Modelling Population Growth - Ecology - Lab Handout, Exercises of Ecology and Environment

Download Modelling Population Growth - Ecology - Lab Handout and more Exercises Ecology and Environment in PDF only on Docsity! Ecology MODELLING POPULATION GROWTH WITH COMPETITION AND PREDATION Note: I may lecture on population regulation at the beginning of lab to bring you up to speed on this. Bring you outline for lectures 11 & 12 so that you are prepared. Be sure that you have read pages 100-103 in Khrone. The equations presented in this handout are elaborations of the one presented on page 102. Introduction Ecology is the study of interactions between organisms and their environment as a means to understand their distribution and abundance. In essence, ecology is the study of populations in nature. The most important, or at least most obvious attribute of a population is its size. Often ecologists (myself included) will conduct experiments to determine how a particular abiotic or biotic factor(s) will impact the life history of an organism. Ideally, we want to quantify the fitness of our research organism. Fitness is not the number of offspring produced by an organism, but rather it is the contribution those offspring make to future generations. That is, an organism’s offspring must survive and reproduce. To assess that, an ecologist would need to follow a population for several generations after their study. This generally does not happen. As a substitute for assessing fitness, ecologists measure fecundity, the rate at which females produce offspring. For a semelparous species or one that has big-bang reproduction, fitness can be measured at a single point in time. At this juncture, an ecologist can do no more than point at changes in fecundity (e.g. an increase) and induce that if the current rate of fecundity is maintained, the population will increase. This is a fairly simplistic approach to understanding the population dynamics of an organism and of course, hardly quantitative. This is why I maintain the opinion that quantitative skills are extremely valuable in biology, including ecology. Our foray in class into population biology represents one way that ecologists attempt to quantify population dynamics. Review of exponential growth and carrying capacity If we start with a population of size Nt and an intrinsic rate of population growth (r) in percent (r = 0.4), we can calculate Nt+1. The discrete (not differential) exponential equation for a population of Nt organisms is (1) Nt+1 = Nt + rNt. This model predicts the size (N) of the population at some time in the future (t+1). However, no population grows exponentially without being limited. If we assume that a population is under density-dependent regulation, then the discrete version of the logistic equation can be expressed as (2) Nt+1 = Nt + rNt       − k k tN . Docsity.com Ecology Although this model seems more realistic in that it considers intraspecific competition, it assumes that the organism under study lives alone in the environment and is the only organism consuming the resources. Incorporation of competition into population models A.J. Lotka and G.F. Gause independently developed a set of models that included competition. They modified equation 2 so that it considered the interspecific effect of competition of species 2 on species 1. The equation they derived is: (3) N1(t+1) = N1 + r1N1       − 1 2211 N-N k k α where r = intrinsic rate of increase N = population size k = carrying capacity α2 = impact of species 2 on species 1 In the above equation, α2N2 represents the competing organisms of species 2 and are expressed as equivalent organisms of the original species. For example, if α2> 1, that means that each individual of species 2 consumes more of species 1’s resources than an individual of species 1. The result is that species 2 depresses the growth of the population of species 1. Similarly if α2< 1, individuals of species 2 consume less of species’ 1 resources than each individual of species 1. The effect of species 1 on species 2 is: (4) N2(t+1) = N2 + r2N2       − 2 1122 N-N k k α Incorporation of predation into competition population models. A.J. Lotka and Vito Volterra independently considered the impact of predation on population dynamics. This builds upon the models that incorporates one population of predators (P) consuming two herbivore populations (H1 and H2). The equations for the herbivores would be: (5) H1(t+1) = H1 + r1H1       − 1 2211 H-H k k α - γ1H1P (6) H2(t+1) = H2 + r2H2       − 2 1122 H-H k k α - γ2H2P And the predator would be (7) P = γ1H1P∈1 + γ2H2P∈2 –DP Docsity.com