Ch 14: Population Growth + Regulation dN/dt = rN dN/dt = rN(K-N)/K

For this lecture, print this pointpoint andbring pg. 77 from manual

Objectives

• 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

Ro < 1 Ro >1Ro =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…

+plants

qx=death rate constant

or lx

Cohort life table: follows fate of individuals born at same time and followed throughout their lives.

mx

See pg. 277

Survival data for a cohort (all born at same time) depends strongly on environment + population density. What type of 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 conditions

Static life table: based on individuals of known age censused at a single time.

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.

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 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 0

0

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

Through time• population size increases fluctuates, then becomes constant

• stable age distribution reached

See pg. 275)

With a stable age distribution,

• Each age class grows (or declines) at same rate ().

• Population growth rate () stabilizes.

• Assumes survival and fecundity = 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 - 4Pg. 80