Suppose that for a change in time d t and change in age d a , the population density is: n ( t + d t , a + d a ) = [ 1 − − m ( a ) d t ] n ( t , a ) That is, during a time period d t the population density decreases by a percentage m ( a ) d t . Taking a Taylor series expansion to order d t gives us that: n ( t + d t , a + d a ) ≈ ≈ n ( t , a ) + ∂ ∂ n ∂ ∂ t d t + ∂ ∂ n ∂ ∂ a d a We know that d a / d t = 1 , since the change of age with time is 1. Therefore, after collecting terms, we must have that: ∂ ∂ n ∂ ∂ t + ∂ ∂ n ∂ ∂ a = − − m ( a ) n