we have seen that a life table allows us to determine the rate of population change as a result of age-specific fecundity and mortality

does the rate of population decrease predicted by Blair's life table actually equal the rate of decrease measured by his censuses of the lizards?

to compare these two rates, we face a problem:   R₀ from the life table is the proportionate change in population size per generation -- the censuses give us the change per year -- what is the relationship between these two rates of change?

the next three sections (down to the fourth horizontal line) answer this question ... it takes some arithmetic ...

to answer this question, first define . . .

• T = length of a generation in years . . . so . . . the proportionate change in number of
  individuals in one generation or R₀ = N_T / N ₀
• (lower-case Greek letter lambda) = proportionate change in number of individuals
  in one year . . . or . . . = N₁ / N₀

now, with some substituting, R₀ = N_T / N₀ = e^rT = ^T . . . or . . . R₀ = ^T

or, we can rearrange terms, thus . . .

= R₀^{1 / T}

here is the answer to our question -- the rate of change in one year equals the rate of change in a generation, raised to the power 1 divided by the length of a generation

so we face a second question -- what is the length of a generation?

generation time T is the average age at which females produce their offspring . . . in other words T = (proportion of all offspring produced at age 1)(1) + (proportion of all offspring produced at age 2)(2) + . . . and so forth

so we could calculate the generation time T if we knew the proportion of a female's offspring produced at every age x

since the expected proportion of a female's offspring produced at age x is the expected number of offspring at age x divided by the expected number of offspring in her lifetime ... or ... l_xm_x / R₀

therefore T = (l_xm_x / R₀ )( x ) with the sum over all ages x

or after rearranging . . .

T = ( xl_xm_x) / R₀

using numbers from the life table T = 1.083 / 0.593 = 1.83 years

. . . and notice how we put the xl_xm_x column in a life table to good use !

now that we know the generation time, we can calculate the expected proportionate change in population size per year ( ) from the life table . . .

= R₀ ^1/T = 0.593 ^1/1.83 = 0.752

we can compare this number with the proportionate change per year ( ) calculated from Blair's censuses . . . because he censused his population for 4 years . . .

⁴ = (final population) / (initial population) = 197 / 250

or after rearranging . . .

= (197 / 250)^1/4 = 0.942

these two estimates of -- one from the life table and one from the censuses -- are not even close to being equal -- they should be equal provided . . .

• the estimates of age-specific mortality and fecundity are correct (no reason to doubt them)
• the age structure of the population was constant (there were only minor fluctuations in the proportions of each age-class)
• reproduction and mortality are the only processes that affect population change (no immigration/emigration) . . .

immigration and emigration to and from Blair's population is the problem -- he had noticed that unmarked individuals appeared on his property every year (13.1% of all lizards aged 2 and over) -- presumably an unknown number of other individuals moved off his property -- he included the immigrants when he estimated the number of eggs laid on his property -- but he did not take into account the emigrants when he estimated survival of lizards -- the marked lizards on his property represented only part of the survivors!

so it is not surprising that from the life table is less than from the censuses

distinguishing between mortality and emigration is often a problem in studies of animal populations!

the life table shows that these lizards live fast and die young . . .

adult females produce 75-100 or so eggs a year and some 75% of all adults die from one year to the next -- mortality in the first year is even worse -- 80% of eggs are eaten by predators (mostly snakes) before they hatch -- 80% of hatchlings die before they reach one year of age -- over the entire life span, high fecundity balances low survival

different species of lizards balance their survival and fecundity in different ways -- there are two general patterns (each with some exceptions) -- these patterns are often called life history strategies . . .

according to this table . . .

• some species of lizards begin reproduction early, at smaller size, and reproduce repeatedly each season -- as a result they have short generation times, high annual fecundity, and low adult survival

• others begin reproduction later, at larger size, reproduce once each season and provide care for offspring (more nutrients or protection) -- they have longer generation times, lower annual fecundity, and higher adult survival

these strategies are associated with different phylogenetic groups of lizards (different phylogenetic subfamilies and families) . . . but (unexpectedly) not with different environments

how come we can find species of lizards with high fecundity and low survival and others with low fecundity and high survival . . . but none with low fecundity and low survival ??? . . . and none with high fecundity and high survival ???

how do human populations compare ? . . . check the life tables for American and Yanamamo women