The Lotka-Volterra predator-prey model

Optimal strategy maximizing bacterial fitness
Fitness= per capita bacterial population growth rate i.e.,
1
C
dC
dt = µ 1S 1
u 1 + µ 2S 2
u 2 ↦→ max
K 1 + S 1 K 2 + S 2 u i
The optimal strategy:
µ 1 S 1
K 1 + S 1
> µ 2S 2
K 2 + S 2
=⇒ u 1 = 1
µ 1 S 1
K 1 + S 1
< µ 2S 2
K 2 + S 2
=⇒ u 1 = 0