# MathBio: R Code for Linear Structured Systems

Code for simulating linear 3d systems: linear3d.R

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by Scott Alister McKinley on February 28, 2014

*Bayesian Inference and MCMC methods*, Math 7770

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Hmm…is the code right? With a yearly juvenile death rate of 99.998% I’m still getting exponential growth on the juvenile population. I’m doing it on the calculator and it shouldn’t be. The other alternative is that I might be using the code in the wrong manner.

I just did it on matlab with my own code and got the same thing. I don’t get it, a yearly death rate of 99.998% should be enough for a stable population, but both adults and juveniles are increasing exponentially.

I think figured out what the problem is. Death rate should be about 99.998% in order for only 1 juvenile in 50,000 to survive, meaning 99.998% of the children born this year will die, but we said graduation rate is 10%, and we are taking this 10% out of the total eggs hatched and adding it to the number of adults each year, instead of only taking into account the surviving 0.002%. In the models we’ve done so far 1 minus the juvenile death rate has still been greater than the graduation rate, so we haven’t run into problems where we are adding dead juveniles to the number of adults, but I guess in this case the model must be fixed to account for that.

So taking that into account now I’m getting some numbers that make sense. With capture rate at 0%, the population is reaching stability after a few years. I am getting, however, that is not possible to reach stability if the capture rate is higher than 0%, and population will eventually go extinct (in hundreds of years, or thousands of years if the capture rate is low enough), unless the capture rate is statistically negligible. I don’t know if that’s correct, but at least it’s not exponential growth anymore.

Hi David, Thanks for your thoughts on this. I’m working on developing a default model with the parameters we discussed in class, and everyone can check their systems against the default. I hope to have something posted sometime this weekend.

One important point though: These linear systems will exhibit unbounded growth because we have not included density-dependence. I was talking to another student this afternoon and based on that conversation I will include a further default model that has a nonlinear logistic growth that will enable some long-term stability at a non-zero population level.

Good work so far!