# Stochastic modelling in python | Statistics

For this project assume that bobcats have a mean birth rate of 0.4 with a standard deviation of 0.1 and a mean survival rate of 0.68 with a standard deviation of 0.07. In this model, assume that these demographic parameters follow a normal distribution. Environmental stochasticity can take many forms. For this project it will take the form of a catastrophe which occurs an average of once every 25 years or 4% of the time. These catastrophes affect both the bobcat birth and bobcat survival rates by decreasing both rates by 30% during the year that the catastrophe occurred. For all parts of this project, assume an initial bobcat population of 100.

1. Deterministic. Construct and run a deterministic model for the bobcats using the birth rate of 0.4 and the survival rate of 0.68, but ignoring all random factors. Graph94 2.7 Projects the population over a 20-year period with these parameters and make a table of this information.

2. Demographic Stochasticity. Create a new model using only the demographic stochastic information. Make a graph and a data table with at least 50 runs for 20 years.

3. Environmental Stochasticity. Now construct a model using only environmental stochasticity. Again construct a data table and graph for at least 50 runs of this case for 20 years.

4. Take the data from the 20th year of both stochastic models and, if necessary, export it to a program that calculates statistics. Make histograms and box plots. Make reports of the following summary statistics: mean, median, 25th and 75th percentiles, standard deviation, range, inter-quartile range, minimum, and maximum. Compare the results from these two models.

5. For each model construct a graph with side-by-side box plots for the first 10 years showing the change in distribution over time. Compare both of these models with each other and with the deterministic model.

6. From the work so far, which stochastic effect is more pronounced? Either construct and analyze a model with both demographic and environmental stochastic effects, or argue that the combined effects will not be significantly different from the individual effects so there is no need to complicate the model.