# Finding population growth rate given initial population and average pubs per female reproduction

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?

## 1 Answer

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.

• thanks. I had similar logic for first year. However, how do I model that offspring of last year will take 1 year to mature and 1 more year to reproduce. Doesn't that effect the formula as major part of population for next year consists of pubs? – usman Feb 18 at 13:54
• @usman. Yes, instead of 1/2 × 6.5 it's 3/7 × 6.5. – William Elliot Feb 18 at 21:47