The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. The equation for a diallelic gene is:
$$p^2 + 2pq + q^2 = 1$$
In population ecology, the logistic model describes how a population grows exponentially at first, but slows as it reaches the carrying capacity of its environment:
$$\frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right)$$