Stochastic Population Growth Model Next, we are going to monitor the population growth of an asexually reproducing single-celled organism, centinia lincolni (pennies). This Centina population has a mortality rate of 50% per year, but all individuals that survive the year divide to produce an additional individual. The very most basic growth model of a closed population is: N+ N-deaths births Rewritten to use rates instead of individuals, this equation becomes: N+ -N,S+N.BS where S is the probability of survival (0.5) and B is the birth rate (1.0). Assume you start with 10 individuals in the population at Time -0. Use the equation above. Howmanyindividuals will be in the populationateimecreaal(mall:a.읔:[email protected]) How many individuals will be in the population at Time 2? Find the population growth rate, λ, and intrinsic rate of increase, r. (recall: λ-N 1. r-In(A) The population is ( increasing/ decreasing/ not changing) The above model describes the long-term average behavior of such a population, but not necessarily how a real population might behave. In a more realistic model, the probability of survival, S, applies to each individual separately, rather than to the population as a whole. Because S is a probability, the outcome of such a model is not pre-determined, and hence is called stochastic (includes randomness), instead of deterministic Start with a small population of Centinia (6 individuals). If we use a deterministic model for Centinia dynamics, what would the population size be after 8 generations? Stochastic Population Growth Model Next, we are going to monitor the population growth of an asexually reproducing single-celled organism, centinia lincolni (pennies). This Centina population has a mortality rate of 50% per year, but all individuals that survive the year divide to produce an additional individual. The very most basic growth model of a closed population is: N+ N-deaths births Rewritten to use rates instead of individuals, this equation becomes: N+ -N,S+N.BS where S is the probability of survival (0.5) and B is the birth rate (1.0). Assume you start with 10 individuals in the population at Time -0. Use the equation above. Howmanyindividuals will be in the populationateimecreaal(mall:a.읔:[email protected]) How many individuals will be in the population at Time 2? Find the population growth rate, λ, and intrinsic rate of increase, r. (recall: λ-N 1. r-In(A) The population is ( increasing/ decreasing/ not changing) The above model describes the long-term average behavior of such a population, but not necessarily how a real population might behave. In a more realistic model, the probability of survival, S, applies to each individual separately, rather than to the population as a whole. Because S is a probability, the outcome of such a model is not pre-determined, and hence is called stochastic (includes randomness), instead of deterministic Start with a small population of Centinia (6 individuals). If we use a deterministic model for Centinia dynamics, what would the population size be after 8 generations?