Lefkovitch Matrix Model Research Articles

Value of combining transect counts and telemetry data to determine short-term population trends in a globally threatened species.

To evaluate conservation interventions, it is necessary to obtain reliable population trends for short (<10 years) time scales. Telemetry can be used to estimate short-term survival rates and is a common tool for assessing population trends, but it has limitations and can be biased toward specific behavioral traits of tagged individuals. Encounter rates calculated from transects can be useful for assessing changes across multiple species, but they can have large confidence intervals and be affected by variations in survey conditions. The decline of African vultures has been well-documented, but understanding of recent trends is lacking. To examine population trends, we used survival estimates from telemetry data collected over 6 years (primarily for white-backed vultures [Gyps africanus]) and transect counts conducted over 8 years (for 7 scavenging raptors) in 3 large protected areas in Tanzania. Population trends were estimated using survival analysis combined with the Leslie Lefkovitch matrix model from the telemetry data and using Bayesian mixed effects generalized linear regression models from the transect data. Both methods showed significant declines for white-backed vultures in Ruaha and Nyerere National Parks. Only telemetry estimates suggested significant declines in Katavi National Park. Encounter rates calculated from transects also showed declines in Nyerere National Park for lappet-faced vultures (38% annual declines) and Bateleurs (18%) and in Ruaha National Park for white-headed vultures (Trigonoceps occipitalis) (19%). Mortality rates recorded and inferred from telemetry suggested that poisoning is prevalent. However, only 6 mortalities of the 26 presumed mortalities were confirmed to be caused by poisoning, highlighting the challenges of determining the cause of death when working across large landscapes. Despite declines, our data provide evidence that southern Tanzania has higher current encounter rates of African vultures than elsewhere in East Africa. Preventing further declines will depend greatly on mitigating poisoning. Based on our results, we suggest that the use of multiple techniques improves understanding of population trends over the short term.

Modeling the Population Demographics &amp; Viability of Imperiled Guzmania monostachia Populations

Guzmania monostachia is a large, long-lived bromeliad whose leaves grow in a rosette pattern and is native to the Americas, but endangered in Florida due to damage caused by the invasive weevil Metamasius callizona. Each G. monostachia rosette can reproduce sexually via flowers or asexually by producing clonal offshoot rosettes. We model the population dynamics and demographic structure of a G. monostachia population using a Lefkovitch matrix model where each state represents a demographic class of rosettes. Model analysis over a range of uncertain parameters show the conditions under which a G. monostachia population is viable in the absence and presence of M. callizona, and the expected demographic structure under those conditions. In particular, our analysis illustrates that proportional reductions in survival have a qualitatively stronger impact on population viability than proportion reductions in clonal fecundity.

Sensitivity analysis of a lake sturgeon population with early life stage density-dependent effects

Lake sturgeon ( Acipenser fulvescens) exhibit a complex life-history strategy where behaviour, including habitat selection, depends on ontogenetic stage. Protection or recovery efforts for one stage may not impact other stages. Stage-structured models have been used to explore the sensitivity of the population to changes in vital rates of individual stages. Recent research demonstrates that juvenile mortality may be lower than estimated in prior modelling efforts and density-dependent. We constructed a Lefkovitch matrix model to reflect an updated understanding of the prerecruitment stages of the lake sturgeon. We then compared the model to a population of lake sturgeon on the Ontario−Minnesota border. Our model predicts that population growth rate, time to equilibrium, and final population size were most sensitive to changes to the survival of early adults, followed by subadults and juveniles. Sensitivity to changes in age-0 survival was very low in contrast to earlier modelling efforts, while sensitivities to juvenile (ages 1–7 years) and subadult (ages 8–23 years) were higher than previously reported values.

Population viability in a host-parasitoid system is mediated by interactions between population stage structure and life stage differential susceptibility to toxicants

The effects of toxicants, such as pesticides, may be more severe for some life stages of an organism than others. However, in most toxicity studies, data is developed for only one life stage, which may lead to misleading interpretations. Furthermore, population stage-structure may interact with differential susceptibility, especially when populations consist of higher proportions of individuals in more susceptible stages at the time of toxicant exposure. We explore the interaction of differential stage susceptibility and stage distribution using a stage-structured Lefkovitch matrix model. We incorporate lab-derived toxicity data for a common parasitoid, the braconid Diaeretiella rapae (M’Intosh), a common natural enemy of the cabbage aphid (Brevicoryne brassicae L.), exposed to the pesticide imidacloprid. We compare population outcomes of simulations in which we vary both the population stage structure along with the susceptibility of each stage to toxicants. Our results illustrate an interaction between differential susceptibility and initial stage distribution, highlighting the fact that both of these demographic features should be considered in interpreting toxicity data and the development of ecological risk assessments.

The Lefkovitch Matrix of Aedes Aegypti with Rainfall Dependent Model for Eggs Hatching

Dengue is known as borne disease that was spread by a species of mosquito which is Aedes aegypti. This disease is considered as a dangerous disease since it can threat human life. Shah Alam city has the high reported dengue cases in Malaysia. Based on this situation, this research was done in order to simulate the population of the mosquito in the city which involved in dengue transmission. A stage-structured of the mosquito life cycle was interpreted into Lefkovitch matrix model which consist of possible rate relating to the mosquito life cycle. The egg hatching rate was set as the main factor which influence the number of mosquito population and it depends on water availability due to rainfall. In this research, the temperature was set as constant because the temperature in Malaysia does not show any significant different compared to the rainfall distribution. The validation of the result was made by doing comparison between the simulations of eggs number with the amount of rainfall in order to see the relationship of the trends for both variables. As a result, the dynamic of dengue cases might be possible related to the trend of rainfall which provide breeding site for the female mosquito to lay eggs which contribute to the increase in the number of mosquito population. However, for the further studies, the researcher should consider other factor such as humidity since it might influence the mosquito life cycle and thus can give more accurate results.

The Simulation of Egg Number of Aedes Aegypti using Stage-Structured Matrix Model

The distribution of rainfall is one of the factors which contribute to the development of Aedes aegypti life cycle. The fluctuation of rainfall might influence the acceleration of Aedes aegypti growth and at same time influence the increase of dengue cases. Many types of mosquitoes strictly need water to lay their eggs therefore in this research, the egg number of Aedes aegypti mosquito was simulated by using stage-structured matrix model. The development of egg numbers were associated with rainfall distribution and mosquito life cycle which consist of egg, larva, pupa, and adult. A stage-structured Lefkovitch matrix model was used for the simulation. An egg hatching function depends on rainfall was one significant parameter rate of matrix model which affect the whole mosquito life cycle. The graphical results were shown to illustrate the relationship between the rainfall and egg number. We found that there was a significant relation between the rainfall, and egg number. However, it is recommended to look for more possible factors such as size of opening container, humidity and temperature which contribute to the development of mosquito in order to acquire more accurate results.

The Simulation of Egg Hatching Trend of Aedes Aegypti Associated with Rainfall Distribution

Aedes aegypti is primary vector of Zika virus, dengue, and chikungunya which go through four different stages of life cycle: Egg, Larva, Pupa, and Adult. The mosquito might be able to lay 100 eggs at a time. The eggs can hatch when there is water and submerged in the water, but it can survive without water almost to 8 months by sticking to the walls of a container. In this research, the trend of egg hatching was simulated by using a stage-structured Lefkovitch matrix model. The matrix model consists of a function of egg hatching which associated and depends on rainfall distribution. The purpose of the function is to identify the relationship between egg hatching and rainfall which provide water to egg. Using the same mathematical model, the population of adult Aedes aegypti has also simulated which the population related to egg simulation and rainfall. The graphical results were shown to illustrate the relationship between the rainfall, egg number and adult Aedes aegypti. We found that there was a significant relationship between the rainfall and these two stages of mosquito life cycle which are egg hatching number and adult Aedes aegypti. However, it is recommended to look for more possible factors such as the size of an opening container and humidity which possible to contribute to the development of mosquito to acquire more accurate results.

Population drivers of aThalia democraticaswarm: insights from population modelling

The small salp, Thalia democratica, is known globally to form dense swarms, yet the physiological and oceanographic factors that influence the magnitude and occurrence of these swarms are poorly understood. In this study, two numerical models were used to explore T. democratica population dynamics. A Lefkovitch matrix model identified that the survival of juvenile oozoids was the most important population metric promoting population growth and a size-structured population model was developed to further explore the dynamics of T. democratica. The size-structured model tracks cohorts of four life stages and incorporates size-dependent reproduction and mortality. Model outputs of average generation time and mean abundances of each life stage corresponded well to previously reported values. Factors that promote juvenile oozoid abundance were the most sensitive parameters influencing salp abundance. A 10-year time-series simulation using this population model identified that salp abundances in the Tasman Sea are proportionally higher in winter and spring, consistent with previous studies. This model shows that temperature and phytoplankton concentration are sufficient drivers of large-scale patterns of salp abundance across season and latitude. These results demonstrate the importance of future research focusing on identifying the environmental conditions that influence the size at which females reproduce.

A stage-based population model for American alligators in northern latitudes

Very little is known about the population dynamics of American alligators in northern latitudes. To better define the characteristics of the northern population, we combined published life-history and vital rate data for studies conducted in North Carolina and South Carolina; for comparison, we gleaned the same information from the literature for the southern (Florida and Louisiana) population. We constructed a 5-stage Lefkovitch matrix model for each population. The models showed that the southern population was stable and slightly increasing (λ = 1.02), whereas the northern population was in decline (λ = 0.870). We integrated potential impacts of climate change into the northern population model to determine how the population might respond to increased temperature and decreased precipitation. An increase in temperature would benefit the northern population; however, a decrease in precipitation or the combined effects of temperature increase and precipitation decrease would negatively affect the viability of the northern population. Two priorities result from modeling these scenarios: 1) a long-term monitoring program is needed to acquire the life-history and vital rate data on the northern population, and 2) current alligator habitat must be conserved or improved to insulate the species from potential drought associated with climate change. © 2014 The Wildlife Society.

Effects of life-history components on population dynamics of the rare endangered plant &amp;lt;i&amp;gt;Davidia involucrata&amp;lt;/i&amp;gt;

In order to estimate the most effect stage and process on population growth and effective conserve the rare endangered plant Davidia involucrata, we analyzed the dynamics and the contributions of life-history components on population dynamics based on Lefkovitch matrix model and sensitivity analysis. The life cycle of Davidia involucrata was divided into six stages (seed, seedling, juvenile, immature, early adult and late adult) based on the species characteristics and published literature data, the survival rates in each life-history stage were simulated using a static life table, and the fecundity of each stage was determined according to sample information. The results showed that the structure of the observed population was not ideal, and the numbers of seedlings and coppice shoots was similar. The population growth rate was influenced largely by individual growth process, and asexual reproduction made a larger contribution to population growth than sexual reproduction. However, sexual reproduction was more important than asexual reproduction, because most asexual reproducing individuals (the coppice shoots) were derived mainly from human destruction (e.g. felling trees). The most important stage was stage V (late adult), associated with seed production and germination. Therefore, conservation of Davidia involucrata populations should focus on stage V and sexual reproduction, in order to improve the seed production and germination rate, and to promote population stability and development.

Comparison of six sewage effluents treated with different treatment technologies—Population level responses in the harpacticoid copepod Nitocra spinipes

Since conventional treatment technologies may fail in removing many micro-pollutants, there is currently a focus on the potential of additional treatment technologies for improved sewage treatment. The aim of the present study was to evaluate six different effluents from Henriksdal Sewage Treatment Plant in Stockholm, Sweden. The effluents were; conventionally treated effluent (chemical phosphorous removal in combination with an activated sludge process, including biological nitrogen removal and a sand filter), with additional treatments individually added to the conventional treatment; active carbon filtration, ozonation at 5 mg l −1, ozonation at 15 mg l −1, ozonation at 5 mg l −1 + moving bed biofilm reactor and irradiation with ultraviolet radiation + hydrogen peroxide. The evaluation was done by characterizing and comparing the effluents using a Lefkovitch matrix model based on a life cycle test with the harpacticoid copepod Nitocra spinipes, combined with analysis of juvenile development and survival over time. The conventionally treated effluent resulted in the most negative effects, leading to the conclusion that all additional treatments in the present study created effluents with less negative impacts on the copepod populations. The ozone treatments with the low dose treatment in particular, resulted in the overall least negative effects. Moving bed biofilm reactor combined with ozone did not improve the quality of the effluent in the sense that slightly more negative effects on the population abundance were seen for this treatment technology compared to ozonation alone. The active carbon treatment had more negative effects than the ozone treatments, most of which could possibly be explained by removal of essential metal ions. The effluent which was treated with ultraviolet radiation + hydrogen peroxide resulted in few developmental and survival effects over time, but still showed negative effects on the population level. Matrix population modeling proved a useful tool for biologically characterizing and comparing the effluents. Basing the assessment either on the individual level data (development and survival over time or total reproductive output) or the population level data (lambda values and projected population abundances) would not have resulted in the same conclusions as combining both analyses. The juvenile development and survival over time allowed for closer monitoring of the important molting process, whereas the population modeling provided an integrated measure of potential effects at the population level. If the dilution of the effluent in the recipient is considered, the biological effects recorded in the present study were not of substantial significance for the copepod populations, regardless of treatment technology.

Demography and life history of Geonoma orbignyana: An understory palm used as foliage in Colombia

Abstract Geonoma orbignyana is a common understory palm, whose leaves are used as foliage in Colombia. This palm has been used for more than 30 years; but there is no information about its life history or conservation status. Our objective was to characterize the life history of this palm and population dynamics of a natural population as a first step to assess the effect of leaf harvesting. More than 1600 palms were monitored from June 1999 to March 2000; we measured growth, mortality, and reproductive success. Population dynamics were evaluated using a Lefkovitch matrix model, and elasticity analysis. Results indicate that G. orbignyana grows at a rate of 1.98 ± 0.047 leaves/year, the palm has a long lifespan, and growth and reproduction are related to light conditions in the forest. The density of this palm is high (108–311 palms/100 m2), which is explained in part by its capacity to continue growing after damage, and to respond to the frequent gap formation in the forest. The population is growing (λ = 1.074, CI = [1.046–1.099]). Survival transitions account for 77% of population growth, a value that is higher compared to other understory plants. Because of the high density, the recovery capacity of these palms, and the correlations found between individual and population performances with forest dynamics, we hypothesize that G. orbignyana behaves as an opportunistic species taking advantage of forest gaps. This palm is a promising non-timber forest product (NTFP) with a high profile for further exploitation, although we recommend that harvesting regimens should consider time of recovery and forest dynamics. Without these considerations mortality could increase in all classes, which will compromise population persistence. Further studies should accurately estimate the recovery time after defoliation as well as to characterize forest dynamics identifying its most important features for population growth.

Time to Reduction: Factors Influencing Management Efficacy in Sterilizing Overabundant White-Tailed Deer

In managing overabundant white-tailed deer (Odocoileus virginianus), fertility control frequently is regarded as a viable alternative to lethal strategies. However, little information is available concerning expected duration of fertility control. Our objectives were to create a flexible model for application in a diverse array of environmental conditions, determine the extent to which various parameters contributed to population growth, and assess the time necessary to reduce a population to a given level. The modeled population was assumed geographically closed without density dependence. Using prospective perturbation analysis on a linear time-invariant Lefkovitch matrix model, survival rates contributed to overall population growth nearly twice that of birth rates. Using numerical analysis, a general relationship between annual sterilization rate, desired population reduction, and time to that reduction was determined. This relationship was nonlinear and showed decreased efficiency per unit effort. Depending on local parameter values, we determined that a population could be reduced by 30% to 60% in 4-10 years if a manager could sterilize 25-50% of available fertile females annually. Thus, sterilization may be a viable option for communities with the financial resources and political will to sterilize.

THE ROLE OF SEED DISPERSERS IN THE POPULATION DYNAMICS OF THE COLUMNAR CACTUS NEOBUXBAUMIA TETETZO

We examined the effect of frugivorous bats and birds on the population dynamics of the giant columnar cactus Neobuxbaumia tetetzo in the Tehuacán Valley, Mexico. Because successful seedling establishment occurs only beneath the canopies of shrubs and trees, we hypothesized that seed dispersal is a key process in the maintenance of its populations. We determined the dispersal effectiveness of different frugivores, considering the quantity and quality components of seed dispersal. We also evaluated the potential effects of each frugivore species on the finite rate of increase of N. tetetzo populations by modifying the fecundity values of a Lefkovitch matrix model. The bat Leptonycteris curasoae had the highest effectiveness whereas the bird Carpodacus mexicanus had the lowest. The estimated finite rates of increase calculated to evaluate the effects of frugivores on the population dynamics of the cactus differ marginally from unity, except when the effect of the bat L. curasoae was analyzed. Our results suggest that the bat Leptonycteris curasoae could be considered the legitimate dispersal agent of N. tetetzo, dispersing seeds directly to safe sites, and thus representing a key species in the ecology of this columnar cactus.

Application of a stage-specific matrix model and length-cohort based analysis to assess the anchovy fishery in Catalan coastal waters (NW Mediterranean Sea)

This study describes trends in anchovy ( Engraulis encrasicolus) population biomass in Catalan coastal waters of the northwestern Mediterranean Sea and relates empirical data to the demographic models in order to understand its dynamics and shed some light for future management of the stock. Classical fisheries models (length-cohort analysis and yield-per-recruit analysis) are applied together with the stage-specific Lefkovitch matrix model to detect population growth. Estimates of rates of growth, mortality, and fecundity were assembled for each biological stage. The results confirm and quantify the importance of early life stages on population trends and indicate how sensitive the overall biomass is to rate variations. Both approaches are consistent in indicating stable biomass conditions at the current exploitation level, even though environmental variability is not considered, and might cause changes. In view of the fishermen's effort reduction, a 10% fishing mortality decrease on the fishery was also examined in a dynamic model to forecast the yields, simulating different stock-recruitment patterns.

Evolution of semelparous and iteroparous perennial plants:: Comparison between the density-independent and density-dependent dynamics

The evolution of the frequency of reproduction in perennial plants is analyzed using the Lefkovitch matrix model. The model describes a population dynamics with a stage-specific pattern of reproduction and mortality of plants. Both the density-independent and density-dependent models are analyzed, and the results of the two models are compared. In the density-independent model, the invasible condition depends on the survival rate at juvenile stage, the emergence rate of seeds and the trade-off curve between the number of seeds and the survival rate of mature plants. The result is qualitatively similar to the studies by Schaffer & Gadgil (1975, in: Ecology and Evolution of Communities.Cambridge, MA: Belknap Press.) and Pianka (1976, Am. Zool. 16,775–784). However, in the density-dependent model, the invasible condition does not depend on those parameters, but on only the trade-off curve. Therefore, the trade-off between the number of seeds and the adult survival rate, and the density-dependence of the dynamics, play an important role in the evolution of the frequency of reproduction. However, there is no significant difference between the results derived from the stage- and the age-structured population models.

The relationship between the transition matrix model and the diffusion model

The diffusion equation model and the Lefkovitch matrix model have been employed independently in plant population ecology in order to analyze the dynamics of growth and size structure. The two models describe the dynamics of size structure in biological populations, and thus there must be some relationship between them. In the present paper, we examine the theoretical relationship between these two models. We demonstrate, on a certain assumption, that the one-step Lefkovitch matrix model corresponds to a difference equation of the diffusion equation and that the two- and three-step Lefkovitch matrix model correspond to difference equations of the 4th- and 6th-order Kramers-Moyal expansions, respectively. It is also shown that 2n moments (the first to the 2n-th moments) of growth rate are necessary and sufficient to rewrite uniquely the n-step Lefkovitch matrix model in terms of the linear combination of the moments. We finally discuss the relationship between the species characteristics of census data and the appropriate types of the Lefkovitch matrix.

An analysis of life history evolution in terms of the density-dependent Lefkovitch matrix model

The evolution of demographic characteristics is considered in terms of the density-dependent Lefkovitch matrix model, which describes a species' population dynamics with a stage-specific pattern of reproduction and mortality. We obtain the invadability condition of a mutant-type into the wild-type population at the equilibrium state. The condition depends on the left and right eigenvectors at the equilibrium state and the difference, between wild-type and mutant-type populations, of the values of elements in the Lefkovitch matrix at the equilibrium state. It is also shown that if elements of the density-dependent Lefkovitch matrix are decreasing functions of population density, then the equilibrium population density increases in the process of natural selection; that is, K-selection acts even on the stage-structured population. The evolution of life history in perennial plants is discussed through two models as an application of the above results. The evolution of perennial plants with no vegetative reproduction is analyzed in the first example. It is shown that whether monocarpic perennials (which reproduce once and die) or polycarpic perennial plants (which reproduce more than once) are favored depends on the cost of a produced seed. The second example concerns perennial plants that reproduce vegetatively. It is shown that whether monocarpic or polycarpic perennial plants are favored depends on the cost of a seed and that where vegetative reproduction is common, polycarpic perennials with no seed reproduction are favored.