l seeking to invade that area. Regular dispersion patterns can also be observed in plants. Random patterns can be found in a variety of organisms (trout in lake or maple trees in a forest). Regardless of which organisms, the number of births almost always has the potential to be greater than the number of deaths. In other words populations of all species have the capacity to grow. That property is crucial importance to the success of all species. However, all species will not increase under all circumstance, but instead they can, given appropriate conditions. There are two models of population growth: the exponential model and the logistic model. One of the most basic models of population biology is the exponential growth equation, which is: )N/)t = rmaxN This equation states that, in a growing population, the rate of change in population size is determined by the maximal intrinsic rate of increase (rmax) multiplied by the number of individuals in that population (N). If a population growth very quickly we called that an exponential increase and its growth curve has a J-chaped called J-chaped curve. A population cannot continue to grow indefinitely because this equation contains additional term called the carrying capacity (K) which is not fixed, but carrying capacity is constantly affected by many factors, both biotic (living) and abiotic (non-living). The logistic population growth predicts that populations will grow rapidly at first. However, as the number of individuals in the population (N) approaches the carrying capacity (K), the population growth rate eventually slows to zero, and the population stabilize at K. The result is a sigmoidal or S-shaped curve which is often divided into three phases: the first is called the lag phase (the period of slow growth that occurs when population numbers are low). The second is the log phase, which occurs when growth rate accelerates and becomes relatively rapid. The third is the saturation p...
