Techniques for the Study of Primate Population Ecology (1981) / Chapter Skim
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PRIMATE POPULATION ANALYSIS
PRIMATE POPULATION ANALYSIS
Pages 135-175
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From page 135... ...
They include the birthrate, death rate, population growth rate, and others. Vital statistics describe the dynamics of a population, or its demography.
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From page 136... ...
Errors in estimates of vital statistics that can arise from faulty age classification are discussed in Chapter 5. Changes in a population can be monitored by making an annual census of animals of all ages by sex and by making a series of annual censuses to find newborn infants.
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From page 137... ...
Therefore, to reduce the error of not counting infants that were born and died in the interval between successive censuses, one should make the census interval as short as possible. Since pregnant females are conspicuous in some primates, the censusing effort can be focused on specific individuals until all adult females in a troop have recently given birth or can be seen nursing infants.
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From page 138... ...
The mean date of birth and its standard deviation are first calculated in terms of the period codes and then converted to their real values in days or dates. Mean date, Mn = 1,162 150 = 7.75 periods, where / = the number of births during a period, and x -- the period code = 7.75 periods X 28 days per period = 217 days after midpoint of period 1 (June 25-July 22)
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From page 139... ...
2/150 149 -Vi2 = 3.85 periods Most birth seasons are skewed in the positive direction -- that is, the frequency of births rises steeply to a peak and then descends in a long tail to the right. In such asymetrical distributions 60 -i 50 40 ~ 30 10 Period code l 2 3 4 5 6 7 8 9 10 ll 12 13 Date Jly Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jly FIGURE 7-1 Distribution of births in toque monkeys at Polonnaruwa, Sri Lanka, from 1968 to 1972.
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From page 140... ...
Median, Md = L f where L = lower limit (in days) of the period in which the median lies = 198 days g = serial number of the median birth minus the cumulative frequency of births up to the upper limit of the period preceding the median period = 75 - 51 = 24 C = period interval = 28 days / = frequency of births in the period containing the median = 55.
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From page 141... ...
Another method for obtaining birth season statistics involves probit analysis. This method is especially useful when regular census work is not possible, because it requires no constant sample size or regular interval between samplings, nor does the beginning or end of the birth season have to be sampled.
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From page 142... ...
The toque monkeys at Polonnaruwa were sampled, and 208 females and 211 males were counted among 419 animals. The equation for the binomial test is where x = the smaller number of observed births (208)
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From page 143... ...
If the observation period spans only 1 yr and females are individually identified, the birthrate is estimated as follows: Birthrate, b = I,/Ft, where 7, = total number of infants born in 1 yr and F, = total number of females observed throughout 1 yr. If females are classified according to different age classes (x)
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From page 144... ...
The estimation of mx from such data is given in Table 7-2 for middleaged adult female toque monkeys. Within each age class, x, the number of years of observation differed between females.
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From page 145... ...
To avoid circularity in analysis, one should base estimates of mx for young adult females on at least 2 yr of observation after the first birth, or on the interbirth interval (Method 2)
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From page 146... ...
and Fecundity Rates (mx) of Females in the Population of Toque Monkeys at Polonnaruwa Between 1968 and 1972" Mean Mean Estimated Age Birthrate Fecundity Age Class (years)
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From page 147... ...
In this table, most ages are grouped into classes and are tabulated according to the birth pulse model discussed under "Birth Seasons." The importance of the censusing methods described earlier can now be understood in terms of the assumptions underlying the construction of an age-structure table, the accuracy of which depends on the adequacy of the sample of the population, the completeness and accuracy of the age and sex class identifications, and the accuracy of the estimate of the birth season. Sampling primate populations is relatively easy (compared with sampling herds of ungulates, for example)
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From page 148... ...
, it is advantageous to census close to the median or mean birth day of the population. These considerations assume, of course, that the average birth day of the population is the same every year and that the standard deviation from the average birth day is low.
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From page 149... ...
Vital statistics are most conveniently expressed as probabilities. The usual statistics given in a life table are as follows: lx = survivorship (or survival)
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From page 150... ...
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From page 151... ...
First, unless the population's birth season conforms exactly to the theoretical birth pulse model and the census was taken on the day of all births for the population for that year, the number of infants born in that year or during the year preceding the census will be underestimated. This can be corrected for, however, by eliminating from the raw data the number of infants less than 1 yr old and substituting an estimate of the number that were born in the season preceding the census.
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From page 152... ...
The statistics are then tabulated for each year of life in a format similar to that in Table 7-5 to give a life table. ESTIMATING VITAL STATISTICS FROM AVERAGED AGE CLASS FREQUENCIES Theoretically, one would wish to have the observed frequencies of females,/,., for each year of life.
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From page 153... ...
The standard notation E"=0 represents the limits of the summation -- in this case, the sum of values for jc from 0 to infinity or the sum of all age classes. Following convention, the limits of the summation will not be shown when all age classes are summed.
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From page 154... ...
= 0.200 X 5 = 1.000. That is, all females of the age class x = 25-29 will, on the average, die before their 30th birthdays.
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From page 155... ...
The average life expectancies of individuals of different age classes are given in Table 7-7 for female toque monkeys. The life expectancy at birth, e0, is the average life expectancy of the entire cohort; for the female toque monkey, e0 = 4.8 yr.
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From page 156... ...
Figures 7-2 and 7-3 show survivorship and mortality rate curves for male and female toque monkeys. The survivorship curves appear in a stepwise fashion because statistics were computed as averages that apply to all ages within TABLE 7-7 Average Life Expectancies for Female Toque Monkeys of Different Age Classes Average Life Expectancy Age Class (years)
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From page 157... ...
FIGURE 7-2 Survival curves for male and female toque monkeys at Polonnaruwa from 1968 to 1972. After Dirtus, 1975.
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From page 158... ...
LIMITATIONS OF AGE DISTRIBUTION DATA FOR CALCULATING VITAL STATISTICS The Effect of Age Distribution on Life-Table Estimates The frequency distribution of ages in a population sample at the time of the census is known as a "standing age distribution" and is usually shown in an age-structure table. In estimating life-table statistics from such data, one assumes that the standing age distribution is equivalent to a "temporal age distribution" of a cohort.
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From page 159... ...
This can be shown as follows. The standing age distribution, Sx, can be expressed as the number of animals in an age class relative to the number of newborn (Caughley, 1977)
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From page 160... ...
might be useful for rejecting or accepting Sx as a basis for estimating vital statistics. Population growth rate (r)
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From page 161... ...
For example, the population of toque monkeys at Polonnaruwa was judged to have had a fairly stable history based on forest ecology, a very constant long-term climatic regime, and short-term population stability. Errors Due to Inaccurate Age Estimates Probably the greatest source of error in estimating vital statistics is faulty age estimation.
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From page 162... ...
Similarly, male infants and juveniles often grow faster than their female age mates. Using the size-to-age relationship of one sex to estimate the ages of the other, or an average growth curve to estimate the ages of either, would tend to overestimate the mortality of the faster-growing males relative to their slower-growing female age mates.
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From page 163... ...
Two alternative methods can be used to estimate vital statistics when no assumptions are required concerning the stability of the age distributions or the rate of population increase at any time. (The methods are given in the next two sections.)
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From page 164... ...
ESTIMATING VITAL STATISTICS FROM STANDING AGE DISTRIBUTIONS SAMPLED AT YEARLY INTERVALS When a standing age distribution is obtained from the same population two or more times at intervals of 1 yr, any two successive samples may be used to calculate life-table statistics. The number of survivors, fx, at the time of the first sample is
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From page 165... ...
• Any two successive samples should be taken at the same time of year, preferably during the birth season, so that in a birth pulse population the ages of animals will be distributed near their birth days. • Since most births are unlikely to occur on the day of sampling (t = 0)
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From page 166... ...
Therefore, RQ can be estimated from lxmx only if the lx schedule was calculated by methods not assuming r = 0. TABLE 7-8 Calculation of Net Reproductive Rate, R0, from Fecundity and Survivorship Schedules of Female Toque Monkeys Age Class (years)
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From page 167... ...
In a birth pulse population where ages are expressed in classes, T -- Y,Sxmxxax, where x = average age of age class x and ax = number of birth pulses of ages in years encompassed by age class x and Sx = fx/fo. ESTIMATING EXPONENTIAL RATE OF POPULATION INCREASE The exponential rate of increase, r, may be estimated from r = log,.
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From page 168... ...
It is a unitary measure expressing how survivorship and fecundity interact to determine how many offspring a female is likely to produce before dying. Young adult females that are just beginning to reproduce have a long life expectancy and will produce more offspring before dying than will older females.
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From page 169... ...
For female toque monkeys of age class x = 10-14, for example, = -- ^ -- X 0.777 = 5.7. The values of vx are plotted against age in Figure 7-5.
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From page 170... ...
For interpreting demographic events within the sample population, it is important to know rates of movement into and out of the population. For example, if a high proportion of males leaves the study population every year, and they are not replaced by an influx of an equal number of males, the mortality of males in the population might be overestimated.
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From page 171... ...
With these distinctions in mind, estimates might be made of rates of transfer between social groups within a population and of those between populations. ESTIMATING RATES OF TRANSFER BETWEEN SOCIAL GROUPS The raw data for estimating rates of intergroup transfer are (1)
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From page 173... ...
For example, from Table 7-10 it is highly unlikely that adult females or infants and young juveniles shift between populations because they appear not to leave their social groups. If we consider a set of troops to constitute the sample population, the number of individuals moving into and out of the population is estimated as follows: Minimum number of emigrations = total of Type 3.
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From page 174... ...
In populations where it can be assumed that immigration and emigration are equal, mortality can be estimated independently of dispersal by applying methods based on standing age distributions. (See "Estimating Vital Statistics from a Stable Standing Age Distribution" and "Estimating Vital Statistics from Standing Age Distributions Sampled at Yearly Intervals," above.)
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From page 175... ...
Such a population has yet to be found in primate demographic studies Lone males and all-male groups must, of course, be incorporated into any valid demographic sample. SUGGESTED READINGS The following are excellent introductions to the study of animal populations: Caughley (1977)
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