Download Population Models: Understanding Dynamics and Growth with Logistic Models and more Slides Ecology and Environment in PDF only on Docsity! Population Models • What is a population? • Populations are dynamic • What factors directly impact dynamics – Birth, death, immigration and emigration • in models we frequently simplify things in order to gain a better understanding of how the rest will work – E.g. a closed vs. open population Docsity.com Population Models • Start with treating time as a ‘discrete’ (geometric population growth) unit rather than continuous (exponential growth) • Is this realistic? Why or why not? Docsity.com Population Models • Because this model does NOT change with population size, it is called density- independent • Furthermore, (b-d) is extremely important • λ is the finite rate of increase Nt+1 = Nt + (b – d)Nt Nt+1 = Nt + RNt Nt+1 = (1+R)Nt Nt+1 = λNt Docsity.com Population Models exponential growth (continuous) • Instantaneous rate of change • Calculate the per capita rate of pop growth • Calculate the size of the pop at any time dN / dt = rN (dN / dt) / N = r Nt = N0ert Docsity.com Logistic Population Models • Here is an example of exponential growth Docsity.com Logistic Population Models • All four parameters (b, b’, d, d’) are assumed to remain constant through time (hence no bt) • How and why should b and d vary with density? Docsity.com Logistic Population Models • We will explore the behavior of populations as numbers change • There is an equilibrium population size Neq = b-d d’-b’ Docsity.com Logistic Population Models • However, is it realistic to think populations will grow exponentially continuously? Docsity.com Logistic Population Models • Now consider the population growth of a species • At some point competition for resources will strengthen, even in the absence of other species dN/dt = rN [1-(N/K)] Intraspecific competition Docsity.com Logistic Population Models • Logistic population models can be used to examine the potential impact of interspecific and intraspecific competition, as well as predator-prey relationships and/or population management (harvesting) • A competitor (or predator) should lower the population numbers of the target species, but by how much? Docsity.com Logistic Population Models • So the equation for population growth is: • Another species (a competitor) has its own population dynamics… • And has the ability to suppress the population of sp1 dN/dt = r1N1 [1-(N1/K1)] dN/dt = r2N2 [1-(N2/K1)] dN/dt = r1N1 [1-(N1/K1) – α1,2 (N2/K1)] Docsity.com Logistic Population Models • Some important model assumptions: • 1) resources are in limited supply (if not, little or no competition, thus no effect) • 2) competition coefficients (α and β) and carrying capacities are constants (otherwise too difficult to predict) • 3) density dependence is linear (adding individuals yields a strict linear impact; equilibrium of non-linear systems complex) Docsity.com Logistic Population Models • It is extremely difficult to get an accurate an accurate estimate of the competition coefficient (α). Why? • Remember, most competition is asymmetrical Docsity.com Logistic Population Models • One could expand upon this equation and include as many species for which as one could get a reasonable estimate of the actual intensity of competition • These same equations could be modified to further capture the effects of other biotic interactions Docsity.com
