Past exam of the short options course of the University of Oxford / 2023 / 9 / a / i / Solution

The terms $r_i{N}_i$ give intrinsic per-capita population growth. The terms $-r_i{N}_i^2/K_i$ model intraspecific crowding in a logistic equation, while $-r_i{b}_{ij}{N}_i{N}_j/K_i$ model interspecific competition. Here $K_i$ is the single-species carrying capacity, and $b_{ij}$ measures the competitive effect of one unit of species $j$ relative to one unit of species $i$ in that species' crowding term. The last term $-\delta N_2$ is per-capita removal of grey squirrels: constant effort, rather than a constant number removed per unit time.

The intrinsic rates $r_1,r_2$ and removal rate $\delta$ have units of inverse time. The capacities $K_1,K_2$ have the same density units as the respective $N_i$; with both densities expressed in the same units, $b_{12},b_{21}$ are dimensionless. The two equations form a Competitive Lotka-Volterra model with density regulation and harvesting.