Problem Decomposition

Exponential Growth 2

One of you lab mates (you may remember them from the For Loops 2 problem) is busy working on insect population dynamics. Initial results suggested that exponential growth was too simplistic for understanding the observed dynamics, so now they need to look at logistic growth. Logistic growth is a lot like exponential growth except that it slows down as the population grows large and eventually asymptotes at a carrying capacity. The basic recursive equation is:

N(t+1)~ = N(t) + r * N(t) * ((K – N(t)) / K)

N(t) is the abundance at a given time step, r is the reproductive rate, and K is the carrying capacity (you can learn a bit more about logistic population growth here). Since we can’t have partial individuals in the real world we should round the calculation in each step up to the nearest integer using the ceil function in the math module.

Your lab mate has compiled data from literature on the reproductive rates and carrying capacity for a number of different individuals for a variety of species. You’ve been teaching them about database structure so they have broken the data into two tables: an individuals table and species table. The database has information on several different taxonomic groups, but for this project your lab mate is only interested in the data for the insects.

Using the average reproductive rate and carrying capacity for each insect species determine the time it takes for the species to reach equilibrium (i.e., carrying capacity) when starting with an initial population size of 10. Once you’ve determined the value for each species, plot the time to equilibrium as a function of the reproductive rate and (on a separate graph) the carrying capacity.

You can either break this problem down into manageable parts yourself (you can use the problem decomposition steps to help) or follow this approach. Turn in the Python code and (if you use one) a database file with any queries that you use.