## Wednesday, July 16, 2008

## Monday, July 14, 2008

I am also reading about logistic models and using them to incorporate a density dependent death rate.

## Monday, June 30, 2008

I also fixed my birth rates (for my linear model) and my seasonal issues after my talk with Heideman. I also keep getting confused on the way to find birth rates for my nonlinear model; my idea was to multiply a reproductive success rate with a meeting rate to give me a "birth rate" but I want to somehow make sure this corresponds with the birth rate info Heideman gave me (4 litters per year, each litter consists of about 4 mice).

I will probably take a break from parameters tomorrow and focus on getting a draft of my lab report done in tech.

## Wednesday, June 25, 2008

Today I met with Professor Heideman and there are some important changes that I need to make to the model. He would like me to incorporate a kind of carrying capacity so that as the population increases there is a greater risk of dying (i.e less nutrients, fewer places to hide, etc.). He also told me that spring, summer, and fall should have similar parameters, while the winter's parameters differ (before I had assumed fall and winter were similar and summer and spring were similar). Next he would like me to add an intermediate group of mice, meaning that there would be a group of mice between P and NP, and that they have a probability of producing half the time in the winter. Adding this group will help with the genetic component of my model; when a NP and P mate there children would become intermediates (assuming heritability is 100%) .

## Monday, June 23, 2008

## Tuesday, June 17, 2008

## Friday, June 13, 2008

Today I found a new paper with a lot of the parameters explicitly written in it; this paper also includes various parameters according to population density, so this may help when I begin to add nonlinear terms.

I also looked at the distriubution of seasons according to the Coordinated Universal Time (UTC), and I found that each seasons begins or ends with a solstice or equinox and lasts for approximately 13 weeks. I think that the seasonal distributions I used in my model (each 13 weeks) is a good estimate for the time being.

I plan to play around with my linear model a little more and then I will add a nonlinear term and try to code that next.

## Monday, June 9, 2008

Today I also spent some time researching parameters. Finding birth rates for separate seasons is difficult, but I am able to find average birth rates, so I may have to make some estimates/talk to Prof Heideman.

I went to the research ethics lecture today led by Prof Heideman. While some of the scenarios in the talk would not apply to math research students, the issues concerning citation and credit were helpful. It was also interesting to see some of the barriers (grants, patents, etc.) that come up during scientific/laboratory research .

## Friday, June 6, 2008

## Wednesday, June 4, 2008

### New Linear Model

## Tuesday, June 3, 2008

I had a meeting with Prof Heideman today which was extremely helpful for the development of my model. Some previous notions have changed, and my model will look different (I will post a new diagram soon). I got a better handle on the meaning and approximate values for many of my parameters; I will also look at some journal articles on

*Peromyscus*to get some more information for my parameters. I plan to continue to meet with Prof Heideman during this summer so that I can make the most representable model.

My plan is to redo my linear model to meet Prof Heideman's expectations and then identify the parameters that need to be changed from a constant to a function dependent on variables such as environment, etc. I plan to start experimenting with matlab shortly.

Lastly, today was our last GIS class; hopefully in the future I will use some of what I have learned in the spatial aspect of my model.

## Monday, June 2, 2008

I have downloaded Latex and will continue to play with it so I get more comfortable with the language. I have unsuccessfully downloaded matlab, and IT is also currently stooped!

While I did not get to do much modeling today, I got some good ideas on where to take my model. I plan on making my linear model nonlinear and writing out the explicit quadratic terms. I also plan on programming my linear model and just doing a couple of simulations (I will probably change my model from continuous to discrete), and hopefully I will try and do a bifurcation diagram for this model, (although this might not be interesting since I will be doing it for a linear model). My goal is that once I talk to Heideman and understand my parameters more clearly that I can build and a nonlinear model and program that.

## Friday, May 30, 2008

Parameters:

Sorry for starting this blog so late! This first week has been pretty productive. I took the model that I had been using and temporarily changed it (I assumed there are only two photosensitive groups instead of a continuum) and diagrammed it to look at the parameters that could possibly come up.

By doing this I realized (with Meagan's help) that there are some more questions I should ask Prof Heideman, i.e. do maturation rates for young->juvenile differ for males vs. females or for photosensitive vs. nonphotosensitive. So I am going to meet with Prof Heideman on Tuesday morning, I may even ask him if I can see the mice!

I also read about a chapter and a half of Dynamic Models in Biology; its been pretty helpful in reviewing some key concepts in modeling. I checked out a couple of other books from the library and read a little bit of the Chaos book.

Meagan taught me how to use the Routh Hurwitz criteria , a way to check for stability for steady states. So after looking at an example, I tried it on my own model (my initial 3 dimension linear ODE); I still have to multiply a large thing out, but it's almost there!

Lastly, today we had our GIS class which was very cool and different, I think this class could eventually help when I need to add my spatial component to my model.