BIO3011: Population Dynamics - Population Genetic Models of Evolution - Biology Assignment Help

Assignment Task:

This week’s practical introduces three simple models of population size change that were originally developed in the fields of population and community ecology. We will start with a model of density-independent population growth, which builds off of the model that we introduced during this week’s workshop. We will then introduce a more realistic model of negative density-dependent growth, in which the direction and magnitude of change in population size is sensitive to the number of individuals already present in the population. Our final model will describe the population dynamics of a pair of species that compete over a common set of resources.

For each model, we will first develop recursion equations to describe change over a single time step of the model (the basic unit of time for this week’s models will be a year). We will then use our recursion equations to carry out simulations of change across many time-steps, using simulation output to make predictions about population size change over time. Though our analyses will focus on computer simulations, I will introduce several mathematical results that are intended to complement and shed further light on our simulation output.

Density-independent population growth

The recursion equation

In the Week 10 Workshop, we introduced a simple, discrete-time model for change in population size. In our initial model, we assumed that: 

• The breeding season occurred early in the year, during which each individual produces an average of b offspring

• A period of mortality occurred after the breeding season (e.g., due to a seasonal pulse in predation, parasitism, or some other seasonally variable environmental stress), in which d is the proportion of individuals that die; 1 – d is the proportion that survives

• A period of migration late in the year, which increases the population size by m 

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