Group 6

Nadine Galler

Kirk M. Soodhalter

Jennifer S. Novak

Project Description:

Develop and simulate a Hastings model for two competing species on a 1-dimensional flat landscape. Then develop the model for the same situation on a curved landscape for 1 and 2 species. Try to incorporate altitude in the probability density, instead of only distance.

The Hastings Model

The Hasting's model assumes the following:

- Discrete time (reproductive cycle, fixed life span, etc)

- Adults are stationary (plants, crabs, etc)

- Juveniles are motile

The Hasting's model is as follows:

where a is the survival rate of the adults per cycle,

the probability density of the juveniles is given by

and m is the number of juveniles reaching adulthood per adult.

Basic Assumptions:

a: = 0 ( adults do not survive from one cycle to the next)

( dispersal rate)

( conservative constant)

m:=1 ( one offspring per adult)

1. Motivation:

1 species on a flat landscape:

2. Two competing species on a flat landscape:

Our original model:

These are the 2 species after the 2nd cycle:

These are the 2 species after the 3rd cycle:

These are the 2 species after the 4th cycle:

Here we changed the competing factor: instead of ( 0.1 , 0.9) we used ( 0.3, 0.7):

Possible modifications to the model:

3. One species on a curved landscape:

These models are not conservative. We conjecture that the conservative model would have:

4. Two species on a curved landscape:

5. One species on a curved landscape with altitude: