Statement
Age distribution is an important population characteristic which influences both natality and mortality. Mortality usually varies with age, and reproduction is quite often restricted to certain age groups, for example, the middle age groups in the higher animals and plants. Consequently, the ratio of the various age groups in a population determines the current reproductive status of the pop- ulation and indicates what may be expected in the future. Usually a rapidly expanding population will contain a large proportion of young individuals, a stationary populatio a more even distribu- tion of age classes, and a declining population a large proportion of old individuals. However, a population may pass through changes in age structure without changing in size. There is evi- dence that populations have a "normal" or stable age distribution toward which actual age distributions are tending. Once a stable age distribution is achieved, unusual increases in natality or mor- tality result in temporary changes, with spontaneous return to the stable situation.
Explanation
In so far as the population is concerned, there are three eco- logical ages, which have been listed by Bodenheimer (1938) as prereproductive, reproductive, and postreproductive. The relative duration of these ages in proportion to the life span varies greatly with different organisms. In modern man, the three "ages" are
172 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CH. 6 relatively equal in length, about a third of his life falling in each class. Primitive man, by comparison, had a much shorter post- reproductive period. Many plants and animals have a very long prereproductive period. Some animals, notably insects, have ex- tremely long prereproductive periods, a very short reproductive period, and no postreproductive period. The May fly (or Ephe- meridae) and the seventeen-year locust are classic examples. The former requires from one to several years to develop in the larval stage in the water and lives but a few days as an adult; the latter has an extremely long developmental history (not necessarily seventeen years, however), with adult life lasting less than a single season. It is obvious, therefore, that the duration of the ecological ages needs to be considered in interpreting data on age distribution.
Lotka (1925) has shown on theoretical grounds that a popula- tion tends to develop a stable age distribution, that is, a more or less constant proportion of individuals of different ages, and that if this stable situation is disrupted by temporary changes in the environment or by temporary influx from or egress to another population, the age distribution will tend to return to the pre- vious situation upon restoration of normal condi.tions. More per- manent changes, of course, would result in development of a new stable distribution. A direct quotation from Lotka is perhaps the best way to clarify the important concept of stable age distribu- tion: " ... the force of mortality varies very decidedly with age, and it might therefore be supposed that any discussion of the rate of increase of a population of organisms must fully take into account the age distribution. This supposition, however, involves an assumption, namely, the assumption that age distribution itself is variable. Now in pOint of fact, age distribution is indeed vari- able, but only within certain restricted limits. Certain age dis- tributions will practically never occur, and if by arbitrary inter- ference or by a catastrophe of nature, some altogether unusual form were impressed upon the age distribution of an isolated pop- ulation, the irregularities would tend shortly to become smoothed over. There is, in fact, a certain stable type of age distribution about which the actual age distribution varies and toward which it returns if through any agency disturbed therefrom. The form of this distribution in an isolated population (i.e., with immigration and emigration negligible) is eaSily deduced. . . ." The mathe- matical proof of this parameter and the method of calculating the
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §6 173
theoretical stable age distribution is beyond the scope of this presentation (see Lotka, 1925, Chapter IX, pages 110-115).
Suffice it to say that life-table data and knowledge of the specilic growth rate (see Sections 2 and 7) are needed to determine the stable age distribution.
The idea of a stable age distribution is an important one. Again, as in the caSe of the maximum natality constant, it furnishes a base for evaluating actual age distributions as they may occur. It is one mare constant that may help us untangle the seemingly bewilder- ing array of variables that occur in nature. The whole theory of a population, of course, is that it is a real biological unit with definite biological constants and definite limits to variations that may occur around or away from these constants.
Examples
A convenient way to picture age distribution in a population is to arrange the data in the form of a polygon or age pYTamid (not to be confused with the ecological pyramids discussed in Chapter 3), the number of individuals or the percentage in the different age classes being shown by the relative widths of successive hori- zontal bars. The upper pyramids in Figure 45 illustrate three hypo- thetical cases: (left) a pyramid with broad base, indicating a high percentage of young individuals; (middle) a bell-shaped polygon, indicating a moderate proportion of young to old; and (right) an urn-shaped figure, indicating a low percentage of young individ- uals. The latter would generally be characteristic of a senile or declining population. The other pyramids in Figure 45 are based on actual and theoretical populations. Those in the middle of the figure show age distribution of a population of meadow voles (left) under conditions of maximum rate of population increase with a stable age distribution, and (right) same population with natality equaling mortality and rate of increase equaling zero.
The rapidly growing population has the much greater proportion of young individuals.
In many warm-blooded vertebrates often only two age classes can be distinguished during the non-breeding season-immatures and adults. Even so, age-distribution data are instructive. In game and fur-bearing vertebrates, the ratio of first year animals to older animals determined during the season of harvest (fall or winter) may aid in estimating natality and survival of young from the previous breeding season and thus provide an index to the popu-
174
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BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: ClIo 6
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Figure 45. Age pyramids. Upper: Three types of age pyramids repre- senting a large, moderate, and small percentage of young individuals in the population. Middle: Age pyramids for laboratory populations of the vole, Microtus agrestis, (left) when expanding at an exponential rate in an unlimited environment, and (right) when birth rates and death rates are equal (data from Leslie and Ransom, 1940). Lower: Extremes in juvenile- adult ratios in pheasants in North Dakota (data from Kimball, 1948) and in muskrats in eastern United States (data from Petrides, 1950).
lation trends. The diagrams at the lower left in Figw-e 45 show the age distribution of ring-necked pheasants in the Dakotas for two specific years. In 1945 the pheasant population was declining.
Since adult mortality was not known to have been excessive, the low proportion of juveniles definitely indicated a poor production andlor survival of young hatched dw-ing the preceding breeding season. In 1947, the ratio of juvenile birds was much higher. If the latter pattern continued and adult mortality did not increase, it
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §6 175
would be safe to predict a rising population level. The diagrams at the lower right in Figure 45 show the highest and lowest ratio of immature to adult muskrats found in studies of 14 different populations scattered in seven states and representing a span of years (data from Petrides, 1950). Thus we see that muskrat popu-
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Figure 46. Age distribution in the commercial catch of herring in the North Sea between 1907 and 1919. The 1904 year class was very large and dOminated the population for many years. (After HjOrt, 1926.)
176 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: ClI. 6
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Figure 47. Age pyramids for man in two localities in Scotland. Series at the left is for a parish with top-heavy age structure by 1931 in a deteriorated habitat. Series at right is for a population in a somewhat healthier environ- ment. Age classes have been reduced to percentage of total population, with males represented at left and females at right of each pyramid. (After Darling, 1951.)
lations at season of trapping varied from 52 to 85 per cent young of the year. The highest figure, 85 per cent, occurred in a popula- tion which had been heavily trapped for the previous few years;
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §7 177
reduction in total population in this manner had apparently re- sulted in increased natality for those individuals surviving. Thus, as Latka would say, tlle population was "spontaneously" returning to a more stable age distribution which would presumedly lie somewhere between the extremes shown.
Fish are good forms for the study of age distribution, because the age of individuals can often be determined from growth rings on the scaks or other hard parts. For the herring of the North Sea it has been determined that the scale method is reliable. Figure 46 shows the percentage of the total commercial catch of herring belonging to different year classes (horizontal axis) for a series of years (from Hjort, 1926). Since young fish are not taken in the commercial nets, only fish older than 5 or 6 years are adequately sampled. Despite the fact that the number of young fish was not known, it is evident from the graph that there was an extremely successful hatch and survival in 1904. Fish of this year dominated the population until 1918 when, at 14 years old, they still out- numbered fish in younger age groupsl This phenomenon of a
"dominant age class" has been repeatedly observed in fish popu- lations which have a very high potential natality rate. When a large year class occurs, reproduction is suppressed for the next several years. Fishery ecologists are currently trying to find out what environmental conditions result in the unusual survival which occurs every now and then.
As final examples, Figure 47 shows a series of interesting age pyramids for human populations in two localities in Scotland. Both populations in 1861 were young and vigorous, and by 1901 they had assumed an age distribution of a stationary population. By 1931 one population had assumed a top-heavy age structure (rela- tively few children, large proportion of old people) as a result of a deteriorated habitat. These figures are interesting, also, in that they show how sex distribution can be pictured along with age distribution.
7. Optimum rates of natural increase and concept of biotic potential and environmental resistance Statement
When the environment is unlimited (space, food, other organ- isms not exerting a limiting effect), the per cent growth rate (i.e., the population growth rate per individual) becomes constant and
178 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: ClI. 6 maximum for the eXisting microclimatic conditions. The value of the growth rate under these favorable population conditions is maximal, is characteristic of a particular population age structure, and is a single index of the inherent power of a population to grow.
It may be designated by the symbol r, which is the exponent in the equation for population growth in an unlimited environment under speCified physical conditions:
AN
AN At
-rN' r - -
At - , -
N(in an unlimited environment)
for short intervals of time, or for cumulative effects over longer periods of time fthe exponential integrated form follows auto- matically from the short time rate form by calculus manipulation) :
No represents the number at time zero, Nt the number at time t and e the base of natural logarithms. The index r is actually the difference between the instantaneous specific natality rate (Le., rate per time per individual) and the instantaneous specific death rate, and may thus be simply expressed:
r=b-d
The overall population growth rate under unlimited enviromnental conditions (,.) depends on the age composition and the specific growth rates due to reproduction of component age groups. Thus, there may be several values of r for a species depending upon population structure. When a stationary and stable age distribu- tion exists, the specific growth rate is called the intrinsic rate of natural increase or rio The maximum value of r is often called by the less specific but widely used expression biotic potential, or reproductive potential. The difference between the maximum r or biotic potential and the rate of increase which occurs in an actual laboratory or field condition is often taken as a measure of the environmental resistance, which is the sum total of environ- mental limiting factors which prevent the biotic potential from being realized.
Explanation
We have now come to the point where we wish to put together natality, mortality, and age distribution-each important but each
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §7 179
admittedly incapable of telling us very much by itself-and corne out with what we really want to know, namely, how is the popula- tion growing as a whole and what would it do if conditions were different, and what is its best possible performance against which we may judge its everyday performances? Chapman (1928) pro- posed the term biotic potential to deSignate maximum reproduc- tive power. He defined it as "the inherent property of an organism to reproduce, to survive, i.e., to increase in numbers. It is sort of the algebraic sum of the number of young produced at each repro- duction, the number of reproductions in a given period of time, the sex ratio and their general ability to survive under given physical conditions." The concept of biotic potential, or reproductive po- tential, suggested by some as more descriptive (see Graham, 1952), has gained wide usage. However, as might be imagined from the very generalized definition given above, biotic potential came to mean different things to different people. To some it came to mean a sort of nebulous reproductive power lurking in the population, terrible to behold, but fortunately never allowed to corne forth because of the forthright action of the environment (i.e., "if unchecked the descendants of a pair of flies would weigh more than the emth in a few years"). To others it came to mean simply and more concretely the maximum number of eggs, seeds, spores, etc., the most fecund individual was known to produce, despite the fact that this would have little meaning in the popula- tion sense in most cases, since most populations do not contain in- dividuals all of which are continually capable of peak production.
It remained for Lotka (1925), Dublin and Lotka (1925), Leslie and Ranson (1940), Birch (1948), and others to translate the rather broad idea of biotic potential into mathematical terms that can be understood in any language (with, sometimes, the help of a good mathematician I). Birch (1948) expressed it well when he said: "If the 'biotic potential' of Chapman is to be given quanti- tative expression in a single index, the parameter r! would seem to be the best measure to adopt since it gives the intrinsic capacity of the animal to increase in an unlimited environment."
At this point the reader may well raise the question: How can there possibly be a Single index to reproductive potential when natality and mortality vary so much with different-age individ- uals? The single index concept stands or falls on two assumptions, (1) that average natality and mortality remain the same for any
180 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: ClI. 6 specific age group when environmental conditions are optimum, and (2) that a population with constant age schedules of natality and mortality in an unlimited environment assumes a fixed age distribution, as was explained in the previous section. At the moment these assumptions seem well grounded, so, until someone proves them wrong, we may play with the intriguing idea of a single index representing the inherent power of increase and the ultimate biotic potential.
The question that now arises is: What kind of data do we need to work out sueh an index as l' or 1';, and can we apply this concept to natural populations, or is it only good for highly Simplified labo- ratory populations? Although natural populations must be ap- proached with caution, if we can estimate natality, the essential data needed to calculate l' are found in the life table. As we have seen, at least approximate life tables may be constructed for such very wild populations as mountain sheep living in rugged Alaska country.
Environmental resistance is another very useful concept first proposed by Chapman. It represents the difference between the potential ability of a population to increase and the actual ob- served performance. If the biotic potential can be nailed down as a specific quantity, then differences between biotic potential or maximum l' and the observed rate of increase could be considered a measure of the environmental resistance, since failure of the population to measure up would be the result of non-optimum factors in the environment decreaSing natality or increasing mor- tality somewhere along the line. In terms of our models, environ- mental resistance can be indicated by adding limiting factors to the exponential growth equation. When a population is stationary or is oscillating back and forth around a mean size, nataHty rate equals mOltality on the average, and the specific growth rate is zero.
In tenns of the growth curves discussed in Section 3, the spe- cific growth rate (t:.N IN t:.t) may be obtained graphically when population growth is exponential. If growth is plotted as loga- rithms or on semi-logarithmic paper, the log of population number plotted against time will give a straight line if growth is exponen- tial; l' is the slope of this line. The unlimited specific growth rate is selected as a measme for comparing populations because it has been observed many times in a variety of organisms that popula-
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §7 181 tions exhibit logarithmic growth at least for a time when there is ample food and no crowding effects, enemies, etc. Under such con- ditions the population as a whole is expanding at a terrific rate even though each organism is reproducing at the same rate as before, i.e., the specific growth rate is constant. Many other phe- nomena such as absorption of light, monomolecular chemical re- actions, and compound interest behave in the same manner.
It is obvious that this unlimited rate of increase cannot continue indefinitely; often it is never realized. The role of environmental resistance in shaping population growt1] form will be considered next.
Examples
Table 14 gives the unlimited rate of natural increase for two insects, two rodents, and man. The values for the rodents and for the insects at 29° C are presumed to be "maximum r" (biotic potential), since populations on which calculations were based
Table 14. Unlimited rate of natural increase of cel·tain species of insects, rodents and man
Finite rme (er ): number r, or instantaneous tim.es population would
rate per female nwltiply in
Organism and conditioll week year week year
Calandral (rice weevil) at optimum
temp. 29· C 0.76 39.6 2.14 1.58 X 10)0
Caland1'al at 23· C 0.43 22.4 1.54 5.34 X 108
Caiandral at 33.5· C 0.12 6.2 1.13 493
Tribolium castaneum2 (Bour beetle) at 28.5·C and 65 per cent relative
humidity 0.71 36.8 2.03 1.06 X 1015
Microtus agrestis3 (English vole)4
optimum laboratory 0.088 4.5 1.09 90
Rattus llorvegicus5 (brown rat) op-
timum laboratory 0.104 5.4 1.11 221
Man,6 white population USA in
1920 0.0055 1.0055
1 From Birch (1948).
2 From Leslie and Park (1949).
a From Leslie and Ranson (1940).
4 Fro~ data presented by Hamilton (1937), it seems likely that the American vole, MIcrotus pell11Sylvlmictls, has a higher biotic potential than its English counler- part, although the value of maximum r has not been Ca !<.:ula ted.
n From Leslie (1945).
6 From Dublin and Latka (1925).