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The total instantaneous mortality rate.  Take the natural log of the number of survivors each age class and calculate the slope of the line.  Z=slope and is always negative.

When there is a constant proportion of each age class in the population, even if there is growth or decline in the total population.  Find by calculating the proportions for each year and comparing the proportions.  If proportions at time t are the same at time t+1, you have reached the stable age distribution.

The number of 1 year olds at time t+1 is equal to the number of adults at time t, times the fecundity, times the survival rate of newborns to age 1.

Z measures the decrease in cohort or age class size over time while r measures the change in population size through time.

Z and r are found by fitting a line to the natural log transformed data of either cohorts or population.  They are instantaneous rates - the slope of the line.

Done by sampling a population and counting the number of individuals in each age class.  Transform the data and fit a line to it.  The slope of the line gives you Z.

The mortality rate is constant across all age classes.  The mortality rate is constant over time.  Population is at a stable lambda.

A cohort analysis requires several years of data.  You follow what cohort through time and plot the number of individuals in that cohort through time.  The slop of the ln of the cohort size is Z.