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In this paper, we deal with Leslie and doubly Leslie matrices of order n. In particular, with the companion and doubly companion matrices. We study three inverse eigenvalues problems which consist of constructing these matrices from the maximal eigenvalues of its all leading principal submatrices. For Leslie and doubly companion matrices, an eigenvector associated with the maximal eigenvalue of the matrix is additionally considered, and for the doubly Leslie matrix also an eigenvector associated with the maximal eigenvalue of leading principal submatrix of order n − 1 is required. We give necessary and sufficient conditions for the existence of a Leslie matrix and a companion matrix, and sufficient conditions for the existence of a doubly Leslie matrix and a doubly companion matrix. Our results are constructive and generate an algorithmic procedure to construct these special kinds of matrices.

In the analysis of economic and social issues of a country (or any larger or smaller socio-economic unit) the demographic dynamics of the considered population often play a crucial role. Very current emergencies in this respect are e.g. ageing, longevity risk, state-run healthcare etc. Over the last decade migration between EU countries also became an important issue, and in recent years the uncontrolled migration from non-EU countries is also a major concern. Therefore, the better theoretical understanding of the evolutionary mechanism of age-classified populations interacting via migration, is a timely modelling-methodological task. This paper is a preliminary demographic methodological contribution to a further research in support of socio-economic modelling and decision making concerning migration issues. It is known that in the framework of the classical age-specific Leslie model, under simple demographic conditions, a closed population in the long term tends to an equilibrium age distribution. As the main theoretical result of the paper, a similar convergence is proved for a system of several populations with migration between them, and this long-term behaviour (convergence theorem) is extended to systems of sex-structured populations. Based on the latter model, medium term projections are also analysed concerning the effect of migration among countries on the development of the old-age dependency ratio (the proportion of pensioner age classes to active ones), which is an aggregate scalar indicator of ageing, a major concern in most industrialized countries. Illustrative simulation analysis is carried out with data from three European countries.

The long-term forecast of energy demand has assumed significant importance in the energy planning of energy-imported cities. However, the required data are usually limited or unavailable. In this paper, we developed a combined model based on Long-range Energy Alternate Planning and econometric models to forecast the energy demand of Hunan province from 2012 to 2030. Based on historical data, population was predicted by Leslie matrix, the industrial structure, traffic turnover and productions of high energy-consuming industries were forecasted by Autoregressive Integrated Moving Average and Vector Autoregressive models. Three scenarios were designed with different energy-saving polices and population growths. The uncertainties of forecasting results were analysed by Monte Carlo method. Results showed the total energy demand increased but the growth rate gradually slowed down under each scenario. In 2030, compared with business as usual scenario, the energy demand in second child scenario only increased 29 thousand tons coal equivalent (tce), showing a slight population growth effect; while the energy demand in energy saving scenario significantly decreased 450 thousand tce, showing a significant potential of energy conservation and efficiency improvement. Although the uncertainty of forecasted results increased over time, the uncertainty was still less than 15 %, showing a good accuracy of this combined model.

Prolonged exposure to a disturbance such as a toxicant has the potential to result in rapid evolution to toxicant resistance in many short-lived species such as daphniids. This evolution may allow a population to persist at higher levels of the toxicant than is possible without evolution. Here we apply evolutionary game theory to a Leslie matrix model for a daphniid population to obtain a Darwinian model that couples population dynamics with the dynamics of an evolving trait. We use the Darwinian model to consider how the evolution of resistance to the lethal or sublethal effects of a disturbance may change the population dynamics. In particular, we determine the conditions under which a daphniid population can persist by evolving toxicant resistance. We then consider the implications of this evolution in terms of the use of daphniids as surrogate species. We show for three species of daphniids that evolution of toxicant resistance means that one species may persist while another does not. These results suggest that toxicant studies that do not consider the potential of a species (or its surrogate) to develop toxicant resistance may not accurately predict the long term persistence of the species.

Removal methods are some of the most common statistical tools for estimating fish abundance in streams and lakes, yet they are prone to produce biased estimates when the assumption of constant capture probability is violated. In response, numerous authors have modified the classic removal models to control for non-constant capture probability. A variety of fish behaviors can cause capture probability to vary across individuals or over time, such as dominance hierarchies, escaping capture or persistent individual differences in capture probability due to activity or aggression; yet knowing exactly which behaviors may affect capture probability is generally unknown. We assessed the robustness of five removal models (i.e., the Leslie model, three behavior-dependent models and a density dependent capture probability model) and their ability to provide consistently accurate and precise abundance estimates irrespective of the exhibited behavior. We fitted each model to catch data generated from five behavioral models that mimicked a range of animal behaviors in a closed population. Additionally, we evaluated the improvements that can be gained by including marked fish in the removal process and in that case, compared estimation models with a Peterson mark-recapture estimation. Results indicate that no single removal model is robust to non-constant capture probability, however, the density-dependent capture probability model performed moderately better than other models when only removal data were used. We found that the addition of marked fish results in a substantial improvement in accuracy and precision across all removal models when mark-recapture assumptions are met. However, these improvements diminished substantially when mark-recapture assumptions were violated. Due to the difficulties in assessing assumptions, our findings suggest that including marked fish in the removal process may unknowingly reduce accuracy and precision of initial abundance estimate and that this type of experimental design should be avoided in many instances.

Assessing the potential impact of additional mortality from anthropogenic causes on animal populations requires detailed demographic information. However, these data are frequently lacking, making simple algorithms, which require little data, appealing. Because of their simplicity, these algorithms often rely on implicit assumptions, some of which may be quite restrictive. Potential Biological Removal (PBR) is a simple harvest model that estimates the number of additional mortalities that a population can theoretically sustain without causing population extinction. However, PBR relies on a number of implicit assumptions, particularly around density dependence and population trajectory that limit its applicability in many situations. Among several uses, it has been widely employed in Europe in Environmental Impact Assessments (EIA), to examine the acceptability of potential effects of offshore wind farms on marine bird populations. As a case study, we use PBR to estimate the number of additional mortalities that a population with characteristics typical of a seabird population can theoretically sustain. We incorporated this level of additional mortality within Leslie matrix models to test assumptions within the PBR algorithm about density dependence and current population trajectory. Our analyses suggest that the PBR algorithm identifies levels of mortality which cause population declines for most population trajectories and forms of population regulation. Consequently, we recommend that practitioners do not use PBR in an EIA context for offshore wind energy developments. Rather than using simple algorithms that rely on potentially invalid implicit assumptions, we recommend use of Leslie matrix models for assessing the impact of additional mortality on a population, enabling the user to explicitly define assumptions and test their importance.

Background For the planning of an effective dog mass vaccination campaign against rabies in Africa, it is crucial to know more about the dog population. In this paper we describe for the first time the dog ecology, demographic structure and population dynamics of a domestic dog population in Bamako, Mali. In 2010 and 2011, we visited 2956 randomly selected compounds. Questionnaire data was collected on the compound and household level and on each dog individually. Dog-owning households were followed every six months during one (dog-owning households identified in 2011) or two years (dog-owning households identified in 2010) for the successive collection of dog demography data. Results We recorded 379 dogs in 279 compounds. The dog human ratio was estimated at 1:121, and the extrapolation of the domestic dog population in Bamako results in an estimate of 14 906 dogs (95% CI 13 041–17 037). The female male ratio was 1:2.8. A high proportion of young dogs was found as a result of a high turnover rate in the population. Mortality within the first year of life was high, and dogs had a life expectancy at birth of 2.5 years. Using a Leslie matrix, we estimated the annual dog population growth to be 20%. Christians were more likely to be dog owners than Muslims. Another factor favouring dog ownership was belonging to the ethnic group of Bobo or Malinke . Dogs were mainly used as watchdogs and fed with household leftovers and garbage. They were most often obtained and given away without remuneration. Conclusions This work contributes vital information towards planning effective and sustainable dog rabies control programmes for the district of Bamako. Due to the high turnover rate, we recommend repeated mass-vaccination campaigns of at least 70% of the owned dogs at yearly intervals. In addition, dog-owners need to be educated on good dog management.

Information on how shark populations respond to fishing mortality ( F ) is critical to developing successful management and conservation strategies. However, data on catch, fishing effort and species abundance are often lacking for shark populations – preventing stock assessments from being conducted. Static demographic models circumvent this issue as they only require life history parameters. Age-structured Leslie Matrix models were developed and applied for silvertip shark Carcharhinus albimarginatus and common blacktip shark Carcharhinus limbatus sampled from heavily fished populations in the Indo-Pacific. Stochasticity was introduced to these models by varying vital rates though Monte Carlo simulations. Varying levels of F were introduced to the analyses to determine how both species respond to fishing pressure. Management scenarios were further developed to determine strategies that could facilitate sustainable harvesting. The demographic estimates demonstrated that without fishing both species would have increasing populations ( λ = 1.06 yr −1 for C. albimarginatus and 1.05 yr −1 for C. limbatus ) until density dependent effects occur. However, both populations would decline when low levels of F (>0.1 yr −1 ) were applied to all age-classes. The matrix elasticities revealed that changes to fertility elements had little effect on λ, while changes in juvenile survival led to the largest changes. However, age-at-first-capture analysis suggests protecting the juvenile life stage of both species would be an ineffective management strategy as both species mature at old ages. An age-at-last-capture analysis suggests these species could be harvested while maintaining increasing populations through a gauntlet fishery. This required F to be restrained to individuals C. limbatus and C. albimarginatus, respectively, until density dependent effects begin to manifest. However, this strategy depends on the ability to successfully protect all other age-classes from fishing – a strategy that may not be pragmatic in developing nations where little regulation occurs.

Demographic models are a powerful means of identifying vulnerable life stages of pest species and assessing the potential effectiveness of various management approaches in reducing pest population growth and spread. In a biological control context, such models can be used to focus foreign exploration or conservation efforts on enemies that attack life stages identified to have the greatest impact, and determine target levels of predation or parasitism that would be necessary to suppress population growth. In this study, we constructed a matrix population model to assess the potential effectiveness of biological controls against the wheat stem sawfly, Cephus cinctus , a major pest of wheat in North America. We calculated the sensitivity of C. cinctus population growth to changes in stage-specific survivorship, to identify the stage at which parasitoid attack would have the largest impact on pest population growth. We also calculated the stage-specific rate of mortality needed to reduce C. cinctus population growth rate to zero, to set targets for conservation biological control approaches. Our model indicates that C. cinctus populations are growing (λ = 1.022), and are predicted to triple in a year in the absence of added control measures. The winter larval stage had the highest elasticities, suggesting this stage is the weakest link in the pest life-cycle, in part reflecting the much longer average duration of the winter compared with the summer larval stage (45 versus 5 weeks). Parasitism levels by native Bracon spp. parasitoids necessary to suppress C. cinctus population growth were the same for summer and overwintering stages (68%). These target parasitism levels far exceeded those typically observed in the field, and conservation measures employed to date suggest that single actions do not bolster parasitism to target thresholds. Thus multiple conservation measures (e.g. reduced tillage, increased cutting height and the provisioning of floral resources) will likely need to be complemented by other management approaches (e.g., host plant resistance), to suppress C. cinctus populations. Our results reinforce previous work demonstrating the utility of matrix models for evaluating the potential efficacy of biological control agents, and further illustrates how they can be used to evaluate, and set targets for, conservation management approaches using specific natural enemies.

Backgrounds: Currently, China has implemented second child policy, and at the same time, many cities in China have Promulgate immigration policy to appeal labor force mainly for talented people, these measures are aim to avoid the aging problems. Chinese population structure has entered the aging era. The ratio of the elderly is increasing to a point where the government must think carefully. Method: The model is based on Leslie model which is dynamic difference equation, the model has two modules: firstly, the prediction of future population structure under existing conditions. Secondly, adding two parameters of second child policy and immigration policy to predict future population structure by using modified Leslie model. Results: We find that just 10 years late, in 2029 the ratio of population over 60 will be 39.45%, far beyond the 10% aging threshold. If adding the parameter of second child policy, the ratio can be 38.1%, 37.9%, 37.7%, 37.5% of different values and when adding immigration policy, the ratio can be 35.1%, 35.4%, 35.8%, 36.1% of different values. We can use the modified model to help the government judge how powerful policies can help balance the population structure. Conclusion: The results above show that if the government does not formulate policies to improve the population structure, the aging problem will continue to deteriorate, the government need to consider implementing pro-natalist Incentive and lowering the threshold of policy. The government should take preventive measures for aging social problems, such as recruit more doctors in advance.

Humans and wildlife are frequently exposed to complex mixtures of chemicals, with exposure rarely causing only one dominant effect. Consequently, there is an urgent need to develop strategies to assess exposures to multiple, hazardous chemicals and effects of such combinations. Here, the maximum cumulative ratio was used as part of a tiered approach to evaluate and prioritize risks of co-exposures to metals in 781 samples of surface water from Tai Lake, China. Multiple metals, including copper, lead, cadmium, nickel and zinc dominated the hazardous effects on aquatic organisms. Based on species sensitivity distributions developed from genus mean chronic values, crustaceans were the most susceptible to effects of metals. Results of a multi-generation experiment demonstrated adverse effects of mixtures of metals at environmentally relevant concentrations on growth and reproduction of the cladocerans, Daphnia magna and Moina macrocopa. Specifically, when exposed to metals body length and total number of offspring produced per adult female were less than the controls. Resistance of D. magna populations to mixtures of metals was significantly less, while, under similar conditions, M. macrocopa exhibited greater capacity to recover and the response to adverse effects occurred earlier. Demographic analysis models constructed using a Leslie matrix, used to predict population dynamics of the cladocerans, revealed that various effects of metal cocktails on individual-level endpoints was related to attenuation at the population level. By integrating all the observations, it was recommended that densities of populations of cladocerans in surface waters could be a useful parameter for indicating possible detrimental effects induced by toxic chemicals. Results of this study provide novel insights into risks posed by simultaneous exposure to multiple metals and reveal their potential adverse long-term effects on sensitive aquatic organisms.

Periodical cicadas, Magicicada spp., are a useful model system for understanding the population processes that influence range boundaries. Unlike most insects, these species typically exist at very high densities (occasionally > 1000/ m2) and have unusually long life-spans (13 or 17 years). They spend most of their lives underground feeding on plant roots. After the underground period, adults emerge from the ground to mate and oviposit over a period of just a few days. Collections of populations that are developmentally synchronized across large areas are known as “broods”. There are usually sharp boundaries between spatially adjacent broods and regions of brood overlap are generally small. The exact mechanism behind this developmental synchronization and the sharp boundary between broods remain unknown: previous studies have focused on the impacts of predator-driven Allee-effects, competition among nymphs, and their impacts on the persistence of off-synchronized emergence events. Here, we present a nonlinear Leslie-type matrix model to additionally consider cicada movement between spatially separated broods, and examine its role in maintaining brood boundaries and within-brood developmental synchrony that is seen in nature. We successfully identify ranges of competition and dispersal that lead to stable coexistence of broods that differ between spatial patches.

Sib cannibalism seems to be paradoxical behaviour, since it decreases the survival rate of the closest relative juveniles, so the rate of sib cannibalism changes the demography of the cannibal phenotype. In the general kin demographic selection model presented here, the long-term growth rate of a phenotype is determined by a Leslie matrix that depends on the life history strategy, and a uniform density-dependent selection process takes place, keeping the total population size at the level of the carrying capacity. Using this model, where different phenotypes are described by different Leslie matrices, we point out that the phenotype optimizing the phenotypic long-term growth rate will select out any other optimizing phenotype. We find that sib cannibalism is adaptive if the sib cannibal can decrease its developmental time, and the shorter development time can increase the rate of survival from sib cannibal juvenile to adult, and also when sib cannibalism increases fecundity in the adult stage. Cannibalism between the closest relatives can be considered as a mutualistic kin strategy when the benefit of cannibalism is greater than the cost of it.

A parametric family of models based on the Weibull model was proposed to describe the age structure of a fossil population. This descriptive approach was combined with a population dynamics model based on the Leslie matrix. The stability and sustainability conditions were algebraically stated to provide an equilibrium equation for any species. The model parameters for a sustainable population were determined via numerical methods. These values represent the survival and mortality profiles for a sustainable population and are comparable between different populations. This approach tests whether an observed mortality profile might correspond to the natural mortality pattern of a stable population. Finally, the model performance was tested for three fossil Bison priscus populations (Il'Skaya, Mauran and Coudoulous) using literature data.

Cohort component models are often used to model the evolution of an age-specific population, and are particularly useful for highlighting the demographic component that contributes the most to the population change. Recently, most of the attention has been devoted to the estimation of four specific demographic components, namely mortality, fertility, emigration and immigration. Many methods take a deterministic viewpoint, which can be quite restrictive in practice. The statistical method that we propose is a multilevel functional data method, where both mortality and migration are modelled and forecast jointly for females and males. The forecast uncertainty associated with each component is incorporated through parametric bootstrapping. Using the historical data for the United Kingdom from 1975 to 2009, we found that the proposed method shows a good in-sample forecast accuracy for the holdout data between 2001 and 2009. Moreover, we produce out-of-sample population forecasts from 2010 to 2030, and compare our forecasts with those produced by the Office for National Statistics.

An estimate of the population growth rate ( γ ) is an essential biological information that can be input into stock assessment models to estimate management quantities for commercial fisheries. Demographic analysis conducted using the Leslie matrix method was used to estimate γ for Indian Ocean blue shark (Prionace glauca), with Monte Carlo simulation used to quantify uncertainty. A harvest analysis was conducted with various selectivity patterns. The results indicated that the productivity of the blue shark was high, with γ = 0 . 26 –0.32 y−1 under the assumption of a one-year reproductive cycle. The steepness of the Beverton–Holt stock-recruitment model was estimated to be 0.72 (0.24–0.87) when the Castro and Mejuto fecundity formular was assumed, and 0.80 (0.65–0.88) when the Fujinami et al. fecundity formular was assumed. Harvest analysis with tuna longline selectivity led to lower sustainable harvest rates, but a higher proportion of biomass removed compared to the selectivity patterns for other fisheries. This study provides crucial prior information on the population growth rate and steepness parameters, which can be incorporated into stock assessments for blue shark. Besides, harvest analysis could be a supplement for data-poor stock assessment and risk analysis, to evaluate a tradeoff among different fisheries when considering a management strategy.

This study aims to investigate the impact of the change in China’s fertility policy from its selective two-child policy to a universal two-child policy on the balance of its Urban Employee Basic Medical Insurance (UEBMI) fund. This study uses data obtained from the 2013 and 2015 China General Society Survey to estimate the Poisson model, and then adopts a bisexual Leslie matrix, estimated adjusted coefficients, and an actuarial model to forecast the current balance and accumulated balance of the UEBMI fund under each of the selective two-child and universal two-child policies up to the year 2060. The primary finding of this study is that this change in fertility policy results in the current balance of the UEBMI fund registering a lower deficit and eventually a surplus. Although this policy change cannot prevent the UEBMI from facing bankruptcy, the deficit in terms of the accumulated balance of the UEBMI fund will decline.

a b s t r a c t To be most effective, the scale of wildlife management practices should match the range of a particular species' movements. For this reason, combined with our inability to rigorously or regularly census moun- tain lion populations, several authors have suggested that mountain lions be managed in a source-sink or metapopulation framework. We used a combination of resource selection functions, mortality estima- tion, and dispersal modeling to estimate cougar population levels in Montana statewide and potential population level effects of planned harvest levels. Between 1980 and 2012, 236 independent mountain lions were collared and monitored for research in Montana. From these data we used 18,695 GPS loca- tions collected during winter from 85 animals to develop a resource selection function (RSF), and 11,726 VHF and GPS locations from 142 animals along with the locations of 6343 mountain lions harvested from 1988-2011 to validate the RSF model. Our RSF model validated well in all portions of the State, although it appeared to perform better in Montana Fish, Wildlife and Parks (MFWP) Regions 1, 2, 4 and 6, than in Regions 3, 5, and 7. Our mean RSF based population estimate for the total population (kittens, juveniles, and adults) of mountain lions in Montana in 2005 was 3926, with almost 25% of the entire population in MFWP Region 1. Estimates based on a high and low reference population estimates produce a possible range of 2784 to 5156 mountain lions statewide. Based on a range of possible survival rates we estimated the mountain lion population in Montana to be stable to slightly increasing between 2005 and 2010 with lambda ranging from 0.999 (SD = 0.05) to 1.02 (SD = 0.03). We believe these population growth rates to be a conservative estimate of true population growth. Our model suggests that proposed changes to female harvest quotas for 2013-2015 will result in an annual statewide population decline of 3% and shows that, due to reduced dispersal, changes to harvest in one management unit may affect population growth in neighboring units where smaller or even no changes were made. Uncertainty regarding dis- persal levels and initial population density may have a significant effect on predictions at a management unit scale (i.e. 2000 km 2 ), while at a regional scale (i.e. 50,000 km 2

In this study, we use entropy related mixing rate modules to measure the effects of temperature on insect population stability and demographic breakdown. The uncertainty in the age of the mother of a randomly chosen newborn, and how it is moved after a finite act of time steps, is modeled using a stochastic transformation of the Leslie matrix. Age classes are represented as a cycle graph and its transitions towards the stable age distribution are brought forth as an exact Markov chain. The dynamics of divergence, from a non equilibrium state towards equilibrium, are evaluated using the Kolmogorov–Sinai entropy. Moreover, Kullback–Leibler distance is applied as information-theoretic measure to estimate exact mixing times of age transitions probabilities towards equilibrium. Using empirically data, we show that on the initial conditions and simulated projection’s trough time, that population entropy can effectively be applied to detect demographic variability towards equilibrium under different temperature conditions. Changes in entropy are correlated with the fluctuations of the insect population decay rates (i.e. demographic stability towards equilibrium). Moreover, shorter mixing times are directly linked to lower entropy rates and vice versa. This may be linked to the properties of the insect model system, which in contrast to warm blooded animals has the ability to greatly change its metabolic and demographic rates. Moreover, population entropy and the related distance measures that are applied, provide a means to measure these rates. The current results and model projections provide clear biological evidence why dynamic population entropy may be useful to measure population stability.

The recently developed macroscopic approach to demography describes the age distribution of mothers and the net maternity function for a given human population entirely in terms of five parameters. Tracking of these parameters provides a number of new tools for analyzing populations and predicting their future states. Within the macroscopic approach, the new concept of generalized Lotka stability is presented in this paper, as an extension of a strong version of classic Lotka stability. The two leading parameters of the macroscopic approach, the Malthusian parameter r and the perturbation s, are computed from population data and plotted in two-dimensional parameter space. Generalized Lotka stability is then defined in terms of the movement of the (r,s)-vector over time. It may be observed in a number of human populations at specific periods of their history.

Conservation of threatened or endangered species relies critically on accurate population counts over time. In practice, many population censuses are conducted by non-governmental organizations or volunteer citizen scientists who are constrained by fiscal and temporal resources. Less than optimal sampling regimens (characterized by infrequent and/or irregular schedules) for conducting population censuses can result in woefully misleading population estimates – and thus have dire consequences for management and conservation. We illustrate this using an East African case study in which 14 years of bird data was collected in the Arabuko-Sokoke Forest in coastal Kenya. We first estimate life history parameters in a discrete matrix model. Desiring a data collection protocol which would lessen observation error and lend to a deeper understanding of population projections and dynamics of a threatened species, we carry out mathematical and statistical modeling efforts with an adaptation of a Leslie model for simulated population estimates stemming from different population sampling schemes. We illustrate how resource managers might take a strategic approach, using simple quantitative models, to develop an optimal sampling scheme that considers important species traits, such as breeding season, and balances the tradeoff between resources and accuracy.

The population vulnerability of a species to pesticides is determined by the risk of its exposure to the pollutant, its sensitivity to the toxicant and the potential to sustain its populations if adversely affected (population resilience). This study uses population modelling to link the life cycle traits of a set of fish species which are highly susceptible to pesticide exposure, to their population resilience as a contribution to the needed identification of representative vulnerable species for higher-tier ecological risk assessment (ERA) of pesticides in Europe. Leslie matrix models for 21 species were parametrized using data from literature on field populations whose resilience was assessed. Phoxinus phoxinus was identified as the species with the least resilient populations for effects on fertility, Lampetra planeri for effects on juvenile survival and Esox lucius for effects on adult survival. Combining the measured effects from standard fish bio-tests with population models of these species would result in an ecologically relevant and protective risk assessment for field conditions in Europe.

Illegal harvest rates of wildlife populations are often unknown or difficult to estimate from field data due to under-reporting or incomplete detection of carcasses. This is especially true for elephants that are killed for ivory or in conflicts with people. We describe a method to infer harvest rates from coarse field data of three population parameters, namely, adult female to male ratio, male old-adult to young-adult ratio, and proportion of adult males in the population using Jensen's (2000) 2-sex, density-dependent Leslie matrix model. The specific combination of male and female harvest rates and numbers can be determined from the history of harvest and estimate of population size. We applied this technique to two populations of elephants for which data on age structure and records of mortality were available-a forest-dwelling population of the Asian elephant (at Nagarahole, India) and an African savannah elephant population (at Samburu, Kenya) that had experienced male-biased harvest regimes over 2-3 decades. For the Nagarahole population, the recorded numbers of male and female elephants killed illegally during 1981-2000 were 64% and 88% of the values predicted by the model, respectively, implying some non-detection or incomplete reporting while for the Samburu population the recorded and modeled numbers of harvest during 1990-1999 closely matched. This technique, applicable to any animal population following logistic growth model, can be especially useful for inferring illegal harvest numbers of forest elephants in Africa and Asia.

The present work describes the application of a non-linear Leslie model for predicting the effects of ionising radiation on wild populations. The model assumes that, for protracted chronic irradiation, the effect-dose relationship is linear. In particular, the effects of radiation are modelled by relating the increase in the mortality rates of the individuals to the dose rates through a proportionality factor C. The model was tested using independent data and information from a series of experiments that were aimed at assessing the response to radiation of wild populations of meadow voles and whose results were described in the international literature. The comparison of the model results with the data selected from the above mentioned experiments showed that the model overestimated the detrimental effects of radiation on the size of irradiated populations when the values of C were within the range derived from the median lethal dose (L50) for small mammals. The described non-linear model suggests that the non-expressed biotic potential of the species whose growth is limited by processes of environmental resistance, such as the competition among the individuals of the same or of different species for the exploitation of the available resources, can be a factor that determines a more effective response of population to the radiation effects.

International audience; The population dynamics of waterbirds constitute an indicator of wetland conservation status. However, waterbird population censuses are difficult to implement because the individuals are very mobile within their range, and some species are elusive or breed in remote areas. Therefore, demographic models based on the estimation of survival and breeding success appear as a reliable alternative to population censuses. Here we present this model-based approach in the case of the French-wintering snipe population (Gallinago gallinago), which breeds mainly in Northern and Eastern Europe. Using a multi-state model to accommodate the mobile nature of waterbirds, we estimate snipe survival using a joint analysis of capture-recapture and ring-recovery data. Then, we use matrix population models to estimate the minimum recruitment rate required to maintain the population at its current size and derive a chart for using ageratio of ringed birds as indicator of population trend. Although we call for more data collection in order to reduce uncertainty, we conclude that occasional declines are likely after years with poor breeding success, but that the French-wintering snipe population is on average stable. Individual-based monitoring data and population modeling make it possible to use waterbirds as indicator species at the flyway scale.

Demographic models are commonly used to study cetacean population dynamics and are characterized by a wide range of age classes. The primary building blocks are age-specific survival or mortality and birth rates, which can be combined using a Leslie matrix protocol to provide estimates of maximum possible rates of increase for population size. In this context, specific mortality data are valuable for modeling the viability of threatened species. Depletion of prey, pollution, and other anthropogenic disturbances are believed to have contributed to the decline of populations, but the evidence is less conclusive for these factors than for bycatch. In an attempt to estimate a population growth rate that incorporates uncertainties in vital parameters, we apply a random Leslie analysis to calculate effective growth rate for the time-dependent mean-value population. Here we provide the algorithm to implement it for a general 13×13 random survival model. An effective growth rate can be characterized by studying the time evolution of the mean-value population vector state (in an age-structured description). We show that the asymptotic behavior of the mean-value vector state, which characterizes the population growth rate when the model has random vital parameters, exhibits a value that is below previously expected potential estimations. We demonstrate the procedure using bibliographic revision data of the harbor porpoise (Phocoena phocoena) in Canadian waters, subjected to incidental mortality. Fil: Caceres Garcia Faure, Manuel Osvaldo. Universidad Nacional de Cuyo; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Area de Energía Nuclear. Instituto Balseiro; Argentina Fil: Cáceres Saez, Iris. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales; Argentina. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche; Argentina

This work is aimed at presenting and discussing a nonlinear Leslie model for predicting the effects of stressors on a biological population whose growth is limited by unfavourable factors such as the competition for the exploitation of the environmental resources. The model was applied to simulate the impact of ionising radiation on populations of mammals living in highly contaminated areas. After a brief review of the main properties of nonnegative matrices, it was demonstrated that the output of the suggested model is asymptotically stable. Analysis of the model results enlightened the importance of indirect systemic effects such as the enhanced capacity, under certain circumstances, of populations in more competitive conditions to resist the harmful influence of a stressor. The proposed model is simple and can be useful for understanding the behaviour of populations affected by radioactive and non-radioactive stressors.

Investigating how individuals are affected by environmental pollution is relatively straightforward, for example through conducting field studies or laboratory toxicity tests. Exploring such effects at a population level is considerably more difficult. Nonetheless, the exploration of population-level effects is important as the outcomes may differ from those seen at the individual level. Eelpout (Zoarces viviparus L.) have been used for several years as a bioindicator for hazard substances in both the field and laboratory tests, and individual effects on reproduction have been reported. However, the influence of these effects at the population level remained unexplored. In this study, four Leslie matrix models were parameterized using data from non-polluted eelpout populations (Skagerrak, Baltic Proper, Gulf of Bothnia and Gulf of Finland). The four sites represent an environmental gradient in salinity. Furthermore, life-history data revealed differences between the sites with growth rate, fecundity, age at maturity and longevity being the most significant. The effect of pollution on natural eelpout populations was then simulated by combining the outputs from the Leslie matrices with data from laboratory and field studies exploring reproductive impairment in contaminated environments. Our results show that despite differences in life-history characteristics between sites, survival of early life stages (i.e. larvae and zero-year-old fish) was the most important factor affecting population growth and persistence for all sites. The range of change in survival of larvae necessary to change population dynamics (i.e. growth) and persistence is well within the range documented in recipient and experimental studies of chemicals and industrial waste waters. Overall, larval malformation resulting from environmental pollution can have large effects on natural populations, leading to population losses and possibly even extinction. This study hereby contributes valuable knowledge by extending individual-level effects of environmental contaminants to the population level.

The yellownose skate ( Dipturus chilensis ) is one of the most important component of the commercial elasmobranch fishery off Chile with an extensive distribution range from 36°44′ S − 55°13′ S. Nevertheless, fishery management for this species does not extend beyond the central zone off Chile (36°44′ − 41°28′ S), leaving the southern zone (41°28′ S − 55°13′ S) without a proper fishing effort regulation. As a result, fishing pressure has increased dramatically in the southern zone, with unknown potential consequences for this elasmobranch population. In the absence of rigorous fishery-biological data, we used a matrix population model to assess yellownose skate demographic traits under different fishing mortality levels. A Leslie matrix model was implemented, where changes in age classes are defined in terms of of life history parameters. Uncertainty was incorporated by applying a Monte Carlo method to survival, age at maturity, and fecundity. Three scenarios were evaluated based on different assumptions about survival, fishing mortality rates, and age at 50% of vulnerability. These scenarios showed a slow growth rate for population abundance (3–15% per year) with no fishing exploitation. The population reaches equilibrium at low mortality levels (0.31 yr −1 ), which is consistent with estimates reported for other rajidae skates. The elasticity analysis indicates that juvenile survival contributes the most to variations in the population growth rate. The sustainable mortality rate has a positive, non-linear relationship with age at 50% of vulnerability. Projections using different selectivity patterns showed that the population abundance is stable only when age-dependent fishing mortality removes individuals of older ages. We concluded that yellownose skate is extremely vulnerable to fishing exploitation and it is remarkably sensitive to juvenile and early life stages survival, implying that management actions are needed to ensure a sustainable exploitation.

The origin of preferences was viewed as related to the dominant eigenvalue of a Leslie matrix modelling reproductive strategies. In a variable environment, however, the coexistence of varying preferences no longer requires optimality, but is identified with the mathematical property of viability: a state of the population is viable if there exists at least one solution starting from it and remaining in the set of constraints until a given time horizon (or forever). The coexistence kernel of two competitors with varying preferences is computed for the case of scalar and 2 × 2 Leslie matrices, with either measurable or differentiable preferences. The homologue of indifference curves is the regulation map, the correspondence associating the set of viable preferences to a given state of the population. Among these viable trajectories, some are also optimal in the sense of dominance discounted in time. These viable optimal solutions are obtained as specific trajectories in an auxiliary dynamic system, and the associated maximal values constitute one boundary of the viability kernel of this auxiliary system (theorem). Hence, the perpetuation of varying preferences allows the diversity of economic preferences, as shown here using the example of the comparative history of fertility from mid-nineteenth century to nowadays in France and England.

In age-classified population models where all parameters are known, the generation time and growth rate are calculated in a straightforward manner. For many populations, some parameters, such as juvenile survival, are difficult to estimate accurately. In a simplified population model where fecundity and survival are constant from the onset of breeding, it is known that generation time may be calculated given only adult survival, age at first reproduction, and the population growth rate. However, the assumption of constant fecundity from the onset of breeding does not hold for many populations. An extended population model allows calculation of generation time with the additional knowledge of the ratio of age-specific fecundities compared to a maximum fecundity rate. When these relative fecundities are unknown, an ad hoc adjustment to the simplified model performs well. When the study population is in an ideal environment, the optimal generation time and maximum growth rate are linked, and both may be approximated knowing only adult survival, age at first reproduction, and the relative fecundities. The maximum growth rate has important conservation implications, and calculating it correctly is therefore important. Improper use of the simplified population model to calculate the maximum growth rate, combined with a simple decision rule, leads to an average overharvest of 36%, and >60% for three of six bird species studied, compared to the full population model. By comparison, using the approximation from the extended or adjusted models results in average overharvests of only 8% (extended model) and 5% (adjusted model), and

In this paper, we consider the diffusive Leslie predator–prey model with large intrinsic predator growth rate, and investigate the change of behavior of the model when a simple protection zone Ω 0 for the prey is introduced. As in earlier work [Y. Du, J. Shi, A diffusive predator–prey model with a protection zone, J. Differential Equations 229 (2006) 63–91; Y. Du, X. Liang, A diffusive competition model with a protection zone, J. Differential Equations 244 (2008) 61–86] we show the existence of a critical patch size of the protection zone, determined by the first Dirichlet eigenvalue of the Laplacian over Ω 0 and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when Ω 0 is above the critical patch size. However, our research here reveals significant difference of the model's behavior from the predator–prey model studied in [Y. Du, J. Shi, A diffusive predator–prey model with a protection zone, J. Differential Equations 229 (2006) 63–91] with the same kind of protection zone. We show that the asymptotic profile of the population distribution of the Leslie model is governed by a standard boundary blow-up problem, and classical or degenerate logistic equations.

Lumbricus terrestris, an abundant and widespread earthworm of temperate regions, plays an important role in soil structure and organic matter turnover, especially in unplowed fields. The prediction of earthworm density is important to accurately assess the role they are playing in soil quality. The population dynamics of L. terrestris have been mainly studied under grassland conditions but little effort has been dedicated to predicting such dynamics in cultivated soils. This paper presents a new model, WORMDYN that simulates the population dynamics of L. terresttis in terms of density. WORMDYN is a stochastic stage-based Leslie matrix model which accounts for vertical migrations. In the model, the earthworm population is divided into four developmental stages (cocoons, juveniles, sub-adults, and adults) and life cycle parameters depend on soil temperature and water content. The model parameters were estimated from the available literature. Experiments were carried out in 2006 and 2007 in plowed and surface tilled plots (Grignon, France) to assess the accuracy of the model predictions of L. terrestris density. The Root Mean Squared Error (RMSE) of the WORMDYN predictions ranged from 0.5 to 19.9 individuals m(-2) in 2006 and from 0.4 to 40.5 individuals(-2) in 2007, depending on the type of soil tillage, the time of year and the developmental stage. The RMSE values of WORMDYN were compared to RMSE values obtained for predictions directly derived from density measurements and from the model of [Svendsen, T.S., Hansen, P.E., Sommer, C., Martinussen, T., Gronvold, J., Holter, P., 2005. Life history characteristics of Lumbricus terrestris and effects of the veterinary antiparasitic compounds ivermectin and fenbendazole. Soil Biol. Biochem. 37, 927-936]. In 2006, WORMDYN performed better for all developmental stages except for adults. In 2007, WORMDYN performed better for juvenile, adult, and total populations in the plowed plot, but the RMSE values of WORMDYN were almost always higher than the values obtained for the other two series of predictions for the unplowed plot. The relatively high RMSE values obtained in 2007 were probably due to some intrinsic factors regulating the population which were not taken into account by the model, like density-dependence and/or competition for food and space. It may also be due to inaccurate estimation of parameter values. A sensitivity analysis was carried out to identify the parameters which should be estimated with a higher precision in order to improve the predictive capabilities of the model. The results showed that the most important parameters are the survival rate of juveniles and the fecundity of adults. (c) 2008 Elsevier B.V. All rights reserved.

A discrete age-structured Bernardelli, Lewis and Leslie (BLL) population model for a single species is formulated under age dependent harvesting condition. Here, after an initial period during which the growth of the species is not much, harvesting is performed. Its rate is proportional to the available bio-mass (number of species) of different age group population and decreases with the age of the species. The modified Leslie matrix for the present models is derived. Stability of the system is studied from the ratio of the population densities at different times. As a particular case, not considering the harvesting of species, the classical age-structured population model of [J.N. Kapur, Stability analysis of continuous and discrete population models, Indian J. Pure Appl. Math. 9 (1976) 702–708] is obtained.

The finite rate of population increase ( λ ) is a fundamental demographic parameter used to assess the dynamics of wild animal populations. Although, abundance data are commonly used, λ may be estimated by survival and fecundity rates using the Lotka equation or Leslie projection matrices. Implicit in the dimensionality of the Leslie matrix and its formulation is an assumption about maximum attainable age. The purpose of this paper is to discuss the difficulties of accurately calculating maximum life expectancy and the implications of alternative values on estimated rates of population change. We also present a simplified expression for the Lotka equation that can be used to estimate λ and its variance under asymptotic survival assumptions. Our evaluation of estimating maximum life expectancy revealed that a much larger sample size is required for species with high ( S ≥ 0.80) versus low annual survival rates ( S ≤ 0.30). Uncertainty in maximum age can also lead to sampling error in λ ˆ and possible bias. Therefore, investigators are encouraged to carefully consider sources used to estimate maximum age expectancy while recognizing that life expectancy is population specific. Specifying the estimation equation used, and the value of maximum age assumed will improve the statistical and biological inferences concerning the rates of population change. Ironically, the asymptotic estimate of λ (i.e., w → ∞ ) will have a smaller sampling error than estimates of λ when age expectancy is unknown. The asymptotic value of λ , when clearly identified, may therefore provide a useful bound, unencumbered by arbitrary and uncertain estimates of maximum life expectancy.

The finite annual rate of population increase ( λ ) is a fundamental demographic parameter that characterizes the relative annual change in animal numbers. Uncertainty in the estimation of λ from demographic population viability analyses (PVAs) has been largely limited to sensitivity analysis, calculating a pseudo-distribution for λ ˆ using Monte Carlo methods, or by use of bootstrap methods. The delta method has been used and suggested by several researchers, but no one has provided the computational means to implement it. In this paper, we present Mathematica code to calculate λ and its variance based on eigenvalue calculations of a Leslie transition matrix. We demonstrate the procedure using data from a Hawaiian hawk ( Buteo solitarius ) study.

We use a periodically forced density-dependent compensatory Leslie model to study the combined effects of environmental fluctuations and age-structure on pioneer populations. In constant environments, the models have globally attracting positive fixed points. However, with the advent of periodic forcing, the models have globally attracting cycles. We derive conditions under which the cycle is attenuant, resonant, and neither attenuant nor resonant. These results show that the response of age-structured populations to environmental fluctuations is a complex function of the compensatory mechanisms at different life-history stages, the fertile age classes and the period of the environment.

In this work, we present an age-structured population model that incorporates individual behaviour. A classical Leslie matrix model is used to describe the population demography. Adults acquire resources required to survive and reproduce by using two contrasted behavioural tactics (hawk versus dove). Individual survival depends on the average cost of fights while individual fecundity depends on the average gain in the competition to access the resource. We investigated variation in fecundity according to the amount of resources available by using two functions: a Holling type function and a threshold function. We aimed to assess the long-term effects of conflicting tactics of resource acquisition on population dynamics. Our model includes two parts: a fast part that describes the encounters and fights involves a game dynamic model based upon the replicator equations in discrete time; and a slow part that describes the long-term effects of conflicting tactics on the population growth rate. The use of aggregation methods allowed us to reduce the proposed initial model into an aggregated model that describes the dynamics of the population (a Leslie matrix model). We analysed the effects of gain and cost parameters on the asymptotic growth rate of the total population.

The risk of roadside verge invasion by transgenic plants is favoured when a cultivated species can persist outside fields as feral populations. We chose oilseed rape as a model species to evaluate the spread of genetically modified herbicide tolerant (GMHT) feral populations under selection pressure (herbicide spraying) in the medium term. We developed a stepwise invasion model that combines stage-structured dynamics (via a leslie matrix) and seed dispersal (via a mixture of two kernels) within an integro-differential equation. Modelling choices were made to conform to our intention to obtain methodological insight about the necessity to integrate long-distance seed dispersal in models of gene flow among oilseed rape. We thus assumed that roadside verges are a one-dimensional and uniformly suitable habitat and that events of dispersal and demography are deterministic. We performed elasticity analyses of population growth rate and invasion speed to highlight the determinants of population demography and spread. Rare events of long-distance dispersal controlled population spread. The risk of road verge invasion by feral populations of GMHT oilseed rape under selection pressure is thus real and does exist, since it was proved experimentally that oilseed rape can be dispersed by vehicles. Models of oilseed rape should then include long-distance seed dispersal otherwise they would underestimate feral population spread. Population growth rate and invasion speed depended on the same demographic transitions, i.e. those including local recruitment (local production of new individuals), but not on the persistence of seeds in the seed bank. Therefore, plant sterilisation would be more efficient to limit feral population spread than selection of cultivars without seed dormancy. The assumptions made about habitat continuity and homogeneity were consistent in the framework of this stepwise approach. However, integrating habitat heterogeneity and stochasticity would improve this invasion model.

Leslie matrix models are discrete models for the development of age-structured populations. It is known that eigenvalues of a Leslie matrix are important in describing the asymptotic behavior of the corresponding population model. It is also known that the ratio of the spectral radius and the second largest (subdominant) eigenvalue in modulus of a non-periodic Leslie matrix determines the rate of convergence of the corresponding population distributions to a stable age distribution. In this paper, we further study the spectral properties of a row-stochastic Leslie matrix A with a near-periodic fecundity pattern of type (k, d, s) based on Kirkland’s results in 1993. Intervals containing arguments of eigenvalues of A on the upper-half plane are given. Sufficient conditions are derived for the argument of the subdominant eigenvalue of A to be in the interval 2 π d , 2 π d - s for the cases where k = 1. A computational scheme is suggested to approximate the subdominant eigenvalue when its argument is in 2 π d , 2 π d - s .

We consider the class of projection matrices arising from the size-classified matrix model for population growth. Suppose that such a matrix M is irreducible, and that the corresponding stable distribution vector is x. We give formulae for the partial derivatives of the entries in x with respect to the demographic parameters in M. Those formulae only require knowledge of the entries in M and the Perron value of M. For the special case that M is a Leslie matrix, we discuss various concavity and order properties of the partial derivatives, and for a large subclass of Leslie matrices, provide bounds on the sizes of the relevant partial derivatives.

The exponent γ(D) of a primitive digraph D is the smallest m such that for each ordered pair of not necessarily distinct vertices (u, v), there exists a u ⇝ v walk of length m. If λ(D) is the set of all cycle lengths, then the circumdiameter of D, denoted dc(λ(D)), is the maximum over all ordered pairs of not necessarily distinct vertices (u, v) of the length of a shortest u ⇝ v walk that intersects cycles of all lengths. It is well known that γ(D) ⩽ ϕ(λ(D)) + dc(λ(D)), in which ϕ(λ(D)) is the Frobenius–Schur index. Several new sufficient conditions and families of digraphs for which equality holds in the above upper bound are given, and some families of digraphs D for which γ(D) = ϕ(λ(D)) + dc(λ(D)) − 1 are defined. Additional sufficient conditions for equality in the above upper bound for γ(D) and a new upper bound for dc(λ(D)) are given for digraphs with large exponent, that is, digraphs on n vertices having γ ( D ) ⩾ ⌊ ( n - 1 ) 2 + 1 2 ⌋ + 2 . The circumdiameter and bounds on the exponent for the digraph of a Leslie matrix are found.

We develop a unified framework for jointly defining population dynamics models and measurements taken on a population. The framework is a state-space model where the population processes are modelled by the state process and measurements are modelled by the observation process. In many cases, the expected value for the state process can be represented as a generalisation of the standard population projection matrix: each sub-process within the state process may be modelled by a separate matrix and the product of these matrices is a generalised Leslie matrix. By selecting appropriate matrices and their ordering, a wide range of models may be specified. The method is fully flexible for allowing stochastic variation in the processes. Process parameters may themselves be modelled as functions of covariates. The structure accommodates effects such as density dependence, competition and predator–prey relationships, and metapopulations are readily modelled. Observations on the population enter through an observation process model, and we show how likelihood functions can be built that reflect both demographic stochasticity (which appears in the state process) and stochastic errors in the observations. Parameter estimation and estimation of state process variables can be conducted using sequential Monte Carlo procedures.

There is a well-established body of literature that deals with population models for modular organisms but that ignores the fragmentation history of individuals. Processes that cause colony damage, such as fragmentation, can result in reduced growth and fecundity and increased mortality of fragments, leading to two classes of colonies—undamaged and damaged. If these classes differ in demographic performance, models ignoring fragmentation history may be inaccurate. We present a general population model for modular organisms, which addresses this issue by including fragmentation history. The model is illustrated using the colonial bryozoan Mucropetraliella ellerii (MacGillivray). We used the model to investigate the impact of additional disturbance of a kind that would damage colonies. We used existing data for two populations living under boulders in the low intertidal zone to parameterise the model. Despite similar population size structures, the population at Point Addis was predicted to be at risk only after very large increases in disturbance, while the Flinders population had a high risk of extinction over 10–15 years, with only a small increase in disturbance. The results suggest that site-specific demographic models may be required when establishing and managing marine protected areas that include this species.

Partial life-cycle models are simplified, matrix-based population models that allow demographic analyses using incomplete demographic data. Number of parameters in most partial life-cycle models are fixed, and this permits direct interspecific comparison of population dynamics and life histories. Because of these desirable properties, partial life-cycle models have recently received substantial applications. However, adequacy of partial life-cycle models has not been investigated using empirical data. I tested the adequacy of a post-breeding census partial life-cycle model by examining whether and to what extent dynamical properties of the age-structured model are retained in the post-breeding census partial life-cycle model. I applied the age-structured Leslie matrix model and a post-breeding census partial life-cycle model to demographic data for 142 populations of mammals, and compared the projected population growth rate (λ), and elasticity of λ to changes in ages at first and last reproduction, juvenile survival, adult survival, and fertility estimated from the two models. Population growth rate estimated from the two models were practically indistinguishable, and elasticities estimated from the two models were very similar. These results suggest that dynamical properties of the age-structured model are generally captured in the partial life-cycle model, and that application of the post-breeding census partial life-cycle model to age-structured or partial demographic data will not substantially compromise precision of analyses nor conclusions of an investigation. These results have substantial implications in basic and applied population ecology, because age-specific demographic data are seldom available for many species of conservation concern, and also because partial life-cycle models permit perturbation analyses involving ages at first and last reproduction using standard analytical techniques.

Management plans for threatened or recovering large vertebrate species that are increasing in population size and range focus on the establishment of viable populations within set temporal limits.New Zealand (Hookers) sea lions ( Phocarctos hookeri) were declared a threatened species in 1997, and New Zealand legislation requires that threatened species of marine mammals must be managed to reduce human-induced mortality and achieve a non-threatened status within 20 years.The present breeding distribution of P. hookeri is highly localised, with over 95% of total annual pup production located at Auckland Islands and almost all of the remainder at Campbell Island.Breeding elsewhere has been ephemeral or restricted to < 10 adult females.The only recorded sustainable breeding at a new location has been at Otago, South Island, New Zealand.This breeding population consisted of a total of four breeding females in 2002 and is derived from one immigrant female that gave birth to her first pup in the 1993/1994 breeding season.The New Zealand Department of Conservation management plan specifies that to achieve a non-threatened status P. hookeri (1) at Otago must increase in the number of breeding females to 510, and (2) must establish 5two new breeding locations within the 20-year time frame, each with 510 breeding females.This study 1) projects the population growth trends at a new location (Otago) to see if it will achieve 510 breeding females within the legislated time frame, and (2) examines the likelihood that other breeding locations will establish elsewhere given the demographic information available for this species.We present 20 deterministic and three stochastic Leslie matrix model scenarios for female population growth for the initial years following the start of breeding at a new location.Our results indicate that (1) a new breeding population derived from one immigrant female is unlikely to reach 10 breeding females in 20 years; this duration is more likely to be 23–41 years (deterministic models) or 23–26 years (stochastic model), (2) the likelihood of two new sites establishing within 20 years is unquantifiable, but the probability is low, and (3) if the legislated outcome and time limit are not revised in the population management plan, the feasibility and effectiveness of re-locating young females could be investigated. # 2003 Elsevier Ltd.All rights reserved.

We studied survival and demography of black bears, Ursus americanus, in Banff National Park (BNP) from 1994 to 2000 to test the efficacy of National Park protection. We monitored 25 radiocollared bears an average of 1.9 years each for a total of 51.8 bear-years. Eighty-two percent of all mortality (n=11) was human-caused, composed of highway mortality (36%), management mortality (27%) and management relocation (18%). Survival was influenced by season and management status. Once bears became a management problem, survival (0.66) was lower than several hunted populations. Adult (0.84) survival was comparable to other unprotected or partly protected populations. Cub (0.64) and yearling (0.67) survival, and reproductive rate (mx=0.47 female cubs/inter-birth interval), was slightly lower than other populations in western North America. We combined survival and reproductive rates in a preliminary post-birth pulse age-class Leslie matrix model and estimated population growth rate as 0.95 (95% simulated C.I. 0.79–1.10). Sensitivity analyses showed λ was most sensitive to changes in adult female survival. Responsible management agencies should reduce adult female highway mortality and the likelihood of becoming a management problem, while continuing monitoring to refine demographic analyses to adequately protect this population.

It is frequently asserted that measures to protect the biotic environment from increased radiation exposures arising from human activities should be focussed on the population rather than the individual. It is, however, difficult (if not impossible) to identify any population-specific attributes that can be affected by radiation exposure directly rather than through the mediation of direct, known and identifiable effects in individual organisms. Indeed, it is often conceded that this difficulty forces attention to be refocussed onto the effects in individuals. Regulatory controls on radioactive waste management and disposal could then be implemented to ensure that any radiation effects in individual native plants and animals remain at, or below, some acceptable level (yet to be defined). Nevertheless, the question remains as to whether such controls would also provide for the protection of the population. An answer to this question depends on the availability of a model that allows the integration of the known effects of radiation exposure on the mortality, morbidity, fertility and fecundity of individuals into an assessment of the possible impact at the population level. The utility of one such approach, the Leslie Matrix Model, is explored in respect of a fish population (the plaice, Pleuronectes platessa). This initial implementation of the population model is simplistic (and, certainly, environmentally unrealistic), but it is concluded that the output from the model does provide some insights into how the population might respond to radiation-induced changes in individual attributes, and that further development in the direction of increased realism is fully warranted.

A Leslie matrix model was developed for a small gray wolf (Canis lupus) population recolonizing an area with abundant resources and uncontrolled by humans. The model was modified to describe population growth in a limited environment using a discrete form of the logistic equation. The density dependent Leslie matrix model was applied to investigate gray wolf population recovery in the Upper Peninsula of Michigan. Estimates from the density dependent matrix model were compared with published winter count estimates from the Michigan Department of Natural Resources. The gray wolf population in the Upper Peninsula of Michigan was projected to reach a total of 929 wolves by the year 2012 with a 95% confidence interval of 662 to 1153 wolves.

A spatially explicit metapopulation model was used to examine the effects of landscape characteristics (patch sizes, interpatch distances, patch productivity) and dispersal behavior (maximum dispersal distance) on the source–sink dynamics of white-tailed deer ( Odocoileus virginianus ) in a simulated landscape. Specifically, the model was used to test the hypothesis that patterns in primary productivity, which affect the growth of deer populations, will interact with, and potentially alter, the effects of landscape structure on metapopulation dynamics. The model, constructed in the STELLA modeling environment, combines a density-dependent Leslie matrix population model with a simple habitat/non-habitat representation of an artificial landscape to simulate the growth and spread of deer populations in a spatial framework. A set of 60 simulations were run, measuring the average net emigration per habitat patch for maximum dispersal distances of 5, 10 and 20 km and under four net primary productivity (NPP) conditions: (1) constant NPP per km 2 ; (2) NPP varying with patch size; (3) NPP varying inversely with patch size; and (4) NPP varying over time. Significant differences were observed for effects of patch size, dispersal distance, NPP conditions and all two- and three-way interactions on patterns of net emigration. Specifically, increasing the maximum dispersal distance led to magnifications in net emigration patterns (i.e. patches exhibiting a positive trend in net emigration became more positive and vice versa). Changes in NPP altered the magnitude of the source–sink trends, sometimes reversing the relationship, particularly for populations in smaller patches. The results illustrate the importance of multiple interacting landscape factors in influencing metapopulation dynamics, indicating that shifting patterns of productivity can significantly alter the source–sink patterns of metapopulations when spatial factors are explicitly considered. Implications for management and conservation, as well as future model improvements, are briefly discussed.