Probabilities of Encounters between Objects in Biological Systems: Meta-observer View

Encounters between objects play a crucial role in creating specific patterns of organization in many biological systems. This paper explores a general, quantitative principle of encounter probabilities, applicable over various levels of organization, as a fundamental step toward a comprehensive theory of biological probability ranging from cells through organisms to ecological communities. Based on the cognizers-system model, a general description of encounter probabilities in a finite position space is derived as a function of the number, or density, of objects with cognitive, selectivity properties incorporated as parameters. There is a prevailing wisdom, as supposed in many scientific thoughts, that the per-unit-time number of encounters between focal and target objects is given as a linear function of the density of target objects. One result shows that this idea does not describe the real nature of encounter probabilities or rates, but only a special case or approximation of a fundamental description. The analysis also explicates conditions for ignoring the presence of non-target objects, and those for the aggregation of two or more different objects into the same type sharing the same cognitive properties in the description of the probabilities.