A biological population is a dynamic and variable entity which changes its age-distribution and variety of individuals with time. It is not a static and invariable pool of items from which sample data is extracted, as is often conveniently assumed by statistical analysis simplification procedures. With respect to the ecological concept of a 'population'... as being a group of individuals of a species inhabiting a given area... there are various numerical parameters that could be considered which would lead to the possibility of symbolizing the situation with some form of mathematical analysis. Obtain some ratio data of numbers with respect to area... for various phases and circumstances of the population... and then decisions could be made as to what values might be construed as being indicative of states of 'underpopulation', 'stability', 'overpopulation' etc. This 'simplification' however would not adequately account for the physical size of the individuals in a population. A small lagoon could be seriously overpopulated by a couple of whales but underpopulated with only a few hundred sea horses. The area at the top of a thin bamboo pole is definitely overpopulated by just one fantail but perhaps not by thousands of bacteria. Same area... overpopulation by one species and underpopulation by another. At the very least therefore, it would be necessary to establish some sort of 'average range' that a particular species tends to occupy and is able to go thru its various phases of development. For some species... like whales and fantails... the average range might be appropriately expressed in units of area, but for others... like sea horses or bacteria... units of volume might make more biological sense. For the most part, the numbers of a biological population will increase or decrease according to the capacity of the species to reproduce individuals... that is to say...to avoid being eaten and to participate in the production of progeny. In many populations however, not all the individual members will have the ability to procreate. Some will be too immature, some will be too old, and some will be either infertile or disinclined. Humans, various social mammals, bees and ants all exhibit age and role differentiation as a developmental characteristic. In fact, if numbers in a specific range can also vary by individuals leaving or by 'foreigners' being integrated, certain exceptional populations like prisons, labour-camps and gold-rush settlements can have a life-cycle without any reproductive capacity whatsoever. As well as the above of course, the chaotic vicissitudes of environment... floods, predation, climate change, food supply, antibiotics, etc... will have a dramatic influence on growth or decline of species numbers in a particular region. Mathematical models, which attempt to describe any numerical patterns in any of the above factors, need to be very sophisticated to adequately account for the life cycle of a population and such simplifications as logistic growth, predator prey differential equations, island biogeography and so on, only manage at best to approximate some parameter or aspect at a particular phase.

Every population is an identifiable entity... just as is a star, continent, weather system, animal, species, empire, economy, institution or artefact... and will have its own unique developmental dynamics that has a life-cycle with a beginning and an end. Determining the 'beginning' or 'end' of a population... whether it is of stars or cephalapods... is no easier than it is for any other entity. Whilst it may seem plausibly obvious that the beginning of a biological population needs the presence of at least one parthenogenetic individual or a pair of sexually active ones... and that the end of a population is indicated by the absence of any individuals... such conditions cannot be universal. Many biological populations are not necessarily sustainable until numbers in excess of one or two are attained, because a level of social cooperation and role distribution may be essential before the numbers of individuals begins to increase. The 'end' of a biological population may similarly be quite difficult to ascertain because although several non-fertile individuals of a previously viable population still remain, never-the-less for all practical purposes it has ceased to exist. The various population types will usually have typically patterned life-cycle phases. One might expect to be able to recognize a 'growth' phase, a 'maturity' phase and and an 'ageing' phase for example... as appears to happen in certain pathogenic microbial invasions, some social insect species and human gold rush exploitation episodes. It also needs to be remembered that populations evolve and diversify within an evolutionary continuity and so beginnings and endings may have very different timescales. Certain bacteria may have populated specific terrestrial regions for aeons, a population of Homo neanderthalis may have only inhabited an area for a few hundreds of years and a virus population may invade a human body and pass thru its entire life cycle in just a few hours.

Because of the essential evolutionary reality of predation and the existential limitation of physical resources, any biological population expansion or contraction will influence associated ecological populations. Populations interact with a variety of other populations... of both the same and different species... by means of such processes as 'competition', 'predation', 'exploitation', 'habitat destruction', and so on. The explosion of one population will provide the opportunity for predator and parasitic exploitation species to also increase... so that for example, a human population expansion will also provoke parallel expansions of cultivated agricultural plants, domestic animals, dogs, cats, mice, flies, and all the multitude of bacteria and viruses that use them as a resource. Similarly, the extinction of one species... like the moa... put pressure on its giant predatory eagle, which may well have been the main factor in the extinction of that creature as well. The ecology of populations is so chaotically complex that statements about 'overpopulation' will not be very significant if narrow simplification perspectives are adopted.

Any statements made about populations are made by humans and are thus anthropocentric by definition. Because the various social and political groupings of humans impose different simplifications on their perception of existence, evaluation statements about populations are thus uncompromisingly biased towards those perspectives of self-interest. The diverse 'scientific', 'economic', 'political', 'palaeontological' , 'ecological' or 'religious' perspectives are each bounded by their own self-imposed limitations which usually ensures the exclusion of the essential considerations of the others. The same totality (of humans say) might be evaluated as an 'underpopulation' by a religious sect that glorified the expansion of god's creation, as an ideal 'optimum population' by a political and economic perspective that aimed to facilitate industrial growth, and as an 'overpopulation' by an ecological point of view that had concluded that the numbers had exceeded the carrying capacity of its ecological niche. The different perspectives are so entrenched within the human social groupings, that any consensus evaluation about populations is virtually impossibly improbable. Suppose the idea of a 'null hypothesis' was borrowed from stochastic mathematics. Suppose that the null hypothesis 'human numbers are in excess of a balanced natural diversity' was proposed to the entire human population. The intransigent and incompatable perspectives intrinsic to the human species will ensure that such a hypothesis will never be either accepted or rejected. Each sector will continue to reject any factors and evidence which are promoted by the other sectors. Humans have evolved is such a manner that greed and self-interest is a dominant genetic component and the relatively few individuals who are prepared to accept a 'cosmic' perspective will have little capacity to compensate for the aspirations of the exploiters. Although ecology and evolution relies upon diversity, such an appreciation is neither present in the awareness, nor deemed to be existentially relevant to the great majority of individuals who are entirely absorbed by the intricacies of human society. The concept of human 'overpopulation' is irrelevant to the majority of the species.

Some biological populations have acquired sophisticated strategies to control their numbers... both up and down... to accord and integrate with the realities of their environmental circumstances. It is certainly possible therefore, that humans in particular might develop the social pressures and technological skills to modify their population numbers to be in a state of equilibrium that is appropriate to the phase of their species evolutionary cycle. The complex variety of human behaviours however, will militate against the effective implementation of any potentially effective strategy. They are clever machine makers, intelligent manipulators, greedy and murderous with respect to resources, absurdly religious and are prepared to indulge in creative speculation. They have devised sophisticated methods of exploiting energy sources but continue to deplete the finite resources of fossil fuel and the evolutionary biomass. They have several population limiting techniques at their disposal, but it will prove impossible to effectively put them into global practice, before irreversible ecological degradation has eventuated.

The stark reality however is that any anthropocentric perspective is entirely irrelevant to 'nature'. The chaotic essence of the cosmos has the capacity to invoke whatever compensatory processes are necessary in order to contain runaway positive feedback events... just as it does for algae blooms, wasp explosions, rodent plagues and nuclear chain reactions. No matter what humans think, the cosmos will react in its own manner to the diminution of its natural diversity.