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## Measurement of Population dynamics, Biology tutorial

Introduction:There are numerous methods to explain populations from field measurements: dynamic and static life tables, and transition matrices. All are based on censusing individuals in groups, classified according to the state (age, size, or stage). They are used to describe population dynamics in relation to demographic processes, and to forecast fate of population. Methods differ in a) convenience of data collection, b) basic assumptions and c) way they deduce population growth rate. Because this also depends on general biology and life cycle of organism, some methods are better for some types of populations, but not for others. Dynamic life tables explain survivorship and fecundity (production of eggs, seeds, or young) at different ages of the cohort. Generally cohort is followed until last member dies.

Stage is very helpful in cohort studies of annual organisms if surviving organisms all pass through comparatively short stages, so that stages barely overlap (occur at same time), and stage and age are connected. Then, transition models are more suitable.

Survivorship:Two types of information are derived from the cohort studies: survivorship curves and population growth rates. Survivorship curves demonstrate how mortality differs with age of individuals of cohort. Age-specific mortality, and age-specific fecundity, is because of changing susceptibilities and capabilities of individual, and variation in environmental exposure. Depending on age at which most of mortality occurs, organisms can have different survivorship curves.

Population growth rate:Population growth rate of the cohort is stated as basic reproductive rate R0 for the generation over its lifetime. Using dynamic life tables is best suitable for semelparous animals or monocarpic plants, particularly annual organisms, as in study on annual plant species Phlox drummondii by Leverich and Levin. These have single cohort per year, and therefore have no overlapping generations. Perennial iteroparous/polycarpic organisms do have overlapping generations that makes method less straightforward, although frequently still useful.

There are two ways to arrive at the basic reproductive rate. The first method is R

_{0}= ΣF_{x}/a_{0}, where ΣF_{x}, the sum of F_{x}'s, is number of offspring over life span of cohort, and a_{0}is first stage. Ratio illustrates relative change in population size/density from one generation of cohort to next. R_{0}is also estimated as R0=Σ l_{x}m_{x}, the sum of l_{x}, the chance of individual surviving to age x, times m_{x}, number of offspring produced during time from age x-1 to x. The benefit of this model is that it is explicit about relation between overall population growth and actual demographic processes that take place through time in the cohort. For annual organisms this sequence of processes tracks changing of seasons. In cohort studies, R_{0}is determined over generation time. If organism is the annual plant or animal, R_{0}also denotes population growth rate R, stated per year: R = R_{0}. In perennial semelparous or monocarpic organisms, R_{0}must be corrected for generation time T (>1 year).Since R

_{0}=R^{T}, so that lnR= (ln R_{0})/T.Though, for organisms with overlapping generations, it is hard to evaluate annual growth rate correctly as generation time T is in fact unknown. Instead of T, R is given by lnR=(ln R

_{0})/T_{c}.R

_{0}is corrected by T_{c}, the average cohort lifespan, which is the average time from the birth of an individual to the birth of one of its offspring, calculated as the sum of lengths of time of the offspring of all individuals divided by the total number of offspring.The presence of three generations at the same time, i.e. if some individuals have produced offspring themselves while their parents are still alive, cannot be incorporated in the equation.

Static life tables:The static life table has age groups in the population at one particular period of time. Therefore, cohorts are not followed in time, but reconstructed using one-time observations. These can be utilized to compute population growth only if the assumption is made. Assumption is that mortality experienced by cohort at any age stays constant in time. Birth rates and age-specific survivorship are supposed to be independent of actual year in which observations are made.

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