A unit of Lasting Forests Sustained forests; sustained profits evolving since March 30, 1999

Let us suppose there is no such thing as a "population." There is not; a population is a mental construct, an abstraction. This is a difficult supposition because the word and concept is such a part of what wildlifers and deer managers know and talk about. Nevertheless, at least temporarily, let us suppose. Wellington (1965:179) said that D. Chitty and he discovered they were both dissatisfied with current population theories and "...disturbed by the tendency of ecologists to treat the populations with which they worked as though they were monolithic structures, instead of collections of individuals."

What is left after "population" is temporarily laid aside a bunch of individual animals, a concrete, observable, bounded entity that almost all rational observers will see similarly. An animal is hardly an abstraction! (Some will debate whether the air in the lungs or moisture in the nasal passage is part of the animal or part of the environment and the difficult question of whether another interior organism is a parasite, mutualist, or ... etc. The boundary problem is real for all systems.)

By attempting to emphasize and to work with the individual animal, it may be possible to avoid some ambiguities and semantic battles waged among "population" and "community" theorists. I shall shift from the individual to the population and back again in order to remain at a relatively realistic level, one that is both observable and testable, and to see if we can push the topic of faunal systems management to its most fundamental, yet realistic level. There is convenience and teaching ease in using population concepts and I shall return to them and use them for those reasons. The other reasons for using population concepts rather than summations of individual existence or their condition now begin to be passe. We now have the computer; previously we had to lump animals together as the population.

The animal is a system. The animal is observed or "given." An animal must occupy three-dimensional space (x,y,z) and it will be observed at an instant t of time or some period (t to t+n). Thus, a fundamental animal can be symbolized as

a_{x y z t}.

The reason why populations have been so passionately sought (and part of the reason lost in the passion) is that the seeker wanted to know the probability of an organism being in some state or condition. The question may simply be "will the animal be here tomorrow?" Rephrased: what is the probability that animal a observed at xyz at time t will be at xyz tomorrow at t + 24? The options are that it may have migrated, a yes/no condition (to where it may have gone is not specified or required), or died (existing in place xyz as carcass of a, no longer a; or moved by a predator).

The question may have been "what is the sex ratio?" and this may be rephrased as "what is the probability of any observed animal a being female." The sex ratio became interesting, of itself, and the reason for seeking it lost. An animal in the trap being examined is certainly a male. No probability question is involved here except at another level, i.e., the goodness of the sex-determination criteria (surprisingly limited in many fauna) and the knowledge and bias of the observer.

The individual becomes:

a _{p q r s x y z t}

where p is the sex; q is the age class or state; r, a dominance, behavioral, or health coefficient; s, a pregnancy coefficient (including zero); xyz, location in space; and t, time. the pqr state determines weight and many rate phenomena (e.g., the probability of moving to the next age class).

Increasingly, I believe that most concepts of population structure and dynamics may (and should) be expressed as the probability of an individual animal existing and, if so, then performing as part of a system.

This point of view suggests looking at many animals, then drawing from those observations, conclusions about an animal. Never certain (that is, having a probability of 1.0) about anything, the faunal system managers nevertheless can proceed to relate to the animal. They must know the animal intimately; they must know many animals in order to draw conclusions or make predictions about any animal.

Averages are used, but in many cases the average animals, some deer, does not exist. I prefer as part of future studies and computer work to concentrate on, or at least emphasize, that the expression is "the probability of condition X" or "the probability of state Y" or "the probability of maximum efficiency." This is not a new formulation by any means, but an emphasis believed to clarify some issues, make certain ideas more easily handled than in the past, and allow the harvest of many ideas and algorithms from fields of science already extensively using probability. In addition, it happens that many animal population phenomena are not normally (bell-shape) distributed. They are highly skewed, so the average or mean statistic may be misleading. Maxima, minima, upper and lower confidence bands, and medians are often the best statistics for expressing deer and things probably affecting them.

This Web site is maintained by R. H. Giles, Jr.
Last revision January 17, 2000.