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Eradicating feral pigs from island ecosystems can assist in restoring damaged biodiversity values and protect commercial industries such as agriculture. Although many feral pig eradications have been attempted, management decisions are often led by practitioner experience rather than empirical evidence. Few interventions have been guided by population models to identify harvest intensity necessary to achieve eradication within a specified time frame, nor have they applied data on control effort and costs to evaluate the relative cost‐effectiveness of proposed control strategies. We used effort and cost data from a feral pig‐control program on Kangaroo Island, South Australia, over 17 months to derive functional‐response relationships between control effort (in hours per pig) and pig abundance for four control methods: (1) ground‐based shooting, (2) trapping with remote triggers, (3) poison baiting, and (4) thermal‐assisted aerial culling. We developed a stochastic Leslie matrix with compensatory density feedback on survival to project population trajectories from an initial population (N0) of 250 female pigs with an estimated island‐wide carrying capacity (K) of 2500 over 3 and 10 years for populations subjected to an annual harvest of 35%–95%. We built functional‐response models to calculate annual effort and cost for six cull scenarios across all harvest rates. We derived total cost and effort over 3‐ and 10‐year projections from the sum of annual cost and effort within the projection intervals. Pig populations were reduced to <10% N0 based on harvest rates >80% and 60% for culls of 3‐ and 10‐year durations, respectively. In all scenarios above, the minimum required harvest rate and the total cost to reduce population to ≤10% of N0 decreased with increasing harvest proportion, with lower total costs incurred over 3 years compared to 10 years. The simulations suggest that the most cost‐effective approach for most scenarios is to maximize annual harvest and complete eradication effort over the shortest periods. [ABSTRACT FROM AUTHOR]

We focus on distinctive data-driven measures of the fate of ongoing epidemics. The relevance of our pursuit is suggested by recent results proving that the short-term temporal evolution of infection spread is described by an epidemicity index related to the maximum instantaneous growth rate of new infections, echoing concepts and tools developed to study the reactivity of ecosystems. Suitable epidemicity indices can showcase the dynamics of infections, together with commonly employed effective reproduction numbers, especially when the latter assume values less than 1. In particular, epidemicity evaluates the short-term reactivity to perturbations of a disease-free equilibrium. Here, we show that sufficient epidemicity thresholds to prevent transient epidemic outbreaks in a spatially connected setting can be estimated by generalizing existing analogues derived when spatial effects are neglected. We specifically account for the discrete nature, in both space and time, of surveillance data of the type typically employed to estimate effective reproduction numbers that formed the bulk of the communication of the state of the COVID-19 pandemic and its controls. After analyzing the effects of spatial heterogeneity on the considered prognostic indicators, we perform a short- and long-term analysis on the COVID-19 pandemic in Italy, showing that endemic conditions were maintained throughout the duration of our simulation despite stringent control measures. Our method provides a portfolio of prognostic indices that are essential to pinpoint the ongoing pandemic in both a qualitative and quantitative manner, as our results demonstrate. We base our conclusions on extended investigations of the effects of spatial fragmentation of communities of different sizes owing to connectivity by human mobility and contact scenarios, within real geographic contexts and synthetic setups designed to test our framework.

We focus on distinctive data-driven measures of the fate of ongoing epidemics. The relevance of our pursuit is suggested by recent results proving that the short-term temporal evolution of infection spread is described by an epidemicity index related to the maximum instantaneous growth rate of new infections, echoing concepts and tools developed to study the reactivity of ecosystems. Suitable epidemicity indices can showcase the dynamics of infections, together with commonly employed effective reproduction numbers, especially when the latter assume values less than 1. In particular, epidemicity evaluates the short-term reactivity to perturbations of a disease-free equilibrium. Here, we show that sufficient epidemicity thresholds to prevent transient epidemic outbreaks in a spatially connected setting can be estimated by generalizing existing analogues derived when spatial effects are neglected. We specifically account for the discrete nature, in both space and time, of surveillance data of the type typically employed to estimate effective reproduction numbers that formed the bulk of the communication of the state of the COVID-19 pandemic and its controls. After analyzing the effects of spatial heterogeneity on the considered prognostic indicators, we perform a short- and long-term analysis on the COVID-19 pandemic in Italy, showing that endemic conditions were maintained throughout the duration of our simulation despite stringent control measures. Our method provides a portfolio of prognostic indices that are essential to pinpoint the ongoing pandemic in both a qualitative and quantitative manner, as our results demonstrate. We base our conclusions on extended investigations of the effects of spatial fragmentation of communities of different sizes owing to connectivity by human mobility and contact scenarios, within real geographic contexts and synthetic setups designed to test our framework. [ABSTRACT FROM AUTHOR]

Matrix population models are essential tools in conservation biology, offering key metrics to guide species management and conservation planning. However, the development of these models is often limited by insufficient life history data, particularly for non-charismatic species. This study addresses this gap by using life history data from FishBase and the FishLife R package, complemented by size-dependent natural mortality estimates, to parameterize age-structured matrix population models applicable to most fish species. The method was applied to 30 fish species common around oil and gas platforms in the Northern Gulf of Mexico, generating seven key metrics: damping ratio, resilience, generation time, stable age distribution, reproductive value, sensitivity matrix, and elasticity matrix. The damping ratio reflects how quickly a population returns to a stable age distribution after a disturbance, while resilience indicates the speed of recovery from perturbations. Generation time captures the average age of reproduction, and the stable age distribution represents the long-term proportion of individuals in each age class. Reproductive value quantifies future reproductive potential by age class. The sensitivity matrix highlights the age-class transitions most affecting population growth, and the elasticity matrix shows the proportional influence of these factors on population growth. The results demonstrate that robust population models can be constructed with limited species-specific data and reveal notable differences in population dynamics among species. For example, species with longer generation times, like the greater barracuda (Sphyraena guachancho), have lower damping ratios, indicating prolonged transient dynamics. In contrast, species such as the round scad (Decapterus punctatus) exhibit shorter generation times and higher damping ratios, suggesting faster returns to equilibrium. These findings underscore the importance of life history variability in shaping conservation strategies. Additionally, metrics like stable age distributions and reproductive values provide insight into population structure and individual contributions to future populations, while sensitivity and elasticity matrices inform management interventions such as size limits in fisheries. By integrating extensive databases and predictive tools, this study offers a scalable approach for developing matrix population models across diverse fish species. This methodology enhances our understanding of fish population dynamics, particularly for data-deficient species, and supports more informed conservation efforts. It also promotes ecosystem-based management by enabling species comparisons through standardized metrics, contributing to the sustainability of marine ecosystems.

Abstract Eradicating feral pigs from island ecosystems can assist in restoring damaged biodiversity values and protect commercial industries such as agriculture. Although many feral pig eradications have been attempted, management decisions are often led by practitioner experience rather than empirical evidence. Few interventions have been guided by population models to identify harvest intensity necessary to achieve eradication within a specified time frame, nor have they applied data on control effort and costs to evaluate the relative cost‐effectiveness of proposed control strategies. We used effort and cost data from a feral pig‐control program on Kangaroo Island, South Australia, over 17 months to derive functional‐response relationships between control effort (in hours per pig) and pig abundance for four control methods: (1) ground‐based shooting, (2) trapping with remote triggers, (3) poison baiting, and (4) thermal‐assisted aerial culling. We developed a stochastic Leslie matrix with compensatory density feedback on survival to project population trajectories from an initial population (N0) of 250 female pigs with an estimated island‐wide carrying capacity (K) of 2500 over 3 and 10 years for populations subjected to an annual harvest of 35%–95%. We built functional‐response models to calculate annual effort and cost for six cull scenarios across all harvest rates. We derived total cost and effort over 3‐ and 10‐year projections from the sum of annual cost and effort within the projection intervals. Pig populations were reduced to 80% and 60% for culls of 3‐ and 10‐year durations, respectively. In all scenarios above, the minimum required harvest rate and the total cost to reduce population to ≤10% of N0 decreased with increasing harvest proportion, with lower total costs incurred over 3 years compared to 10 years. The simulations suggest that the most cost‐effective approach for most scenarios is to maximize annual harvest and complete eradication effort over the shortest periods.

This article aims to identify the possibilities of combining existing approaches in ecology with the challenges of the labor market in the current era of digitalization and to identify what qualitative changes the labor market may undergo under the impact of digital knowledge acquisition. This article contains original ideas as it proposes a methodology framework that combines the long-known population prediction model in ecology (the Leslie matrix) with empiric economic methods for labor studies. The proposed framework, which includes a two-stage empirical approach and employs the Leslie matrix, can help determine how digital knowledge can affect the quality of structural changes occurring in labor. The proposed approach is useful for policymakers for various purposes, such as predicting structural changes in a labor market, assessing the effectiveness of state support programs, and for the private sector, big corporations, and state administration bodies to predict the possibilities of changes in job structure resulting from digital knowledge acquisition.

Periodical cicadas live 13 or 17 years underground as nymphs, then emerge in synchrony as adults to reproduce. Developmentally synchronized populations called broods rarely coexist, with one dominant brood locally excluding those that emerge in off years. Twelve modern 17-year cicada broods are believed to have descended from only three ancestral broods following the last glaciation. The mechanisms by which these daughter broods overcame exclusion by the ancestral brood to synchronously emerge in a different year, however, are elusive. Here, we demonstrate that temporal variation in the population density of generalist predators can allow intermittent opportunities for new broods to invade, even though a single brood remains dominant most of the time. We show that this mechanism is consistent, in terms of the type and frequency of brood replacements, with the distribution of periodical cicada broods throughout North America today. Although we investigate one particularly charismatic case study, the mechanisms involved (competitive exclusion, Allee effects, trait variation, predation, and temporal variability) are ubiquitous and could contribute to patterns of species diversity in a range of systems. [ABSTRACT FROM AUTHOR]

We estimated the size-dependent mortality of chub mackerel, Scomber japonicus, for the entire life stages from egg to adult by using a Leslie matrix model based on their fecundity, assuming the steady-state and the bigger-is-better hypothesis. The daily body size was determined by the temperature-dependent Gompertz–Laird and the temperature-independent von Bertalanffy growth equation. The derived constant for size-specific instantaneous mortality was 0.11 day−1 cm in fork length. The estimates of age-specific mortality ranged from 8.04 yr−1 for age 0 to 1.04 yr−1 for age 6 +. Our simulations showed that as the growth rate increases, the mortality decreases, and the recruitment level increases as the ambient water temperature from the egg to larval stages increases from 14 to 22 °C. Comparisons of the length frequencies derived from our Leslie matrix with the catch data suggested that our theoretically derived mortality is reliable enough for the purpose of stock assessment for fisheries management. We expect our approach will be applied in developing bio-physical coupling models for evaluating and projecting the influences of climate change and warming ocean on fish stocks. [ABSTRACT FROM AUTHOR]

More than 33 skate species have been registered in the Southwestern Atlantic Ocean (SAO) 34°S, where hotspots of the endemic threatened marine chondrichthyans with high scientific and conservation priorities have been detected. The lack of species-specific landing data highlights the importance of biological data-based methods to determine the vulnerability and productivity of skate species. In this work, we estimated the demographic parameters for the skates Atlantoraja castelnaui, Rioraja agassizi, Sympterygia bonapartii, and Zearaja brevicaudata in SAO, by implementing Leslie matrix models. The finite rate of population growth (ʎ) for the four skate's species ranged from 1.036 (Z. brevicaudata) to 1.196 (R. agassizi). Elasticity analyses and the performance of different harvest strategies show that reducing juvenile catches appears to be one of the most effective management actions for these species since they result in higher survivorship of age classes with more influence in λ. Differences in the biological productivity of the skates suggest that, to achieve sustainable exploitation of skates, the commitment of all stakeholders to improve species-level information is necessary. [ABSTRACT FROM AUTHOR]

Matrix population models (MPMs) are powerful tools for translating demographic and life history information into a form that can be used to address a wide range of research topics, such as projecting population dynamics, evaluating stressor impacts on populations, and studying life history evolution. However, the reliability of such studies depends on the MPM being constructed in a way that accurately reflects the species’ life history. We highlight three errors commonly encountered in published MPMs: (1) failing to include survival in the fertility coefficient; (2) introducing a one-year delay in age at first reproduction; and (3) incorrectly calculating the growth rate out of a stage class. We review the sources of such errors and provide new analyses revealing the impact of such errors on model predictions, using lionfish and American alligator models as examples. To quantify the prevalence of such errors we examined and scored the original publications underlying the models in the COMADRE Animal Matrix Database. The first two errors were found in 34% and 62%, respectively, of the published studies; nearly all were in models that used a “postbreeding census” representation of the life cycle (in which newborns—eggs, neonates, fledglings, etc.—are explicitly included). Of the studies where stages may last longer than one time step, 53% constructed the growth rate using inappropriate formulas for estimating the asymptotic population growth rate or its sensitivity to demographic parameters. These results suggest that further efforts may be required to educate biologists on the construction of MPMs, perhaps in concert with the development of new software tools. Furthermore, the conclusions of many studies that are based on MPMs may need to be re-examined, and synthetic studies using the COMADRE Database need to be accompanied by careful examination of the underlying studies.

Matrix population models (MPMs) are powerful tools for translating demographic and life history information into a form that can be used to address a wide range of research topics, such as projecting population dynamics, evaluating stressor impacts on populations, and studying life history evolution. However, the reliability of such studies depends on the MPM being constructed in a way that accurately reflects the species’ life history. We highlight three errors commonly encountered in published MPMs: (1) failing to include survival in the fertility coefficient; (2) introducing a one-year delay in age at first reproduction; and (3) incorrectly calculating the growth rate out of a stage class. We review the sources of such errors and provide new analyses revealing the impact of such errors on model predictions, using lionfish and American alligator models as examples. To quantify the prevalence of such errors we examined and scored the original publications underlying the models in the COMADRE Animal Matrix Database. The first two errors were found in 34% and 62%, respectively, of the published studies; nearly all were in models that used a “postbreeding census” representation of the life cycle (in which newborns—eggs, neonates, fledglings, etc.—are explicitly included). Of the studies where stages may last longer than one time step, 53% constructed the growth rate using inappropriate formulas for estimating the asymptotic population growth rate or its sensitivity to demographic parameters. These results suggest that further efforts may be required to educate biologists on the construction of MPMs, perhaps in concert with the development of new software tools. Furthermore, the conclusions of many studies that are based on MPMs may need to be re-examined, and synthetic studies using the COMADRE Database need to be accompanied by careful examination of the underlying studies.

Seasonal variations in age class sizes involve those of births and those of mortality across ages. They affect censuses and, consequently, rates involving numbers by age. As their analytical expression becomes inextricable, a simulation of aging cohorts by months of age shows that mortality oscillations for human populations are not sufficient to prevent age classes from oscillating approximately like associated births, contrary to what previous literature suggests. The amplification converges after damping, and the level reached depends on the amplification of mortality oscillations relative to births between 0 and 6 months of age. The damping rate depends mainly on the amplification of the mortality of 0–5 months compared to births. The application to 1896 South Russian data shows that age class sizes vary during the year like the births of the associated cohorts and that the numbers counted at the census vary strongly according to the month of the census. [ABSTRACT FROM AUTHOR]

It is crucial to take into account the dynamics of the species while investigating how a species may survive in an environment. A species can be classified as either semelparous or iteroparous depending on how it reproduces. In this article, we present a model, which consists of two semelparous species by considering two age classes. We specifically discuss the effects of density-dependent in the interaction between the two semelparaous species and examine the equilibria of the system in the absence and presence of harvesting in the system. Then, the local stability of the equilibria is also investigated. A modified Leslie matrix population model with the addition of density-dependent in the equation is used. The model is analyzed in the presence and absence of competition between these species. We assume that density-dependent only occurred in the first age class of both species and that harvesting only occurred in the second age class of both species. Then, we assume that competition only occurs in the first age class in both species in the form of interspecific and intraspecific competition. This assumption is intended to simplify the complexity of the problem in the model. Our results show that there are three equilibria in the model without competition and four equilibria in the model with the competition. Hence, the presence of competition has influenced the number of equilibria. We also investigate the relation between the stability of the equilibria with the net reproduction rate of the system. Furthermore, we found the condition for the local stability of the co-existence equilibrium point, which is related to the degree of interspecific and intraspecific competition. This theory may be applied to investigate the dynamics of natural resources, whether in the absence of human exploitation and in the presence of various strategies in managing the exploitation of the resources, such as in fisheries industries.

Women are under-represented in academic staff in universities worldwide. Our work builds on other studies of ‘demographic inertia'. We find that time will not bridge the gender representation gap in academia, and echo others in saying bold actions are required to reach parity. Our work then uses New Zealand's unique system of scoring individual research performance to test empirically which levers universities should pull, and in which combinations. We combine individual research performance scores with 20 years of data from one university to parametrize a rank-structured mathematical model using Leslie matrices. Our model compares three key levers of change at universities' disposal—hiring, promotion and attrition. We apply the model to a bifurcated population of university staff—those with high research activity, and those who are moderately active—based on their national research quality score. We then test levers in various combinations that management could pull to improve gender representation. We find that the solutions are different for the high versus moderate research performers. For individuals with high research activity, universities should concentrate on equitable hiring practices. For those with more moderate research activity, more equitable promotion practices hold the key.

• Explored the factors affecting Cisco reintroduction using a Lesile Matrix Model. • Periodicity of 'boom' years of recruitment need to be at least every 5 years. • Egg and fry survival rates were strong determinants of population growth. • Number stocked only affected rate of population growth, not final trajectory. • Increasing adult survival allows for more margin on recruitment periodicity. Recent food web changes led to an opportunity to reintroduce (fingerling stocking) Cisco in central Lake Huron. We examined 9 factors affecting the ability of stocked Cisco fingerlings to survive, and reproduce and for their progeny to survive and reproduce. These values (obtained from the literature) were applied to a stochastic Leslie Matrix model and projected forward 30 years. The mean terminal eigenvalue (λ) of the final 10 years was used to indicate if the resulting wild population would continue to increase or decrease and thresholds for each variable. Recovery success was sensitive to survival rates especially in early life stages. Numbers stocked and the rate of homing by hatchery fish only affected the rate of recovery. Adult survival, if adjusted up, helped compensate for many of the earlier life stages lower survival rates. Simulations indicated the likelihood of successful establishment of ongoing natural reproduction if periodicity of boom years of reproduction were at least once every 5 years on average, but higher adult survival rates can relax this requirement allowing for an expanding population at less frequent periodicities. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper analyses the financial sustainability of the Croatian pension system after the reform that was adopted on January 1, 2019. The Croatian pension system as we know it today was started in 1999 with a reform that created the three pillars of the pension system. Over the next twenty years, Croatian economic and social conditions shifted in an unexpected way and a new reform was needed to ensure financial stability is maintained. In this paper I will analyse population trends in Croatia and forecast movements up to 2060. Afterwards, I will analyse the net government cash flow generated from the pension system, by using the forecast population numbers. The beginning year of the forecast horizon is 2018, as some data were not yet available for this year. I use stochastic methods to perform my analysis.

ABSTRACT Associated microorganisms (“microbiota”) play a central role in determining many animals’ survival and reproduction characteristics. The impact of these microbial influences on an animal’s fitness, or population growth, in a given environment has not been defined as clearly. We focused on microbiota-dependent host fitness by measuring life span and fecundity in Drosophila melanogaster fruit flies reared individually with 14 different bacterial species. Consistent with previous observations, the different bacteria significantly influenced the timing of fly life span and fecundity. Using Leslie matrices, we show that fly fitness was lowest when the microbes caused the flies to invest in life span over fecundity. Computational permutations showed that the positive fitness effect of investing in reproduction was reversed if fly survival over time was low, indicating that the observed fitness influences of the microbes could be context dependent. Finally, we showed that fly fitness is not influenced by bacterial genes that shape fly life span or fly triglyceride content, a trait that is related to fly survival and reproduction. Also, metagenome-wide association did not identify any microbial genes that were associated with variation in fly fitness. Therefore, the bacterial genetic basis for influencing fly fitness remains unknown. We conclude that bacteria influence a fly’s reproductive timing more than total reproductive output and that (e.g., environmental) conditions that influence fly survival likely determine which bacteria benefit fly fitness. IMPORTANCE The ability of associated microorganisms (“microbiota”) to influence animal life history traits has been recognized and investigated, especially in the past 2 decades. For many microbial communities, there is not always a clear definition of whether the microbiota or its members are beneficial, pathogenic, or relatively neutral to their hosts’ fitness. In this study, we report the influence of individual members of the microbiota on Drosophila melanogaster fitness using Leslie matrices that combine the microbial influences on fly survival and reproduction into a single fitness measure. Our results are consistent with a previous report that, in the laboratory, acetic acid bacteria are more beneficial to the flies than many strains of lactic acid bacteria. We add to the previous finding by showing that this benefit depends on fly survival rate. Together, our work helps to show how the microbiota of a fly influences its laboratory fitness and how these effects may translate to a wild setting.

Abstract Feral cats are some of the most destructive invasive predators worldwide, particularly in insular environments; hence, density‐reduction campaigns are often applied to alleviate the predation mortality they add to native fauna. Density‐reduction and eradication efforts are costly procedures with important outcomes for native fauna recovery, so they require adequate planning to be successful. These plans should include empirical density‐reduction models that can guide yearly culling quotas, and resource roll‐out for the duration of the culling period. This ensures densities are reduced over the long term and that resources are not wasted. We constructed a stochastic population model with cost estimates to test the relative effectiveness and cost‐efficiency of two main culling scenarios for a 10‐year eradication campaign of cats on Kangaroo Island, Australia: (a) constant proportional annual cull (one‐phase), and (b) high initial culling followed by a constant proportional maintenance cull (two‐phase). A one‐phase cull of at least 0.35 of the annual population size would reduce the final population to 0.1 of its original size, while a two‐phase cull with an initial cull of minimum 0.6 and minimum 0.5 maintenance cull would reduce the final population to 0.01 of its initial size within the 10‐year time frame. Cost estimates varied widely depending on the methods applied (shooting, trapping, aerial poison baits, Felixer™ poison‐delivery system), but using baiting, trapping and Felixers with additional shooting to meet culling quotas was the most cost‐effective combination (minimum cost: AU$19.56 million; range: AU$16.87 million–AU$20.69 million). Our model provides an adaptable and general assessment tool for cat reductions in Australia and potentially elsewhere, and provides relative culling costs for the Kangaroo Island campaign specifically.

Feral cats are some of the most destructive invasive predators worldwide, particularly in insular environments; hence, density‐reduction campaigns are often applied to alleviate the predation mortality they add to native fauna. Density‐reduction and eradication efforts are costly procedures with important outcomes for native fauna recovery, so they require adequate planning to be successful. These plans should include empirical density‐reduction models that can guide yearly culling quotas, and resource roll‐out for the duration of the culling period. This ensures densities are reduced over the long term and that resources are not wasted. We constructed a stochastic population model with cost estimates to test the relative effectiveness and cost‐efficiency of two main culling scenarios for a 10‐year eradication campaign of cats on Kangaroo Island, Australia: (a) constant proportional annual cull (one‐phase), and (b) high initial culling followed by a constant proportional maintenance cull (two‐phase). A one‐phase cull of at least 0.35 of the annual population size would reduce the final population to 0.1 of its original size, while a two‐phase cull with an initial cull of minimum 0.6 and minimum 0.5 maintenance cull would reduce the final population to 0.01 of its initial size within the 10‐year time frame. Cost estimates varied widely depending on the methods applied (shooting, trapping, aerial poison baits, Felixer™ poison‐delivery system), but using baiting, trapping and Felixers with additional shooting to meet culling quotas was the most cost‐effective combination (minimum cost: AU$19.56 million; range: AU$16.87 million–AU$20.69 million). Our model provides an adaptable and general assessment tool for cat reductions in Australia and potentially elsewhere, and provides relative culling costs for the Kangaroo Island campaign specifically. [ABSTRACT FROM AUTHOR]

Marked tillers of Heteropogon contortus, Trachypogon spicatus, Tristachya leucothrix and Harpochloa falx were sampled regularly over a two-year period in Highland Sourveld burnt annually in winter and biennially in spring. Parameters recorded were height of shoot apex, tiller mass, number of new lateral tillers and time of flowering. Monitoring of marked tillers before and after each burn enabled the life history of populations of tillers to be followed. In all species investigated, flowering was found to be of minimal importance with most tillers remaining vegetative until death. Shoot apices remained close to the soil surface (<20 mm) enabling them to survive frequent burns. All species exhibited smooth survivorship curves, suggesting that dramatic fluctuations in climate and severe defoliation, as by fire, had little impact on mortality. The differential response of the four grass species was explained by their different reproductive capacities and reproductive rates. The predicted responses to fire regime were verified by changes that took place at the study area from 1981 to 2019, showing the importance of applying appropriate burning regimes to maintain the bud bank. A biennial spring burn was best for maintaining these important grass species at current levels of abundance in the KwaZulu-Natal Drakensberg. [ABSTRACT FROM AUTHOR]

The timing of life-history traits may have strong influences on the evolution of life cycles and on population demography. This is especially true of the age at which females first reproduce (Cole's principle). We examined whether the age at which females first reproduce influences fitness in Columbian ground squirrels (Urocitellus columbianus), for which females varied in the age at which they initially produce weaned offspring, from ages 1 through 5 years. With 148 females with complete known life spans in a 28-year data set, we examined four fitness measures: individual fitness (λ ind), individual fitness relative to the pattern of growth of the population (λ rel), lifetime reproductive success (LRS), and LRS relative to the total LRS for each female's cohort (LRSrel). These metrics were calculated for offspring produced at the time of weaning and offspring that survived to emerge after their first hibernation period. Individual fitness (λ ind) was significantly associated with population growth during a female's lifetime (λ Leslie; R 2 = 0.523, P < 0.0001), indicating the need to adjust individual fitness for demonstrated changes in population growth and thus producing a relative individual fitness index (λ rel). We regressed λ rel on age at first reproduction, and found significant selection favoring earlier reproductive success (β ± SE = −0.20 ± 0.06; R 2 = 0.306, P < 0.0001). When using an earlier (offspring at weaning) versus later (those that survived their first hibernation) measure of fecundity, we found that the latter introduced considerable variation, likely environmental, into the estimate of selection. This greatly weakened the regression of relative fitness on the age at first successful reproduction. LRS and LRSrel exhibited nonsignificant changes with age at first reproduction. Finally, those females that reproduced successfully at younger ages had similar litter sizes but significantly shorter life spans than females that matured when older, perhaps reflecting costs to early reproduction. [ABSTRACT FROM AUTHOR]

Size limits are a common fisheries management strategy that are applied to many fisheries and species. Most size limits use a minimum legal size to protect adult fish as per the 'reproduce at least once' paradigm, where stock collapse becomes impossible if every adult can produce one spawner prior to harvest. These approaches can be useful in fisheries where determining catch is difficult and therefore catch limits can be ineffective and potentially cause stock decline.Shark longline fisheries can be complicated to manage due to a deficiency of species‐level reporting. Catch limits are therefore difficult to determine, creating a need for other management measures. Here, three different size‐based management approaches were tested using the shark longline fishery from Papua New Guinea as a case study. These approaches included minimum size, maximum size and harvest slot approaches.Age‐structured Leslie matrix models revealed a broad range of productivities for 12 commonly caught species, ranging from low population growth rates of 1% per year for pelagic thresher sharks Alopias pelagicus to >33% per year for blue sharks Prionace glauca. Therefore, different harvest strategies were required for each species to be fished sustainably. However, management could be applied by grouping similar and easily distinguishable groups of species together.Synthesis and applications. The most pragmatic harvest strategy for all shark species included in this study was to limit harvest to mature individuals using minimum legal sizes. This provided sufficient resilience for all species to tolerate higher levels of fishing mortality than the Papua New Guinea (PNG) longline fishery could impose. Legal minimum lengths were derived from the largest length‐at‐maturity within each species group. However, while this produced a sustainable harvest strategy, issues with selectivity, post‐release mortality, interactions with other fisheries, economic viability and illegal, underreported and unregulated fishing were challenges to restricting fishing to the correct size classes and overall management efficacy. Therefore, while theoretically viable harvest strategies were outlined, it is apparent that size limits would not ensure that these shark species are fished sustainably. Therefore, the PNG longline fishery cannot operate sustainably if it were to reopen using size limits as its sole management strategy. [ABSTRACT FROM AUTHOR]

Augmentative biological control (ABC) is crucial for the integrated pest management (IPM) of greenhouse pests. The proper calculation of natural enemy:pest release ratio (NEPRR) stands out among the various challenges of ABC. Often, most NEPRR calculations only take into account the predation/parasitism efficiency of natural enemies, while disregarding pest population growth capacity, population structure and/or economic thresholds. In a model system consisting of Trichogramma pretiosum Riley parasitizing eggs of Tuta absoluta (Meyrick) on greenhouse tomatoes, we investigated whether a stage‐structured Lefkovitch matrix could be used to determine suitable NEPRRs. The results suggested that these matrix models can potentially provide more precise and realistic predictions of NEPRRs since they account for differential pest population growth over time as a response to natural enemy action. The matrix models could also allow us to choose an adaptable NEPRR based on parameters such as the period the grower wishes to keep the pest population below economic threshold. [ABSTRACT FROM AUTHOR]

This paper develops a method for studying bifurcations that occur in a neighborhood of the extinction equilibrium in nonlinear semelparous Leslie matrix models. The method uses a Lotka–Volterra equation with cyclic symmetry to detect the existence and to evaluate the stability of bifurcating equilibria and cycles. An application of the method provides sharp stability conditions for both a single-class cycle and a positive equilibrium bifurcating from the extinction equilibrium. The stability condition for a bifurcating single-class cycle confirms that the periodicity observed in periodical insects occurs if competition is more severe between than within age-classes. The developed method is also used to investigate two examples of nonlinear semelparous Leslie matrix models incorporating predator satiation. The investigation shows that a single-class cycle, which is associated with the periodicity in periodical insects, is a unique stable cycle in a neighborhood of the extinction equilibrium if the density effects in survival probabilities are identical among age-classes. [ABSTRACT FROM AUTHOR]

Tujuan penelitian ini adalah menentukan banyaknya populasi wanita di Provinsi Jawa Timur berdasarkan angka kelahiran dan harapan hidup menggunakan nilai eigen dan vektor eigen serta untuk mengetahui distribusi umur pembatas menggunakan model matriks Leslie. Vektor eigen digunakan untuk menentukan banyaknya populasi wanita dari masing-masing interval umur, sedangkan nilai eigen digunakan untuk menentukan laju pertumbuhan penduduk. Metode penelitian yang digunakan pada Tahap pertama adalah menentukan subjek penelitian dan Tahap Kedua adalah (a) mengumpulkan data penelitian (b) analisis data dan terakhir menarik kesimpulan. Data penelitian ini diperoleh dari BPS Provinsi Jawa Timur yaitu jumlah penduduk wanita dari tahun 2010-2015. Hasil penelitian ini adalah model matriks Leslie untuk populasi wanita di Provinsi Jawa Timur adalah model diskrit yang dibagi atas empat belas interval umur yang dikonstruksi menggunakan angka kesuburan dan harapan hidup. Simpulan penelitian menunjukkan bahwa jumlah populasi wanita di Provinsi Jawa Timur cenderung mengalami peningkatan dengan nilai eigen positif yang lebih besar dari satu atau dengan kata lain laju pertumbuhan wanita di Provinsi Jawa Timur cenderung bernilai positif . Keberhasilan model matriks Leslie adalah penerapannya dalam kasus untuk memprediksi jumlah populasi wanita di Provinsi Jawa Timur pada tahun 2021 dengan menggunakan Program MAPLE 16. Application of The Leslie Matrix on Birth Rate and Life Expectancy of Women in East Java Province Abstract This research aimed to determine the number of female population in East Java Province based on birth rate and life expectancy using eigenvalues and eigenvectors and to know the age distribution of limiter using Leslie matrix model. The eigenvectors are used to determine the number of female populations of each age interval, while the eigenvalues are used to determine population growth rates. The research method used in the first phase is to determine the subject of research and Phase Two is (a) collect research data (b) data analysis and last draw conclusions. The data of this study were obtained from BPS of East Java Province, namely the number of female population from 2010-2015. The result of this research is Leslie's matrix model for female population in East Java Province is a discrete model that is divided into fourteen age intervals constructed using fertility and life expectancy. The research conclusion showed that the number of female population in East Java Province tends to increase with positive eigen value which is greater than one or in other words the growth rate of women in East Java Province tends to be positive. The success of Leslie's matrix model is its application in cases to predict the number of female populations in East Java Province by 2021 using the MAPLE 16 Programe.

This research aims to determine the number of female residents in Trenggalek Regency in 2021 based on data on birth rate and life expectancy. The use of eigenvalues and eigenvectors aims to determine the dividing age distribution by Leslie matrix model. The eigenvectors are used to determine the number of female populations of each age interval, while the eigenvalues are used to determine population growth rates. The research method used is to determine the subject of research. The next stage is to collect research data, then analyze the data and last draw conclusions. The research data is obtained from BPS Kabupaten Trenggalek and BPS East Java Province that is data of woman population from year 2010-2015. The result of this research using Leslie matrix model for female population in Trenggalek Regency that is discrete model. The discrete model is divided into fourteen age intervals constructed using the birthrate and life expectancy. The conclusions of the study showed that the number of female population in Trenggalek Regency tended to increase with positive eigen value greater than one. In other words, the growth rate of female population in Trenggalek Regency tends to be positive. The success of Leslie's matrix model is the application of case studies in predicting the number of female populations in Trenggalek District by 2021 using the MAPLE 16 Program.

Population matrix models are important tools in resource management, in part because they are used to calculate the finite rate of growth (“dominant eigenvalue”). But understanding how a population matrix model converts life history traits into the finite rate of growth can be tricky. We introduce interactive software (“IsoPOPd”) that uses the characteristic equation to display how vital rates (survival and fertility) contribute to the finite rate of growth. Higher-order interactions among vital rates complicate the linkage between a management intervention and a population’s growth rate. We illustrate the use of the software for investigating the consequences of three management interventions in a 3-stage model of white-tailed deer (Odocoileus virginianus). The software is applicable to any species with 2- or 3-stages, but the mathematical concepts underlying the software are applicable to a population matrix model of any size. The IsoPOPd software is available at: https://cwhl.vet.cornell.edu/tools/isopopd.

Abstract We quantify the expected demographic benefit to a seabird of conservation concern, the ashy storm‐petrel Oceanodroma homochroa, from the proposed eradication of introduced house mice Mus musculus on the South Farallon Islands, California. A key objective of the eradication is to reduce storm petrel predation by burrowing owls Athene cunicularia, which stopover on the island during their fall migration. Mouse trapping and field surveys of both owls and depredated storm petrel carcasses conducted during 2000–2012 reveal a strongly seasonal, inter‐related pattern among the three species: When owls arrive during the fall, mice are super‐abundant and the overwhelming choice of prey for those owls that remain. In the winter, the mouse population crashes just as storm petrels begin to arrive in large numbers; owls that remain on the island switch to preying upon storm petrels until May, when they depart to breed. Capture–recapture analyses of storm petrels showed (1) annual adult survival was inversely related to owl abundance, especially during January–April, and (2) storm petrels demonstrated a declining trend in abundance 2006–2012. The latter was associated with low rates of adult survival, high abundance of overwintering burrowing owls, and high incidence of depredated storm petrels. To evaluate projected impacts to storm petrels of a change in owl predation, we developed a Leslie matrix model, incorporating environmental stochasticity. We modeled future storm petrel population trajectories, allowing for different levels of owl‐mediated predation. Our results suggest that a reduction in owl abundance, a projected consequence of the elimination of mice, has the potential to substantially reduce overall storm petrel mortality, thereby reducing storm petrel declines and increasing the likelihood of stable trends in the future. While long‐term benefits to storm petrels of mouse eradication are apparent, the risk of increased predation due to prey‐switching by owls also needs to be addressed. This study highlights uncertainty of outcomes, which must be considered in evaluating management impacts. This study demonstrates the value of concurrent, continuous, long‐term datasets in providing a quantitative basis for management to aid the conservation of species of concern.

In this paper, we ascertain the validity of a diffusion approximation for the frequencies of different types under recurrent mutation and frequency-dependent viability and fertility selection in a haploid population with a fixed age-class structure in the limit of a large population size. The approximation is used to study, and explain in terms of selection coefficients, reproductive values and population-structure coefficients, the differences in the effects of viability versus fertility selection on the fixation probability of an advantageous mutant. [ABSTRACT FROM AUTHOR]

Population matrix models are important tools in resource management, in part because they are used to calculate the finite rate of growth (``dominant eigenvalue'). But understanding how a population matrix model converts life history traits into the finite rate of growth can be tricky. We introduce interactive software (``IsoPOPd') that uses the characteristic equation to display how vital rates (survival and fertility) contribute to the finite rate of growth. Higher-order interactions among vital rates complicate the linkage between a management intervention and a population's growth rate. We illustrate the use of the software for investigating the consequences of three management interventions in a 3-stage model of white-tailed deer (Odocoileus virginianus). The software is applicable to any species with 2- or 3-stages, but the mathematical concepts underlying the software are applicable to a population matrix model of any size. [ABSTRACT FROM AUTHOR]

Matrix population models (MPMs) are powerful tools for translating demographic and life history information into a form that can be used to address a wide range of research topics, such as projecting population dynamics, evaluating stressor impacts on populations, and studying life history evolution. However, the reliability of such studies depends on the MPM being constructed in a way that accurately reflects the species' life history. We highlight three errors commonly encountered in published MPMs: (1) failing to include survival in the fertility coefficient; (2) introducing a one-year delay in age at first reproduction; and (3) incorrectly calculating the growth rate out of a stage class. We review the sources of such errors and provide new analyses revealing the impact of such errors on model predictions, using lionfish and American alligator models as examples. To quantify the prevalence of such errors we examined and scored the original publications underlying the models in the COMADRE Animal Matrix Database. The first two errors were found in 34% and 62%, respectively, of the published studies; nearly all were in models that used a "postbreeding census" representation of the life cycle (in which newborns—eggs, neonates, fledglings, etc.—are explicitly included). Of the studies where stages may last longer than one time step, 53% constructed the growth rate using inappropriate formulas for estimating the asymptotic population growth rate or its sensitivity to demographic parameters. These results suggest that further efforts may be required to educate biologists on the construction of MPMs, perhaps in concert with the development of new software tools. Furthermore, the conclusions of many studies that are based on MPMs may need to be re-examined, and synthetic studies using the COMADRE Database need to be accompanied by careful examination of the underlying studies. [ABSTRACT FROM AUTHOR]

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A general framework for threshold parameters in population dynamics is developed using the concept of target reproduction numbers. This framework identifies reproduction numbers and other threshold parameters in the literature in terms of their roles in population control. The framework is applied to the analysis of single and multiple control strategies in ecology and epidemiology, and this provides new biological insights. [ABSTRACT FROM AUTHOR]

In addition to their unusually long life cycle, periodical cicadas, Magicicada spp., provide an exceptional example of spatially synchronized life stage phenology in nature. Within regions ("broods") spanning 50,000-500,000 km2, adults emerge synchronously every 13 or 17 years. While satiation of avian predators is believed to be a key component of the ability of these populations to reach high densities, it is not clear why populations at a single location remain entirely synchronized. We develop nonlinear Leslie matrix-type models of periodical cicadas that include predation-driven Allee effects and competition in addition to reproduction and survival. Using both analytical and numerical techniques, we demonstrate the observed presence of a single brood critically depends on the relationship between fecundity, competition and predation. We analyze the single-brood, two-brood and all-brood equilibria in the large life span limit using a tractable hybrid approximation to the Leslie matrix model with continuous time competition in between discrete reproduction events. Within the hybrid model, we prove that the single-brood equilibrium is the only stable equilibrium. This hybrid model allows us to quantitatively predict population sizes and the range of parameters for which the stable single-brood and unstable two-brood and all-brood equilibria exist. The hybrid model yields a good approximation to the numerical results for the Leslie matrix model for the biologically relevant case of a 17-year life span. [ABSTRACT FROM AUTHOR]

• We model multilevel selection in the context of host-symbiont interactions. • We analyze the evolutionary stability of coexistence between an obligate symbiont and its host. • The Leslie matrix can capture the changes in the life history traits of an organism. • Invading mutants can be introduced as a new dimension in resident dynamical systems. The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduced a conceptual model to study the stable coexistence and coevolution of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. Using an age-structured Leslie model for the host, we demonstrated how the obligate symbiont could modify the host's life history traits (survival and fecundity) and the long-term growth rate of the infected lineage. When the symbiont is vertically transmitted, we found that the host and its symbiont could maximize the infected lineage's evolutionary success (multi-level selection). Our model showed that symbionts' effect on host longevity and reproduction might differ, even be opposing, and their net effect might often be counterintuitive. The evolutionary stability of the ecologically stable coexistence was analyzed in the framework of coevolutionary dynamics. Moreover, we found conditions for the ecological and evolutionary stability of the resident host-symbiont pair, which does not allow invasion by rare mutants (each mutant dies out by ecological selection). We concluded that, within the context of our simplified model conditions, a host-symbiont system with mixed-mode transmission is evolutionarily stable unconditionally only if the host can maximize the Malthusian parameters of the infected and non-infected lineages using the same strategy. Finally, we performed a game-theoretical analysis of our selection situation and compared two stability definitions. [ABSTRACT FROM AUTHOR]

There are many factors in the current phase of the COVID-19 pandemic that signal the need for new modeling ideas. In fact, most traditional infectious disease models do not address adequately the waning immunity, in particular as new emerging variants have been able to break the immune shield acquired either by previous infection by a different strain of the virus, or by inoculation of vaccines not effective for the current variant. Furthermore, in a post-pandemic landscape in which reporting is no longer a default, it is impossible to have reliable quantitative data at the population level. Our contribution to COVID-19 post-pandemic modeling is a simple mathematical predictive model along the age-distributed population framework, that can take into account the waning immunity in a transparent and easily controllable manner. Numerical simulations show that under static conditions, the model produces periodic solutions that are qualitatively similar to the reported data, with the period determined by the immunity waning profile. Evidence from the mathematical model indicates that the immunity dynamics is the main factor in the recurrence of infection spikes, however, irregular perturbation of the transmission rate, due to either mutations of the pathogen or human behavior, may result in suppression of recurrent spikes, and irregular time intervals between consecutive peaks. The spike amplitudes are sensitive to the transmission rate and vaccination strategies, but also to the skewness of the profile describing the waning immunity, suggesting that these factors should be taken into consideration when making predictions about future outbreaks., Competing Interests: Declaration of competing interest The authors declare no conflict of interest., (Copyright © 2023 Elsevier Inc. All rights reserved.)

Periodical cicadas are enigmatic organisms: broods spanning large spatial ranges consist of developmentally synchronized populations of 3-4 sympatric species that emerge as adults every 13 or 17 years. Only one brood typically occupies any single location, with well-defined boundaries separating distinct broods. The cause of such synchronous development remains uncertain, but it is known that synchronous emergence of large numbers of adults in a single year satiates predators, allowing a substantial fraction of emerging adults to survive long enough to reproduce. Competition among nymphs feeding on tree roots almost certainly plays a role in limiting populations. However, due to the difficulty of working with such long-lived subterranean life stages, the mechanisms governing competition in periodical cicadas have not been identified. A second process that may affect synchrony among periodical cicadas is their ability to delay or accelerate their emergence as adults by 1 year and accelerate it by 4 years (stragglers). We develop a nonlinear Leslie matrix-type model that describes cicada dynamics accounting for predation, competition, and stragglers. Using numerical simulations, we identify conditions that generate dynamics in which a single brood occupies a given geographical location. Our results show that while stragglers have the potential for introducing multiple sympatric broods, the interaction of interbrood competition with predation-driven Allee effects creates a system resistant to such invasions, and populations maintain developmental synchrony. [ABSTRACT FROM AUTHOR]

Abstract: Harbor seals in Iliamna Lake, Alaska, are a small, isolated population, and one of only two freshwater populations of harbor seals in the world, yet little is known about their abundance or risk for extinction. Bayesian hierarchical models were used to estimate abundance and trend of this population. Observational models were developed from aerial survey and harvest data, and they included effects for time of year and time of day on survey counts. Underlying models of abundance and trend were based on a Leslie matrix model that used prior information on vital rates from the literature. We developed three scenarios for variability in the priors and used them as part of a sensitivity analysis. The models were fitted using Markov chain Monte Carlo methods. The population production rate implied by the vital rate estimates was about 5% per year, very similar to the average annual harvest rate. After a period of growth in the 1980s, the population appears to be relatively stable at around 400 individuals. A population viability analysis assessing the risk of quasi‐extinction, defined as any reduction to 50 animals or below in the next 100 years, ranged from 1% to 3%, depending on the prior scenario. Although this is moderately low risk, it does not include genetic or catastrophic environmental events, which may have occurred to the population in the past, so our results should be applied cautiously. [ABSTRACT FROM AUTHOR]