The Range‐Resident Logistic Model: A New Framework to Formalise the Population‐Dynamics Consequences of Range Residency

Models of population dynamics are substantially non-Markovian in nature and exhibit behavior for memory effects. This research study investigates the logistic growth model from population dynamics under both classical and non-classical (fractional) differential operators using actual statistical data. For the non-classical differential operator, the operator called conformable fractional derivative having order β in the sense of Liouville-Caputo (LC) of order α is employed while taking care of its dimensional consistency. Working parameters including conformable fractional derivative order β, LC having order α, growth rate ζ, and carrying capacity Φ have been optimized, and the results are compared with those of classical one. Error rate suggests the superiority of the fractional conformable logistic model whose solutions are investigated for uniqueness via fixed point theory. Numerical simulations using Adams' iterative technique recently proposed for the conformable fractional derivative are illustrated in figures for a thorough understanding of the model's behavior, along with a statistical summary for the operators. An attractive chaotic attractor is observed in the fractional logistic model when ζ ≥ 4.023. Cumulative effects of growth rate and carrying capacity on the population's change in the logistic model are also investigated with 3D graphics.

Propensity score can be described as a probability of certain treatments conditional to the given observed covariates. Propensity score is one of the known methods to allows an observational study emulating certain characteristics from that of a randomized trial. The most common method used to estimate this score is the logistic regression model. Logistic regression can be used to model the probability of a certain event. With the advancement that is happening to spatial statistics, one can also build a logistic regression model that takes into consideration to that of spatial dependence. Thus, accommodate the spatial effect that is likely happening on observation data that came from different places. Problem arises from this model, that is the estimation of the parameters on the spatial logistic model. EM algorithm which is needed for this problem, still requires another adjustment since the expectation in the E-step is not available in closed form. Variational method modification is then proposed as an alternative for this problem. This paper reviews the propensity score estimation using spatial logistic regression and discusses the variational method as an alternative method to tackle the problem in estimating the parameters on the spatial logistic regression model in a theoretical study.

The logistic model has long been used in ecological modelling for its simplicity and effectiveness. Variations on the logistic model are prolific but, to date, there are a limited number of models that incorporate the stochastic nature of the carrying capacity. This study proposes a modification to the logistic model to incorporate a second differential equation which describes the changes in the carrying capacity, thus treating the carrying capacity as a state variable. The carrying capacity is modelled via a stochastic differential equation that accounts for stochastic ('noisy') variations in the finite resources that the population relies on. The extinction probability distribution, expected solution paths, variance of the solution paths, and distribution of the population are computed using the Monte Carlo method. References R. B. Banks. Growth and Diffusion Phenomena . Springer, 1994. doi:10.1007/978-3-662-03052-3 F. Brauer and C. Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology . Springer, 2001. doi:10.1007/978-1-4614-1686-9 A. Tsoularis and J. Wallace. Analysis of logistic growth models. Math. Biosci. , 179:21–55, 2002. doi:10.1016/S0025-5564(02)00096-2 S. Oppel, G. Hilton, N. Ratcliffe, C. Fenton, J. Daley, G. Gray, J. Vickery and D. Gibbons. Assessing population viability while accounting for demographic and environmental uncertainty. Ecology , 95:1809–1818, 2014. doi:10.1890/13-0733.1 J. E. Cohen. Population growth and earth's human carrying capacity. Science , 269:341–346 1995. doi:10.1126/science.7618100 J. M. Cushing. Periodic time-dependent predator-prey systems. SIAM J. Appl. Math. , 32:82–95 1977. doi:10.1137/0132006 B. D. Coleman. Nonautonomous logistic equation as models of the adjustment of populations to environmental change. Math. Biosci. , 45:159–173, 1979. doi:10.1016/0025-5564(79)90057-9 J. Vandermeer. Seasonal ioschronic forcing of Lotka Volterra equations. Prog. Theor. Phys. , 96:13–28, 1996. doi:10.1143/PTP.96.13 H. M. Safuan, Z. Jovanoski, I. N. Towers and H. S. Sidhu. Exact solution of a non-autonomous logistic population model. Ecol. Model. , 251:99–102, 2013. doi:10.1016/j.ecolmodel.2012.12.016 P. Del Monte-Luna, B. W. Brook, M. J. Zetina-Rejon and V. H. Cruz-Escalona. The carrying capacity of ecosystems. Global Ecol. Biogeogr. , 13:485–495, 2004. doi:10.1111/j.1466-822X.2004.00131.x H. Safuan, I. N. Towers, Z. Jovanoski and H. S. Sidhu. A simple model for the total microbial biomass under occlusion of healthy human skin. 19th International Congress on Modelling and Simulation , Perth, Australia, December 2011, 733–739. http://mssanz.org.au/modsim2011/AA/safuan.pdf H. M. Safuan, I. N. Towers, Z. Jovanoski and H. S. Sidhu. Coupled logistic carrying capacity model. EMAC2011, ANZIAM J. , 53:C172–C184 2012. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/4972 H. M. Safuan, H. S. Sidhu, Z. Jovanoski and I. N. Towers. Impacts of biotic resource enrichment on predator-prey population. B. Math. Biol. , 75:1798–1812, 2013. doi:10.1007/s11538-013-9869-7 H. M. Safuan, H. S. Sidhu, Z. Jovanoski and I. N. Towers. A two-species predator-prey model in an environment enriched by a biotic resource. CTAC2012, ANZIAM J. , 54:C768–C787, 2014 . http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6376 S. M. Henson and J. M. Cushing. The effect of periodic habitat fluctuations on a nonlinear insect population model. J. Math. Biol. , 36:201–226, 1997. doi:10.1007/s002850050098 V. Mendez, I. Llopis, D. Campos and W. Horsthemke. Extinction conditions for isolated populations affected by environmental stochasticity. Theor. Popul. Biol. , 77:250–256, 2010. doi:10.1016/j.tpb.2010.02.006 P. Foley. Predicting extinction times from environmental stochasticity and carrying capacity. Conserv. Biol. , 8:124–137, 1994. http://www.jstor.org/stable/2386727 D. J. Higham. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. , 43:525–546, 2001. doi:10.1137/S0036144500378302 C. W. Gardiner. Handbook of Stochastic Methods , 2nd ed. Springer, 1985. http://trove.nla.gov.au/version/46588286

The existence of spatial effects should not be ignored because it will reduce the goodness of the model. One type of regression analysis that is quite widely used is logistic regression analysis. Spatial logistic regression modelling incorporates spatial effects into the logistic regression model with the expectation that the residuals generated from the model are independent or there is no autocorrelation. The purpose of this study was to obtain the results of spatial autocorrelation testing using a spatial logistic regression model with a Euclidean matrix approach. The results of the study were applied to natural disaster mitigation data in Kupang Regency, Nusa Tenggara Timur Province in 2020, where the distribution of areas in Kupang Regency by village/urban village has spatial autocorrelation. Spatial autocorrelation testing was carried out with Moran's I test to determine the presence of spatial autocorrelation. In this study, a standardized Euclidean distance matrix approach was used to accommodate this spatial effect. The results of the autocorrelation test of the binary spatial logistic model with the Euclidean distance matrix approach were able to accommodate the spatial effect.

When the spatial response variables are discrete, the spatial logistic autoregressive model adds an additional network structure to the ordinary logistic regression model to improve the classification accuracy. With the emergence of high-dimensional data in various fields, sparse spatial logistic regression models have attracted a great deal of interest from researchers. For the high-dimensional spatial logistic autoregressive model, in this paper, we propose a variable selection method with for the spatial logistic model. To identify important variables and make predictions, one efficient algorithm is employed to solve the penalized likelihood function. Simulations and a real example show that our methods perform well in a limited sample.

BackgroundThe Brownian bridge movement model (BBMM) provides a biologically sound approximation of the movement path of an animal based on discrete location data, and is a powerful method to quantify utilization distributions. Computing the utilization distribution based on the BBMM while calculating movement parameters directly from the location data, may result in inconsistent and misleading results. We show how the BBMM can be extended to also calculate derived movement parameters. Furthermore we demonstrate how to integrate environmental context into a BBMM-based analysis.ResultsWe develop a computational framework to analyze animal movement based on the BBMM. In particular, we demonstrate how a derived movement parameter (relative speed) and its spatial distribution can be calculated in the BBMM. We show how to integrate our framework with the conceptual framework of the movement ecology paradigm in two related but acutely different ways, focusing on the influence that the environment has on animal movement. First, we demonstrate an a posteriori approach, in which the spatial distribution of average relative movement speed as obtained from a “contextually naïve” model is related to the local vegetation structure within the monthly ranging area of a group of wild vervet monkeys. Without a model like the BBMM it would not be possible to estimate such a spatial distribution of a parameter in a sound way. Second, we introduce an a priori approach in which atmospheric information is used to calculate a crucial parameter of the BBMM to investigate flight properties of migrating bee-eaters. This analysis shows significant differences in the characteristics of flight modes, which would have not been detected without using the BBMM.ConclusionsOur algorithm is the first of its kind to allow BBMM-based computation of movement parameters beyond the utilization distribution, and we present two case studies that demonstrate two fundamentally different ways in which our algorithm can be applied to estimate the spatial distribution of average relative movement speed, while interpreting it in a biologically meaningful manner, across a wide range of environmental scenarios and ecological contexts. Therefore movement parameters derived from the BBMM can provide a powerful method for movement ecology research.Electronic supplementary materialThe online version of this article (doi:10.1186/s40462-015-0043-8) contains supplementary material, which is available to authorized users.

Event Abstract Back to Event Fisheries management through optimal sustainable policies with constant effort in random environments Nuno M. Brites1* and Carlos A. Braumann1, 2 1 Centro de Investigação em Matemática e Aplicalções, Instituto de Investigação e Formação Avançada, Universidade de Évora, Portugal 2 Departamento de Matemática, Universidade de Évora, Portugal To describe the growth of a harvested population when the environment is subjected to random fluctuations one can use Stochastic Differential Equation models. We consider logistic and Gompertz models for the average natural growth to which we subtract a harvesting yield term based on a constant or variable fishing effort. There is previous work on the optimal design of the harvesting policy with the purpose of maximizing the expected accumulated profit (discounted by a depreciation rate) over a finite time horizon. We consider a quite general profit structure which includes linear prices per unit yield and linear costs per unit effort. The harvesting efforts of the optimal policies vary with the randomly varying population size and such policies can, under certain conditions, even be of bang-bang type. These policies are not applicable to harvesting since they need to constantly evaluate population size and require very frequent randomly determined changes in harvesting effort. Our approach, based on sustainable and applicable fishing policies, leads to sustainability of the population and to a stationary distribution of the population size and do not require evaluation of population size. We determine the constant harvesting effort policy that optimizes the expected sustainable profit per unit time and check what we lose profitwise by using this policy instead of the optimal inapplicable policy with variable effort. Using Monte Carlo simulations, we show that, for common situations, our approach is almost as profitable as the first. Acknowledgements Nuno M. Brites and Carlos A. Braumann belong to the Centro de Investigação em Matemática e Aplicações, Universidade de Évora, a research centre supported by FCT (Fundação para a Ciência e a Tecnologia, Portugal). The first author holds a PhD grant from FCT (ref. SFRH/BD/85096/2012). Keywords: Fishing effort, optimal sustainable policy, logistic model, Gompertz model, stochastic differential equations Conference: IMMR | International Meeting on Marine Research 2016, Peniche, Portugal, 14 Jul - 15 Jul, 2016. Presentation Type: Oral presentation Topic: Fisheries and Management Citation: Brites NM and Braumann CA (2016). Fisheries management through optimal sustainable policies with constant effort in random environments. Front. Mar. Sci. Conference Abstract: IMMR | International Meeting on Marine Research 2016. doi: 10.3389/conf.FMARS.2016.04.00113 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 14 Apr 2016; Published Online: 13 Jul 2016. * Correspondence: Dr. Nuno M Brites, Centro de Investigação em Matemática e Aplicalções, Instituto de Investigação e Formação Avançada, Universidade de Évora, Évora, Évora, 7000-671, Portugal, brites@uevora.pt Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Nuno M Brites Carlos A Braumann Google Nuno M Brites Carlos A Braumann Google Scholar Nuno M Brites Carlos A Braumann PubMed Nuno M Brites Carlos A Braumann Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

U Based on a systematic analysis of the theoretical development of Biostatistics and ecological mathematics at home and abroad, several representative ecological mathematical models are summarized. The respective research fields of Biostatistics and ecological mathematics, as well as the lack of their intersection and integration, are reviewed. The logistic model and GM (1, 1) The statistical modeling method and principle of the model, the logistic model group with correlation relationship and the two species Lotka Volterra model are estimated by two-way difference generalized weighted least square method, and applied to practical problems. Mathematical ecology in biological mathematics includes biostatistics and mathematical models of ecological population, which are mostly in the form of differential equations. Biostatistics and ecological population mathematical model (differential equation) have a long history of development in their respective research fields, with complete system, rich content and perfect theory. However, how to cross and integrate the research of these two directions, so as to promote the development of Biostatistics and biological population mathematical model, and then solve more practical specific problems, ecological population mathematical model generally only Qualitative description and analysis of the population. The parameters of the ecological population mathematical model (differential equation) are estimated by using the method and principle of Biostatistics, and the initial prediction value and parameter estimation are optimized in the logistic model and GM (1,1) model from various directions and angles, so that the ecological population differential equation model has further expansion and specific application.

Many animal personality traits have implicit movement‐based definitions and can directly or indirectly influence ecological and evolutionary processes. It has therefore been proposed that animal movement studies could benefit from acknowledging and studying consistent interindividual differences (personality), and, conversely, animal personality studies could adopt a more quantitative representation of movement patterns.Using high‐resolution tracking data of three‐spined stickleback fish (Gasterosteus aculeatus), we examined the repeatability of four movement parameters commonly used in the analysis of discrete time series movement data (time stationary, step length, turning angle, burst frequency) and four behavioral parameters commonly used in animal personality studies (distance travelled, space use, time in free water, and time near objects).Fish showed repeatable interindividual differences in both movement and behavioral parameters when observed in a simple environment with two, three, or five shelters present. Moreover, individuals that spent less time stationary, took more direct paths, and less commonly burst travelled (movement parameters), were found to travel farther, explored more of the tank, and spent more time in open water (behavioral parameters).Our case study indicates that the two approaches—quantifying movement and behavioral parameters—are broadly equivalent, and we suggest that movement parameters can be viewed as “micropersonality” traits that give rise to broad‐scale consistent interindividual differences in behavior. This finding has implications for both personality and movement ecology research areas. For example, the study of movement parameters may provide a robust way to analyze individual personalities in species that are difficult or impossible to study using standardized behavioral assays.

The rapid growth of opioid abuse and the related mortality across the United States has spurred the development of predictive models for the allocation of public health resources. These models should characterize heterogeneous growth across states using a drug epidemic framework that enables assessments of epidemic onset, rates of growth, and limited capacities for epidemic growth. We used opioid overdose mortality data for 146 North and South Carolina counties from 2001 through 2014 to compare the retrodictive and predictive performance of a logistic growth model that parameterizes onsets, growth, and carrying capacity within a traditional Bayesian Poisson space-time model. In fitting the models to past data, the performance of the logistic growth model was superior to the standard Bayesian Poisson space-time model (deviance information criterion: 8,088 vs. 8,256), with reduced spatial and independent errors. Predictively, the logistic model more accurately estimated fatality rates 1, 2, and 3 years in the future (root mean squared error medians were lower for 95.7% of counties from 2012 to 2014). Capacity limits were higher in counties with greater population size, percent population age 45-64, and percent white population. Epidemic onset was associated with greater same-year and past-year incidence of overdose hospitalizations. Growth in annual rates of opioid fatalities was capacity limited, heterogeneous across counties, and spatially correlated, requiring spatial epidemic models for the accurate and reliable prediction of future outcomes related to opioid abuse. Indicators of risk are identifiable and can be used to predict future mortality outcomes.

Sichuan Province preserves numerous rare and ancient species of plants and animals, making it an important bio-genetic repository in China and even the world. However, this region is also vulnerable to fire disturbance due to the rich forest resources, complex topography, and dry climate, and thus has become one of main regions in China needing wildfire prevention. Analyzing the main driving factors influencing wildfire incidence can provide data and policy guidance for wildfire management in Sichuan Province. Here we analyzed the spatial and temporal distribution characteristics of wildfires in Sichuan Province based on the wildfire spot data during 2010–2019. Based on 14 input variables, including climate, vegetation, human factors, and topography, we applied the Pearson correlation analysis and Random Forest methods to investigate the most important factors in driving wildfire occurrence. Then, the Logistic model was further applied to predict wildfire occurrences. The results showed that: (1) The southwestern Sichuan Province is a high-incidence area for wildfires, and most fires occurred from January to June. (2) The most important factor affecting wildfire occurrence is monthly average temperature, followed by elevation, monthly precipitation, population density, Normalized Difference Vegetation Index (NDVI), NDVI in the previous month, and Road kernel density. (3) The Logistic wildfire prediction model yielded good performance, with the area under curve (AUC) values higher than 0.94, overall accuracy (OA) higher than 86%, true positive rate (TPR) values higher than 0.82, and threat score (TS) values higher than 0.71. The final selected prediction model has an AUC of 0.944, an OA of 87.28%, a TPR of 0.829, and a TS of 0.723. (4) The results of the prediction indicate that extremely high danger of wildfires (probability of fire occurrence higher than 0.8) is concentrated in the southwest, which accounted for about 1% of the area of the study region, specifically in Panzhihua and Liangshan. These findings demonstrated the effectiveness of the Logistic model in predicting forest fires in Sichuan Province, providing valuable insights regarding forest fire management and prevention efforts in this region.

Current research on gas discharge theory has made significant development in terms of numerical simulation, but its analytical description of streamer mechanism remains overly simplified, as it is still based on the electron avalanche model characterized with the exponential growth and infinite breakdown current. This paper presents a simple analytical method of gas discharge based on the classic logistic model and covers four aspects. First, it gives the exact definition of generation and mortality rate of electron number, establishes a logistic differential equation and a logistic iteration model for streamer mechanism, and derives deterministic analytical and iterative solution. Second, we also extend the mortality rate to include negative value, thus allowing the logistic model to describe both exponential growth and S shape growth scenarios, and provide criteria for categorizing spark breakdown, Townsend discharge, and stable discharge (glow, arc, aka saturated streamer). Third, the logistic differential model can be transformed into an iterative model. From that we derive the criteria for evaluating discharge instability. Last, although our model is 1-D, but it is still practical and easy to use given its clear analytical expression of underlying physical mechanism.

This paper uses Logistic model for renewable energy markets under different ownership systems were studied. Logistic model is one of the core theoretical ecology Population Growth Model. According to the market characteristics of renewable energy, our coverage under different ownership system of renewable resources is into the oligopoly market. Through the establishment of a linear dynamic system, the Logistic model was added thereto, analyzed under different ownership systems dynamic Nash equilibrium, and numerical simulation test. Conclusion: (1) Under private ownership, while alive fixation rate of natural increase, the equilibrium point (0,0); endogenous natural growth rate is variable: the overall image offset occurs. In the numerical simulation, changes from 0 to 0.8333, changes from 0 to 1.3333, indicating that in a changing market, the impact of the dynamics of the natural growth rate of renewable resources market equilibrium can not be ignored, and the increase in the number of manufacturer resources sustainable use of both the potential positive effects, may bring negative effects. (2) Under public ownership, within the natural growth rate of raw fixed discount rate of two intersection (2.5,3.1); changes and is declining. In the numerical simulation, from the intersection of (2.5,3.1) down to (1.2,0.7), indicating an increase in the number of manufacturers will give sustainable use of resources brought about negative effects, and when it reaches a certain number, the ecological disaster will be inevitable.

This paper examines spatial variations of urban growth patterns in Chinese cities through a case study of Dongguan, a rapidly industrializing city characterized by a bottom-up pattern of development based on townships. We have employed both non-spatial and spatial logistic regression models to analyze urban land conversion. The non-spatial logistic regression has found the significance of accessibility, neighborhood conditions and socioeconomic factors for urban development. The logistic regression with spatially expanded coefficients significantly improves the orthodoxy logistic regression with lower levels of spatial autocorrelation of residuals and better goodness-of-fit. More importantly, the spatial logistic model reveals the spatially varying relationship between urban growth and its underlying factors, particularly the local influence of environment protection and urban development policies. The results of the spatial logistic model also provide clear clues for assessing environmental risks to take the local contexts into account.

The logistic growth model with proportional harvesting is a population growth model that takes into account harvesting factors. In real life, not all conditions can be known with certainty, such as different growth rates in each population and harvest rates depending on the needs of the harvester. To overcome these conditions, there is a concept that accommodates the problem of uncertainty, namely the fuzzy concept. This concept can be induced into a logistic model with proportional harvesting which assumes the intrinsic growth rate and the harvest rate is expressed by fuzzy numbers. The purpose of this research is to form a logistic model with fuzzy proportional harvesting, analyze the stability of the model, and form a numerical simulation. This study uses the alpha-cut method to generalize the intrinsic growth rate and harvest rate from crisp numbers to fuzzy numbers, then the Graded Mean Integration Representation (GMIR) method to defuzzify the model, and the linearization method to analyze the stability of the model. The results of this study obtained a logistic model with proportional harvesting. Then the model was developed into a logistic model with fuzzy proportional harvesting by assuming the intrinsic growth rate and the harvest rate expressed by fuzzy numbers. From the model obtained 2 equilibrium points, namely the first equilibrium point is unstable and the second equilibrium point is asymptotically stable under certain conditions. Model simulation is given to show illustration of stability analysis. From the simulation, it can also be shown that the higher the graded mean value, the lower the population.