Ecology-Duckweed Population Growth Introduction Reproduction is a fundamental characteristic of living things. All organisms are capable of population growth under some set of possible conditions. Depending upon their life history, some organisms are capable of much more rapid population growth than others. Ecologists study population growth, to understand how the biology of organisms interacts with environmental conditions to produce periods of population growth, stability, and decline, and to understand the factors that ultimately limit the growth of populations. Exponential growth For a continuously reproducing population, exponential growth is an excellent firstapproximation of population growth. When resources are not limiting, and interspecific competition is at a minimum, many populations of organisms grow exponentially. This generally occur when populations are at densities far below their environmental carrying capacity (see below), although some populations, especially birds and mammals, may actually decline if densities are too low, because individuals cannot find mates or engage in other social behaviors necessary for their reproduction. This is called the Alee effect. In exponential growth models, births and deaths take place continuously. In calculus terms: DN/DT=bN-dN • Where: • b is the per capita birth rate • d is the per capita death rate This model ignores immigration and emigration for the time being. Thus: dN/dT=rN r, the instantaneous population growth rate,=b-d)

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you can integrate this to get the exponential growth formula that follows... N(t)=N0ert

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where r is the exponential growth parameter N0 is the starting population t is the time elapsed

Note: if r=0 if the population is constant, r>0 if population is increasing, r