end of the 18th and beginning of 19th century. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model. According to Malthus, assuming that the conditions (the environment) remain constant (ceteris paribus), a population will grow (or decline) exponentially. This principle provided the basis for the subsequent predictive theories, such as the demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic model. A more general model formulation was proposed by F. J. Richards in 1959, further expanded by Simon Hopkins, in which the models of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation. The Lotka–Volterra predator-prey equations are another famous example, as well as the alternative Arditi–Ginzburg equations. Exponential vs. Logistic Growth When describing growth models, there are two types of models that can be used: exponential and logistic. When the per capita rate of increase takes the same positive value regardless of population size, then it shows exponential growth. When the per capita rate of increase decreases as the population increases towards a maximum limit, then the graph shows logistic growth. Fisheries and wildlife management In fisheries and wildlife management, population is affected by three dynamic rate functions. Natality or birth rate, often recruitment, which means reaching a certain size or reproductive stage. Usually refers to the age a fish can be caught and counted in nets. Population growth rate, which measures the growth of individuals in size and length. More important in fisheries, where population is often measured in biomass. Mortality, which includes harvest mortality and natural mortality. Natural mortality includes non-human predation, disease and old age. If N1 is the number of individuals at time 1 then where N0 is the number of individuals at time 0, B is the number of individuals born, D the number that died, I the number that immigrated, and E the number that emigrated between time 0 and time 1. If we measure these rates over many time intervals, we can determine how a population's density changes over time. Immigration and emigration are present, but are usually not measured. All of these are measured to determine the harvestable surplus, which is the number of individuals that can be harvested from a population without affecting long-term population stability or