V

In the matter of population growth there not only "ought to be a law" but six years of research has plainly shown that there is one. This is not the place for recondite statements in mathematical shorthand, but fortunately it is possible to state the law of population growth in plain language, without resort to mathematical symbols. It may be put in this way:

Growth occurs in cycles. Within one and the same cycle, and in a spatially limited area or universe, growth in the first half of the cycle starts slowly but the absolute increment per unit of time increases steadily until the mid-point of the cycle is reached. After that point the increment per unit of time becomes steadily smaller until the end of the cycle. In a spatially limited universe the amount of increase which occurs in any particular unit of time, at any point of the single cycle of growth, is proportional to two things, viz: (a) the absolute size already attained at the beginning of the unit interval under consideration, and (b) the amount still unused or unexpended in the given universe (or area) of actual and potential resources for the support of growth.

The latter element (b) wants a little further explaining. In the case of human population growth the unused and unexploited store of resources for subsistence will include such things as the amount of agricultural land still untilled, or not cultivated to the maximum of productivity. New discoveries of improved agricultural methods, or of chemical methods of making food synthetically, will at once increase the importance of this factor in the case. The result will be either to move up somewhat the upper limiting value of the population attainable in the current cycle of growth, or, if the potential addition is larger, to start the population off upon a new cycle of growth. Factor (b), in the case of human population may

also mean such things as the potential development of transportation, power resources, etc. In fact, it was the unexpected development of just such things as these, making possible the birth and growth of large scale industrialism, which upset Malthus's calculations as to the time when population saturation would make its effects uncomfortably felt. In the case of a simple experimental population like that of yeast cells the (b) element means practically the still unused amount of sugar and salts remaining in the given limited volume of solution in which the cells are growing. Its value can be quantitatively determined in this simple case, by chemical analysis of the solution at successive stages of the growth cycle. For obvious reasons it cannot be accurately measured in the case of human populations. In the case of the growth in size of a single individual organism, like the white rat earlier discussed, the meaning of this factor (b) is somewhat more difficult to define. It probably signifies the still remaining potentiality of the system of mutually inter-dependent cells and organs to expand in space without losing effective biological touch with each other. Just as in the case of human population it has been found possible, by appropriate procedures, to move to a higher level the upper limit to the growth in size of an individual organism within a single cycle. I refer to such matters as the influence of endocrine secretions upon growth. This, however, takes us into a large and important field of experimental biology, which cannot be discussed here.

Having got some insight into the underlying law according to which population growth occurs, and having found that this is of a sort capable of mathematical expression, we are able to approach the general problem of population along several pathways not previously open. We can, for example, upon a more adequate scientific basis than mere guess-work, predict future populations, or estimate past populations, outside the

range of known census counts. This has been done in the diagrams presented earlier. The theoretical curve which is believed to express the law of population growth has been extended, in each of the diagrams for human population, in the form of dotted lines, to the ends of the current cycle of growth. These dotted lines represent the probable future (and past) populations on the assumption, be it clearly understood, that no fundamental alteration in factor (b), as stated above in the definition of the law, occurs prior to the completion of the present cycle of growth. If such alteration does occur, then the predictions based upon the absence of such alterations during the past history of the present cycle, obviously become worthless. The whole case has to be reconsidered in the light of the changed conditions. But if no such alterations occur before the completion of the present cycle of growth, the maximum population, in this cycle, of the several countries discussed will presumably be, in round numbers, about as follows:

Undue absolute weight is not to be given these predictions. It is extremely probable, I should think, that events like scientific discoveries, military conquest, etc., will alter factors (b) for nearly or quite every country in the world during the next hundred years say. The figures really express what the probable future populations would be if the conditions of the nineteenth century were to remain permanently unaltered. For the next ten or twenty years in the future the predictions given by the curves are undoubtedly highly accurate in most cases. But longer range predictions could be taken seriously only by someone who denies the fact of any and all evolution.

CHAPTER II

THE GROWTH OF EXPERIMENTAL

POPULATIONS

OF DROSOPHILA

I

In the preceding chapter it was shown that the growth of one of the simplest populations conceivable from a biological standpoint, one made up of individuals of the unicellular plant Saccharomyces commonly called yeast, followed with remarkable exactness the logistic curve. The simplicity of the case is in respect of several particulars. In the first place the individuals composing a population of yeast are each a single cell, microscopic in size, and but little differentiated. In the second place their environment is relatively simple and homogeneous. They live in a solution, which is not merely their environing and supporting medium, but also their food. Their life is in some part what ours would be if all the food necessary for our existence were derivable from the air which surrounds us, and if this food were taken from the air by our bodies by purely chemical means, without knowledge or effort on our part. In actual fact, of course the environment of any terrestrial animal is a much more complex and heterogeneous matter than is that of the yeast. There intervenes a soilplant cycle between the animal which must have food and the inorganic world (see Lotka 157 for a detailed discussion of this and related cycles). Food has to be sought, and in the case of some animals, notably the highest, cultivated, if population is to make any considerable growth. The distance be

tween an experimental population of yeast and any human population whatever, is biologically great.

is sometimes called It is the small fly,

Let us therefore take an intermediate step and examine experimentally the growth of population in the case of a multicellular animal, much higher than yeast in the biological scale, but still a great deal lower than man. For this purpose a suitable creature is the fruit-fly, or as it the vinegar fly, Drosophila melanogaster. which looks to casual observation much like a diminutive replica of the common house fly, and is seen in swarms around decaying or fermenting fruit, or liquids like cider and vinegar made from fruit and left freely exposed to the air. Its suitability for laboratory experimentation arises from several considerations. In the first place it breeds rapidly and its life cycle is short. A female fly lays a good many eggs: under suitable conditions from 25 up to 40 or 50 a day for a period of at least 10 days. These eggs hatch in from 24 to 48 hours into little larvae or maggots, which squirm around in and feed upon the decaying vegetable material in which they are laid, for three or four days. They then seek a dry spot, settle down and transform into the next stage in which they have their being, the pupal. From each pupa emerges in about four or five days a fully formed adult fly or imago, which promptly mates and, if a female, starts laying eggs in from 12 to 24 hours. So then a whole generation, from adult (imaginal) parent to adult (imaginal) offspring occupies, on the average and under suitable conditions of food and temperature, only about 10 or 11 days.

A second advantage of Drosophila for experimentation lies in the relatively simple and easily standardized husbandry which suffices to meet its needs. The flies may be satisfactorily grown in ordinary half-pint milk bottles, stoppered with a loosely packed wad of cotton wool, like a bacterial culture