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

The Theory of Island Biogeography (MacArthur & Wilson 1967)

Near

Far

log Area

log

S

Colonization

= dispersal Ext

inct

ion

= d

rift

Dispersal brings new species

Dispersal allows populations to occur/persist in unsuitable habitat, elevating local diversity

+

-

Fitness dif (A-B)

+

-

A wins B wins

no dispersal

Freq(A)0 1 Freq(A)0 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

+

-

Fitness dif (A-B)

+

-

A wins B wins

Small competitive advantage for A Big competitive advantage for B

dispersal(per capita)

Dispersal interacts with selection:A local advantage can translate into regional dominance

+

-

Fitness dif (A-B)

+

-

A wins B wins

Big competitive advantage for A Small competitive advantage for B

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] <- 1COMa[(J/2+1):J] <- 2

COMb <- vector(length=J)COMb[1:J/2] <- 1COMb[(J/2+1):J] <- 2

# dispersal ratem <- 0.2

# set number of “years” to run simulations & empty matrix for datanum_years <- 50prop_1 <- matrix(0,nrow=J*num_years,ncol=2)

# run modelfor (i in 1:(J*num_years)) {

# chose cell for deathdeath_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))]

elseCOMa[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)/Jprop_1[i,2] <- sum(COMb==1)/J

}

Limited dispersal allows drift to create differences between

communities

0 500 1000 1500 2000 2500

0.0

0.2

0.4

0.6

0.8

1.0

Time

Fre

q(A

)

0 500 1000 1500 2000 25000

.00

.20

.40

.60

.81

.0

Time

Fre

q(A

)

Mean local richness = 1Regional richness = 2

Mean local richness = 1.5Regional richness = 2

Limited dispersal allows drift to create differences between communities (and vice versa)

2 simulations of 2 communities with 2 species (A & B) Jlocal = 50, m = 0

High beta diversity; Regional richness will eventually be 1 or 2

0 500 1000 1500 2000 2500

0.0

0.2

0.4

0.6

0.8

1.0

Time

Fre

q(A

)

0 500 1000 1500 2000 25000

.00

.20

.40

.60

.81

.0

Time

Fre

q(A

)

Limited dispersal allows drift to create differences between communities (and vice versa)

2 simulations of 2 communities with 2 species (A & B) Jlocal = 50, m = 0.2

Mean local richness = 2Regional richness = 2

Mean local richness = 2Regional richness = 2

Low beta diversity; Regional richness will eventually be 1

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)

Freq(A)0 1

(This type of dynamic is probably quite common in nature: r-K species)

Good colonizer

Good competitor

Succession

2 species many species

- 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

+

-

Complex frequency-dependence

Fitness dif. (A-B)

Freq(A)0 1

sp. A colonizes first and dominates before sp. B gets there

sp. B colonizes first and dominates before sp. A gets there

Expected equilibrium if…

( priority effects & multiple stables states)

A framework for incorporating dispersal into community ecology

Leibold et al. (2004, Ecology Letters)

Patch dynamics(showing competition-colonization tradeoff)

Leibold et al. (2004, Ecology Letters)

Species sorting

Mass effectsNeutral

Dispersal + Selection (freq.

dependent locally)

Dispersal + Selection

(constant locally, spatially

heterogeneous)

As in (b) but with higher dispersal

Dispersal + drift

The metacommunity framework(examples with 2 competing species, 3 patches)

Key questions for determining community consequences of

dispersal:

(1) The composition of the dispersers

(2) The selection/drift regime where the dispersers arrive