I am creating a nonlinear version of my 5 stage class model. I am also working on a toy model (1 dimensional) to test out different ways of representing density dependent death rates. I will be meeting with Heideman tomorrow so I will probably ask him more about parameters and make sure the changes I have made so far look alright. I will also be working on my abstract that is due Friday.

It has been awhile since I have posted and quite a few things have changed. After my presentation on Friday I got some good feedback on what to change/add. I am coding a new model where I still have three stage classes but now the Young Adults (the middle class) will no longer reproduce; they represent a dispersing group of mice. I will now be calling them the Weaned (W) stage class. So now I have Juvenile, Weaned, and Adult. I have also added two new stage classes that represent Adult females that are lactating or are pregnant (they cannot reproduce so they are separate from the Adult class)

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

Today was a little frustrating. I had thought I got my maturation rates down awhile ago, but when I was checking back on all my rates I discovered that the way I had calculated the maturation rates did not seem correct. I had manually calculated them (w help of matlab) using the info that mice sexually mature in about six weeks (42 days). Hopefully I can fix this soon, even though at the moment I am confused on how to go about doing so.

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.

I have been varying my maturation rate of the young adults to adults (I found data that suggested mice in warmer climates mature sexually faster) and I have found some interesting results when I differ the maturation rates between the P and NP(the NP population explodes, while the P seems not to). I also fixed a latex problem that I have been having for awhile.

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%) .

Sorry I have not posted in awhile. I have put my "basic" nonlinear model into matlab and it is up and running. I have been trying to find birth rate terms in terms of copulation attempts per couple* pregnancy success rate. This birth rate needs to incorporate both males and females since my nonlinear model depends on both sexes (and it is the only way my units cancels out). I found a couple papers that may help with this kind of data. I also found some interesting information about maturation rates; mice in warmer climate mature faster than mice in colder climates, while the difference is only about a weeks time, it could impact my data, so I plan to play around with this in my matlab model. I am now going to work on developing a carrying capacity (I need to decide what I want it to depend upon i.e nutrients, rainfall, etc.) A critical depending factor for this would include the diet of white footed mice; I found that the main sources of food throughout the year are insects, but additionally in the spring and summer they eat fruit and in the winter and fall they eat seeds/green vegetation.

Now that I have got my linear model down, I have coupled my two populations (photo and non-photosensitive) together and created a basic nonlinear model. In this model all age classes are split into NP and P, and the Adult class is also split into male and female. A lot of new parameters arise from this, however some of these may collapse after I talk to Prof Heideman. Right now I am working on creating all my equations and making a parameter/variable table in Tech. Once I have this done (it may take awhile), I will start putting this model into matlab to analyze it. Later on I will add nonlinear functions to make additional models, for example my birth rate may become a function of both the number of NP and P and nutrients.

I realized yesterday that my matlab code for my linear model was not accurately representing my model; when I made all the birth rates zero the Juvenile population never died off, which is what should have occured. The problem has now been corrected (my itterations were not properly working) and my graphs look quite different from the ones I had showed Meagan and Prof Day at our meeting on Wed. (Prof. Day I can email you my new pictures!). I looked at the stable age distribution and the dominant eigenvalue and found that the population will reach an unstable steady state and explode (this was conducted by using my parameters I had found in papers).

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.