destabilize globally stable equilibria. We discuss when hydra effects may occur, more specifically, we determine when the adult population size can increase at equilibrium in response to an increase in its per-capita mortality rate as a consequence of threshold harvesting. A rigorous 2-parameter bifurcation diagram is given for semelparous populations, which helps to understand the general case when adult survivorship rates are low. Numerical results complement the bifurcation analysis in the general case.