Stage-structured Population Model Research Articles

Estimated development times for stage-structured marine organisms are biased if based only on survivors

Stage duration is a key parameter in modeling population dynamics of stage-struc-tured populations, however stage duration can be difficult to estimate accuratelybecause calculations are based on survivors and fail to account for mortality. Herewe show a method by which development time and stage duration can be adjustedafter accounting for within-stage mortality. As an example, we use a previouslypublished data set on stage-specific abundances of the euphausiid, Euphausia pacificafrom four laboratory-incubated cohorts, raised from egg to juvenile stage. We useda stage-structured population model along with an inverse algorithm to estimatestage durations, both with and without considering mortality rates. Results suggestthat the overall stage duration from egg to furcilia was 48 days when mortalitywas considered, and 60 days when mortality was not included. Stage-specificmortality rates were generally lower than 10% per day for those stages with rela-tively high mortality rates (egg and naupliar stages and furcilia VI–VII) and ,4%for other developmental stages. However, the difference between the estimateswith and without considering mortality rates did not show a clear relationshipwith stage-specific mortality rates. More robust models that can incorporate thevariability in developmental pathways and physiological changes that occur duringthe molting process may be necessary to further investigate how age distributionwithin stage and mortality influence the estimation of stage duration.KEYWORDS: Euphausia pacifica; stage duration; stage-specific mortalitystage-structured population model; inverse technique

Persistence of Pathogens with Short Infectious Periods in Seasonal Tick Populations: The Relative Importance of Three Transmission Routes

BackgroundThe flaviviruses causing tick-borne encephalitis (TBE) persist at low but consistent levels in tick populations, despite short infectious periods in their mammalian hosts and transmission periods constrained by distinctly seasonal tick life cycles. In addition to systemic and vertical transmission, cofeeding transmission has been proposed as an important route for the persistence of TBE-causing viruses. Because cofeeding transmission requires ticks to feed simultaneously, the timing of tick activity may be critical to pathogen persistence. Existing models of tick-borne diseases do not incorporate all transmission routes and tick seasonality. Our aim is to evaluate the influence of seasonality on the relative importance of different transmission routes by using a comprehensive mathematical model.Methodology/Principal FindingsWe developed a stage-structured population model that includes tick seasonality and evaluated the relative importance of the transmission routes for pathogens with short infectious periods, in particular Powassan virus (POWV) and the related “deer tick virus,” emergent encephalitis-causing flaviviruses in North America. We used the next generation matrix method to calculate the basic reproductive ratio and performed elasticity analyses. We confirmed that cofeeding transmission is critically important for such pathogens to persist in seasonal tick populations over the reasonable range of parameter values. At higher but still plausible rates of vertical transmission, our model suggests that vertical transmission can strongly enhance pathogen prevalence when it operates in combination with cofeeding transmission.Conclusions/SignificanceOur results demonstrate that the consistent prevalence of POWV observed in tick populations could be maintained by a combination of low vertical, intermediate cofeeding and high systemic transmission rates. When vertical transmission is weak, nymphal ticks support integral parts of the transmission cycle that are critical for maintaining the pathogen. We also extended the model to pathogens that cause chronic infections in hosts and found that cofeeding transmission could contribute to elevating prevalence even in these systems. Therefore, the common assumption that cofeeding transmission is not relevant in models of chronic host infection, such as Lyme disease, could lead to underestimating pathogen prevalence.

Effects of cannibalism on a basic stage structure

In this paper, we discuss the effects of cannibalism on a basic stage-structured population model for a single species. A threshold condition for extinction versus persistence is obtained, and numerical simulations of the population dynamics are presented. These simulations suggest that cannibalism has a stabilizing effect on the population, promoting equilibrium of the adult population level.

Discrete host-parasitoid models with Allee effects and age structure in the host

We study a stage-structured single species population model with Allee effects. The asymptotic dynamics of the model depend on the maximal growth rate of the population as well as on its initial population size. We also investigate two models of host-parasitoid interaction with stage-structure and Allee effects in the host. The parasitoid population may drive the host population to extinction in both models even if the initial host population is beyond the Allee threshold.

Marine reserves and the evolutionary effects of fishing on size at maturation

Abstract Miethe, T., Dytham, C., Dieckmann, U., and Pitchford, J. W. 2010. Marine reserves and the evolutionary effects of fishing on size at maturation. – ICES Journal of Marine Science, 67: 412–425. Size-selective fishing may induce rapid evolutionary changes in life-history traits such as size at maturation. A major concern is that these changes will reduce population biomass and detrimentally affect yield and recruitment. Although marine reserves have been proposed as a tool for fisheries management, their evolutionary implications have as yet attracted little scrutiny. A simple model is used to investigate whether marine reserves can be expected to mitigate the evolutionary impacts of fishing on maturation size. The adaptive dynamics of size at maturation are analysed based on a stage-structured population model including size-selective fishing and marine reserves with different retention rates. As has been shown before, imposing greater fishing mortality on the largest individuals promotes an evolutionary change towards smaller maturation size. In the model, protecting part of a fish stock using a marine reserve can prevent such fisheries-induced evolution, and this protection critically depends on the type and extent of movement between the reserve and the fished area. Specifically, although the frequent movement of large adults increases catches of large adult fish outside a marine reserve, it also reduces the reserve's effectiveness in preventing fisheries-induced evolution. In contrast, when there is exchange between protected and fished areas through juvenile export alone, a marine reserve can effectively prevent evolution towards smaller maturation size, but does so at the expense of reducing the yield of large adult fish. Differences in the movement behaviour of successive life stages need to be considered for marine reserves, to help make fisheries more sustainable evolutionarily.

Stochastic development in biologically structured population models

Variation in organismal development is ubiquitous in nature but omitted from most age- and stage-structured population models. I give a general approach for formulating and analyzing its role in density-independent population models using the framework of integral projection models. The approach allows flexible assumptions, including correlated development times among multiple life stages. I give a new Monte Carlo numerical integration approach to calculate long-term growth rate, its sensitivities, stable age-stage distributions and reproductive value. This method requires only simulations of individual life schedules, rather than iteration of full population dynamics, and has practical and theoretical appeal because it ties easily implemented simulations to numerical solution of demographic equations. I show that stochastic development is demographically important using two examples. For a desert cactus, many stochastic development models, with independent or correlated stage durations, can generate the same stable stage distribution (SSD) as the real data, but stable age-within-stage distributions and sensitivities of growth rate to demographic rates differ greatly among stochastic development scenarios. For Mediterranean fruit flies, empirical variation in maturation time has a large impact on population growth. The systematic model formulation and analysis approach given here should make consideration of variable development models widely accessible and readily extendible.

Zooplankton population model coupled to a biogeochemical model of the North Western Mediterranean Sea ecosystem

A stage structured population (SSP) model based on Fennel's [Fennel, W., 2001. Modelling copepods with links to circulation models. Journal of Plankton Research, 23, 1217–1232] equations is applied to Centropages typicus (Kröyer), a dominant copepod species of the North Western Mediterranean Sea (NWMS) and a prey of small pelagic fish. The model considers five groups of stages and development rates are represented by a mechanistic formulation depending on individual specific growth in each stage. Individual growth is calculated from the individual energy budget depending on food availability and temperature. This SSP copepod model is then coupled in one way to a biogeochemical model of the NWMS based on Baklouti et al.’s [Baklouti, M., Diaz, F., Pinazo, C., Faure, V., Quéginer, B., 2006. Investigation of mechanistic formulations depicting phytoplankton dynamics for models of marine pelagic ecosystems and description of a new model. Progress in Oceanography. 71, 1–33] model of phytoplankton processes. Both models have been embedded into the modular numerical tool (Eco3 M) dedicated to biogeochemical modelling. The parameterisation of the physiological processes contributing to the individual metabolic carbon budget and the body weight of C. typicus is based on a recent compilation of the biology of this species. The model delivers stage-dependent growth and development rates which agree with observations in stable food and temperature culture conditions between 13 and 20 °C. An annual cycle of C. typicus population dynamics has been simulated at the DYFAMED offshore sampling station in the Ligurian Sea (NWMS). Simulations deliver consistent seasonal patterns of abundance and biomass as well as a realistic number of generations (6), adult body weight and female egg production. Finally, the SSP model is substituted by a bulk population variable of C. typicus inducing differences in the synchronicity of the simulated standing stock mainly in spring. The role of C. typicus in the production of detritic matter through faecal pellet production, the parameterisation of the bulk population model and the need to take demographic features into account are discussed. The representation of demographic fluxes has been successfully achieved in Eco3 M allowing to enlarge its potential use for an “end to end” food web approach.

The effects of a single stage-structured population model with impulsive toxin input and time delays in a polluted environment

Uncontrolled contribution of pollutant to the environment has led many species to extinction and several others are at the verge of extinction. This article deals with the dynamics of a single stage-structured population model with impulsive toxin input and time delays (including constant individual maturation time delay and pollution time delay) in a polluted environment, in which we assume that only the mature individuals are affected by pollutants. We obtain conditions for the global attractivity of the population-extinction periodic solution and the permanence of the population. We show that maturation time delay and impulsive toxin input can bring great effects on the dynamics of the system, and pollution time delay is harmless. Numerical simulations confirm our theoretical results.

Model complexity affects transient population dynamics following a dispersal event: a case study with pea aphids

Stage-structured population models predict transient population dynamics if the population deviates from the stable stage distribution. Ecologists' interest in transient dynamics is growing because populations regularly deviate from the stable stage distribution, which can lead to transient dynamics that differ significantly from the stable stage dynamics. Because the structure of a population matrix (i.e., the number of life-history stages) can influence the predicted scale of the deviation, we explored the effect of matrix size on predicted transient dynamics and the resulting amplification of population size. First, we experimentally measured the transition rates between the different life-history stages and the adult fecundity and survival of the aphid, Acythosiphon pisum. Second, we used these data to parameterize models with different numbers of stages. Third, we compared model predictions with empirically measured transient population growth following the introduction of a single adult aphid. We find that the models with the largest number of life-history stages predicted the largest transient population growth rates, but in all models there was a considerable discrepancy between predicted and empirically measured transient peaks and a dramatic underestimation of final population sizes. For instance, the mean population size after 20 days was 2394 aphids compared to the highest predicted population size of 531 aphids; the predicted asymptotic growth rate (lamdamax) was consistent with the experiments. Possible explanations for this discrepancy are discussed.

Assessing threats to species at risk using stage‐structured state–space models: mortality trends in skate populations

Population models are needed to assess the threats to species at risk and to evaluate alternative management actions. Data to support modeling is limited for many species at risk, and commonly used approaches generally assume stationary vital rates, a questionable assumption given widespread ecosystem change. We describe a modeling approach that can be applied to time series of length composition data to estimate vital rates and test for changes in these rates. Our approach uses stage-structured population models fit within a Bayesian state-space model. This approach simultaneously allows for both process and observation uncertainty, and it facilitates incorporating prior information on population dynamics and on the monitoring process. We apply these models to populations of winter skate (Leucoraja ocellata) that have been designated as "endangered" or "threatened." These models indicate that natural mortality has decreased for juveniles and increased for adults in these populations. The declines observed in these populations had been attributed to unsustainable rates of bycatch in fisheries for other groundfishes; our analyses indicate that increased natural mortality of adults is also an important factor contributing to these declines. Adult natural mortality was positively related to grey seal (Halichoerus grypus) abundance, suggesting the hypothesis that increased adult mortality reflected increased predation by expanding grey seal herds. Population projections indicated that the threatened population would be expected to stabilize at a low level of abundance if all fishery removals were eliminated, but that the endangered population would likely continue to decline even in the absence of fishery removals. We note that time series of size distributions are available for most marine fish populations monitored by research surveys, and we suggest that a similar approach could be used to extract information from these time series in order to estimate mortality rates and changes in these rates.

Simulating the evolution of glyphosate resistance in grains farming in northern Australia

The evolution of resistance to herbicides is a substantial problem in contemporary agriculture. Solutions to this problem generally consist of the use of practices to control the resistant population once it evolves, and/or to institute preventative measures before populations become resistant. Herbicide resistance evolves in populations over years or decades, so predicting the effectiveness of preventative strategies in particular relies on computational modelling approaches. While models of herbicide resistance already exist, none deals with the complex regional variability in the northern Australian sub-tropical grains farming region. For this reason, a new computer model was developed. The model consists of an age- and stage-structured population model of weeds, with an existing crop model used to simulate plant growth and competition, and extensions to the crop model added to simulate seed bank ecology and population genetics factors. Using awnless barnyard grass (Echinochloa colona) as a test case, the model was used to investigate the likely rate of evolution under conditions expected to produce high selection pressure. Simulating continuous summer fallows with glyphosate used as the only means of weed control resulted in predicted resistant weed populations after approx. 15 years. Validation of the model against the paddock history for the first real-world glyphosate-resistant awnless barnyard grass population shows that the model predicted resistance evolution to within a few years of the real situation. This validation work shows that empirical validation of herbicide resistance models is problematic. However, the model simulates the complexities of sub-tropical grains farming in Australia well, and can be used to investigate, generate and improve glyphosate resistance prevention strategies.

Demographic consequences of anthropogenic influences: Florida black bears in north-central Florida

Anthropogenic habitat fragmentation poses a serious threat to conservation of large carnivores, due to their extensive movements and potential conflicts with humans. We studied the population ecology of Florida black bears ( Ursus americanus floridanus) for 6 years in two study areas in north-central Florida: Ocala National Forest (ONF), a contiguous forested habitat, and an adjacent residential community of Lynne, a fragmented habitat with substantial human activities. We estimated age-specific survival and fecundity rates of bears using data from radio-collared bears, and parameterized and analyzed stage-structured matrix population models for the two study sites and also for data pooled from both sites. Annual survival rates of adult females were lower in Lynne (0.776 ± 0.074) than in ONF (0.966 ± 0.023). While cub survival rates were higher in Lynne (0.507 ± 0.135) than in ONF (0.282 ± 0.109), the rates at both sites were substantially lower than those reported for other black bear populations. Age-specific fecundities did not vary between sites. The asymptotic population growth rate for ONF was greater than one, whereas that for Lynne was less than one. Our results suggest that anthropogenic influences (primarily road density and vehicular traffic, through their effect on adult survival) can substantially affect the population dynamics of Florida black bears and other large carnivores with large home ranges. We recommend efforts such as constructing highway underpasses, which could reduce road-related mortalities, to ensure long-term persistence of Florida black bears facing threats from rapidly increasing human influences.

Harvesting on a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin

In the natural world, there are many species whose individual members have a life history that they take them with two distinct stages: immaturity and maturity. In particular, we have in mind mammalian populations and some amphibious animals. We improve the assumption of a single population as a whole. It is assumed that the immature individuals and mature individuals are divided by a fixed period. This paper concentrates on the study of a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin at fixed moments. Furthermore, the mature individuals are harvested continuously. We show that the population goes extinct if the harvesting rate is beyond a critical threshold. Conditions for the extended permanence of the population are also examined. From the biological point of view, it is easy to protect species by controlling the harvesting amount, impulsive period of the exogenous input of toxin and toxin impulsive input amount, etc. Our results provide reasonable tactics for biological resource management.

Persistence of structured populations in random environments

Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.

Multistate capture–recapture analysis under imperfect state observation: an application to disease models

Summary 1 Multistate capture–recapture models are frequently used to estimate the survival and state transition parameters needed to parameterize stage-structured population models, tools that are important for conservation and management. Typically, such models assume that all encountered individuals can be assigned to a particular state without error or ambiguity, a requirement which is difficult to meet in practice. Model extensions to relax this assumption would increase the richness of ecological data sets available for estimating life-history and stage-transition parameters with multistate models. 2 One relatively common analytical approach when confronted with ambiguity in state determination is to censor all encounters where the state of an animal cannot be ascertained. Here, we present an alternative approach, which uses a hidden Markov (or multievent) modelling framework that can incorporate data from encounters of unknown state. Using simulation, we show that our approach leads to estimators of state-specific survival and transition probabilities that are more precise, and sometimes considerably so, than methods based on censoring. 3 We demonstrate our approach using field data from a study of the dynamics of conjunctivitis in the house finch Carpodacus mexicanus Muller. A fundamental challenge in modelling disease dynamics involves the estimation of the rates of entry and exit from one or more disease states, which can be complicated when disease state is uncertain. We show that incorporating data from unknown states made substantial improvements to parameter precision. 4 Synthesis and applications. Missing or incomplete records are an unfortunate but common feature of many ecological field studies, often diminishing the quality and quantity of data. Our approach of treating state as a hidden Markov process allows such records to be used, increasing the precision of survival and state transition parameters in multistate mark–recapture studies. Our approach is more general than other approaches in the literature, and does not require specialized sampling designs or ancillary information to inform state assignment. We suggest that ecologists consider using this modelling approach instead of censoring records whenever state information is missing.

Dynamic heterogeneity in life histories

Longitudinal data on natural populations have been analysed using multistage models in which survival depends on reproductive stage, and individuals change stages according to a Markov chain. These models are special cases of stage-structured population models. We show that stage-structured models generate dynamic heterogeneity: life-history differences produced by stochastic stratum dynamics. We characterize dynamic heterogeneity in a range of species across taxa by properties of the Markov chain: the entropy, which describes the extent of heterogeneity, and the subdominant eigenvalue, which describes the persistence of reproductive success during the life of an individual. Trajectories of reproductive stage determine survivorship, and we analyse the variance in lifespan within and between trajectories of reproductive stage. We show how stage-structured models can be used to predict realized distributions of lifetime reproductive success. Dynamic heterogeneity contrasts with fixed heterogeneity: unobserved differences that generate variation between life histories. We show by an example that observed distributions of lifetime reproductive success are often consistent with the claim that little or no fixed heterogeneity influences this trait. We propose that dynamic heterogeneity provides a 'neutral' model for assessing the possible role of unobserved 'quality' differences between individuals. We discuss fitness for dynamic life histories, and the implications of dynamic heterogeneity for the evolution of life histories and senescence.

A single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin

In this paper, we concentrates on the study of a single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin. A globally attractive condition for the population-extinction boundary periodic solution of the investigated system is obtained. Sufficient criteria on the permanence of the population are derived.

Modeling population dynamics of two cockroach species: Effects of the circadian clock, interspecific competition and pest control

The German cockroach Blattella germanica is obviously one of the most spread household pests in the world, and is now virtually impossible to sustain outside human constructions. The double-striped cockroach B. bisignata, on the other hand, is limited to Southeast Asia and mostly living in the open space, yet is able to establish in cockroach-free households, too. In this article, we develop a stage-structured population model of these two species to explore (i) whether their circadian clocks impact their long-term population dynamics, (ii) which of these species is a superior competitor, and (iii) how stringent potential pest control strategies have to be to significantly impact established populations of the German cockroach. The results of the model are as follows. Firstly, phase shifts in the light-to-dark cycle did not affect cockroach population dynamics unless males and females were out of phase and their mate finding abilities rather limited. In addition, for the hypothesized circadian clock genotypes, the shorter is the inactivity period relative to the activity one or the less arrhythmic is the population, the more viable the population is and the quicker it grows to large numbers. Secondly, the German cockroach was the superior competitor: it was able to invade and drive out established populations of the double-striped cockroach and prevent any invasion of the latter. Finally, only a significant and simultaneous reduction in a number of most sensitive German cockroach parameters resulted in species extirpation. Only carefully designed and data-based models of German (and double-striped) cockroach population dynamics can be helpful in our quest to win the fight over this unwelcome but very sturdy species.

Demographic Response of a Grassland Rodent to Environmental Variability

We used stage-structured matrix population models, derived from 3 years with disparate levels of precipitation, to assess the potential effects of climate change on annual population growth (k) of deer mice (Peromyscus maniculatus). Populations of deer mice increased during a year of normal precipitation (k ¼ 1.69 6 0.02 SE) and a wet year (k ¼ 1.03 6 0.02), but declined in a dry year (k ¼ 0.34 6 0.02). Life-table response experiment analyses indicated that reduced survival of adults in the dry year, and reduced survival of pups and juveniles in the wet year, exerted the greatest influence on variation in population growth. Stochastic models that projected populations of deer mice for a 50-year period predicted that populations would not be able to persist if mean annual precipitation was reduced � 11% by increasing the frequency of dry years. Furthermore, the stochastic population growth rate declined more quickly when the probability of a normal year was reduced, simulating increased variability in rainfall, relative to other scenarios examined. Our stochastic models indicate that a relatively small reduction in mean precipitation could result in substantial population declines of P. maniculatus in the mixed-grass prairie of central North America.

Hard clam Meretrix lusoria to Hg-stressed birnavirus susceptibility revealed through stage-structured disease transmission dynamics

The purpose of this study was to assess the effects of mercury (Hg) on birnavirus infection in the farmed hard clam ( Meretrix lusoria) populations. A stage-structured matrix population model was linked with a nonlinear epidemiological dynamics of host–pathogen model to quantify the effects of increased Hg-stressed birnavirus on population dynamics of disease in hard clam populations. Bioenergetics was incorporated into population stage-structured model to enhance life cycle toxicity assessment on constraining reproduction and growth in life stages of hard clams. We delineated three qualitatively distinct scenarios of virus only, Hg + virus, and virus + Hg. Within a range of disease transmissibility drawn from analysis of Hg-stressed birnavirus in hard clams, different transmissibility led to simulated outbreaks characterized by basic reproductive number ( R 0) depicting the allowance population numbers to contain disease spread for all three scenarios. This study suggested that recognizing which of the scenarios best describing a situation in the field could aid in planning disease management and in choosing the most efficient and feasible strategy. The present simple model captured the essential dynamics and its flexible enough to integrate effects occurring at varying temporal scales based on biologically plausible and empirically grounded dynamical models. We were confident that the model could be easily adapted for other aquaculture species and encourage researchers to use the model to diagnose the population-level risk of toxic chemical-stressed pathogen on these species.