POPULATION ECOLOGY

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POPULATION ECOLOGY
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ANNOUNCEMENTS

• Office Hours
• NEXT Mon Wed following lecture (3 -5 pm)
• Final Exam Is In ONE WEEK
• Final will consist of 50 new material
• Review exams I II

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ANNOUNCEMENTS

• Next section (Population Ecology) requires basic
  math skills
• NO CALCULATORS!!!!

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ECOLOGY

• Ecology
• The study of how populations interact with their
  environment

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LEVELS OF BIOLOGY

• Individuals
• Populations
• Group of individuals of same species occupying
  given area
• Communities
• Ecosystems
• Global Biosphere

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POPULATION CHARACTERISTICS

• Demographics
• Vital statistics of a population
• Pop Size
• Total number of indiv.s in pop
• Pop Density
• Number of indiv.s per unit area
• Age Structure
• Number of individuals in each age category

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PROPERTIES OF POPULATIONS

• Parameters
• Birth rate b
• Death rate d
• Immigration I
• Arrival of new residents from another pop
• Emigration E
• Permanent movement of individuals out of pop

• b I add individuals to a pop
• d E remove them

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PROPERTIES OF POPULATIONS

• Assuming NO Immigration/Emigration
• If b gt d, then population is growing
• If b lt d, then population is decreasing
• If b d, then population is stable

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PROPERTIES OF POPULATIONS

• More Parameters
• N Population size
• t Time
• ? N Change in population size
• ? t Change in time

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POPULATION GROWTH MODELS

• Two Models
• Logistic Growth
• Exponential Growth

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MALTHUSIAN GROWTH

• Thomas Malthus (1798)
• Believed that population growth (geometric
  growth) would exceed the food supply
• Result people will run out of food!

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MALTHUSIAN GROWTH
987654321
Food
People
Number Of People Food Units
1 2 3 4 5 6
Days
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EXPONENTIAL (Geometric) GROWTH
987654321

• Population Growth as Compound Interest
• You have 100 in the bank at
• compound interest of 10 per day
• After 1 day you will have
• After 2 days you will have

Of Individuals
1 2 3 4 5 6
Days
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EXPONENTIAL GROWTH MODEL

• To calculate population growth, you have to look
  at
• Per capita rate of growth
• Analogous to the compound interest rate
• Number of individuals in the population at time t
  
• Analogous to the amount of in the bank at time
  t.

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High r
EXPONENTIAL GROWTH
500
Moderate r
400
300123 Q
Population size (N)
Low r
200
100
Very low r
0
1
5
0
2
3
4
6
7
8
9
10
Generations
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EXPONENTIAL GROWTH MODEL
Exponential Growth

Number Of Individuals
r 0.47
Time

• r Intrinsic rate of natural increase
• Physiological ability of an individual to
  contribute to population growth
• r b d

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POPULATION GROWTH PROBLEMS

• Birth, Death Intrinsic Increase
• Ex 2,000 mice in a cornfield
• 1,000 babies are born in a single month
• Whats the per capita birth rate (number of
  babies born per individual in the population per
  month)?

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POPULATION GROWTH PROBLEMS

• Birth, Death Intrinsic Increase
• Suppose 200 mice die in the same month
• What's the per capita death rate (number of
  deaths per individual in the population per
  month)?

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POPULATION GROWTH PROBLEMS

• Birth, Death Intrinsic Increase
• What is the per capita rate of increase (r )?

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POPULATION GROWTH PROBLEMS

• Under Optimal (Exponential) Conditions
• What is the overall rate of population growth?
  (?N/?t OR dN/dt)

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POPULATION GROWTH PROBLEMS

• Next month, the population of mice should be
  composed of ____________ individuals ?
• (HINT think of compound interest example!)
• 
  

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POPULATION GROWTH PROBLEMS

• Continuously Expanding Cockroach Population
• If rmax 0.09 roaches/day, what is the rate of
  population growth when the population consists of
  1000 cockroaches?

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ASSUMPTIONS OF EXPONENTIAL MODEL

• No variation between individuals
• Closed population
• Constant b d
• Reproduction at physiological capacity
• Population growth is continuous continues
  indefinitely
• Abundant food resources
• Growth is density-independent

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SHORTCOMINGS OF THE EXPONENTIAL
MODEL

• Exponential Growth Cannot Be Sustained!
• No pop. can continue to grow indefinitely
• All pops eventually reach carrying capacity of
  their habitat
• At high densities, growth becomes
  density-dependent

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DENSITY DEPENDENT FACTORS

• Factors That Intensify as Population Size
  Increases
• Accumulation of wastes
• Predation (sometimes)
• Competition
• Stress?
• Phermonal inhibition?

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DENSITY-DEPENDENT FACTORS

• Populations Subject to Density Regulation
• Negative feedback on growth rate as result of
  density
• b and d change due to crowding
• births decrease
• deaths increase
• Realized Growth lt rmax
• Result logistic growth

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HIGH POPULATION DENSITY DECREASED
SURVIVORSHIP
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HIGH POPULATION DENSITY DECREASED
FECUNDITY
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THE LOGISTIC MODEL

• Predicts Limited Population Growth
• Population size limited by available resources
• Food
• Minerals
• Water
• Habitat
• Refuge from predators
• Carrying Capacity (K)
• Limit beyond which environment cannot support
  additional individuals

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LOGISTIC MODEL OF POPULATION GROWTH Incorporates
carrying capacity (K) of environment
K
K
Population size
Time
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LOGISTIC MODEL

• Rate of Population Change
• dN/dt rmax N (K-N)
• 
  K

• As N approaches K, resources are more limited
• Population growth slows and eventually stops
  when N K
• (K-N) proportion of unused resources
• K

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LOGISTICAL PROBLEMS

• Back To The Roaches
• If the cockroaches were in an environment with a
  carrying capacity of 1500 individuals, how would
  this affect population growth rate (when N
  1,000 roaches)?

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NOT ALL GROWTH IS DENSITY DEPENDENT

• Factors Unrelated to Population Size
• Weather
• Pollution

Thrip population growth over a year
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THE TRUE SITUATION

• Most populations are probably regulated by a
  MIXTURE of density-dependent and
  density-independent factors

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TIME LAGS

• A change in environment does not result in
  instantaneous change in pop size or growth rate
• Pop. may have delayed response to events that
  occur
• Tendency to overshoot K and generate oscillations

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LIFE HISTORY TRAITS AGE STRUCTURE

• Age Structure of a Population is Important
• Individuals at diff. ages reproduce differently
• In humans, elderly and newborns dont reproduce
• Individuals may be more vulnerable to death at
  diff. ages

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HUMAN AGE STRUCTURE

• Age Structure
• Developed nations have age distribution that
  tends to
• be even
• Developing nations have age distribution that is
  bottom- heavy
• Mostly young individuals

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More-Developed Countries
100
1998 data
95
90
85
2050 projections
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
20
20
40
40
60
60
(In millions)
Females
Males
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Less-Developed Countries
100
95
1998 data
90
85
2050 projections
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
100
100
200
200
300
300
(in millions)
Females
Males
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LIFE HISTORY TRAITS SURVIVORSHIP CURVES

• Type I
• High survivorship of young (parental care)
• Ex Mammals
• Type II
• Death rate is constant at all ages
• Ex Birds, lizards, small mammals
• Type III
• Indeterminate growth
• High mortality of young
• Many offspring typically produced, little if any
  parental care
• Ex Trees, frogs, plants, marine invertebrates

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LIFE HISTORY TRAITS SURVIVORSHIP CURVES
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Three General Types of Survivorship Curves
1000
High survivorship
Type l
100
Type ll
Low survivorship
Number of survivors (Nx)
Low survivorship
Steady survivorship
10
1
Type lll
High survivorship
0.1
Age
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LIFE HISTORY TRAITS FECUNDITY CURVES

• Type I
• Reproduction is low at start of life and towards
  end
• Ex Humans
• Type II
• Fecundity increases with age (size?)
• Ex Fish
• Type III
• Reproduction begins at certain age and continues
  until death
• Ex Insects

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LIFE HISTORY TRAITS LIFE TABLES

• Life Tables
• Tracks representative sample (cohort) through
  time
• Divides population into age classes
• Tracks number of offspring born within age
  classes
• m(x) female offspring produced per mother
• Assigns risk of mortality within each age class
• l(x) chance of survival from 0 ? x

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LIFE TABLES

• A LIFE TABLE

l(x) survivorship m(x) fecundity
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LIFE TABLES

• l(x)
• Survivorship from age 0? x
• m(x)
• Average number of female babies born per female
  age x
• Sum l(x)m(x)
• Net Replacement Rate
• Average number of female babies born to a female
  in her lifetime
• Probability of living from age A ? age B
• l(x) for B/ l(x) for A

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LIFE TABLE PROBLEMS

• Use the Life Table (shown previously) to Answer
  the
• Following
• Each individual will replace themselves with how
  many individuals?
• Whats the probability of living from 1?2 years
  old?
• Whats the probability of living from 2?3 years
  old?

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LIMITATIONS OF THE LIFE TABLE

• Some Species Develop Through Various Life
  Stages
• Animals may not spend equal time in each stage
• Ex Frogs and insects

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LIFE TABLES CONSERVATION

• Life Tables
• Summarize probability that an individual will
  survive reproduce in any year over course of
  its lifetime
• Can be used to make population projections and
  guide conservation programs

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POPULATION EXTINCTION

• In the Simplest Terms, Probability of Pop.
  Extinction Depends On
• Birth rates (b)
• Death rates (d)
• Immigration (I)
• Emigration (E)
• Number of individuals in population (N)

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POPULATION EXTINCTION

• Population Viability Analysis (PVA)
• Model that estimates likelihood that a pop. will
  avoid extinction for a given time period
• I E taken into account
• Also models stochastic events that threaten
  population

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POPULATION EXTINCTION

• Population Viability Analysis (PVA)
• Populations are considered viable if they have
• 95 probability of surviving for at least 100
  years
• Currently used by natural resource managers
• Ex Golden Lion Tamarins

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Population Viability Analysis
80
High immigration
60
Population size
40
Low immigration
20
No immigration
0
10
20
50
30
40
60
90
100
0
80
70
Years