Deterministic Population Models Research Articles

Temperature-dependent development of Helicoverpa armigera (Lepidoptera: Noctuidae) at constant temperatures: instar pathways and stage transition models with semifield validation.

Temperature-dependent development of Helicoverpa armigera (Hüber) fed with an artificial diet was studied at different temperatures. The instar pathway (IPW) defined as the number of instars prior to pupation significantly affected larval development time, with higher IPW leading to longer larval development time. The IPW was determined at the fifth instar to proceed to 6-7 IPW, when the development time of fifth instar was largely shortened. Accordingly, the development time after the fourth instar was combined (i.e., the fifth-seventh instar) as a single stage to simplify the various IPW and applied to develop phenology models. In linear models, the lower threshold temperature (LT) and thermal constant (degree-days, DD) for each stage were estimated. DD based on the common LT of 10.7 °C were 43, 287, and 191 DD for eggs, larvae, and pupae, respectively. DD model (253.6 DD with LT 10.3 °C for larvae and 181.5 DD with 11.6 °C for pupae) showed good performance in predicting the 50% occurrences of pupae and adults. In nonlinear models, stage transition (ST) models were constructed using the development rate and distribution models to simulate the proportion of individuals shifted from one stage to the next stage. The ST model showed good performance, indicating an average discrepancy of 1.74 days at 25%, 50%, 75%, and 90% adult emergence. Our models developed here will be useful to predict the phenology of H. armigera in the field and to construct a deterministic population model in the future.

Accounting for bias in prevalence estimation: The case of a globally emerging pathogen

Abstract Accurate quantification of infection parameters is necessary to ensure effective surveillance, investigation and mitigation of infectious diseases. However, hosts and pathogens are often imperfectly observed and key epidemiological parameters, such as infection prevalence, can be biased if this observational uncertainty is not properly accounted for. Here, we evaluated the combined effects of imperfect pathogen detection and host pseudoreplication on the estimation of infection prevalence of the pathogen Batrachochytrium dendrobatidis (Bd) in the southern Darwin's frog (Rhinoderma darwinii). This pathogen causes amphibian chytridiomycosis, a panzootic disease responsible for the greatest documented loss of biodiversity due to an infectious disease. From November 2018 to March 2019, we made 1085 captures of 641 R. darwinii individuals in two areas of Southern Chile. Captured frogs were individually identified to eliminate host pseudoreplication, skin‐swabbed twice in sequence, and each swab was analysed in duplicate using a real‐time polymerase chain reaction (qPCR) assay to detect Bd. To provide a robust estimate of period prevalence, we used a Bayesian multiscale occupancy model that considers pathogen imperfect detection arising from both sampling and diagnostic testing processes. Finally, using a deterministic matrix population model, we illustrated how the method chosen to estimate prevalence influenced our conclusions regarding the impact of Bd infection on host population trajectories. Our results showed that Bd prevalence could be underestimated by 55% if false negatives and host pseudoreplication were not accounted for. Host pseudoreplication had a greater impact on prevalence underestimation than pathogen imperfect detection in our study. This underestimation in prevalence changed our interpretation of the impacts of Bd infections on our model species, from a nearly stable population using the naïve period prevalence to a declining one using our robust estimate. Synthesis and applications. These results highlight the importance of using robust inferences to inform disease risk assessments and to efficiently allocate limited resources during mitigation strategies of infectious diseases. The methods used here can be applied to a wide range of host–pathogen systems, and will be of interest to both researchers and practitioners aiming to investigate and mitigate the impacts of infectious diseases on free‐ranging populations.

Construction, stochastization and computer study of dynamic population models “two competitors - two migration areas”

When studying deterministic and stochastic population models, the actual problems are the formalization of processes, taking into account new effects caused by the interaction of species, and the development of computer research methods. Computer research methods make it possible to analyze the trajectories of multidimensional population systems. We consider the “two competitors - two migration areas” model, which takes into account intraspecific and interspecific competition in two populations, as well as bidirectional migration of both populations. For this model, we take into account the variability of the reproduction rates of species. A formalized description of the four-dimensional model “two competitors - two migration areas” and its modifications is proposed. Using the implementation of the evolutionary algorithm, a set of parameters is obtained that ensure the coexistence of populations under conditions of competition between two species in the main area, taking into account the migration of these species. Taking into account the obtained set of parameters, a positive stationary state is found. Two-dimensional and three-dimensional projections of phase portraits are constructed. Stochastization of the model “two competitors - two migration areas” is carried out based on the method of self-consistent one-step models constructing. The Fokker-Planck equations are used to describe the structure of the model. A transition to a four-dimensional stochastic differential equation in the Langevin form is performed. To carry out numerical experiments, a specialized software package is used to construct and study stochastic models, and a computer program based on differential evolution is developed. Algorithms for generating trajectories of the Wiener process and multipoint distributions and modifications of the Runge-Kutta method are used. In the deterministic and stochastic cases, the dynamics of the trajectories of populationmigration systems is studied. A comparative analysis of deterministic and stochastic models is carried out. The results can be used in modeling of different classes of dynamic systems.

Linking mathematical models and trap data to infer the proliferation, abundance, and control of Aedes aegypti

Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this paper, we develop a deterministic mosquito population model, estimate model parameters by using local entomological and temperature data, and use the model to calibrate the mosquito trap data from 2017 to 2019. We further use the model to compare the Ae. aegypti population and evaluate the impact of rainfall intensity in different urban built environments. Our results show that rainfall affects the breeding sites and the abundance of Ae. aegypti more significantly in tourist areas than in residential places. In addition, we apply the model to quantitatively assess the effectiveness of vector control strategies in Miami-Dade County.

Non-genetic resistance facilitates survival while hindering the evolution of drug resistance due to intraspecific competition

Rising rates of resistance to antimicrobial drugs threaten the effective treatment of infections across the globe. Drug resistance has been established to emerge from non-genetic mechanisms as well as from genetic mechanisms. However, it is still unclear how non-genetic resistance affects the evolution of genetic drug resistance. We develop deterministic and stochastic population models that incorporate resource competition to quantitatively investigate the transition from non-genetic to genetic resistance during the exposure to static and cidal drugs. We find that non-genetic resistance facilitates the survival of cell populations during drug treatment while hindering the development of genetic resistance due to competition between the non-genetically and genetically resistant subpopulations. Non-genetic resistance in the presence of subpopulation competition increases the fixation times of drug resistance mutations, while increasing the probability of mutation before population extinction during cidal drug treatment. Intense intraspecific competition during drug treatment leads to extinction of susceptible and non-genetically resistant subpopulations. Alternating between drug and no drug conditions results in oscillatory population dynamics, increased resistance mutation fixation timescales, and reduced population survival. These findings advance our fundamental understanding of the evolution of resistance and may guide novel treatment strategies for patients with drug-resistant infections.

Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2.

We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.

An Interactive Teaching Tool Describing Resistance Evolution and Basic Economics of Insecticide-Based Pest Management.

Simple SummaryTo attract bright, creative, and curious students to the academic fields of applied entomology and sustainable food production, instructors of undergraduate and graduate student courses should discuss experiences with lectures and lab sessions and share effective interactive teaching tools. This communication describes how a simple population model in an Excel spreadsheet can be used in teaching both insecticide resistance evolution and basic economics of insecticide-based pest management. A tutorial video and the model as an Excel spreadsheet are freely available. Through hands-on experience with this and similar interactive teaching tools, students will acquire fundamental knowledge about basic structures population models and they will acquire experience with quantitative data interpretation. Teachers can use this tool and accompanying tutorials to demonstrate how models can be used to describe and visualize complex interactions between insect genetics and crop management. Furthermore, data from published studies can be analyzed and discussed using this interactive teaching tool.Effective teaching of complex concepts relies heavily on the ability to establish relevance of topics and to engage students in a constructive dialogue. To connect students with abstract concepts and basic theory, instructors foster and facilitate an engaging teaching environment. Population modeling is a cornerstone in applied entomology. However, it is also a topic and skill set that requires both basic mathematical and biological knowledge, and it may be perceived by students as being abstract and exceedingly theoretical. As a way to introduce entomology students at both that undergraduate and graduate levels to hands-on experience with population modeling, a well-established and widely used deterministic genetic population model is presented as an interactive teaching tool. Moreover, the general model describes three genotypes (SS = homozygous susceptible, SR = heterozygous, and RR = homozygous resistant) during 30 discrete and univoltine generations under a shared population density dependence (carrying capacity). Based on user inputs for each genotype (survival, fitness cost, reproductive rate, emigration, and immigration) and an initial resistance allele frequency, model outputs related to resistance evolution are produced. User inputs related to insecticide-based pest management (pest density action threshold, crop damage rate, insecticide treatment costs, and profit potential) can also be introduced to examine and interpret the basic economic effects of different insect pest management scenarios. The proposed model of resistance evolution and basic economics of pest management relies on a large number of important simplifications, so it may only have limited ability to predict the outcomes of real-world (commercial) scenarios. However, as a teaching tool and to introduce students to a well-known and widely used genetic population model structure, the interactive teaching tool is believed to have considerable utility and relevance.

Abstract 227: Association between treatment response classification and resistance in metastatic prostate cancer patients treated with enzalutamide

Abstract Introduction: Treatment resistance contributes importantly to clinical response of metastatic prostate cancer (mPC) patients. We hypothesize that patients with more resistant lesions would lead to more unfavorable treatment response. The goal of this study was to use a computational model to investigate the association between treatment response and individual lesion resistance to enzalutamide therapy. Materials and Methods: A deterministic population model was used to simulate dynamics of drug-sensitive and drug-resistant cells in individual lesions. Intrinsic and acquired resistance were taken into account. Model parametrization, assuming patient and lesions specific parameters, was performed by benchmarking the model to lesion-level burden of 365 lesions extracted from 18F-NaF PET of 7 mPC patients. Distributions of patient and lesion characteristics and model parameters were estimated using a maximum likelihood estimation. With Monte Carlo random sampling of a sample population of 1000 patients lesion-level characteristics were chosen. Afterwards, model simulated lesion-level burden. Lesions were classified as completely responding, partial responding (iPR), stable disease (iSD), progression disease (iPD) and new disease (iND) based on simulated lesion-level burden and measured uncertainties. The proportion of visible lesions (iPR, iSD, iPD and iND) consisting of only drug-resistant cells (NL) was calculated for individual patient. The percentage of patients having higher NL in comparison to the proportion of lesions classified as iSD, iPD, and iND was calculated. All the calculations were performed at 0.5, 1 and 2 years. Results: With Monte Carlo random sampling dynamics of a total of 36185 lesion burden was simulated. Median proportion of lesions classified as iSD, iPD, and iND at 0.5, 1 and 2 years was 0.56, 0.50, 0.54, respectively. Median NL at 0.5, 1 and 2 years was 0.09 (range: 0-1), 0.57 (range: 0.1-1) and 0.82 (range: 0.27-1), respectively. 1%, 59% and 90% of patients had higher NL in comparison to the occupancy of iSD, iPD, and iND at year 0.5, 1 and 2, meaning that some percentage of lesions classified as iPR disease are completely resistant. Median proportion of lesions classified as iPR disease and being completely resistant is 0.18, 0.17 and 0.3 at year 0.5, 1 and 2. Conclusions This work presents a computational model as a useful complementary tool in standard treatment response and therapy efficiency assessment. Contrary to our hypothesis, the results show that significant proportion of lesions classified as favorable responding disease contain only drug-resistant cells. Citation Format: Maruša Turk, Damijan Valentinuzzi, Robert Jeraj. Association between treatment response classification and resistance in metastatic prostate cancer patients treated with enzalutamide [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 227.

Initial abundance and stochasticity influence competitive outcome in communities.

Predicting competitive outcomes in communities frequently involves inferences based on deterministic population models since these provide clear criteria for exclusion (e.g. R* rule) or long-term coexistence (e.g. mutual invasibility). However, incorporating stochasticity into population- or community-level processes into models is necessary if the goal is to explain variation in natural systems, which are inherently stochastic. Similarly, in systems with demographic or environmental stochasticity, weaker competitors have the potential to exclude superior competitors, contributing to what is known as 'competitive indeterminacy'. The importance of such effects for natural communities is unknown, in part because it is difficult to demonstrate that multiple forms of stochasticity are present in these communities. Moreover, the effects of multiple forms of stochasticity on competitive outcomes are largely untested, even in theory. Here, we address these issues by examining the role of stochasticity in replicated communities of flour beetles (Tribolium sp.). To do so, we developed a set of two-species stochastic Ricker models incorporating four distinct forms of stochasticity: environmental stochasticity, demographic stochasticity, demographic heterogeneity and stochastic sex determination. By fitting models to experimental data, and simulating fit models to examine long- term behaviour, we found that both the duration of transient coexistence and the degree of competitive indeterminacy were sensitive to the forms of stochasticity included in our models. These findings suggest the current estimates of extinction risk, coexistence and time until competitive exclusion in communities may not be accurate when based on models that exclude relevant forms of stochasticity.

Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan.

This article presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this article, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

Forest management legacies affect demographics and population dynamics of spruce grouse in northern Maine

Conserving wildlife in managed forests requires knowledge of the interplay between species’ ecology and forestry practices. Spruce grouse (Falcipennis canadensis) are obligate residents of North American conifer forests with a southern range terminus in the northern U.S. We studied survival and reproduction of spruce grouse from 2012 through 2018 in north-central Maine, USA, within a landscape managed extensively for commercial forest products. We used radio telemetry data from 151 unique spruce grouse to monitor nest survival, brood success, and mortality of two age classes (juvenile and adult), and related these factors to a geospatial layer of stand harvest histories that provided a record of the timing and method of silvicultural treatments over the previous 30 years. We evaluated how demographic rates were affected by these forest practices, constructed stage-structured models of spruce grouse population growth, and used these models to quantify potential effects of management legacy on population dynamics. Nests in clearcuts with post-harvest treatments (herbicide and pre-commercial thinning) had lower success than those located in other stand types. Success of broods during summer increased with greater use of residual stands (unharvested for > 31 years), however, juvenile spruce grouse that made greater use of residual stands following independence had reduced survival. Adults that used a greater proportion of clearcuts lacking post-harvest treatments had the greatest annual survival. Deterministic and stochastic population models predicted values of λ < 1.0, suggesting population decline, and we found that λ was most sensitive and elastic to survival of adult females. Combined results from demographic analyses and our population model showed that greater use of untreated clearcuts by adult females had the largest potential to increase population growth, and that a stable to increasing growth rate (λ ≥ 1.0) could be achieved with particular combinations of stand use at different life stages. In this system the demographic mechanisms affecting relationships between forest management and spruce grouse population dynamics were complex. Ongoing changes in forest practices within the region may shift forests away from conifer-dominated composition, with negative consequences for the future status of the species.

Queuing model of axonal transport

The motor-driven intracellular transport of vesicles to synaptic targets in the axons and dendrites of neurons plays a crucial role in normal cell function. Moreover, stimulus-dependent regulation of active transport is an important component of long-term synaptic plasticity, whereas the disruption of vesicular transport can lead to the onset of various neurodegenerative diseases. In this paper we investigate how the discrete and stochastic nature of vesicular transport in axons contributes to fluctuations in the accumulation of resources within synaptic targets. We begin by solving the first passage time problem of a single motor-cargo complex (particle) searching for synaptic targets distributed along a one-dimensional axonal cable. We then use queuing theory to analyze the accumulation of synaptic resources under the combined effects of multiple search-and-capture events and degradation. In particular, we determine the steady-state mean and variance of the distribution of synaptic resources along the axon in response to the periodic insertion of particles. The mean distribution recovers the spatially decaying distribution of resources familiar from deterministic population models. However, the discrete nature of vesicular transport can lead to Fano factors that are greater than unity (non-Poissonian) across the array of synapses, resulting in significant fluctuation bursts. We also find that each synaptic Fano factor is independent of the rate of particle insertion but increases monotonically with the amount of protein cargo in each vesicle. This implies that fluctuations can be reduced by increasing the injection rate while decreasing the cargo load of each vesicle. Statement of SignificanceThe motor-driven intracellular transport of vesicles to synaptic targets in the axons and dendrites of neurons plays a crucial role in normal cell function. Moreover, stimulus-dependent regulation of active transport is an important component of long-term synaptic plasticity, whereas the disruption of vesicular transport can lead to the onset of various neurodegenerative diseases. In this paper we investigate how the discrete and stochastic nature of vesicular transport in axons contributes to fluctuations in the accumulation of resources within synaptic targets. Almost all previous studies of axonal transport have focused on deterministic population models, or on stochastic models of a single motor particle searching for a target. The novel feature of the current paper is to take a target-centric viewpoint, which focuses on the accumulation of resources within synaptic targets under multiple search-and-capture events. In particular, building on previous work by the author on cytoneme-based morphogenesis, he develops a general framework for studying synaptic resource accumulation based on queuing theory. Two major results of the paper are as follows: (i) the discrete nature of vesicular transport can lead to Fano factors that are greater than unity (non-Poissonian) across the array of synapses, resulting in significant fluctuation bursts. (ii) Each synaptic Fano factor is independent of the rate of particle insertion but increases monotonically with the amount of protein cargo in each vesicle. This implies that fluctuations can be reduced by increasing the injection rate while decreasing the cargo load of each vesicle. A wide range of possible extensions of the basic model are highlighted in the discussion.

Optimization Problems for Models of Harvesting a Renewable Resource

We consider models of exploited populations defined by equations with random parameters. For the deterministic population model we study the resource share control problem of maximizing profit. For the probabilistic model we propose a mining method providing an estimate of the average profit from below by the largest possible number. Bibliography: 7 titles.

Life on the edge: common slow pace of life but contrasted trajectories of alpine rock ptarmigan populations at their southern margin

Investigating how and why the life history and demographic traits of a species vary across its range is fundamental to understand its evolution and population ecology and then develop sustainable management recommendations. At the margins of a species' distribution range, populations are expected to exhibit a slower pace of life than in core areas, making them less able to withstand pressures that impact survival. To explore these questions, we estimated age and sex-dependent seasonal survival probabilities using 305 radio-tagged birds monitored over a 18-year period in two alpine rock ptarmigan populations at the southern limit of their distribution, one in the Alps and one in the Pyrenees. We also estimated fecundity of both populations and then conducted sensitivity analysis as well as population viability analyses using deterministic and stochastic population models. Annual survival probability was high in both populations (0.65 for adults and 0.60 for juveniles), but reproductive success was much lower in the Alps (0.55 chicks per hen in the Alps vs 1.19 in the Pyrenees). The results showed that adult survival was the most sensitive demographic parameter. While population in the Pyrenees was stable (λ=1.01; 0.87–1.16), the other in the Alps appeared to be strongly declining (λ=0.81; 0.72–0.91) and this difference was clearly driven by differences of fecundity. While our findings confirm that our peripheral populations are associated with a slower pace of life, they present the particularity to be situated both at the edge and at high altitude. A more systematic study of peripheral population at higher latitude or on island may provide new insight on inter-pop variations of pace of life that would be useful for manager of these cold-adapted species. Key-words: Life history traits, demography, matrix model, telemetry, population viability analysis, age-class survival, fecundity.

Title: Recruitment is key to understanding amphibian’s different population-level responses to chytrid fungus infection

Understanding why related species have differing population-level responses to threats can be key to identifying conservation options for declining populations. However, this is difficult when multiple threats are implicated. Chytrid fungus (Batrachochytrium dendrobatidis: Bd) is implicated in at least 500 amphibian population declines globally, although few tangible options exist to mitigate pathogen impacts. Other threatening processes also invariably operate on most amphibians. Non-native fish, for example, can contribute to amphibian declines and may exacerbate Bd impacts. We disentangled the impacts of Bd and non-native fish upon two stream breeding frog species with differing conservation statuses to reveal vital rates that are crucial for species persistence. Litoria spenceri are threatened and historically occurred at elevations between 300–1100m asl in southeastern Australia. Litoria lesueurii are non-threatened and sympatric with L. spenceri at some sites. Using mark-recapture derived demographic rates known to correlate with climate and elevation, discrete-time deterministic population models were constructed for each species at high, moderate and low elevation sites, and multiple management scenarios. Our study reveals that age to maturation, clutch size and egg-year 1 survival influenced interspecific and intraspecific population-level responses of the two frogs to Bd impacts. Importantly, our results highlight that an amphibian population’s capacity to counteract Bd-mediated adult mortality is clearly constrained by other threats and environment interactions that moderate species recruitment. Furthermore, understanding limits to recruitment may help identify Bd mitigation strategies. In our study, disease mitigation may be best achieved at some sites by enhancing recruitment through non-native fish management.

Twenty-year assessment of Lignum-vitae (Guaiacum sanctum, Zygophyllaceae) in the Palo Verde National Park of Costa Rica

Introduction: The Lignum-vitae (Guaiacum sanctum; Zygophyllaceae) of Mesoamerica and the Greater Antilles, is threatened over much of its range. We evaluated whether a G. sanctum population in the Palo Verde National Park of Costa Rica is viable in the long term. Methods: Using two demographic studies, one in 1997 and the other in 2017, we estimated survival and fecundity rates for each tree age class, population growth rate (lambda), and vital rates elasticities, and we used a density-independent deterministic population model to project the long-term trend of that population. Results: The estimated vital rates during the last 20 years suggested that this population is rapidly decreasing. Although some age classes increased in abundance, seedlings are rare and the plants that recruited in 1997 have not yet reached reproductive maturity. Our results suggest that the current abundance of G. sanctum within the national park may not be a good indicator of its long-term conservation status, and from our population viability analysis, we estimated that the population we studied would decrease to less than 1 % of its current size within the next 200 years. Conclusions: Landscape-scale ecosystem deterioration affecting the greater PVNP region, such as loss of seed dispersers and suppression of disturbances, may offset the passive protection of G. sanctum within park boundaries. Relying on the overall strict protection afforded by the location of the population within the Palo Verde National Park may not be sufficient to conserve this population of G. sanctum. We recommend that more proactive experimental protection and/or restoration measures, possibly including disturbance treatments, be implemented within a research program.

Recombination and mutational robustness in neutral fitness landscapes.

Mutational robustness quantifies the effect of random mutations on fitness. When mutational robustness is high, most mutations do not change fitness or have only a minor effect on it. From the point of view of fitness landscapes, robust genotypes form neutral networks of almost equal fitness. Using deterministic population models it has been shown that selection favors genotypes inside such networks, which results in increased mutational robustness. Here we demonstrate that this effect is massively enhanced by recombination. Our results are based on a detailed analysis of mesa-shaped fitness landscapes, where we derive precise expressions for the dependence of the robustness on the landscape parameters for recombining and non-recombining populations. In addition, we carry out numerical simulations on different types of random holey landscapes as well as on an empirical fitness landscape. We show that the mutational robustness of a genotype generally correlates with its recombination weight, a new measure that quantifies the likelihood for the genotype to arise from recombination. We argue that the favorable effect of recombination on mutational robustness is a highly universal feature that may have played an important role in the emergence and maintenance of mechanisms of genetic exchange.

Long time behaviors of single-species population models with psychological effect and impulsive toxicant in polluted environments

In this paper, we formulate and study the single-species population models with impulsive toxicant input in polluted environments. For the deterministic single-species population model, the threshold between persistence and extinction is established for single-species population. For the stochastic single-species population model, there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by μ̄ is established, which mainly determines the persistence or extinction of the single-species. Numerical simulations are carried out to support our theoretical results.

Accounting for environmental change in continuous-time stochastic population models

The demographic rates (e.g., birth, death, migration) of many organisms have been shown to respond strongly to short- and long-term environmental change, including variation in temperature and precipitation. While ecologists have long accounted for such nonhomogeneous demography in deterministic population models, nonhomogeneous stochastic population models are largely absent from the literature. This is especially the case for models that use exact stochastic methods, such as Gillespie’s stochastic simulation algorithm (SSA), which commonly assumes that demographic rates do not respond to external environmental change (i.e., assumes homogeneous demography). In other words, ecologists are currently accounting for the effects of demographic stochasticity or environmental variability, but not both. In this paper, we describe an extension of Gillespie’s SSA (SSA + ) that allows for nonhomogeneous demography and examine how its predictions differ from a method that is partly naive to environmental change (SSAn) for two fundamental ecological models (exponential and logistic growth). We find important differences in the predicted population sizes of SSA + versus SSAn simulations, particularly when demography responds to fluctuating and irregularly changing environments. Further, we outline a computationally inexpensive approach for estimating when and under what circumstances it can be important to fully account for nonhomogeneous demography for any class of model.

Metapopulation Modelling of Threatened Plants to Assess Conservation Status and Determine Minimum Viable Population Size

Use of metapopulation modelling in conservation of threatened plants has been demonstrated in this article taking Paris polyphylla Smith as an example. The metapopulation data collected from Sikkim Himalaya over a period of four years were analysed using RAMAS Metapop 5.0 software. Demographic projection, assessment of extinction probability, population viability analysis, and analysis of impact of disturbance on the metapopulation were undertaken. The metapopulation had 11 populations of which seven were in continuous forest (CF) and four were in forest fragments (FF). All the analyses were done in two model scenarios, viz. base-model (M1) representing the disturbed condition, and alternate model (M2) representing the undisturbed condition for three distinct layers of P. polyphylla populations, i.e. CF, FF in isolation, and collectively as metapopulation. The outputs of the deterministic population models in respect of CF and FF populations revealed that both the populations had contribution of growth and survival of plants to such decline was greater than the fecundity in both the models. Stochastic simulations revealed an extinction risk of >10% in 100 years in M1 scenario, which put the species under vulnerable category. The extinction risk of metapopulation significantly varied between the two models (M1 = 0.85; M2 = 0.42), conforming the hypothesis that disturbance and forest fragmentation have detrimental effect on the persistence of P. polyphylla . Recovery of species was most promising when reproductive individuals were introduced to the M2 model. Thus, both introduction of individuals in the field and protection of the populations with emphasis on the reproductive subset would result in achieving minimum viable population size or low threat status of the species.