Slide 1Slide 2Slide 3Ch 11: Population Growth + Regulation 2 dN/dt = rN dN/dt = rN(K-N)/KObjectivesAssumptions of the exponential modelAssumptions of logistic model:How fast a population grows depends on its age structure.Age structure varies greatly among populations with large implications for population growth.Slide 10Population Growth:(age structure known)Life Table: A Demographic Summary Summary of vital statistics (births + deaths) by age class; Used to determine population growth See Pg. 221 for Life Table example…Values of , r, and Ro indicate whether population is decreasing, stable, or increasingLife 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. 221 for Life Table example…Slide 15Slide 16Slide 17Survival data for a cohort (all born at same time) depends strongly on environment + population density. What type of lx curve?What are advantages and disadvantages of a cohort life table?Static life table: based on individuals of known age censused at a single time.Static life table: avoids problem of variation in environment; can be constructed in one day (or season)Practice…Problem Set 2-3 (see pg. 220) Complete columns 2 + 4Slide 23How 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.Through timeWith a stable age distribution,*** What is a stable age distribution for a population and under what conditions is it reached?For Tuesday Problem Set 2: 3 - 4 Pg. 220 For Thursday Problem Set 3 Pg. 223-225Qu ickTime™ and aTIFF ( Un comp ressed ) d ecomp ressorare n eeded to see t h is pict u re.QuickTi me™ and aTI FF (Uncompre ssed) de compressorare ne ede d to see thi s picture .Fall 2010 IB Workshop Seriessponsored by IB academic advisorsIB Opportunities in C-UThursday, Sept. 164:00-5:00pm G30 Foreign Languages Bldg.There are many local opportunities for volunteering/internships! Representatives in fields from medicine to ecology will speak with students!Next lecture Ch 10 + 12: Population Structure and Dynamics bring outline! Complete Prob Set 2:3-4Ch 11: Population Growth + Regulation 2 dN/dt = rN dN/dt = rN(K-N)/KObjectives• Add age structure to population growth models• Do Life Table Analysis to predict:• population growth + doubling time• life expectancy + generation time• Survivorship Curves• Life table and stable age distributionAssumptions of the exponential model•1. No resource limits•2. Population changes as proportion of current population size (∆ per capita)• ∆ x # individuals -->∆ in population;•3. Constant rate of ∆; constant birth and death rates•4. All individuals are the same (no age or size structure)1, 2, 3 are violated in logistic modelAssumptions of logistic model:•Population growth is proportional to the remaining resources (linear response).•All individuals can be represented by an average (no age structure considered).•Continuous resource renewal (constant E).•Instantaneous responses to crowding. . ***•K and r are specific to particular organisms in a particular environment.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 classAge structure varies greatly among populations with large implications for population growth.Changes in birth and death rates lead toChanging age structures.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 growthSee Pg. 221 for Life Table example…Values of , r, and Ro indicate whether population is decreasing, stable, or increasingRo < 1 Ro >1Ro =1Life 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. 221 for Life Table example…Survivorship curves:qxlxCohort life table: follows fate of individuals born at same time and followed throughout their lives.Survival data for a cohort (all born at same time) depends strongly on environment + population density. What type of lx curve?What are advantages and disadvantages of a cohort life table?Advantages: •Describes dynamics of an identified cohort•An 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 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 conditionsStatic life table: based on individuals of known age censused at a single time.Static life table: avoids problem of variation in environment; can be constructed in one day (or season)Practice…Problem Set 2-3 (see pg. 220)Complete columns 2 + 4 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.1. Fill in this cohort life table.2. Is the population increasing or decreasing? Show formula used.3. How many female offspring does a female mouse have in her lifetime?4. At what precise age does a mouse have her first child? Show formula used.5. Draw a graph (see pg 226) showing the lx curve for this mouse population. Label axes carefully. What type of curve is it? Explain. x nx lx mx lxmx xlxmx 0-1Etc… 1000 1.0 0 0How 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. 227Through time•population size increases fluctuates, then becomes constant• stable age distribution reached(See pg. 228)With a stable age distribution,•Each age class grows (or declines) at same