Ch 14: Population Growth + Regulation dN/dt = rN dN/dt = rN(K-N)/K For this lecture, print this pointpoint and bring pg. 77 from manual

Objectives models Do Life Table Analysis to predict: Add age structure to population growth models Do Life Table Analysis to predict: population growth + doubling time life expectancy + generation time Surivorship Curves Life table and stable age distribution

How fast a population grows depends on its age structure. When birth and death rates vary by age, must know age structure = proportion of individuals in each age class

Age structure varies greatly among populations with large implications for population growth.

Population Growth:(age structure known) How much is a population growing? per generation = Ro instantaneous rate = r per unit time =  What is doubling time?

Life Table: A Demographic Summary Summary of vital statistics (births + deaths) by age class; Used to determine population growth See Pg. 77 for Life Table for example…

Values of , r, and Ro indicate whether population is decreasing, stable, or increasing Values in graph = lambda - not r Ro < 1 Ro =1 Ro >1

Life Expectancy: How many more years can an individual of a given age expect to live? How does death rate change through time? Both are also derived from life table… Use Pg. 77 Life Table for example…

Survivorship curves: note scales… qx=death rate constant or lx Type II = death rate is constant = qx C52.3; make sure scale = log with top = 1.0 or 1000 % of max life span = time (standardized for different organisms) +plants

Cohort life table: follows fate of individuals born at same time and followed throughout their lives. See pg. 277 mx Often do life tables with only females, because of fecundity of males is unknown. lx = #/no always divide by no Sx = survivorhship as in Leslie matrix GB (and homework) mx (not bx) for fecundity,and not mortality

Survival data for a cohort (all born at same time) depends strongly on environment + population density. What type of curve? Hence a problem in basing population projections on cohort life table.

What are advantages and disadvantages of a cohort life table? Describes dynamics of an identified cohort An accurate representation of that cohort’ behavior Disadvantages: Every individual in cohort must be identified and followed through entire life span - can only do for sessile species with short life spans Information from a given cohort can’t be extrapolated to the population as a whole or to other cohorts living at different times or under different conditions Sessile - or if mobile, intensive work catching every tagged animal each year…

Static life table: based on individuals of known age censused at a single time. Dall mountain sheep. Size of horm increases with age.

Static life table: (see pg Static life table: (see pg. 280) avoids problem of variation in environment; can be constructed in one day (or season) n = 608

Practice…Problem Set 2-2 (see pg. 79) In the population of mice we studied, 50% of each age class of females survive to the following breeding season, at which time they give birth to an average of three female offspring. This pattern continues to the end of their third breeding season, when the survivors all die of old age.

Fill in this cohort life table. Is the population increasing or decreasing? Show formula used. How many female offspring does a female mouse have in her lifetime? At what precise age does a mouse have her first child? Show formula used. Draw a graph showing the surivorship curve for this mouse population. Label axes carefully. What type of curve is it? Explain. x nx lx mx lxmx xlxmx 0-1 Etc… 1000 1.0

How does population size change through time How does population size change through time? How does age structure change through time?

How to use a life table to project population size and age structure one time unit later. See pg. 275

population size increases  fluctuates, then becomes constant See pg. 275) Through time population size increases  fluctuates, then becomes constant stable age distribution reached Any population growing exponentially will with time reach a SAD. The population size is different, based on initial size, but the RATE of pop. Growth is the same, no matter what size you start with.

With a stable age distribution, Each age class grows (or declines) at same rate (). Population growth rate () stabilizes. Assumes survival and fecundity = constant. Note log scale of population size…slopes are same if SAD and pop increase is plotted on log scale Any change in birth or death rate alters SAD - new rate of population growth At SAD, proporiton in each age class is constnat (even as pop = increasing Lambda becomes constant

*** What is a stable age distribution for a population and under what conditions is it reached? SAD = pop in which the proportions of individuals in the age classes remain constant through time Population can achieve a SAD only if its age-specific schedule of survival and fecundity rates remains constant through time. Any change in these will alter the SAD and population growth rate

Problem Set 2 - 4 Pg. 80