A Further Note on the Mathematical Theory of Population Growth

TIME RELATIONS OF GROWTH : III. GROWTH CONSTANTS DURING THE SELF-ACCELERATING PHASE OF GROWTH

Growth curves consist, in all cases, of two major segments. The first major segment is, in the case of higher animals and plants, made up in turn of several (probably five) shorter segments during each of which growth takes place at a constant percentage rate. The transitions between the successive stages are abrupt, the abruptness being of the order of metamorphosis in cold blooded animals. It has been made clear in the first paper of this series that the time rate of growth following the major inflection declines at a constant percentage rate. The junction between the two major segments occurs at puberty in animals and flowering in plants. The two major segments are not symmetrical about the major inflection. The slope of the segment following the inflection is always less than the slope of the segment preceding the inflection. The major inflection does not occur in the center of the growth curve. The instantaneous rate of growth at the beginning of growth is of the order of 100–200 per cent per day (i.e. the body weight is doubled in from 7 to 17 hours). It may be mentioned that 2 months after conception the rate of growth in man is only 8 per cent per day. This is contrary to all the published statements. Thus, Minot concluded that growth begins at 1000 per cent per day; Jackson concluded that in man, growth during the 1st month takes place at 57.5 million per cent per month; during the 2nd month 990 per cent per month; during the 3rd month 390 per cent per month (8 per cent per day is only 240 per cent per month). The reason for the discrepancy between the values derived, by the method adopted by the writer, and the values given in the literature is explained by Fig. 1.