One such example which represents two interacting populations is the predator-prey model that was independently developed by mathematicians Alfred J. Sophisticated models of population dynamics include variables representing real-world interactions between distinct populations. By incorporating a carrying capacity that represents the limiting resources of a population, logistic models consider a more realistic relationship between an organism and its environment. As the population nears its carrying capacity, its growth begins to decrease, until the number of individuals reaches or briefly exceeds carrying capacity and subsequently maintains a size near carrying capacity. Therefore, the growth rate of the logistic growth is variable as opposed to the constant growth rate of the exponential model. Populations of many species follow a logistic growth pattern, where the growth rate of the population is dependent on its current size.

Natural populations may exceed carrying capacity only briefly, before the lack of resources leads to increased death rates and/or decreased reproduction. When more individuals exist in an area than the area can support, the carrying capacity is said to be exceeded. The maximum number of individuals in a population that can be supported based on the resources in the environment is known as the carrying capacity ( K). Geometric or exponential growth cannot go on forever, as eventually resources like food or space will be exhausted, and organisms begin to die more quickly or slow reproduction. For instance, Escherichia coli can double its population in approximately 20 minutes, whereas the rate for Syntrophobacter fumaroxidans is 140 hours 2. Some bacteria can grow and divide very rapidly, and thus would be able to reach large population numbers relatively quickly. At this rate it would only take 23 generations to produce over a million offspring from 2 initial offspring under exponential growth. With a growth rate of 0.05, 5% of individuals produce one offspring in the next generation. Exponential Growthįor a population that follows an exponential growth pattern, population ecologists can estimate the number of individuals in the next generation based on the size of the initial population and the growth rate, which represents the proportion of new offspring produced per individual for each generation. For example, under optimal growing conditions, bacteria follow an exponential growth pattern, with each organism producing two additional reproducing organisms in the next generation 1. Geometric or exponential growth can only occur when resources are readily available and in unlimited supply. However, logistic growth models are density-dependent, therefore the growth rate of the population is dependent on how many individuals are currently in the population. Exponential population models are density-independent, meaning that per capita birth rates and death rates will remain constant regardless of how many individuals are in the population, therefore these populations increase to infinity. Two simple models of population growth are exponential (geometric) growth models and logistic growth models. Population ecologists build models to predict how the size of populations will change over time. If the opposite is true and the death rate is greater than the birth rate, the population is in decline and if it continues to decrease it will eventually go extinct. That is, more offspring are being produced than individuals are dying.

A population grows when its birth rate is greater than its death rate. A particularly important feature that is studied by ecologists is the rate at which a population grows or declines. Population ecology is the study of how population size and age distribution change over time through interactions with other species and the environment as well as with individuals of their own species. To persist, a population must either grow or maintain its size. An ecological population is a group of individuals of a single species living in an area at the same time.

Predator population vs prey population