Theoretical community models:
Incorporating dispersal
Community consequences of dispersal
• Dispersal brings new species
• Dispersal allows persistence in unsuitable habitat
(“sinks”)
• Dispersal can counteract (or reinforce) local
selection
• Dispersal can counteract drift (flipside: limited
dispersal allows communities to drift apart)
• If dispersal ability is negatively correlated with
competitive ability (i.e., there is a tradeoff) across
species, stable coexistence can be maintained
Dispersal brings new species
log S
The Theory of Island Biogeography (MacArthur & Wilson 1967)
log Area
Dispersal allows populations to occur/persist
in unsuitable habitat, elevating local diversity
0
Fitness
dif (A-B)
Freq(A)
1
0
+
+
-
A wins
Freq(A)
B wins
no dispersal
1
Dispersal allows populations to occur/persist
in unsuitable habitat, elevating local diversity
Fitness
dif (A-B)
+
+
-
A wins
B wins
dispersal
(per capita)
Dispersal interacts with selection:
Can allow an inferior competitor to overcome a
selective disadvantage
Fitness
dif (A-B)
+
+
-
A wins
B wins
dispersal
(per capita)
Dispersal interacts with selection:
A difference in dispersal balanced by a difference in
selective advantage
Small competitive advantage for A
Fitness
dif (A-B)
Big competitive advantage for B
+
+
-
A wins
B wins
dispersal
(per capita)
Dispersal interacts with selection:
A local advantage can translate into regional dominance
Big competitive advantage for A
Fitness
dif (A-B)
Small competitive advantage for B
+
+
-
A wins
B wins
dispersal
(per capita)
(1) A bunch of “patches”
(2) A single (and
different) species has
selective advantage in
each patch
(3) Small differences
among species in
“fitness” (# propagules
contributed to regional
“pool”)
no difference in
degree of local
selection
variants
of (3)
# Set initial communities (e.g., 25 individuals of sp. 1 + 25 of sp. 2; J = 50)
J <- 50 # must be an even number
COMa <- vector(length=J)
COMa[1:J/2] <- 1
COMa[(J/2+1):J] <- 2
COMb <- vector(length=J)
COMb[1:J/2] <- 1
COMb[(J/2+1):J] <- 2
# dispersal rate
m <- 0.2
Limited dispersal allows drift to
create differences between
communities
# set number of “years” to run simulations & empty matrix for data
num_years <- 50
prop_1 <- matrix(0,nrow=J*num_years,ncol=2)
# run model
for (i in 1:(J*num_years)) {
# chose cell for death
death_cell <- ceiling(J*runif(1))
# pick randomly between two sites for a death; chose replacer from
# other site with probability m; from same site with probability (1-m)
if (runif(1) > 0.5) {
if (runif(1) > m)
COMa[death_cell] <- COMa[ceiling(J*runif(1))]
else
COMa[death_cell] <- COMb[ceiling(J*runif(1))]
} else {
if (runif(1) > m)
COMb[death_cell] <- COMb[ceiling(J*runif(1))]
else
COMb[death_cell] <- COMa[ceiling(J*runif(1))]
}
prop_1[i,1] <- sum(COMa==1)/J
prop_1[i,2] <- sum(COMb==1)/J
}
Limited dispersal allows drift to create differences
between communities (and vice versa)
0.6
0.4
Freq(A)
0.6
0.2
0.4
0.0
0.2
0.0
Freq(A)
0.8
0.8
1.0
1.0
2 simulations of 2 communities with 2 species (A & B)
Jlocal = 50, m = 0
0
500
1000
1500
2000
Time
Mean local richness = 1
Regional richness = 2
2500
0
500
1000
1500
2000
Time
Mean local richness = 1.5
Regional richness = 2
High beta diversity; Regional richness will eventually be 1 or 2
2500
Limited dispersal allows drift to create differences
between communities (and vice versa)
0.6
0.4
Freq(A)
0.6
0.2
0.4
0.0
0.2
0.0
Freq(A)
0.8
0.8
1.0
1.0
2 simulations of 2 communities with 2 species (A & B)
Jlocal = 50, m = 0.2
0
500
1000
1500
2000
Time
Mean local richness = 2
Regional richness = 2
2500
0
500
1000
1500
2000
Time
Mean local richness = 2
Regional richness = 2
Low beta diversity; Regional richness will eventually be 1
2500
Stable coexistence can be maintained if there is a trade-off among
species between competitive ability and colonization ability
Pseudo-code for 2 species
A is a good disperser & poor competitor; B is the opposite
for loop
Kill a bunch of individuals
Each species sends out a bunch of dispersers (A > B, per capita)
If A lands in an empty cell, it occupies it
If A lands in a B cell, it dies
If A lands in an A cell, non-event
If B lands in an empty cell, it dies (or has low prob of occupying it)
If B lands in an A cell, it kicks out A and occupies the cell
If B lands in a B cell, non-event
stop for loop
If A (good disperser) gets too common, then B will kick it out
almost anywhere B lands
If B (good competitor) gets too common, it will have few places
to colonize, and empty cells will accumulate for A to colonize.
Negative frequency-dependence
Fitness
dif (A-B)
+
0
Freq(A)
1
(This type of dynamic is probably quite common in nature: r-K species)
many species
2 species
Good competitor
Good colonizer
Succession
- Predators cause prey to go locally
extinct, which in turn causes predator to
go extinct
- Prey better at getting to empty sites
- Predators “chase” prey through space,
but prey stay one step ahead
= stable coexistence
Is the effect of dispersal on
communities stochastic?
The trajectory of community dynamics (abundances of
multiple species) can be greatly changed colonization
order or by the presence/absence of particular species
We don’t know who’s coming next (i.e., arriving via
dispersal)
Therefore, the effect of dispersal on communities is
(partly) stochastic
Expected equilibrium if…
sp. B colonizes first
and dominates before
sp. A gets there
sp. A colonizes first
and dominates before
sp. B gets there
+
Complex
frequencydependence
Fitness
dif. (A-B)
0
Freq(A)
1
( priority effects & multiple stables states)
A framework for incorporating dispersal into community ecology
Leibold et al. (2004, Ecology Letters)
The metacommunity framework
(examples with 2 competing species, 3 patches)
Patch dynamics
(showing competitioncolonization tradeoff)
Dispersal +
Selection (freq.
dependent locally)
Mass effects
As in (b) but with
higher dispersal
Leibold et al. (2004, Ecology Letters)
Species sorting
Dispersal +
Selection
(constant locally,
spatially
heterogeneous)
Neutral
Dispersal + drift
Key questions for determining
community consequences of
dispersal:
(1) The composition of the dispersers
(2) The selection/drift regime where
the dispersers arrive