Population dynamics

1
Population dynamics

• Final slides about logistic model
• A review of the in-class exercise
• Cohort vs. Static Life Tables
• Why should you care about these calculations?
• A case study of where this made a difference
• A special case Small populations
• Why they are more vulnerable to extinction

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Logistic
3
Logistic
4
Logistic
New recruits each timestep
5
Logistic
6
Logistic
Rate of popn growth per individual (NOT CONSTANT)
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Population abundance (N)
Time
Highest population increase at intermediate
densities
dN/dt
Density (N)
Declining per capita contribution
dN/dt/N
Density (N)
8
Desert tortoises, Gopherus spp.
Mark-recapture data following individuals over 3
surveys (one survey every 5 years) Static life
tablewith some cohort info
sx (survival) from stage x to x1
0.27
0.24
0.24
0.10
0.21
0.11
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Desert tortoises, Gopherus spp.
bx
Juveniles (0-5)
Young Adults (6-10)
Middle age (11-15)
Older Adults (16-20)
sx
sx
sx
1
10.24 0.24
10.240.1 0.024
10.240.10.110.003
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Desert tortoises, Gopherus spp.
Mark-recapture data following individuals over 3
surveys (one survey every 5 years)
1.48
18.6
0.70
7.8
Generation time, G Sxlxbx / R0
18.6/1.48 12.53
7.8/0.70 11.20
Intrinsic rate of population growth
ra ln(R0) / G
ln(1.48)/12.53 0.03
ln(0.70)/11.20 -0.03
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Why?? Poaching/Harvest Egg predators Beach
development Collision with ships Fishing bycatch
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Crouse builds a model based on life-table (matrix
model)
Crouse et al. 1987 Ecology
Eggs/hatch 1yr
Sm juveniles 7yrs
Lg. juveniles 8yrs
Subadults 6yrs
Adults gt32yrs
Norbert Wu
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She systematically changed the survival and
fecundity rates.. -projected the population
growth rate into the future (r) -which one
results in the biggest change in r -determines
the most sensitive life-stage for population
growthfocus protection efforts
Even 100 survival of eggs/hatchlings doesnt
reverse decline!
Where should we invest conservation efforts to
reverse population decline?
Norbert Wu
changed survival by 10 (0.67 to 0.77)
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How to make models more realistic?

• Deterministicthis is what weve considered so
  far (demographic rates dont change)
• Stochastic- adding random noise or variation in
  rates makes the models more realistic (but also
  more complex)
• Especially important for accurately predicting
  small populations
• Most endangered species, some exploited species

15
Three reasons why populations may fail to
increase from low density

• rlt0 (deterministic decline at all densities)
• Depensation individual performance declines at
  low population size (deterministic decline at low
  densities)
• Below Minimum Viable Population susceptible to
  stochastic decline
• (demographic, environmental, genetic)

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Depensation

• Positive density dependence-- individuals do
  worse at low population size
• Resources are not limiting, but
• Mates difficult to find (Allee effect)
• Lack of neighbors may reduce foraging or breeding
  success, vulnerability to predators (flocking,
  schooling)

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Red abalone
Mechanism of depensation At low densities
successful spawning declines.mates too far away
Consequence of depensation Population growth
rate is LOWER with fewer individuals
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Deterministic decline in Snake R. Chinook salmon
across a wide range of densities (rlt0)
Kareiva et al. 2000 Science
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Draw a hypothetical graph of fecundity as a
function of population size for passenger pigeons
No density dependence
As would be the case for density-independent
population growth (geometric/exponential)
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Draw a hypothetical graph of fecundity as a
function of population size for passenger pigeons
Density dependent population regulation (logistic)
Births/individual/year
Population density (N)
Carrying capacity (K) when dN/dt/N0
21
Draw a hypothetical graph of fecundity as a
function of population size for passenger pigeons
Depensation
Births/individual/year
Density dependent population regulation (not
logistic)
Population density (N)
Carrying capacity (K) when dN/dt/N0
22
Small populations

• Dynamics governed by uncertainty
• compared to large population (law of averages)
• Demographic stochasticity random variation in
  sex ratio at birth, number of deaths, number
  reproducing
• (individual-levelbut when few individuals can
  have a big effect)
• Environmental stochasticity decline in
  population numbers due to natural disasters or
  more minor environmental events
• (effect of ENSO for Galapagos penguins?)

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Galapagos penguins and ENSO

• Galapagos penguin declines
• (IUCN Red List)
• -northern most penguin species
• -highly dependent on abundant fish (upwelling)
• 1982-1983 El Nino event 77 reduction in
  population
• 1988-1989 El Nino event 66 reduction in
  population
• Other factors fishing, exotic egg predators,
  oil spills

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Small populations

• Genetic stochasticity loss of genetic variation
  due to small numbers in reproducing population
• Inbreeding depression
• Reduction in genetic diversity
• Genetic drift
• Genetic problems probably occur slower than
  demographic problems at small population sizes
• BUT, reduced genetic variation has big effects
  for recovering populations (genetic bottlenecks)