<P> where N is the number of individuals measured as biomass density, a is the maximum per - capita rate of change, and K is the carrying capacity of the population . The formula states that the rate of change in population size (dN / dT) is equal to growth (aN) that is limited by carrying capacity (1--N / K). </P> <P> Population ecology builds upon these introductory models to further understand demographic processes in real study populations . Commonly used types of data include life history, fecundity, and survivorship, and these are analysed using mathematical techniques such as matrix algebra . The information is used for managing wildlife stocks and setting harvest quotas . In cases where basic models are insufficient, ecologists may adopt different kinds of statistical methods, such as the Akaike information criterion, or use models that can become mathematically complex as "several competing hypotheses are simultaneously confronted with the data ." </P> <P> The concept of metapopulations was defined in 1969 as "a population of populations which go extinct locally and recolonize". Metapopulation ecology is another statistical approach that is often used in conservation research . Metapopulation models simplify the landscape into patches of varying levels of quality, and metapopulations are linked by the migratory behaviours of organisms . Animal migration is set apart from other kinds of movement; because, it involves the seasonal departure and return of individuals from a habitat . Migration is also a population - level phenomenon, as with the migration routes followed by plants as they occupied northern post-glacial environments . Plant ecologists use pollen records that accumulate and stratify in wetlands to reconstruct the timing of plant migration and dispersal relative to historic and contemporary climates . These migration routes involved an expansion of the range as plant populations expanded from one area to another . There is a larger taxonomy of movement, such as commuting, foraging, territorial behaviour, stasis, and ranging . Dispersal is usually distinguished from migration; because, it involves the one way permanent movement of individuals from their birth population into another population . </P> <P> In metapopulation terminology, migrating individuals are classed as emigrants (when they leave a region) or immigrants (when they enter a region), and sites are classed either as sources or sinks . A site is a generic term that refers to places where ecologists sample populations, such as ponds or defined sampling areas in a forest . Source patches are productive sites that generate a seasonal supply of juveniles that migrate to other patch locations . Sink patches are unproductive sites that only receive migrants; the population at the site will disappear unless rescued by an adjacent source patch or environmental conditions become more favourable . Metapopulation models examine patch dynamics over time to answer potential questions about spatial and demographic ecology . The ecology of metapopulations is a dynamic process of extinction and colonization . Small patches of lower quality (i.e., sinks) are maintained or rescued by a seasonal influx of new immigrants . A dynamic metapopulation structure evolves from year to year, where some patches are sinks in dry years and are sources when conditions are more favourable . Ecologists use a mixture of computer models and field studies to explain metapopulation structure . </P>

Who define ecology as the study of structure and function of nature