## Further Reading

The estimation of 'generation time' is an important part of the demographic analysis of populations because it is a measure of the time required for a newborn to become a parent and this influences a population's potential for growth. As reviewed in two books on demography by Hal Caswell and Tom Ebert, the word 'generation' is generally defined as the average age that a female from any given population gives birth to her first female offspring. It is therefore equivalent to the time that it takes a population to increase by a factor equal to the net reproductive output of those females.

More specifically, at least four definitions of the term generation, and ways of estimating its length (generation time), have been proposed. The first is to calculate the time Trequired for a population to increase by a factor of R0 (its net reproductive rate), with T = ln R0/ln A = ln R0/r, with A being the finite rate of increase of the population. The other three estimates are (1) the mean age of females bearing offspring in a cohort subject to no mortality; (2) the mean age (^1) of the females bearing offspring produced by a cohort over its lifetime (also known as the mean length of a generation, and not requiring a stable age distribution); and (3) the mean age (A) of the females bearing pups produced by a population at the stable age distribution - for this last one, in a stationary population with A = 1.0, M1 = A. Somewhat surprisingly, values of T are _ not always the same as those obtained using the other three approaches, even though these latter three are all estimates of the mean ages of reproductively active females in the population.

While the concept of generation and generation time (or length) has been an important, but varying, concept over the years, ways of calculating it have also varied. Generation times can be calculated either through the use oflife tables or projection matrices. Early authors defined generation time as the mean length of a generation (or the average time from the birth ofa mother to the birth ofher first female offspring), and used it as T in the exponential growth equation Nt = NoerT. Then, from their definition of the net reproduction rate as Nt/No = R0, they solved for r = ln R0/T and T = ln R0/ r. But, it was then pointed out that the mean length of a generation cannot be obtained until the best value of r is obtained. This ultimately resulted in the equation T = ^ xlxmx/^2,lxmx, which has commonly been used in many other papers and textbooks to explain how to calculate generation times. Many demographers have considered that a female parent in her lifetime produces R0 daughters, where R0 is the net reproductive rate as explained in the paragraph above. Then, generation time should be the length oftime it takes for the stable population to increase by the factor R0. The above estimation of generation time (and other parameters) involves the creation of life tables - a more classic approach to demography. A more contemporary approach to demography is to use Lefkovitch (stage-based) and Leslie (age-based) projection matrices.

Demographic analyses are useful for understanding the population dynamics of many organisms. The role of generation time in these analyses is crucial in understanding the interaction between age- or stage-specific survivorship and reproductive-output functions. Such approaches have been used to produce estimates of generation time for many types of organisms including algae, flowering plants, invertebrates, fishes, reptiles, birds, and mammals.

'Generation length' is positively correlated with body size (see Figure 1), leading some authors to categorize this as a 'generation-time law'. The mathematical relationship is that the generation time increases with body size at a power of approximately one-fourth of the body mass. This pattern appears to exist across taxa. However, this may not be necessarily the case within taxa such as fishes. Also, body size (measured as weight or length) in a variety of organisms is also positively related to reproductive output (e.g., clutch weight or volume, number of eggs per female parent), hatchling weight (egg or other product), gestation (or brood) time, maturation time, and maximum life span. However, the intrinsic rate of increase can be either negatively or not related to body size and 'generation length'.

Relative to its use in population dynamics of fished or exploited populations, the position of the inflection point of population growth curves (a measure of where 'maximum sustainable yield' (MSY) or 'Catch' can be attained) is related to the rate of increase per 'generation' (rT), and that this relationship is independent of body size. These relationships, often employing size at maturation rather than actual generation times, have also been employed to better understand how the life-history traits of many organisms have evolved.

The concept of 'generation time' has been used extensively by the World Conservation Union (IUCN) as part of their process of categorizing the status of species and their populations worldwide. They state ''Generation may be measured as the average age of parents in the population.'' and that ''This is greater than the age at first breeding, except in taxa where individuals breed only

100 years

10 years ar er n e

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Sequoia Birch • « White shark Human • * StriPed bass

Turtle *

Elephant Rhino

Bear

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Crab

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Mouse

Whale

Kelp

Drosophila

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E. coli

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Figure 1 The relationship of body size and generation time for several groups of living organisms.

once.'' 'Generation time' is used to categorize the conservation status of species when determining whether they are declining by a certain percentage in abundance ''over the last 10 years or three generations, whichever is the longer.'' This enables the IUCN to decide whether a species should be placed on the Red List and categorized as 'critically endangered' (CR: 80%), 'endangered' (EN: 50%), or 'vulnerable' (VU: 20%). Therefore, in this process, the accuracy of both the estimates of population abundance and 'generation time' estimates is extremely important.

'Generation time' also comes into play when calculating rebuilding times for overexploited species in fisheries, both in the United States and worldwide. Under precautionary approaches, scientists at the National Marine Fisheries Service (NMFS) of the United States Department of Commerce have stated that if the rebuilding time (time it takes for the stock to reach the biomass that produces MSY under zero fishing mortality) exceeds 10 years, then the generation time must be added to it to estimate a new rebuilding period.

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