Analyzing and Projection of Future Bangladesh Population Using Logistic Growth Model
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Population Ecology: Theory, Methods, Lenses Dr. Bill Fagan
Population ecology: Theory, methods, lenses Dr. Bill Fagan Population Ecology & Spatial Ecology A) Core principles of population growth B) Spatial problems and methods for modeling them C) Integrodifference equations as a robust platform Population Ecology & Spatial Ecology A) Core principles of population growth B) Spatial problems and methods for modeling them C) Integrodifference equations as a robust platform Socio – Environmental Issues: 1. Fisheries 2. Invasive Species 3. Biological Control 4. Ecological Footprints 5. Critical Patch Size / Reserve Design A) Core principles of population growth Berryman: On principles, laws, and theory in population ecology. Oikos. 2003 1) Exponential population growth as a null baseline. What causes deviations from that ? The Basics of Discrete Time Models Have Form Nt1 f Nt , Nt1, Nt2 ,... where N is the thing you are measuring and t is an index representing blocks of time. Constant time step = 1 unit (year, month, day, second) Time is discrete, #’s need not be In many cases Nt1 f Nt Reduced Form Status next time step depends only on where system is now. history is unimportant Alternatively: N t 1 f N t , N t 1 , N t 2 ... history is important wide applicability 1) Many ecological phenomenon change discretely - insects don’t hatch out all day long, only in morning - rodents are less mobile near full moon - seeds germinate in spring daily censuses 2) Data were collected at discrete times yearly censuses The Simplest Discrete Time Model N t1 N t “Geometric” Growth Equation N Thing we -
Ecological Principles and Function of Natural Ecosystems by Professor Michel RICARD
Intensive Programme on Education for sustainable development in Protected Areas Amfissa, Greece, July 2014 ------------------------------------------------------------------------ Ecological principles and function of natural ecosystems By Professor Michel RICARD Summary 1. Hierarchy of living world 2. What is Ecology 3. The Biosphere - Lithosphere - Hydrosphere - Atmosphere 4. What is an ecosystem - Ecozone - Biome - Ecosystem - Ecological community - Habitat/biotope - Ecotone - Niche 5. Biological classification 6. Ecosystem processes - Radiation: heat, temperature and light - Primary production - Secondary production - Food web and trophic levels - Trophic cascade and ecology flow 7. Population ecology and population dynamics 8. Disturbance and resilience - Human impacts on resilience 9. Nutrient cycle, decomposition and mineralization - Nutrient cycle - Decomposition 10. Ecological amplitude 11. Ecology, environmental influences, biological interactions 12. Biodiversity 13. Environmental degradation - Water resources degradation - Climate change - Nutrient pollution - Eutrophication - Other examples of environmental degradation M. Ricard: Summer courses, Amfissa July 2014 1 1. Hierarchy of living world The larger objective of ecology is to understand the nature of environmental influences on individual organisms, populations, communities and ultimately at the level of the biosphere. If ecologists can achieve an understanding of these relationships, they will be well placed to contribute to the development of systems by which humans -
Concept of Population Ecology
Mini Review Int J Environ Sci Nat Res Volume 12 Issue 1 - June 2018 Copyright © All rights are reserved by Nida Tabassum Khan DOI: 10.19080/IJESNR.2018.12.555828 Concept of Population Ecology Nida Tabassum Khan* Department of Biotechnology, Faculty of Life Sciences and Informatics, Balochistan University of Information Technology Engineering and Management Sciences, Pakistan Submission: May 29, 2018; Published: June 06, 2018 *Corresponding author: Nida Tabassum Khan, Department of Biotechnology, Balochistan University, Quetta, Pakistan, Tel: ; Email: Abstract Population ecology deals with the study of the structure and subtleties of a population which comprises of a group of interacting organisms of the same specie that occupies a given area. The demographic structure of a population is a key factor which is characterized by the number of is growing, shrinking or remain constant in terms of its size. individual members (population size) present at each developmental stage of their cycle to identify whether the population of a specific specie Keywords: Population size; Population density; Gene pool; Life tables Introduction of random genetic drift therefore variation is easily sustained Population ecology deals with the study of the structure in large populations than in smaller ones [10]. Natural selection and subtleties of a population which comprises of a group of selects the most favorable phenotypes suited for an organism interacting organisms of the same specie that occupies a given survival thereby reducing variation within populations [11]. area [1]. Populations can be characterized as local which is a Population structure determines the arrays of demographic group of less number of individuals occupying a small area or variation such as mode of reproduction, age, reproduction met which is a group of local populations linked by disbanding frequency, offspring counts, gender ratio of newborns etc within/ members [2]. -
A Model for Bio-Economics of Fisheries
International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 2 Issue 2, February- 2013 A Model for Bio-Economics of Fisheries G. Shanmugam 1, K. B. Naidu 2 1Associate Professor, Dept of Mathematics, Jeppiaar Engineering College, Chennai, 2Professor, Department of Mathematics, Sathyabama University, Chennai Abstract. In this paper a model for growth of fish, a model for fishing economics and delay model for fishing are considered. The maximum sustainable yield for fishing is obtained. In the delay model the three cases of equilibrium population being equal to (or) greater then (or) less then the ratio of carrying capacity and rate of growth are considered. 1 Introduction The World population is growing at enormous rate, creating increasing demand for food. Food comes from renewable resources. Agricultural products are renewable resources, since every season new crops are produced in farms. Fisheries are a renewable resource since fish are reproduced in lakes and seas. Forests are renewable resources since they reproduce periodically. As these resources are renewable, the quality of the resources will certainly degrade, leading to shortage. Over fishing will lead to decline in fisheries. Global warming again has an impact on the growth of agriculture, fisheries and forests. It is imperative that we should manage these resources economically to prevent a catastrophic bust in our global economy. Mathematical bio-economics is the mathematical study of the management of renewable bio resources. It takes into consideration not only economic factors like revenue, cost etc., but also the impact of this demand on the resources. IJERTIJERT One of the mathematical tools used in bio economics is differential equations. -
Critical Review of the Literature on Marine Mammal Population Modelling Edward O
Nova Southeastern University NSUWorks Marine & Environmental Sciences Faculty Reports Department of Marine and Environmental Sciences 9-1-2008 Critical Review of the Literature on Marine Mammal Population Modelling Edward O. Keith Nova Southeastern University Oceanographic Center Find out more information about Nova Southeastern University and the Halmos College of Natural Sciences and Oceanography. Follow this and additional works at: https://nsuworks.nova.edu/occ_facreports Part of the Marine Biology Commons, and the Oceanography and Atmospheric Sciences and Meteorology Commons NSUWorks Citation Edward O. Keith. 2008. Critical Review of the Literature on Marine Mammal Population Modelling .E&P Sound & Marine Life Programme : 1 -63. https://nsuworks.nova.edu/occ_facreports/93. This Report is brought to you for free and open access by the Department of Marine and Environmental Sciences at NSUWorks. It has been accepted for inclusion in Marine & Environmental Sciences Faculty Reports by an authorized administrator of NSUWorks. For more information, please contact [email protected]. Critical Review of the Literature on Marine Mammal Population Modeling Prepared by Nova Southeastern University www.soundandmarinelife.org Revised Final Report Critical Review of the Literature on Marine Mammal Population Modeling (JIP 22-07-19) Edward O. Keith Oceanographic Center Nova Southeastern University 8000 N. Ocean Drive Dania Beach, FL 33004 [email protected] 954-262-8322 (voice) 954-262-4098 1 September 2008 1 Table of Contents A. Executive summary 3 B. Introduction 3 1. Purpose 4 2. Objectives 4 3. Scope 5 C. Types of population models 1. H0 vs. Model Selection/GLMs/GAMs 6 2. Exponential/Logistical 8 3. Multinomial 10 4. -
Diffusive Logistic Population Growth with Immigration
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Applied Mathematics Letters 18 (2005) 261–265 www.elsevier.com/locate/aml Diffusive logistic population growth with immigration S. Harris∗ College of Engineering and Applied Sciences and Marine Sciences Research Center, SUNY, Stony Brook, NY 11794, United States Received 1 March 2003; accepted 1 March 2003 Abstract We study diffusive logistic growth with immigration for a habitat surrounded by a hostile environment. The focus of our interest is the effect of immigration on the critical habitat length required for survival of the population. As expected, we find that this is reduced when immigration occurs. We also briefly consider the much simpler case where both immigration and emigration take place in an isolated habitat. © 2005 Elsevier Ltd. All rights reserved. Keywords: Diffusive logistic growth; Immigration; Critical length; Emigration 1. Introduction Various approaches have been taken to model the distribution of populations. These differ in several important respects, especially as regards the treatment of the dispersal process. Metapopulation models [1]provide a global description of a complex habitat whose evolution is determined by the colonization (i.e. immigration into) and extinction of its component patches. In contrast, reaction–diffusion models [2–4]provide a local description of individual isolated patches. The fusion of these two approaches would be desirable [5], and our purpose here is to consider one of the specific issues that must be resolved before such an ambitious goal can be reached. Existing results for reaction–diffusion models describing individual patches are almost exclusively limited to describing habitats in which there is no immigration. -
Projections of Global Carrying Capacity - Graeme Hugo
THE ROLE OF FOOD, AGRICULTURE, FORESTRY AND FISHERIES IN HUMAN NUTRITION – Vol. III - Projections of Global Carrying Capacity - Graeme Hugo PROJECTIONS OF GLOBAL CARRYING CAPACITY Graeme Hugo Professor of Geography, University of Adelaide, Australia Keywords: Carrying capacity, optimum population, population pressure, renewable resources, resource exploitation, economic development, fossil fuels, hunter-gatherers, ecological sustainability, cereal grains, consumption Contents 1. Introduction 2. The Reality of Projected Population Growth 3. Responses to Population Pressure on Resources 4. Optimum Populations 5. Food Production Outlook 6. Projections of Global Carrying Capacity 7. Conclusion Glossary Bibliography Biographical Sketch Summary The term carrying capacity is applied largely to animal populations as the maximum number of individuals in a particular species that can be indefinitely supported by the resources in a particular area. In animal contexts the carrying capacity is determined by the amount of food available, the number of predators, and the rate at which the environment can replace the resources that are used by the population. In applying this concept to humans there are two differences. First, human beings have the capacity to innovate and to use technology and to pass innovations on to future generations, so they have the capacity to redefine upward the limits imposed by carrying capacity. Second, human beings need and use a wider range of resources than food and water in the environment. Hence, human carrying capacity is a function of the resources in an area, the consumption level of those resources, and the technology used in exploitingUNESCO them. Therefore, there is –a grEOLSSeat deal of difficulty experienced in operationalizing or measuring human carrying capacity globally or regionally. -
Community-Based Population Recovery of Overexploited Amazonian Wildlife
G Model PECON-41; No. of Pages 5 ARTICLE IN PRESS Perspectives in Ecology and Conservation xxx (2017) xxx–xxx ´ Supported by Boticario Group Foundation for Nature Protection www.perspectecolconserv.com Policy Forums Community-based population recovery of overexploited Amazonian wildlife a,∗ b c d e João Vitor Campos-Silva , Carlos A. Peres , André P. Antunes , João Valsecchi , Juarez Pezzuti a Institute of Biological and Health Sciences, Federal University of Alagoas, Av. Lourival Melo Mota, s/n, Tabuleiro do Martins, Maceió 57072-900, AL, Brazil b Centre for Ecology, Evolution and Conservation, School of Environmental Sciences, University of East Anglia, Norwich Research Park, Norwich NR47TJ, UK c Wildlife Conservation Society Brasil, Federal University of Amazonas, Av. Rodrigo Otavio, 3000, Manaus 69077-000, Amazonas, Brazil d Mamiraua Sustainable Development Institute (IDSM), Estrada da Bexiga 2584, Fonte Boa, Tefé, AM, Brazil e Centre for Advanced Amazon Studies, Federal University of Para, R. Augusto Correa 01, CEP 66075-110, Belém, PA, Brazil a b s t r a c t a r t i c l e i n f o Article history: The Amazon Basin experienced a pervasive process of resource overexploitation during the 20th-century, Received 3 June 2017 which induced severe population declines of many iconic vertebrate species. In addition to biodiversity Accepted 18 August 2017 loss and the ecological consequences of defaunation, food security of local communities was relentlessly threatened because wild meat had a historically pivotal role in protein acquisition by local dwellers. Keywords: Here we discuss the urgent need to regulate subsistence hunting by Amazonian semi-subsistence local Hunting regulation communities, which are far removed from the market and information economy. -
Math 636 - Mathematical Modeling Discrete Modeling 1 Discrete Modeling – Population of the United States U
Discrete Modeling { Population of the United States Discrete Modeling { Population of the United States Variation in Growth Rate Variation in Growth Rate Autonomous Models Autonomous Models Outline Math 636 - Mathematical Modeling Discrete Modeling 1 Discrete Modeling { Population of the United States U. S. Population Malthusian Growth Model Programming Malthusian Growth Joseph M. Mahaffy, 2 Variation in Growth Rate [email protected] General Discrete Dynamical Population Model Linear Growth Rate U. S. Population Model Nonautonomous Malthusian Growth Model Department of Mathematics and Statistics Dynamical Systems Group Computational Sciences Research Center 3 Autonomous Models San Diego State University Logistic Growth Model San Diego, CA 92182-7720 Beverton-Holt Model http://jmahaffy.sdsu.edu Analysis of Autonomous Models Fall 2018 Discrete Modeling U. S. Population | Discrete Modeling U. S. Population | Joseph M. Mahaffy, [email protected] (1/34) Joseph M. Mahaffy, [email protected] (2/34) Discrete Modeling { Population of the United States Discrete Modeling { Population of the United States Malthusian Growth Model Malthusian Growth Model Variation in Growth Rate Variation in Growth Rate Programming Malthusian Growth Programming Malthusian Growth Autonomous Models Autonomous Models United States Census Census Data Census Data United States Census 1790 3,929,214 1870 39,818,449 1950 150,697,361 Constitution requires census every 10 years 1800 5,308,483 1880 50,189,209 1960 179,323,175 Census used for budgeting federal payments and representation -
Carrying Capacity
CarryingCapacity_Sayre.indd Page 54 12/22/11 7:31 PM user-f494 /203/BER00002/Enc82404_disk1of1/933782404/Enc82404_pagefiles Carrying Capacity Carrying capacity has been used to assess the limits of into a single defi nition probably would be “the maximum a wide variety of things, environments, and systems to or optimal amount of a substance or organism (X ) that convey or sustain other things, organisms, or popula- can or should be conveyed or supported by some encom- tions. Four major types of carrying capacity can be dis- passing thing or environment (Y ).” But the extraordinary tinguished; all but one have proved empirically and breadth of the concept so defi ned renders it extremely theoretically fl awed because the embedded assump- vague. As the repetitive use of the word or suggests, car- tions of carrying capacity limit its usefulness to rying capacity can be applied to almost any relationship, bounded, relatively small-scale systems with high at almost any scale; it can be a maximum or an optimum, degrees of human control. a normative or a positive concept, inductively or deduc- tively derived. Better, then, to examine its historical ori- gins and various uses, which can be organized into four he concept of carrying capacity predates and in many principal types: (1) shipping and engineering, beginning T ways prefi gures the concept of sustainability. It has in the 1840s; (2) livestock and game management, begin- been used in a wide variety of disciplines and applica- ning in the 1870s; (3) population biology, beginning in tions, although it is now most strongly associated with the 1950s; and (4) debates about human population and issues of global human population. -
Smith's Population Model in a Slowly Varying Environment
Smith’s Population Model in a Slowly Varying Environment Rohit Kumar Supervisor: Associate Professor John Shepherd RMIT University CONTENTS 1. Introduction 2. Smith’s Model 3. Why was Smith’s Model proposed? 4. The Constant Coefficient Case 5. The Multi-Scaling Approach 6. The Multi-Scale Equation and its implicit solution using the Perturbation Approach 7. Smith’s parameter, c , varying slowly with time using Multi- Timing Approximations 8. Comparison of Multi-Timing Approximations with Numerical Solutions 9. Conclusion 1 1. Introduction Examples of the single species population models include the Malthusian model, Verhulst model and the Smith’s model, which will be the main one used in our project (Banks 1994). The Malthusian growth model named after Thomas Malthus illustrates the human population growing exponentially and deals with one positive parameter R , which is the intrinsic growth rate and one variable N (Banks 1994). The Malthusian growth model is defined by the initial-value problem dN RN, N(0) N . (1) dT 0 The Malthusian model (1) generated solutions NT()that were unbounded, which was very unrealistic and did not take into account populations that are limited in growth and hence, the Verhulst model was proposed (Bacaer 2011; Banks 1994). This model suggested that while the human population nurtured and doubled after some time, there comes a stage where it tends to steady state (Bacaer 2011). The Verhulst model is defined by the initial-value problem, dN N RN1 , N(0) N0 . (2) dT K Here, R is the intrinsic growth rate, N is the population size and K is the carrying capacity. -
Stochastic Predation Exposes Prey to Predator Pits and Local Extinction
130 300–309 OIKOS Research Stochastic predation exposes prey to predator pits and local extinction T. J. Clark, Jon S. Horne, Mark Hebblewhite and Angela D. Luis T. J. Clark (https://orcid.org/0000-0003-0115-3482) ✉ ([email protected]), M. Hebblewhite (https://orcid.org/0000-0001-5382-1361) and A. D. Luis, Wildlife Biology Program, Dept of Ecosystem and Conservation Sciences, W. A. Franke College of Forestry and Conservation, Univ. of Montana, Missoula, MT, USA. – J. S. Horne, Idaho Dept of Fish and Game, Lewiston, ID, USA. Oikos Understanding how predators affect prey populations is a fundamental goal for ecolo- 130: 300–309, 2021 gists and wildlife managers. A well-known example of regulation by predators is the doi: 10.1111/oik.07381 predator pit, where two alternative stable states exist and prey can be held at a low density equilibrium by predation if they are unable to pass the threshold needed to Subject Editor: James D. Roth attain a high density equilibrium. While empirical evidence for predator pits exists, Editor-in-Chief: Dries Bonte deterministic models of predator–prey dynamics with realistic parameters suggest they Accepted 6 November 2020 should not occur in these systems. Because stochasticity can fundamentally change the dynamics of deterministic models, we investigated if incorporating stochastic- ity in predation rates would change the dynamics of deterministic models and allow predator pits to emerge. Based on realistic parameters from an elk–wolf system, we found predator pits were predicted only when stochasticity was included in the model. Predator pits emerged in systems with highly stochastic predation and high carrying capacities, but as carrying capacity decreased, low density equilibria with a high likeli- hood of extinction became more prevalent.