I am new to mathematical modeling and having trouble modelling the following population growth scenario:
- Starting population: $100$ individuals
- Average age: $7$ years
- Assumption: population equally distributed among sexes and ages
- Females reproduce: once per year
- Average per litter: $6.5$ pubs
- Females pubs become sexually active after $1$ year
Question # 1: What will be population growth model for $7-10$ years and yearly growth rate? What kind of techniques and mathematical models can be used in this situation?
Question # 2: What if I want to model interaction with predators and how that will affect population growth?
Let n be the number of dogs. 6n/7 are mature.
In one years time there are 3n/7 × 6.5 pups and n/7 dogs die.
Population at the end of the year is n + 3n/7 × 6.5 - n/7.
Let a = 1 + 3/7 × 6.5 - 1/7, the rate of population increase.
In k years the population is na$^k$.
To account for predation, diminish a.
If for every 100 dogs, d dogs are eaten by cats
then substract d/100 from a.