```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
• 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 =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
+plants
Cohort life table: follows fate of individuals bor
at same time and followed throughout their
See pg. 277
lives.
mx
Survival data for a cohort (all born at same
time) depends strongly on environment +
population density. What type of curve?
of a cohort life table?
• Describes dynamics of an identified cohort
• An accurate representation of that cohort’
behavior
• 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
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
lxmx
mx
0-1
Etc…
1000
1.0
xlxmx
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
See pg. 275)
Through time
• population size increases
•  fluctuates, then becomes constant
• stable age distribution reached
With a stable age distribution,
• Each age class grows (or declines) at same ra
().
• 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 agespecific 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
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