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

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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
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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

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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

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Age structure varies greatly among populations
with large implications for population growth.
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Population Growth(age structure known)

• How much is a population growing?
• per generation Ro
• instantaneous rate r
• per unit time ?
• What is doubling time?

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Life Table A Demographic Summary Summary of
vital statistics (births deaths)
by age class Used to determine population
growthSee Pg. 77 for Life Table for example
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Values of ?, r, and Ro indicate whether
population is decreasing, stable, or increasing
Ro lt 1
Ro gt1
Ro 1
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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
tableUse Pg. 77 Life Table for example
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Survivorship curves note scales

• qxdeath rate constant

or lx
plants
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Cohort life table follows fate of individuals
born at same time and followed throughout their
lives.
See pg. 277

mx
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Survival data for a cohort (all born at same
time) depends strongly on environment
population density. What type of curve?
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What are advantages and disadvantages of a cohort
life table?

• Advantages
• 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 cant be
  extrapolated to the population as a whole or to
  other cohorts living at different times or under
  different conditions

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Static life table based on individuals of known
age censused at a single time.
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Static life table (see
pg. 280) avoids problem of variation in
environment can be constructed in one day
(or season)
n 608
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PracticeProblem 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.

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• 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 0



0
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How does population size change through
time?How does age structure change through
time?
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How to use a life table to project population
size and age structure one time unit later.
See pg. 275
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Through time
See pg. 275)

• population size increases
• ? fluctuates, then becomes constant
• stable age distribution reached

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With a stable age distribution,

• Each age class grows (or declines) at same rate
  (?).
• Population growth rate (?) stabilizes.
• Assumes survival and fecundity constant.

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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

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Problem Set 2 - 4Pg. 80