Parameters in the competitive Lotka-Volterra model for red and grey squirrels

I am trying to create a simple model of how the population of red and grey squirrels in Scotland will change using the competitive Lotka-Volterra model. I know there are approximately 120 000 red squirrels today. However, I need to figure what the biological parameters would be.

In the model $\alpha_{12}$ is a parameter which describes how population 2 (red squirrels) affects population 1 (grey squirrels). I think the grey squirrels are more harmful to the red squirrels than vice versa so maybe $\alpha_{21}=2$ and $\alpha_{12}=1/2$?

And the growth rate $r$ of a population is birth minus death rate, so I think it is reasonable that $r$ is between $-0.1$ and $0.1$. If I could find a graph of population size I could estimate the growth rate as the slope of a secant line in a time interval.

• Your remark about the sign of the "autonomous" reproduction rates $r$ is odd. In the competetive Lotka-Volterra model, the population of red squirrels $x_1(t)$ solves $${dx_1 \over dt} = r_1x_1\left(1-\left({x_1+\alpha_{12}x_2 \over K_1}\right) \right)$$ where $\alpha_{12}$ is positive since it describes a competition effect and $K_1$ is positive since it describes the effective size of the population of red squirrels in the absence of grey squirrels. But if $r_1<0$, the evolution of the red squirrels in isolation, ... – Did Jan 10 '17 at 0:01
• ... given by $${dx_1 \over dt} = r_1x_1\left(1-{x_1 \over K_1} \right)$$ is such that $x_1(t)\to\infty$ for every $x_1(0)>K_1$ and $x_1(t)\to0$ for every $x_1(0)<K_1$, which seems absurd. Please explain. – Did Jan 10 '17 at 0:02
• – Remi.b Feb 4 '17 at 14:03