AGE STRUCTURE AND SURVIVORSHIP Populations, whether animal or plant, vary in their proportions of young and old individuals. Time units such as weeks, months, or years can describe ages. Or individuals can be assigned to qualitative age classes such as nestling, juvenile, subadult, and adult, or egg, larva, pupa, and adult. The proportions of individuals belonging to the various age groups are collectively referred to as the age structure or age distribution of the population. Three different procedures may be used for obtaining the age structure of a population. The vertical approach follows a particular cohort. A cohort is a group of individuals born within the same time interval. Thus, by knowing the age of cohort members, you can follow their survival until all have died. The horizontal approach uses data on all ages within a given population at one time; that is all cohorts in the population are examined at the same time. In the latter method, one assumes a stable age structure and constant birth and death rates. A third approach involves knowing the age at death for members of a population. Such data are commonly obtained for a game species. Knowledge of age structure is important, for the age distribution of a population affects its growth and dynamics. From a knowledge of age structure, a table of age-specific mortality, survivorship, and life expectancy can be constructed – a life table. In 1
Transcript
AGE STRUCTURE AND SURVIVORSHIP
Populations, whether animal or plant, vary in their proportions of young and old individuals. Time units such as weeks, months, or years can describe ages. Or individuals can be assigned to qualitative age classes such as nestling, juvenile, subadult, and adult, or egg, larva, pupa, and adult. The proportions of individuals belonging to the various age groups are collectively referred to as the age structure or age distribution of the population.
Three different procedures may be used for obtaining the age structure of a population.
The vertical approach follows a particular cohort. A cohort is a group of individuals born within the same time interval. Thus, by knowing the age of cohort members, you can follow their survival until all have died.
The horizontal approach uses data on all ages within a given population at one time; that is all cohorts in the population are examined at the same time. In the latter method, one assumes a stable age structure and constant birth and death rates.
A third approach involves knowing the age at death for members of a population. Such data are commonly obtained for a game species.
Knowledge of age structure is important, for the age distribution of a population affects its growth and dynamics. From a knowledge of age structure, a table of age-specific mortality, survivorship, and life expectancy can be constructed – a life table. In addition, population growth rates may be estimated from data on births per female in the population.
LIFE TABLE
To construct a life table we must be able to determine the age of the organisms in questions and distribute the population members into age classes or age intervals. Age intervals can
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vary according to the longevity of the organism. For small rodents or lagomorphs the age interval may be one month, for deer one year, for humans five years. For insects age categories may be instars or life history stages. We need information on survival, mortality, or rate of mortality by age classes for a given population. Data on survivorship in each age class provide the information needed for survivorship column, lx.
Table 1. A Life Table. The data in the x and Lx columns were obtained from a population of animals. Then, all other columns of data were derived from them, as described in the text.
Life TablesIn a life table various statistics are compiled for each age class, or cohort (designated x). Data are commonly collected as numbers of individuals in each age class. Lx is the number of individuals in age class x. It is assumed that Lx is the number alive at the middle of age class x (for example, in above table, 33 individuals assumed to be 0.5 year old, even though the true ages of the 33 might range between 0 and 1 year old).
We designate lx as the number of individuals alive at e beginning of age class x. Thus, Lx may be defined as
Lx = ( l x + l x+1) (1) 2
(i.e., Lx is the number alive at the midpoint of age class x), and
lx = 2Lx – lx+1 (2)
For example, in Table 1.
Lo = 33L1 = 16
2
L2 = 9L3 = 4L4 = 1L5 = 0
Since L5 = 0, we can set l5 = 0. Then by applying Equation 2,
The age-specific survival rate (sx) for age interval x is the proportion of individuals alive at the start of the interval who do not die during that interval period. In other words, sx is the probability of surviving age interval x:
We can calculate age-specific life expectancy (commonly done for human populations) as follows. Let us define Tx, as the number of time units left for all individuals to live from age x onward; this is obtained by summing Lx values as follows:
Life expectancy represents the average additional length of time that an individual will live, once it has reached age x.
To compare different populations, the numbers dying (dx) or surviving (lx) are often expressed as numbers per 100 or per 1000 individuals entering the population at age 0; that is, 10 is set to 100 or 1000, and all other life-table entries are expressed relative to this value. For the example in our table, we have 10 = 46 and 11 = 20. If we set 10 = 100, then we would have an 11
value of (20/46) x (100) = 43.5. In order words, for every 100 in-dividuals born into the population, 43.5 survive to age 1. If we begin with 10 = 100, then of course dx = 100.
In the above example, the data collected were six values of Lx, from which we computed all the values of lx, dx, qx, sx, Tx, and ex. If, instead, the data collected were lx’s, then all of the Lx’s would have been calculated by Equation 1, and the other quantities would have been ascertained using Equations 4 through 9. If the original data were values of dx, then we would have used Equation 4 to determine l0 and then, for x > 0,
The remaining life-table statistics would be computed using Equations 5 through 9.
Although the construction of a life table is straightforward, given data on survival of various age classes, the life table may be inaccurate or invalid. Especially questionable are life tables based on capture-recapture of marked or banded individuals. Life tables based on such data involve two assumptions:
1. Annual survival rate is age-specific; it varies only by age and not by year.
2. Recovery rates are constant over all ages and all years. Rarely are these assumptions met. In fact, annual survival rates, especially among birds, do vary by year, often influenced more by weather than by age.
Survivorship Curves
Various types of graphs may be constructed from life-table data, including mortality rate curves, life expectancy curves, and survivorship curves. Most widely used among ecologists, the survivorship curve is prepared by plotting (usually on semilogarithmic graph paper) the logarithm of the number of survivors against age. For comparative purposes use lx data bases on 100 or 1000. From this graphical presentation, three basic types of curves are recognizable.
In the type 1 survivorship curve, there is a high survival rate of the young and a low survival rate after a particular old age. In the type 2 curve, a constant rate of’ mortality occurs at all ages (a constant percentage of population decreases each time period).
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The type 3 curve shows a high juvenile mortality and a relatively low rate of mortality thereafter. Most populations exhibit survivorship curves between types and 2 or between types 2 and 3. Some adult birds approach type 2, and modern humans approach type 1. Including data from very early life stages (even eggs) tends to introduce type 3 curve characteristics.
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FECUNDITY TABLE
If we know the productivity of each age class of females, mx, determined by litter counts, brood counts, placental scars, young fledged, and so on, we can construçt a fecundity table.
The fecundity table includes the age categories, x; age-specific survivorship from the female life table, lx; age-specific productivity, mx; the mean number of female young produced by each female of age x, lxmx; which is mx weighted by survivorship. The sum of the lxmx column gives the net reproductive rate, Ro.
Added to the fecunditv table is another column xlxmx, which records the values obtained by multiplying the lxmx by the appropriate age. The sum of this column is used to compute the rate of increase.
In Table 2, age categories have been converted to mean age to permit the correction calculation of xlxmx, starting with year class 0. Some female gray squirrels may produce a litter late in the year of their birth.
The value of R0 (1.169) is just above the replacement rate that would be expected in an unhunted gray squirrel population. A hunted population would have a higher reproductive rate and few, if any, individuals in the 5 to 7 year age classes.
lx = age-specific survivorship from the female life tablemx = age-specific productivitylxmx = the mean number of female young produced by each female of age xRo = net reproductive rate
Table 2. Fecundity table for the Gray Squirrel Population
In keeping with our earliest interpretation of Ro, this value of Ro indicates that the population is growing and that each individual produces on the average 1.169 offspring. Remember that if Ro is less than 1.0, then the population would be expected to decline, and if it exactly 1.00, then the population should remain constant in size.
RATE OF INCREASE
Given a life table and a fecundity table, we can determine the rate of increase, rm, for a population in a particular environment.An approximation of r can be obtained by the equation
r = l xmx log e l xmx
xlxmx
For the squirrel population an approximation is
r = 1.169 (0.1561) = 0.049 3.709
Another method requires more calculations but gives the same result. The first step is to determine mean generation time
Tc = xl xmx
Ro
For the squirrels
Tc = 3.709/1.169 = 3.173
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To find an approximate value of rm the following formula applies:
When generations are overlapping, the length of a generation is not clear. One way to visualize the generation length in this case is as the average age of an individual when offspring are born.
Where Tc is the generation length or mean generation time.
Tc = 3.173
REPRODUCTIVE VALUE
The life table and fecundity table provide the data needed to calculate the reproductive values of females age x in the population.
The reproductive value is the relative number of female offspring that remain to be born to each female age x.
To state it differently, it is the number of offspring that will be produced by a female from age x until the end of her life. It can be estimated relative to the reproductive value of the female at birth, vo, which is 1 by the formula given by the geneticist R.A. Fisher.
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vx/vx = rrx / lx e-ry lymy
y=x
Because the reproductive value of a female at birth is 1, vo can be removed from the formula. The formula can also be written as
vx = e rx e-ry lymy
lx y=x
where y = all ages a female passes through from age x on up. Essentialy the formula states that the number of female offspring produced at any one moment of time by females aged x and over is divided by the number of females of age x at any one moment.
To calculate reproductive values for females of each age class (Table 3).
1. Add the e-rx lxmx column from the bottom up to obtain a value for e-ry lymy for each age class
2. Divide this value by e-rx lx for each age class. The reproductive values for the squirrel population are graphed in Figure 1. Note that the reproductive values rise and fall by age.
Table 3. Determination of reproductive values for squirrel population
