Malthus’ law

One sees that N approaches 1/)S as r -> oo. Equation (29) is a more realistic form than Malthus law, since there is now a stationary phase following exponential growth. 

Clearly the foregoing result is better than that obtained from Malthus law. However, any model such as Eq. (23) or (24) is suspect because it does not account for the effect of environment on growth, or the reciprocal effect of growth on environment this will be considered shortly. Also experimental data exist which cannot be reconciled with such models. Finn and Wilson (F2), in a study of the continuous propagation of yeast, found that under certain conditions there did not appear to be any steady state rather, the population density oscillated about some mean value, with a well-defined frequency. This brings the question of stability into the discussion we will show that Eq. (23) is incompatible with the existence of the phenomenon observed by Finn and Wilson. 

Models of population growth are analogous to chemical reaction rate equations. In the model developed by Malthus in 1798, the rate of change of the population N of Earth is dN/dt = births — deaths. The numbers of births and deaths are proportional to the population, with proportionality constants b and d. Derive the integrated rate law for population change. How well does it fit the approximate data for the population of Earth over time given below ... 

Malthus further argued, The race of plants and the race of animals shrink imder this great restrictive law. And the race of man cannot, by any efforts of reason, escape from it. Among plants and animals its effects are waste of seed, sickness, and premature death. Among mankind, misery and vice. How then has the world for 200 years stayed the prediction of Malthus ... 

---