Statement
Natality is the inherent ability of a population to increase.
Natality rate is equivalent to the "birth rate" in the terminology of hwnan population study (demography); in fact, it is simply a broader telm covering the production of new individuals of any organism whether such new individuals are ''born,'' "hatched,"
"germinated," "arise by division," or what not. Maximum (some-
ORGANIZATION AT THE SPECmS POPULATION LEVEL: §4 161
times called absolute or physiological) Mtality is the theoretical maximum production of new individuals under ideal conditions (i.e., nO ecological limiting factors, reproduction being limited only by physiological factors); it is a constant for a given popula- tion. Ecological or realized natality (or just plain "natality," with- out qualifying adjective) refers to population increase under an actual or specific environmental condition. It is not a constant for a population but may vary with the size and composition of the population and the physical environmental conditions. Natality is generally expressed as a rate determined by diViding the number of new individuals produced by time (6N,,/ D.t, the absolute natal- ity rate) or as the num bel' of new individuals per unit of time per unit of population [( D.N,,/D.t )/N, the per cent natality rate].
Explanation
Natality can be measured and expressed in a number of ways. Following the notation in the preceding section we have:
D.N ... = natal-ity,-productionofnewindividttalsil1thepopttlation. (1)
6N- n = B or nata l't I y rate per umt tIme. . .
6t . (2)
6N" 1 l't . . . d"d 1
- _. = ) or nata 1 y rate per umt hme per Jl1 IV] ua .
ND.t ( 3)
N may represent the total population or only the reproductive part of the population. With higher organisms, for example, it is cus- tomary to express natality rate per female. With all the different
"kinds" of birth rates it is c1ear that confusion can easily result un- less the concept used is c1early deflned, preferably by using stand- ard mathematical notations as above. Which concept is used will depend on the available data and the type of comparisons or predictions which one wishes to make.
Although the same notations may be used in referring to natality rate and population growth rate, the two are not the same because 6.N represents somewhat different quantities in the two cases.
With respect to natality, 6N n represents new individuals added to the population. Natality rate is zero, or always positive. With re- spect to growth raite 6.N represents the net increase or decrease in the population, which is the result not only of natality but of mortality, emigration, immigration, etc. Growth rate may be either negative or positive, since the population may be either in-
162 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CH. 6 creasing or decreasing. Population growth rate will be considered in Sections 7 and 8.
Maximum natality, as indicated in the above statement, is the theoretical upper limit which the population, or the reproductive portion of the population, would be capable of producing under ideal conditions. As might be imagined, it is difficult to deter- mine but is of interest for two reasons. (1) It provides a yardstick for comparison with the realized natality. Thus, a statement that natality of a population of mice was 6 young per female per year would mean more if it was known to what extent this might be higher if conditions were less limiting. (2) Being a constant, maximum natality is useful in setting up equations to determine or to predict the rate of increase in a population, as we shall see in subsequent sections. For practical purposes maximum natality can be approximated by experimental methods. For example, the highest average seed production achieved in a series of experi.
ments with alfalfa, in which the most favorable known conditions of moisture, temperature, and fertilizer were combined, could be taken as maximum natality for that particular population. Another method of establishing a base is to observe the reproductive rate of a population when it is placed in a favorable environment, or when major limiting factors are temporarily nonoperative. If a small group of paramecia, for example, is placed in a new batch of favorable media, the maximum reproductive rate achieved would be a good measure of maximum natality rate. This method can often be used in the field, if the ecologist is alert, since in nature there are often fortuitous circumstances when limiting fac- tors are temporarily relaxed. As we shall point out later, many natural populations regularly exhibit maximum natality for brief seasonal or other periods. Reproductive performance during such favorable periods would be a practical approximation of maximum natality. Since the value of maximum natality concept lies in its use as a constant against which variable observed natalities may be compared, any reasonable estimate could be used so long as conditions under which it was made are defined.
It should be repeated that natality, and the other concepts dis- cussed in this section, refer to the population and not to isolated individuals. The average reproductive capacity should be taken as the measure of natality, and not the capacity of the most pro- ductive or least productive individual. It is well known that occa·
sional individuals in a population will exhibit unusual reproduc- tive rates, but the performance of such individuals would not be
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §4 163
a fair measure of the maximum possibilities of the population as a whole. Furthermore, in some populations the highest reproductive rate may occur when the population denSity is low, but in others -some of the higher vertebrates with complicated reproductive patterns, for example-the highest rate may occur when the popu- lation is medium sized or even relatively large (Allee effect, see Section 14 and Figure 64). Thus, the best estinlate of the maxi- mum natality should be made not only when physical factors are not limiting but also when population size is optimum. We shall see more about this business of a population acting as a limiting factor on itself in the next few sections.
Examples
In Table 12 two examples are worked out, one from field and one from laboratory data, to illustrate concepts of maximum- realized natality and absolute-specific natality rate. Maximum na- tality is based on somewhat arbitrary condWons, as must always be the case, but these conditions are clearly defined in the table.
The ecological natalities are actual measurements. From these examples we see that the insect considered here has an enormously greater natality than does the vertebrate, but the latter realizes a greater percentage of its potential under the conditions listed. For comparisons, it is more satisfactory to use the specific rate (i.e., so many eggs, young, etc., per female per time unit). In the case of the bluebird, the exact number of females in the population was not known so that rate calculations shown in Part III of the table are approximations. It should also be pointed out that bluebird females may actually lay more than 15 eggs per season, if one or more of her sets are destroyed. Under ideal conditions, however, no eggs would be lost and three broods of 5 each would theoreti- cally be all that a female could phYSiologically manage during a season. The bluebird data also demonstrate a striking seasonal variation in natality; fewer eggs are laid in late broods and more of the eggs laid are infertile, fail to hatch, or are lost in other ways.
Seasonal variation in natality is almost a universal phenomenon, as is also variation due to differences in the age and sex distribu- tion in the population.
One problem in comparing the natality of different species populations rests in the difficulty of measuring natality at com- parable stages in the life history; this is espeCially true of organ- isms such as insects and birds which have complicated life his-
164 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CR. 6
Table 12. Comparison of maximum and realized natality of two species
Expressed as natality rate per time (B) and natality rate per time per female (b) l. Field population of bluebirds (Sialia sialis) in city park, Nashville, Tenn., 1938
(from Laskey. 1939):
Max. natality Ecological or realized natality rate Total eggs Eggs produced Young fledged
laid No. % max. No. % max.
1st brood 1701 170 100 123 72
2nd brood 1751 163 93 90 51
3rd brood 1651 122 74 52 32
Total for year 5101 455 89 265 52
1 Calculated by multiplying 5 times number nests attempted; nve eggs per set is average number which the popUlation is able to produce in the most favorabh:
part of the season.
rI. Laboratory population of flour beetles (Triboliu11l confusum), 18 pairs for 60 days (approx. one generation) (from Park, 1934);
Max. natality Ecological or realized natality rate Total eggs Eggs produced Larvae produced
laid No. % max. No. % max.
Fresh Hour 11,9881 2,617 22 773 6
Old or "conditioned" flour2 11,9881 839 7 205 2
1 Determined by average rate of 11.1 eggs per female per day which is average of two 60 day cultures held under optimulTl conditions (see Table 4, in Park, Gins- burg, and Horwitz. 1945).
2 Flour in which a previous culture has been living; contains metabolic or "waste products." This situation might he si.milar to one in nature where the organism does not conti.nually have the benefit of "unused" environment.
Ill. Natality of bluebird and flour beetle populations (ilN,,/Nilt) ;
Bluebird: Maximum specific natality rate eggs per female per year
15
Flour beetle: Maximum natality rate
Fresh flour Condition flour
eggs per female per day 11.1
11.1
expressed as specific rates
Realized speCific natality per female Eggs Fledged young
13.4 7.8
Realized natality per female Eggs Larvae
2.40 0.61
0.73 0.19
tories. Thus, in one case the number of eggs might be known whereas in another case only the number of larvae or independent young could be determined. In comparing one species and popula- tion with another, it is, therefore, important to be sure there is a comparable basis.
s .
MortalityStatement
Mortality refers to death of individuals in the population. It is more or less the antithesis of natality with some parallel subcon-
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §5 165 cepts. Mortality rate is equivalent to "death rate" in human demography. Like natality, mortality may be expressed as the number of individuals dying in a given period (deaths per time), or as a specific rate in terms of the percentage of the total popula- tion or any part thereof. Ecologica.l 01' realized mortality-the loss of individuals under a given environmental condition-is, like ecological natality, not a constant but varies with population and environmental conditions. There is a theoretical minimum mor-
tality, a constant for a popnlation, which represents the loss under ideal or nonlimiting conditions. That is, even under the best con- ditions individuals would die of "old age" determined by their physiological longevity which, of course, is often far greater than the average ecologicallol1gevity.
Explanation and examples
Natality and mortality are complex population characteristics which may be expressed in a number of ways. To prevent con- fusion, therefore, the general term "mortality" needs to be quali- fied and, wherever possible, expressed by definite mathematical symbols, as indicated in previous sections. Generally, specific mortality is expressed as a percentage of the initial population dying within a given time.o Since we are often more interested in organisms that survive than in those that do not, it is often more meaningful to express mortality in terms of the reciprocal sur- vival rate. As with natality, both the minimum mortality rate (theoretical constant) and the actual or ecological mortality rate (variable) are of interest, the former to serve as a base or "meas- uring stick" for comparisons. Since even under ideal conditions individuals of any population die of "old age," there is a minimum mortality which would occur under the best possible conditions that could be devised, and this would be detennined by the aver- age physiological longevity of the individuals. In most populations in nature the average longevity is far less than the phYSiologically inherent life span, and, therefore, actual mortality rates are far
~reater than the minimum. However, in some populations or for brief periods in others, mortality may, for all practical purposes, reach a minimum, and thus provide opportunity for practical measurement under population conditions.
o As with other rates we have been discussing, mortality rate can be ex- pressed as a per eent of average population instead of the initial population;
this would be of interest in situations where denSity changed greatly during the period of measurement.
166 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CH. 6
Table 13. Life table for the Dall Mountain sheep (Ovis D. Dallit
Based on known age at death of 608 sheep dying before 1937 (both sexes com- bined). t Mean length of lite 7.09 years.
x x' d. 1. lOOOq. e.
Expeclution of Number .,,,r .. Morlality life, or mean
Age as pcr vi'lling at be, rale per life·,ime reo
unt devia· Number dy. ginning of IhollJmld mai'ling to lion from j,18 in age age in/erttal ali'Ve al be- those altain- Ifge m.an l'n~lh interval oul out of 1000 g;'min~ of ing age inter·
(YearJ) of life of 1000 horn born age infer val .al (ytar!)
0-0.5 -100 .54 1000 54.0 7.06
0.5-1 -93.0 145 946 153.0
1-2 -85.9 12 801 15.0 7.7
2-3 - 71.8 13 789 16.5 6.8
3-4 - 57.7 12 776 15.5 5.9
4-5 -43.5 30 764 39.3 5.0
5-8 -29.5 46 734 62.6 4.2
6-7 - 15.4 48 688 69.9 3.4
7-8 - 1.1 69 640 108.0 2.6
8-9 +13.0 132 571 231.0 1.9
9-10 +27.0 187 439 426.0 1.3
10-11 +41.0 156 252 619.0 0.9
11-12 +55.0 90 96 937.0 0.6
12-13 +69.0 3 6 500.0 1.2
13-14 +84.0 3 3 1000 0.7
• From Deevey (1947); data from Murie (1944).
t A small number of skulls without horns, but judged by their osteology to be- long to sheep nine years old or old r, have been apportioned pro rata among the older age classes.
Since mortality varies greatly with age, especially in the higher organisms, specific mortalities at as many different ages or life history stages as possible are of great interest inasmuch as they enable us to determine the forces underlying the crude, overall population mortality. A complete picture of mortality in a popu- lation is given in a systematic way by the life table, a statistical device developed by students of human populations. Raymond Pearl first introduced the life table into general biology by apply- ing it to data obtained from laboratory studies of the fruit fiy, Drosophila (Pearl and Parker, 1921). Deevey (1947) has assem- bled data for the construction of life tables for a number of natural populations, ranging from rotifers to mountain sheep. As a result of improved methods of marking and censusing of natural populations, it is often possible to determine at regular intervals the individuals surviving out of an initial population of known size. Such data are then comparable with data obtained from laboratory populations living in a Simplified environment. Ap- proximate life tables may also be constructed for natural popula-
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §5 167
tions if the age at death is known or if the age structure (that is, proportion of different ages) can be determined at intervals.
As an example, let us take the Dall mountain sheep (Table 13).
The age of these sheep can be determined from the horns. When a sheep is killed by a wolf or dies for any other reason, its hams remain preserved for a long period. Adolph Murie spent several years in intensive field study of the relation between wolves and mountain sheep in Mt. McKinley National Park, Alaska. During this period he picked up a large series of horns, thus providing admirable data on the age at which sheep die in an environment subject to all the natural hazards, including wolf predation (but not including predation by man, as sheep were not hunted in the McKinley National Park). As shown in Table 13, the life table consists of several columns, headed by standard notations, giving lID the number of individuals out of a given population (1,000 or any other convenient number) which survive after regular time intervals (day, month, year, etc.-see column x); (dID) the number dying during successive time intervals; (q~) the death or mortal- ity rate during successive intervals (in terms of initial population at beginning of period); and (elD) the life expectancy at the end of each interval. As may be seen from Table 13, the average age is better than seven years, and if a sheep can survive the first yeal'
'"
Q: o
III
o
~oo
~ 100
'"
:::.
() ~o
..
:t...
II:II.
~ 10 o ",
:;: ~ Q: :::.
'"
~ OALl SHeEP
~---.. o H[RAING GUl.-1..
... " ... ., rLOSCVLARIA
I'T---~---~~~----,_---~~~
-100 0 +100 +200 +300
PERCENT. DEVIATION FROM MEAN LENGTH OF LIFE
Figure 42. Survivorship curves for the Dall mountain sheep, the sessile rotifer (Floscuwria conifera) and the herring gull, age being expressed as percentage deviation from the mean length of life. (After Deevey, 1947.)
168 BASIC ECOLOGICAL PRINCIPLES AND CONCEPTS: CR. 6
100
10
Figure 43. Several types of survivorship curves plotted on the basis of survivors per thousand log scale (vertical coordinate) and age in relative units of mean life span (horizontal coordinate). (After De vc)" 1950.)
or so, its chances of survival are O'ood until relative old age, de- spite the abundance of wolves and the other vicissitudes of the environment.
Curves plotted from life-table data may be very instructive.
When data from column Lx are plotted with the time interval on the horizontal coordinate and the number of survivors on the vertical coordinate, the resulti11g curve is called a survivorship curve. If a semilogarithmic plot is used (as in Figure 42), with the time interval on the horizontal coordinate expressed as a percentage of the mean length of life (see column Xl, Table 13), species of widely different life spans may be compared. Further- more, a straight line on a semilogarithmic plot indicates a con- stant specific rate of survival. In Figure 42 the survivorship curve for the mountain sheep is highly convex. A rather different situa- tion is seen in the case of the herring gull, for which a survivor- ship curve i also plotted. Here we see that mean length of life is short in proportion to maximum length. The survival rate in the gull is more nearly constant for middle age groups.
The three basic types of survivorship curves are shown in Figure 43. If the average physiological longevity were to be realized, the
ORGANIZATION AT THE SPECIES POPULATION LEVEL: §5 169
curve would be highly convex and sharp-angled, all individuals living out their inherited life span and dying more or less all at once. A close approach to this has been obtained by Pearl with
"starved fruit flies." That is, when flies of a genetically homozy- gous strain were given no food on emerging from the pupa, they all lived out their inherited span and all died within a very short time (Fig. 43). If the specilic mortality rate at all ages is con- stant, the survivorship curve will be a straight, diagonal line (on scmi-log plot), as shown for hydra (Fig. 43). Finally, a concave curve indicates a high mortality during the young stages. In the oyster, for example, mortality is extremely high during the free- swimming larval stage; once the individual is attached to a favor- able substrate, the life expectancy improves considerably!
The shape of the survivorship curve may vary with the density of the population, as shown in Figure 44. Data On age structure were used by Taber and Dasmann (1957) to construct the curves for two stable deer populations living in the chaparral region of California. As may be seen in the figure, the survivorship curve
III
a: o
>
LOW DENSITY
;: 100 a:
50
HIGH
2 4 6 8 YEARS
B LACK -TAIL DEER SURVIVORSHI P CURVE S
Figure 44. Survivorship curves for two deer stable populations living in the chaparral region of California. The high density population (about 64 deer per square mile) is in a managed area where an open shrub and herbaceous cover is maintained by controlled burning, thus providing a greater quantity of browse in the form of new growth. The low density population (about 27/sq. mi.) is in an unmanaged area of old bushes un- burned for 10 years. Recently burned areas may support up to 86 deer/sq. mi.
but the population is unstable and hence surVivorship curves can not be con- structed from age distribution data. (Mer Taber and Dasmann, 1957.)