Models of Population Growth

<h1>Text Preview</h1> <p>Suppose a pair of rabbits breed just once a year, producing a litter of 8 rabbits. If each new rabbit becomes mature after one year and also breeds yearly, the population of rabbits over a 10-year period would grow to 5 million. </p> <p>Theoretically, all populations can grow in this fashion, but the growth usually slows down because of environmental limitations. For example, the rabbits would run out of space, out of food, or would meet predators that would reduce the population again.</p> <p>The number of individuals an environment can support over time is called its carrying capacity. Carrying capacity is denoted by capital K.</p> <p>Let’s look at the growth of our rabbit population in graphical terms. </p> <p>If we plotted the rabbits’ population size over each generation, we’d see that the growth is exponential, producing an exponential growth curve and mathematically this looks like the graph shown here.</p> <p>The rate of population growth, or the change in population size over a given time interval, can be expressed as the number of births during the time interval minus the number of deaths. If N represents the population size and t represents the time interval, we get the differential equation:</p> <p>dN/dt = rN</p> <p>where r represents the number of births minus deaths.</p> <p>In other words, the change in population over a given time interval equals the rate of population growth multiplied by the population size.</p> <p>In an ideal population, r, the population growth rate, is always at its maximum—we call this rmax. </p> <p>We know that real populations don’t grow exponentially. If they did, the first species that ever existed would have filled the whole universe by now! So how do we model population growth more accurately?</p> <p>We need to modify our equation to incorporate changes in r as the population approaches its carrying capacity, K. . The revised equation looks like this: </p> <p>dN/dt = rmaxN(K– N)/K </p> <p>Notice that as the population size, N, gets larger, the population growth rate, r, gets smaller.</p> <p>If we set rmax at 1.0, we get a curve that looks like this. It is called a logistic growth curve. </p> <p> Logistic growth affects natural selection. At high population densities, organisms that can survive with few resources are at an advantage. These populations, in which natural selection is assisted by the carrying capacity, are called K-selected populations. At low population densities, selection favors organisms that can reproduce rapidly. These populations, in which natural selection is helped by the growth rate, are called r-selected populations.</p> <p>Now that we’ve looked at the theoretical modeling of populations, let’s look at the real-life factors that can affect the growth of populations. </p> <p id="TextCopyright">Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education</p>