Presentation on theme: "Ch 14: Population Growth + Regulation dN/dt = rN dN/dt = rN(K-N)/K"— Presentation transcript:
1Ch 14: Population Growth + Regulation dN/dt = rN dN/dt = rN(K-N)/K For this lecture,print this pointpoint andbring pg. 77 from manual
2Objectives models Do Life Table Analysis to predict: Add age structure to population growthmodelsDo Life Table Analysis to predict:population growth + doubling timelife expectancy + generation timeSurivorship CurvesLife table and stable age distribution
3How 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
4Age structure varies greatly among populations with large implications for population growth.
5Population Growth:(age structure known) How much is a population growing?per generation = Roinstantaneous rate = rper unit time = What is doubling time?
6Life 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…
7Values of , r, and Ro indicate whether population is decreasing, stable, or increasing Values in graph = lambda - not rRo < 1Ro =1Ro >1
8Life 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…
9Survivorship curves: note scales… qx=death rate constantor lxType II = death rate is constant = qxC52.3; make sure scale = log with top = 1.0 or 1000% of max life span = time (standardized for different organisms)+plants
10Cohort life table: follows fate of individuals born at same time and followed throughout their lives.See pg. 277mxOften do life tables with only females, because of fecundity of males is unknown.lx = #/no always divide by noSx = survivorhship as in Leslie matrixGB (and homework) mx (not bx) for fecundity,and not mortality
11Survival 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.
12What are advantages and disadvantages of a cohort life table? Describes dynamics of an identified cohortAn accurate representation of that cohort’ behaviorDisadvantages:Every individual in cohort must be identified and followed through entire life span - can only do for sessile species with short life spansInformation 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 conditionsSessile - or if mobile, intensive work catching every tagged animal each year…
13Static life table: based on individuals of known age censused at a single time. Dall mountain sheep.Size of horm increases with age.
14Static 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
15Practice…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.
16Fill 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.xnxlxmxlxmxxlxmx0-1Etc…10001.0
17How does population size change through time How does population size change through time? How does age structure change through time?
18How to use a life table to project population size and age structure one time unit later. See pg. 275
19population size increases fluctuates, then becomes constant See pg. 275)Through timepopulation size increases fluctuates, then becomes constantstable age distribution reachedAny 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.
20With 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 scaleAny change in birth or death rate alters SAD - new rate of population growthAt SAD, proporiton in each age class is constnat (even as pop = increasingLambda becomes constant
21*** 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 timePopulation 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 SADand population growth rate