Leslie Matrix Research Articles

Ecotoxicological risk assessment of metal cocktails based on maximum cumulative ratio during multi-generational exposures

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.

Another approach for Leslie model via linear difference equations

We explore here an approach to study the Leslie model, describing the growth of the discrete age structured populations. Our main tool is based upon properties of some linear difference equations. Involving the analytical and combinatorial aspects of solutions of these equations, we establish new formulas for the entries of the population vector and derive their asymptotic behavior. Significant illustrative examples and applications are given.

Age, growth and demography of the silky shark Carcharhinus falciformis from the southwestern Atlantic

The silky shark Carcharhinus falciformis is considered one of the least productive pelagic shark species. The estimation of growth and demographic parameters presented here is fundamental to a sound knowledge of population status of the species in the Atlantic Ocean. Data was collected through an onboard observer program of the Brazilian chartered pelagic longline fishing fleet that operates in the Equatorial Southwestern Atlantic. Vertebral analysis produced the von Bertalanffy growth parameters for pooled sexes L∞ = 283.05 cm; k = 0.0987 yr-1 and t0 = -3.47 yr. Males reached sexual maturity at 8.6 yr and females at 9.9 yr. Longevity was estimated at 27.2 yr. Age structure analysis indicated that 80.5% of the catch was composed of juveniles, with recruitment to the fishery from the first year of life (age 1+). These biological parameters are responsible for the species’ low resistance to fishing pressure, and our demographic analysis (Leslie Matrix) shows an annual population decline of 12.7% yr-1 under the current fishing scenario for the period analyzed. Therefore, conservation measures must be enacted to reestablish the population of silky sharks to safe levels for the maintenance of this species in the South Atlantic.

The Uniaxial Limit of the Non-Inertial Qian–Sheng Model for Liquid Crystals

In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model.

Viability of the vaquita, Phocoena sinus (Cetacea: Phocoenidae) population, threatened by poaching of Totoaba macdonaldi (Perciformes: Sciaenidae)

Introduction: Despite extensive science-based conservation policy recommendations, with fewer than 20 individuals remaining, the vaquita (Phocoena sinus) -endemic to the Gulf of California- is the world’s most endangered marine mammal due to incidental catch in fishing nets and whether it can recover is unclear. Objective: Assess expectations for vaquita over the next two decades. Methods: We identified factors affecting the vaquita, constructed life tables, derived demographic parameters for different scenarios and conducted a population viability analysis using stochastic age-structured matrix Leslie models. Results: Analytical results indicate that the vaquita net growth rate is particularly sensitive to juvenile survival. We find that intensive, ongoing bycatch in gillnets used to poach totoaba (Totoaba macdonaldi) over the past decade brought the vaquita population to its current critically low size. Currently this seems to be exacerbated by demographic stochasticity and a potential Allee effect. Conclusions: If totoaba poaching is eliminated immediately, demographically, vaquita can recover; its long-term survival will depend on its uncertain genetic status, although a recent study found encouraging results in this regard.

Application of the Leslie Matrix to Predict the Number and Growth Rate of Women in West Java 2021

Data from the Central Statistics Agency 2019 collected that the total population of women in Indonesia is less than male, which is 131.48 million people if compared to the total male population, which is 132.68 million population. This matter is directly relation to the total female population in West Java which is also less than the male population around 24031252.0 female and 24652609.0 male population(Badan Pusat Statistika, 2019).This should be the focus of the government to balance the population growth of women and men in West Java because of the role of women being central in the population growth of the people of West Java. The targets of the development plan contained in the RPJM 2005-2025 is to improve the quality of human resources, including the role of women in development. The growth of the female population is an important thing that must be observed, considering the role of women is determining the development of the human population in the future, because without the role of women the population will not be able to develop. This encourages researchers to predict the number and rate of female population growth in West Java in 2021. The Leslie matrix is a matrix used to predict the number and growth rate of a population. By applying the Leslie matrix to predict the number and growth rate of women in West Java in 2021, it can be concluded that the number of female populations in West Java is around tends to increase.

A framework for variance analysis of customer equity based on a Markov chain model

This study proposes a framework for variance analysis of customer equity (CE) based on a Markov chain model called the Leslie matrix, developed in mathematical biology. Because customer lifetime value represents the net present value of customer derived cashflow, CE can be characterized as a forward-looking measure. Numerous studies have addressed the use of CE for planning. However, few studies have utilized CE for control. When CE is used as a basis for control, variance analysis is indispensable. In the proposed framework, CE variance is divided into three parts: customer payoff variance, customer lifecycle variance, and customer state variance. Thereafter, customer lifecycle variance is further broken down into customer acquisition, retention, and expansion. The aforementioned framework was applied to membership customers of a Japanese resort hotel chain. The results revealed that customer retention was a major cause of CE variance, whereas customer acquisition and expansion had a smaller impact.

Prediction of the Number of Women Population in Medan City 2025 by Using the Leslie Matrix

Population problems can cause problems, both in terms of political, economic, socio-cultural life, defense and security, as well as other aspects of life concerning the use of natural resources and the environment. By knowing the population growth rate, the Medan city government can implement a policy to anticipate social problems that may arise. This study aims to determine the number and rate of female population growth in the city of Medan in 2025. The Leslie matrix model is a model that can be used to predict the number and rate of female population growth. The step taken to predict the number of population p in the following year is to form a column vector whose entry is the initial number of population for each age class. Next look for n (t + p) which is the total population for the following year using the formula n(t+p)=Apn(t) where A is the Leslie matrix. Furthermore, to predict the population growth rate using the Leslie matrix is to find the positive eigenvalues λ of the matrix A. Based on positive eigenvalues λ, three cases occur, namely: 1) the population will tend to increase if λ>1; 2) the population will tend to decline if λ<1 ; 3) the population will tend to be stable if λ=1. Based on data analysis, the total female population in the city of Medan in 2025 is 1,576,294. Furthermore, the eigenvalues of λ=1,3673 which mean that the number of female populations in the city of Medan tends to increase.

Prediction of the number of Women Population in Medan City 2025 by using The Leslie Matrix

The Leslie matrix model is a model used to predict the number and rate of female population growth. This study aims to determine the number and rate of female population growth in the city of Medan in 2025 based on data on birth rates and life expectancy. The eigenvector is used to determine the number of female populations at each age interval, while the eigenvalues are used to determine the population growth rate. To determine the number of female populations from each age interval, a positive eigenvalue is sought. Based on positive eigenvalues, three cases occur, namely: 1) the population will tend to increase if; 2) the population will tend to decline if; 3) the population will tend to be stable if. Based on the research results, the eigenvalues were obtained λ = 1,3673 which means the number of the female population in the city ofMedan tends to increase

Stationary Shear Flows of Nematic Liquid Crystals: A Comprehensive Study via Ericksen–Leslie Model

We apply the Ericksen–Leslie dynamic model to investigate stationary solutions of planar shear flows for nematic liquid crystals. Nematic material is extremely rich and involves several parameters to characterize the basic local properties. The Ericksen–Leslie model of the nematic material includes Frank’s parameters for Oseen–Frank energy and Leslie’s dynamic parameters. Even in this simple setting of shear flows, the dynamics supported by the material exhibit quick rich behavior. With the aid of a Hamiltonian formulation and phase plane portraits, we are able to provide a rather complete picture about the possible solutions. In particular, we establish the existence of multiple solutions for the boundary value problem in many situations. We also try to explain the physical reasons for some of the results.

Age-specific survival and reproductive rates of Mediterranean monk seals at the Cabo Blanco Peninsula, West Africa

We provide the first complete set of survival rate estimates for the Endangered Mediterranean monk sealMonachus monachusfrom birth into adulthood, as well as the first age-specific reproductive rates for the species. From 2002 to 2016, we obtained individual seal live encounter data through non-invasive monitoring techniques that were analyzed to estimate vital rates of Mediterranean monk seals of the Cabo Blanco (Western Sahara/Mauritania) population. From birth to age 2 mo, when pups molt, survival averaged 0.59, ranging from 0.41 to 0.74 among cohorts. From birth to 1 yr and from 1 to 2 yr, median estimated survival rates were 0.46 and 0.75, respectively. Beyond 2 yr, survival estimates differed by sex: 0.94 for males and 0.97 for females. From 2005 to 2016, we estimated a mean gross reproductive rate of 0.71. The youngest parturient females were 3 yr old. Fitted age-specific reproductive rates increased beginning at age 3 yr and exceeded 0.80 from age 6 to 17 yr. Despite low survival during the first 2 mo of life, the aggregate vital rates of the population are favorable for growth; a Leslie matrix containing our survival and fecundity estimates yielded an intrinsic growth rate of 1.058. Increasing abundance and favorable vital rates are a testament to the efficacy of the many measures taken to promote the conservation of this population.

Demographic and harvest analysis for blue shark (Prionace glauca) in the Indian Ocean

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.

Vital rates of small reef corals are associated with variation in climate

AbstractWith coral cover declining on most tropical reefs, efforts are intensifying to understand the mechanisms by which environmental stressors are driving populations into demographic deficit. Here, the population dynamics of sexual cohorts of small corals (≤ 4 cm diameter) in St. John, US Virgin Islands were used to test the hypothesis that the association of vital rates with environmental conditions has changed over 22 yr. The annual fate of 3999 corals at six sites and 7–9 m depth were used to populate Leslie Matrices and calculate assemblage growth rates (λ, without recruitment), mortality of the smallest corals, and graduation from the largest size class. Vital rates were tested for associations with temperature, the number of days with seawater warmer than 29.4°C (i.e., hot days), and rainfall. Transition probabilities varied among years, and usually more corals remained in their original size class than moved among size classes. Corals in the smallest size class had the highest mortality rate (42% yr−1), λ had a grand mean of 0.688, and there were trends for λ to vary with the number of hot days and rainfall through quadratic relationships. The linear dependence of λ on rainfall over consecutive 3‐yr periods declined over two decades, suggesting that this colony size‐defined coral assemblage has undergone phenotypic change in their responsiveness to varying environmental conditions.

A Note on Migration Perturbation and Convergence Rates to a Steady State

Using tools developed in the Markov chains literature, we study convergence times in the Leslie population model in the short and middle run. Assuming that the population is in a steady-state and reproduces itself period after period, we address the following question: how long will it take to get back to the steady-state if the population distribution vector was affected by some shock as, for instance, the “brain drain”? We provide lower and upper bounds for the time required to reach a given distance from the steady-state.

Concentration-cancellation in the Ericksen\u2013Leslie model

We establish the subconvergence of weak solutions to the Ginzburg–Landau approximation to global-in-time weak solutions of the Ericksen–Leslie model for nematic liquid crystals on the torus {mathbb {T}^2}. The key argument is a variation of concentration-cancellation methods originally introduced by DiPerna and Majda to investigate the weak stability of solutions to the (steady-state) Euler equations.

Robust ℓ₁-Controller Design for Discrete-Time Positive T–S Fuzzy Systems Using Dual Approach

In this article, a new approach is proposed for stability analysis and controller design of nonlinear discrete-time positive systems by means of the Takagi&#x2013;Sugeno fuzzy model. The closed-loop stability and the positivity constraint are guaranteed by synthesizing a linear co-positive Lyapunov function and by applying the parallel distributed compensation controller. In contrast to the state-of-the-art approaches for ensuring the <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-stability of the positive system which are based on bilinear matrix inequalities, the proposed optimal robust control design under <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-induced performance is derived based on linear programming framework. It has been shown that the computational complexity of the proposed optimization problem can be effectively reduced. Finally, a numerical example and the Leslie population model are adopted to show the capabilities of the proposed method.

Bifurcation and Chaos of a Discrete-Time Population Model

A Leslie population model for two generations is investigated by qualitative analysis and numerical simulation. For the different parameters a and b in the model, the dynamics of the system are studied, respectively. It shows many complex dynamic behavior, including several types of bifurcations leading to chaos, such as period-doubling bifurcations and Neimark–Sacker bifurcations. With the change of parameters, attractor crises and chaotic bands with periodic windows appear. The largest Lyapunov exponents are numerically computed and can verify the rationality of the theoretical analysis.

Can multi‐species shark longline fisheries be managed sustainably using size limits? Theoretically, yes. Realistically, no

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

Stock assessment and potency of sustainable yield of glass eel (Anguilla spp.) in Cimandiri River Estuary, West Java

The demand for glass eel (Anguilla spp.) as a source of seeds for aquaculture activities depended on natural catches continue to increase. It has caused glass eel fishing activities to increase and potentially affect the biological condition and sustainability of fishing activities. The study aims to assess the potential stock, maximum sustainable yield (MSY) and the level of utilization of glass eel in the Cimandiri river estuary, West Java. The data were obtained from data on fisherman catches in the period 2014-2018. Potential stock calculation using the CPUE method is based on the Leslie model. Calculation of MSY based on the surplus production model from Schaefer. Utilization rates are determined based on the percentage of actual catch to the total allowable catch (TAC). The results of the study obtained an estimated glass eel potential stock of 4,575 kg. The maximum sustainable yield (MSY) was 991.20 kg.years−1 and the effort (fMSY) was 1050 trip.years−1. The average of glass eel production was 725.55 kg.years−1 and fishing effort 1031 trip.years−1. The TAC which set at 80% from the MSY was 792.96 kg.years−1. The average of the utilization rate of glass eel reached 91.50%. Utilization rates exceeding the TAC value occurred in 2014 and 2017. Management of glass eel fisheries is needed through limiting fishing efforts and the number of catches.

A New Method of Data Encryption based on One to One Functions

Due to the rapid growth of computer networks, critical highly confidential information shared across these networks. Accordingly, securing such information from unauthorized intruders has become a vital issue in the field of information technology. In this paper, we present a new algorithm for encrypting and decrypting English plain text based on the well-known Caesar's algorithm and a special type of functions called One to One function. The proposed algorithm is referred to as the One to One function algorithm (OtO). The OtO belongs to a symmetric key concept where the same key is used in both encryption and decryption processes. In the OtO algorithm, the triplet (K, a, b) represent the private keys. To speed up the proposed OtO computation, the value of K is calculated based on Fibonacci sequence, on eigenvalues, Leslie matrices and Markov chain. This private key K only knew to the transmitter and receiver and considered one of the private keys used in the encryption process. When the message arrives at the receiver, it uses the inverse function of the proposed one to one function that used at the transmitter. The proposed OtO algorithm is conducted using MATLAB and its efficiency is checked in terms of encrypted time, decrypted time, and Avalanche Effect. We think that the obtained results are acceptable compared to famous algorithms DES, 3DES, AES and RSA.