1. Population Ecology
Goal of Population Ecology is to Describe the Composition of Populations Through Time and Understand Population Fluctuations
Number of Animals
Year

2. Describing Population Composition
Sex Ratio
Age Ratio
Genetic Composition
Spatial Structuring

3. Sex Ratio Indicates Important Processes in Population
Population growth potential--greater male bias = less growth ability (sexual species)
Breeding System
Dispersal
(Data from Marzluff and Balda 1992)
Sex Ratio (Males:Females)
in Flock of Pinyon Jays

4. Age Pyramids Summarize Age Structure
Differ for Increasing, Steady, and Declining Populations
Indicate Bad Years, Bottlenecks in Reproduction, etc.
Proportion
in each
age class
Increasing
Population
Stable
Population
Declining
Population

5. Pinyon Jays Were Studied for 20 Years
Long-term studies of marked animals are needed to get accurate population growth and composition information.

6. Age Structure Reflects Relative Productivity of Cohorts
Young (cohort) from productive years constitute large proportion of population for many years (1977, 1978)
A poor year of reproduction continues to be echoed in population as a missing cohort (1976)
300
1978
1977
Number
of Jays
in Flock
1976 50
YEAR
(Marzluff & Balda 1992)

7. Importance of Indirect and Direct Selection Depends on Genetic Composition of Population
Number of
Relatives
in Flock
Age of Focal Individual
(Marzluff & Balda 1992)

8. Describing Change in Population Size
Managers are usually concerned with monitoring population SIZE---So, How do WE Quantify CHANGE in Population Size??
(Lack 1966)
Density of Great Tits in 4 Areas
Year

9. Population size and rates of growth
Nt = population size at time t
Nt+1 = population size at time t+1
Nt+1 = Nt + Births + Immigration – Deaths -Emigration
Growth rates:
r = exponential growth rate
λ (‘lambda’) = intrinsic population growth rate 4

10. Population growth “BIDE” Reproduction, births, natality (B)
Immigration (I)
Emigration (E)
Population
Mortality, death (D)
“BIDE” 4

11. Age-specific birth rates
A fecundity schedule for Chamois from New Zealand.
Age (yrs) N # Female births per
pregnant female
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>
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12. Survivorship curves for male & female moose on Isle Royale
females
Survivors (lx)
males
Age at Death (years)

13. Emigration and Immigration
Juvenile dispersal: movement from place of birth to place of breeding
Breeding dispersal: movement by adults from one place of breeding to another
Birds: Female dispersing sex
Mammals: Male dispersing sex

14. American Robin post-fledging movements
From same site, larger scale, most mobile species

15. Population Growth k Carrying capacity (k) Exponential N N Logistic
time
time
Classic growth curve,
unlimited resources
Classic growth curve,
limited resources (k) 6

16. The Simplest Quantification of Population Growth Assumes Exponential Growth
Nt=N0ert-----let t = 1 year
N1=N0er
er=N1/N0===Lambda, Finite rate of Increase
Lambda goes from 0 (extinction) to 1 (stable growth) to positive infinity (Exponential growth of various magnitude)

17. Exponent Indicates the Magnitude of Change
er=N2/N1---Take ln (natural log, loge) of both sides to get:
r = ln(N2/N1)
varies from negative infinity (decrease) to 0 (Stable) to positive infinity (increase)
r, the exponential multiplier, = Intrinsic (instantaneous) rate of increase

18. Exponents provide consistent quantification of magnitude of change
Doubling and halving of population produces same exponent multiplier of change----sign of multiplier changes
N1=50 ---N2=100--doubling
er = (lamda) = 100/50 = 2
r = ln (2) = .693
N1=100--N2=50---halving
er = (lamda) = 50/100 = 0.5
r = ln (0.5) = -.693

19. Units of r and lambda Units of lambda are obvious
numbers per unit time
restricted to the unit it was calculated over
t = 1 year, then rate is change per year
Units of r not obvious
it is a multiplier, not a rate
“growth multiplier of ln(#s) per unit time”
not restricted to unit it was calculated over
r from 1 year can be transformed to r for each day by dividing by 365, etc.

20. Lambda and r Both present the same information in varying formats
Population increases at lambda per unit time or r at any instant in time
r is useful because it can be transformed to fit time interval of interest, lambda is more intuitive

21. Unlimited Growth Australian rabbit (European hare)
1859: 24 hares introduced (for human food?)
1865: over 20,000 hares were harvested, actual
population much greater.
Mid-1800’s to mid-1900’s: major problem with too
many hares; caused habitat destruction and
reduction in native mammals
2000: still present, local problems 8

22. Carrying capacity
Rabbits exceeded k
No rabbits
Rabbit-proof fence

23. Carrying capacity
Carrying capacity (k): the number of organisms that can be supported by a given area; the actual number of organisms fluctuates near this
# of
Animals (N) k
time

24. Adding A Limit to Population Growth
More Realistic than Exponential Growth
Growth is adjusted as population approaches carrying capacity (K) of the environment
Population growth simply stops at K
Population crashes after resource is consumed
Population growth is under negative feedback as it approaches K and gradually reaches K

25. Population Growth is Gradually Reduced as Carrying Capacity is Reached; Resources Renew Independently of Population Size
Inflection Point
Logistic Growth
simple favorite in wildlife management
Rate of Increase is only a function of Population Density
Assumes resources are not damaged by large populations
Wildebeast don’t affect grass roots K #s
Ln (#s)
Time

26. Logistic Math
Verhulst (1838) and Pearl & Reed (1920) independently derived equation
Verhulst-Pearl Equation (Sigmoidal Growth)
dN/dt = derivative form of change in N with respect to time
dN/dt = rmN(1-N/K)
dN/dt = rmN = exponential growth
As N approaches K, N/K approaches 1. Therefore rmN(1- N/K) approaches 0

27. With K and Typical Seasonal Patterns of Reproduction, There is Often A “Doomed Surplus”
Mink control distribution of muskrats
those in poor sites including dispersers are eaten
Predators often take the young, homeless, sick, injured, dispersing, or old individuals
so effect on species or community is less
Good Sites
Poor Sites
High Pops
Density of Muskrats
Low
Pops
Deep
Water
Dry
Upland
(Errington 1946)

28. Logistic Growth Model May be Used to Calculate Harvest
Maximum Sustainable Yield is at Inflection Point
Growth is Maximum and Population is at Largest Size
Larger Populations Start to Have Slower Growth K
Maximum
Yield
=1/2 K #s
Ln (#s)
Time

29. Another View of Logistic Growth
Inflection Point
Max Sustainable
Yield
Growth rate starts slow, peaks, and ends slow
Maximum Sustainable Yield is at rate of fastest population growth
dN/dt K N

30. Assumptions of Logistic Growth
All individuals contribute equally to population growth--equal reproduction regardless of age or sex
Growth rate is constant regardless of environmental variation
K is constant--not affected by growth
Reduction in growth as population approaches K is linear and instantaneous (no time lags)

31. Populations fluctuate due to
Density dependent factors
Ex: Predation, competition, habitat availability
change population growth in predictable ways
N is driven by population density
Density independent factors
Random or Stochastic events
Ex. Weather, accidents
Breeding
Improve definition of deterministic
Today we will focus on deterministic factors
Stochastic events happen all the time. Scary with small population
14 aug 2007

32. Reindeer
(caribou)
# young
produced
Bighorn sheep
Population density (top) or size (bottom)

33. Population regulation: food
High food addition
Low food
addition
Townsend’s vole
No food
added
Shaded area is winter

34. Population regulation: food
Population cycles: Ex. peaks in lynx populations show time lag behind peaks in snowshoe hare populations
Snowshoe hare
Population size
Lynx
Time (years) 10

35. Population regulation: climate

36. Population regulation: competition
Competition – demand by 2 or more individuals of the same or different species for a common resource
Between 2 individuals of same species: Intraspecific
Between 2 individuals of different species: Interspecific
Limited supply of resource: Exploitation
Not limited but interaction detrimental: Interference

37. Inter- or Intraspecific competition
Inter- or Intraspecific competition? Exploitation or Interference competition?

38. Population regulation: competition