Populations: Variation in time and space

1
Populations Variation in time and space

• Ruesink Lecture 6
• Biology 356

2
Temporal variation

• Due to changes in the environment (e.g., ENSO,
  seasons) OR
• Due to inherent dynamics
• Lag times
• Predator-prey interactions (LATER)

3
Figure 15.11
Oscillations occur when population growth occurs
faster than density dependence can act
population overshoots
4
Figure 15.13
Larval food is limited Larvae do not have enough
food to reach metamorphosis unless larval density
is low
adults
larvae
5
Figure 15.14
If food is limited for adults, then they cannot
lay high densities of eggs. Low densities of
larvae consistently survive.
6
Three reasons why populations may fail to
increase from low density

• rlt0 (deterministic decline at all densities) OR
• Depensation individual performance declines at
  low population size (deterministic decline at low
  densities) OR
• Below Minimum Viable Population stochastic
  decline

7
Depensation

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

8
Deterministic decline in Pacific salmon across a
wide range of densities (rlt0)
Kareiva et al. 2000
9
Passenger Pigeon Millions to billions in North
America prior to European arrival 1896 250,000
in one flock Probably required large flocks for
successful reproduction 1900 last record of
pigeons in wild 1914 Martha dies
Deterministic extinction from low population size
10
Draw a hypothetical graph of fecundity as a
function of population size for passenger pigeons
11
Draw a hypothetical graph of fecundity as a
function of population size for passenger pigeons
No density dependence
Births/individual/year
Population density (N)
12
Draw a hypothetical graph of fecundity as a
function of population size for passenger pigeons
Carrying capacity when dN/dt/N0
Births/individual/year
Population density (N)
13
Draw a hypothetical graph of fecundity as a
function of population size for passenger pigeons
Depensation
Births/individual/year
Population density (N)
14
Heath hen (Picture is related prairie
chicken) 1830 only on Marthas Vineyard 1908
reserve set up for 50 birds 1915 2000
birds 1916 Fire eliminated habitat, hard winter,
predation, poultry disease 1928 13 birds, just 2
females 1930 1 bird remained
Stochastic extinction
15
Small populations

• Dynamics governed by uncertainty
• Large populations by law of averages
• Demographic stochasticity random variation in
  sex ratio at birth, number of deaths, number
  reproducing
• Environmental stochasticity decline in
  population numbers due to environmental disasters
  or more minor events

16
Small populations

• Genetic problems also arise in small populations
• Inbreeding depression
• Reduction in genetic diversity
• Genetic problems probably occur slower than
  demographic problems at small population sizes

17
Minimum viable population

• Population size that has a high probability of
  persisting into the future, given deterministic
  dynamics and stochastic events

18
Initial population size
What is the minimum viable population of Bighorn
Sheep, based on model results?
19
Spatial variation

• No species is distributed evenly or randomly
  across all space

20
Figure 15.15
Individuals may be clumped due to underlying
habitat heterogeneity
21

• Individuals may also occur in a clumped
  distribution due to habitat fragmentation by
  human activities

22
Population

• Group of regularly-interacting and interbreeding
  individuals

23
Metapopulation

• Collection of subpopulations
• Spatially structured
• Previously weve talked about population
  structure in terms of differences among
  individuals Age structure

24
Metapopulation

• Dynamics of subpopulations are relatively
  independent
• Migration connects subpopulations (Immigration
  and Emigration are non-zero)
• Subpopulations have finite probability of
  extinction (and colonization)

25
Metapopulation dynamics

• Original classic formulation by R. Levins 1969
• dp/dt c p (1-p) - e p
• p proportion of patches occupied by species
• 1-p proportion of patches not occupied by
  species

26
Metapopulation dynamics

• dp/dt c p (1-p) - e p
• c colonization rate (probability that an
  individual moves from an occupied patch to an
  unoccupied patch per time)
• e extinction rate (probability that an occupied
  patch becomes unoccupied per time)

27
Metapopulation dynamics
28
Metapopulation dynamics
29
Metapopulation dynamics
30
Metapopulation dynamics
31
Metapopulation dynamics
32
Metapopulation dynamics
33
Metapopulation dynamics
34
Classic metapopulations

• At equilibrium, dp/dt 0 and p 1 - e/c
• Metapopulation persists if eltc
• Specific subpopulation dynamics are not modeled
  (but can be) only model probability of
  extinction of entire metapopulation

35
Classic metapopulations

• Lesson 1 Unoccupied patches or disappearing
  subpopulations can be rescued by immigration
  (Rescue Effect)
• Lesson 2 Unoccupied patches are necessary for
  metapopulation persistence

36
In real populations

• Subpopulations can vary in
• Size
• Interpatch distance
• Population growth type
• D-D or D-I
• value of r
• Quality

37
Figure 15.16
38
Figure 15.17a
39
Figure 15.17b
40
Classic metapopulation

• Subpopulations have independent dynamics and are
  connected by dispersal

41
Mainland-Island metapopulation

• R. MacArthur and E.O. Wilson 1967
• 1 area persists indefinitely and provides
  colonists to other areas that go extinct

42
Source-Sink metapopulation

• R. Pulliam 1988
• In sources, Rgt1
• In sinks, Rlt1
• Sinks persist because they are resupplied with
  individuals from sources

43
Source-Sink metapopulation

• Do all subpopulations with high l have high
  density?
• Which would contribute more to conservation, high
  l or high density?