Stage-structured Population Research Articles

Pathogens stabilize or destabilize depending on host stage structure.

A common assumption is that pathogens more readily destabilize their host populations, leading to an elevated risk of driving both the host and pathogen to extinction. This logic underlies many strategies in conservation biology and pest and disease management. Yet, the interplay between pathogens and population stability likely varies across contexts, depending on the environment and traits of both the hosts and pathogens. This context-dependence may be particularly important in natural consumer-host populations where size- and stage-structured competition for resources strongly modulates population stability. Few studies, however, have examined how the interplay between size and stage structure and infectious disease shapes the stability of host populations. Here, we extend previously developed size-dependent theory for consumer-resource interactions to examine how pathogens influence the stability of host populations across a range of contexts. Specifically, we integrate a size- and stage-structured consumer-resource model and a standard epidemiological model of a directly transmitted pathogen. The model reveals surprisingly rich dynamics, including sustained oscillations, multiple steady states, biomass overcompensation, and hydra effects. Moreover, these results highlight how the stage structure and density of host populations interact to either enhance or constrain disease outbreaks. Our results suggest that accounting for these cross-scale and bidirectional feedbacks can provide key insight into the structuring role of pathogens in natural ecosystems while also improving our ability to understand how interventions targeting one may impact the other.

Productivity drives the dynamics of a red kite source population that depends on immigration

Local population dynamics are driven by local processes such as temporal variation of productivity, survival, emigration and population stage structure, and by processes originating from outside the local population, such as immigration. Populations may operate as sources that contribute more individuals than have died or as sinks that depend on neighbouring populations. Knowing demographic processes driving the dynamics of a local population and the significance of a local population in a system of multiple populations is crucial for understanding population dynamics and requires detailed demographic analyses. We studied demographic drivers in a red kite Milvus milvus population located in Germany that was monitored for 34 years using integrated population modelling. We specified the model in such a way that the numbers of experienced breeders, local recruits, locally born non‐breeders and immigrants are estimated explicitly, applied a retrospective perturbation analysis to identify the demographic drivers and assessed the source‐sink status of the population. The study population increased on average by 1% per year. The number of breeders was about double than the number of locally born non‐breeders, and the number of experienced breeders exceeded the number of local recruits and immigrants by a factor of six to nine. The retrospective analysis identified productivity, i.e. the number of fledglings per breeding pair, as the main demographic driver, followed by adult survival and immigration. As other studies show close links between food supply and productivity, it is likely that food supply plays a critical role in red kite population dynamics. The study population contributed more individuals than it lost through mortality, but due to emigration of locally born individuals it was not self‐sustainable and depended on immigration. This quantifies the population as a dependent source and shows that red kite populations are linked across large spatial scales.

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.

Modeling temporal dynamics of genetic diversity in stage-structured plant populations with reference to demographic genetic structure

Predicting temporal dynamics of genetic diversity is important for assessing long-term population persistence. In stage-structured populations, especially in perennial plant species, genetic diversity is often compared among life history stages, such as seedlings, juveniles, and flowerings, using neutral genetic markers. The comparison among stages is sometimes referred to as demographic genetic structure, which has been regarded as a proxy of potential genetic changes because individuals in mature stages will die and be replaced by those in more immature stages over the course of time. However, due to the lack of theoretical examination, the basic property of the stage-wise genetic diversity remained unclear. We developed a matrix model which was made up of difference equations of the probability of non-identical-by-descent of each life history stage at a neutral locus to describe the dynamics and the inter-stage differences of genetic diversity in stage-structured plant populations. Based on the model, we formulated demographic genetic structure as well as the annual change rate of the probability of non-identical-by-descent (denoted as η). We checked if theoretical expectations on demographic genetic structure and η obtained from our model agreed with computational results of stochastic simulation using randomly generated 3,000 life histories. We then examined the relationships of demographic genetic structure with effective population size Ne, which is the determinants of diversity loss per generation time. Theoretical expectations on η and demographic genetic structure fitted well to the results of stochastic simulation, supporting the validity of our model. Demographic genetic structure varied independently of Ne and η, while having a strong correlation with stable stage distribution: genetic diversity was lower in stages with fewer individuals. Our results indicate that demographic genetic structure strongly reflects stable stage distribution, rather than temporal genetic dynamics, and that inferring future genetic diversity solely from demographic genetic structure would be misleading. Instead of demographic genetic structure, we propose η as an useful tool to predict genetic diversity at the same time scale as population dynamics (i.e., per year), facilitating evaluation on population viability from a genetic point of view.

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.

Propagation of invasive plant species in the presence of a road

Invasive plant species pose a significant threat to biodiversity and the economy, yet their management is often resource-intensive and expensive, and further research is required to make control measures more efficient. Evidence suggests that roads can have an important effect on the spread of invasive plant species, although little is known about the underlying mechanisms at play. We have developed a novel mathematical model to analyse the impact of roads on the propagation of invasive plants. The integro-difference equation model is formulated for stage-structured population and incorporates a road sub-domain in the spatial domain. The results of our study reveal, that, depending on the definition of the growth function in the model, there are three distinct types of behaviour in front of the road. Roads can act as barriers to invasion, lead to a formation of a beachhead in front of the road, or act as corridors allowing the invasive species to invade the domain in front of the road. Analytical and computational findings on how roads can impact the spread of invasive species show that a small change in conditions of the environment favouring the invasive species can change the case for the road, allowing the invasive species to invade the domain in front of the road where it previously could not spread.

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.

Discrete-time models for interactive wild and sterile mosquitoes with general time steps

Different from the discrete-time population models based on evolution of generations or life cycles, we formulate discrete-time homogeneous and stage-structured models with time steps in more general settings such that survivals are included at each time step. We assume that sterile mosquitoes are released and their number in the field is kept at a constant level. We study the interactive dynamics of wild and sterile mosquitoes where only sexually active sterile mosquitoes are considered. We determine threshold values of releases and investigate the interactive dynamics for both homogeneous and stage-structured populations. Numerical examples are provided to confirm and demonstrate the obtained theoretical results.

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.

Competition and resource depletion shape the thermal response of population fitness in Aedes aegypti

Mathematical models that incorporate the temperature dependence of lab-measured life history traits are increasingly being used to predict how climatic warming will affect ectotherms, including disease vectors and other arthropods. These temperature-trait relationships are typically measured under laboratory conditions that ignore how conspecific competition in depleting resource environments—a commonly occurring scenario in nature—regulates natural populations. Here, we used laboratory experiments on the mosquito Aedes aegypti, combined with a stage-structured population model, to investigate this issue. We find that intensified larval competition in ecologically-realistic depleting resource environments can significantly diminish the vector’s maximal population-level fitness across the entire temperature range, cause a ~6 °C decrease in the optimal temperature for fitness, and contract its thermal niche width by ~10 °C. Our results provide evidence for the importance of considering intra-specific competition under depleting resources when predicting how arthropod populations will respond to climatic warming.

A Stage-Structured Fishery Model for African Catfish and Nile Tilapia Feeding on Two Food Resources with Harvesting

In this paper, a fishery model for African catfish and Nile tilapia is formulated. This model is used to compare financial profit and biomass outtakes in a two-species system versus single species systems. We consider a stage-structured fish population model consisting of the aforementioned fish species together with two food resources. The model dynamics include cannibalism, predator-prey, feeding, reproduction, maturation, development, mortality, and harvesting. We prove consistency of the model in the sense that the solutions will stay bounded and nonnegative over time. Conditions for local stability of fish-free equilibrium point are established. The simulation results reveal asymptotically stable solutions with coexistence of African catfish, Nile tilapia, and two food resources. The major conclusion from our findings is that fisheries should culture both species to maximize the biomass outtake and financial profit.

Discrete stage-structured tick population dynamical system with diapause and control.

A discrete stage-structured tick population dynamical system with diapause is studied, and spraying acaricides as the control strategy is considered in detail. We stratify vector populations in terms of their maturity status as immature and mature subgroups. The immature subgroup is divided into two categories: normal immature and diapause immature. We compute the net reproduction number $ R_0 $ and perform a qualitative analysis. When $ R_0 < 1 $, the global asymptotic stability of tick-free fixed point is well proved by the inherent projection matrix; there exists a unique coexistence fixed point and the conditions for its asymptotic stability are obtained if and only if $ R_0 > 1; $ the model has transcritical bifurcation if $ R_0 = 1. $ Moreover, we calculate the net reproduction numbers of the model with constant spraying acaricides and periodic spraying acaricides, respectively, and compare the effects of the two methods on controlling tick populations.

Single-species population models with stage structure and partial tolerance in polluted environments.

We propose stage-structured single-species population models with psychological effects and partial tolerance in polluted environments in this paper. First, the conditions of extinction and the time for extinction are investigated respectively. Especially, the time for extinction takes longer as the value of the psychological effects increases. Then the weak persistence in the mean around the pollution-free equilibrium and the stochastic permanence have been derived under some moderate conditions. Further, the existence of a periodic solution for the periodic single-species population has been determined. The corresponding numerical simulations verify the efficiency of the main theoretical results.

Simulation of Stage-structured population growth of Myzus persicae (Suzler) (Hemiptera: Aphididade) based on age-stage, two sex life table

The age-stage specific growth rate and fecundity of Myzus persicae obtained from an age-stage, two-sex life table analysis were used to simulate the growth of stage-structured population under two scenario of initial population structure for five temperature regimes. The first scenario was started with a newly born nymph and the second scenario was started with the youngest female. In both scenario, the population growth increased with shorter life cycle in the respective order: 17°C &lt; 20°C &lt; 23°C &lt; 26°C &lt; 29°C. In this study, computer simulation based on the agestage, two sex life table demonstrate it’s advantages for revealing stage-structured population growth. Information on the growth of a stage-structured population is critical for deciding the timing of intervention in integrated pest management approach.

Cost-benefit evaluation of management strategies for an invasive amphibian with a stage-structured model

Management strategies for invasive populations should be designed to maximise efficacy and efficiency, i.e. to accomplish their goals while operating with the least resource consumption. This optimisation is often difficult to achieve in stage-structured populations, because costs, benefits and feasibility of removing individuals may vary with stage. We use a spatially-explicit stage-structured model to assess efficacy of past, present and alternative control strategies for invasive guttural toads, Sclerophrys gutturalis, in Cape Town. The strategies involve removal of variable proportions of individuals at different life-history stages and spatial scales. We also quantify the time necessary to implement each strategy as a proxy of financial resources and we correct strategy outcomes by implementation of time to estimate efficiency. We found that the strategy initially pursued in Cape Town, which did not target any specific stage, was less efficient than the present strategy, which prioritises adult removal. The initial strategy was particularly inefficient because it did not reduce the population size despite allocating consistent resources to remove eggs and tadpoles. We also found that such removal might be detrimental when applied at high levels. This counter-intuitive outcome is due to the ‘hydra effect’: an undesired increase in population size caused by removing individuals before overcompensatory density dependence. Strategies that exclusively remove adults ensure much greater management efficiency than those that also remove eggs and tadpoles. Available management resources should rather be allocated to increase the proportion of adult guttural toads that are removed or the spatial extent at which this removal is pursued.

Mortality estimate driven by population abundance field data in a stage-structured demographic model. The case of Lobesia botrana

Simulating the population dynamics of a stage-structured population requires the knowledge of development, mortality and fecundity rate functions characterizing the species. In general, development and fecundity can satisfactorily be estimated starting from literature data. Unfortunately, this is often not the case for the mortality function due to the lack of experimental data. To overcome this problem, we estimate the mortality rate function from field data on the abundance of the species. The mortality is expressed as a linear combination of cubic splines and the estimation method allows to determine its coefficients taking into account the observations measurement error. Moreover, the variability in the estimate is quantified using the confidence bands for both mortality and dynamics. The presented method allows obtaining a more flexible shape for the mortality rate functions compared with previous methods applied to the same pest. The method has been applied to the case of Lobesia botrana, the main pest in the European vineyards, with abundance data collected for five consecutive years in an experimental field in the North of Italy. Data collected over three years are used to estimate the mortality and to analyse the variability in the estimate and its effects on the population dynamics, while the other two datasets are used to validate the model simulating the dynamics using the estimated mortality.

Dynamics of a new stage-structured population model with transient and nontransient impulsive effects in a polluted environment

In this paper, we consider a new stage-structured population model with transient and nontransient impulsive effects in a polluted environment. By using the theories of impulsive differential equations, we obtain the globally asymptotically stable condition of a population-extinction solution; we also present the permanent condition for the investigated system. The results indicate that the nontransient and transient impulsive harvesting rate play important roles in system permanence. Finally, numerical analyses are carried out to illustrate the results. Our results provide effective methods for biological resource management in a polluted environment.