Evolution involves two processes working in tandem:

1. Mutation, where organisms change randomly.
2. Selection, where organisms survive based on fitness.

There are broadly speaking two strategies for dealing with this reality:

1. Quantity (r-selection): produce many offspring, each with low probability of survival.
2. Quality (K-selection): invest more in fewer offspring, each with higher probability of survival and a longer lifespan.

$$\frac{dN}{dt} = rN(1-\frac{N}{K})$$

where N is the population, r is the maximum growth rate, K is the carrying capacity of the local environment, and dN/dt, the derivative of N with respect to time t, is the rate of change in population with time.