Discrete Population Growth Lab Report Example | Topics and Well Written Essays - 500 words - 1

Discrete Population Growth - Lab Report Exampley, during a period of an extremely populous generation resources are brought to scarcity and life and reproduction are made harder for individuals, leading to a decline in nation numbers. These ideas are well reflected by modeling the situation with a function assuming low set on both ends of the range of argument, and high values in and around its center.The equation below is a simple example of this kind of model, using a multivariate parameter k to account for variable reproductive strength of different species and/or a given species in different environments. The equation predicts the size of (n+1)-th population pn+1 as a measuring stick considered dependent only on the size of n-th population pnUsing the program Grapher by R. Decker, the first 100 terms of the sequence generated by equation 1 were generated and plan for several initial situations characterized by different combinations of p0 and k. Graphs in visits 1 to 4 show four situations combining the values of 0.5 and 0.8 for p0 and 1.5 and 2.5 for k. The graphs make clear the sequence converges quite a quickly under these conditions. The limit values are 0.33 for k = 1.5 and 0.6 for k = 2.5, regardless of p0. This behaviour is seen for k values between 1 and 3.The graph in Figure 5 is different in that there are two values between which the population numbers keep alternating. The graph has been produced for values k = 3.2, p0 = 0.5. Experimenting with the program proved such behaviour is characteristic for values of k between 3.0 and 3.4 (see also Figure 6).For values of k exceeding 3.4, the lines observed in Figure 5 become increasingly split or blurred (see Figures 7 and 8) until k = 3.6, where the alternating course of the sequence gives way to chaotic behaviour (see Figures 9, 10, 11 and 12). In this range, changing the value of k by only 0.001 has profound impact on the sequence terms (compare Figures 9 and 10, and Figures 11 and 12).Figur e 12, produced for k = 4.0, reveals an