Fisher Information in Ecological Systems

Fisher information is being increasingly used as a tool of research into ecological systems. For example the information was shown in Chapter 7 to provide a useful diagnostic of the health of an ecology. In other applications to ecology, extreme physical information (EPI) has been used to derive the population-rate (or Lotka-Volterra) equations of ecological systems, both directly [

1

] and indirectly (Chapter 5) via the quantum Schrodinger wave equation (SWE). We next build on these results, to derive (i) an uncertainty principle (8.3) of biology, (ii) a simple decision rule (8.18) for predicting whether a given ecology is susceptible to a sudden drop in population (Section 8.1), (iii) the probability law (8.57) or (8.59) on the worldwide occurrence of the masses of living creatures from mice to elephants and beyond (Section 8.2), and (iv) the famous quarter-power laws for the attributes of biological and other systems. The latter approach uses EPI to

derive the simultaneous quarter-power behavior

of all attributes obeyed by the law, such as metabolism rate, brain size, grazing range, etc. (Section 8.3). This maximal breadth of scope is allowed by its basis in information, which of course applies to all types of quantitative data (Section 1.4.3, Chapter 1).