1.1. The first task is to generate a deterministic version of the logistic growth curve in R. Hint: you can modify the code that was presented for the exponential growth model in “Growth curves in R”. The equation of logistic model is described in the narrated PowerPoint on “Population growth curves”.
1.2. Using graphs to communicate your results, describe how the dynamics of the population change for different values of the model parameters. Hint: choose default values for your parameters and then for each select at least one higher value and lower value than the default.
1.3. Describe the main assumptions of the model, and provide a critical analysis of the use of the logistic model to inform invasive species management, drawing on your own examples from the literature. Hint: consider what the limitations of the model are, and how the logistic model has been used in other studies.
Part 2 Spatial spread models
2.1. Develop an individual-based stochastic spread model for an invasive species that can be run over multiple simulations. Hint: You can modify the code from topic 6 on “An individual based model in R” from a single run to multiple runs.
2.2. Explore the model by producing maps of the probability that each patch becomes occupied by the end of the simulated time (this time is arbitrary but should be chosen not too early or late in the invasion so there is some variability, and all probabilities are not zero or 1). Hint: this probability can be determined from the proportion of simulations in which the patch became occupied. You will have to ensure you store this value in a vector as the simulations progress.
2.3. Describe the main assumptions of the model, and provide a critical analysis of how individual based models can be used to design targeted surveillance and control programs for invasive species. Hint: the model presented here is simplistic, what are its limitations and what additions could be made to the model to enable its use in practice? Draw on examples from the literature where this has been done.
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