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. Copyright 2001 Academic Press.