source-sink dynamics. remember, all landscapes are heterogeneous at some scale consequently, patch...

Source-Sink Dynamics


• Remember, all landscapes are heterogeneous at some scale

• Consequently, patch quality is heterogeneous

• All else being equal, individuals occupying superior habitat should have greater reproductive success


• Sources are areas or location where local reproductive success is greater than local mortality (r >0)

• Sinks are areas where individuals are reproducing, but the net reproductive rate is <0 (not replacement)

• Sinks will eventually become extinct if they do not receive immigrants from other areas.


• Why would individuals leave an area of higher quality?

• We get spatial dynamics of individuals dispersing from sources to sinks

r > 0


• Remember from our population growth models: Nt = Bt –Dt + It –Et

• In our previous models, we treated I and E as neglible

• However, in source-sink dynamics, the movement of individuals is paramount to understanding population dynamics at the landscape scale Nt+1 = Nt + (b – d + i –e )Nt


• To make population projects of a source-sink system, we need to know the numbers of individuals in each habitat type, as well as the BIDE factors for each habitat type


• Let’s examine the source

• Birth rate bt = Bt/Nt and Bt = btNt

• Immigration rate it = It/Nt and It = itNt

• Death rate dt = Dt/Nt and Dt = dtNt

• Emigration rate et = Et/Nt and Et = etNt

• If you assume constant per capita rates, we can lose all the “t’s” on rates

Nt+1 = Nt + (b – d + e – I )Nt


• Remember R = b + i - d – e• So Nt+1 = Nt +RNt

• ΔNt = RNt

• ΔNt /Nt = R (per capita rate of change)• Nt+1 = (1 + R)Nt (impact of R at time t)• Nt+1 = λNt • When λ=1, the population remains

constant


• Without dispersal, a source can be defined as a subpopulation where λ>1. this occurs only when b>d.

• A sink can be defined as λ<1, which occurs when b<d

• A source or sink population is in dynamic equilibrium when B+I-D-E = 0

• For a sink to be in equilibrium, e>i


• How is the equilibrium size of the greater population (source and sink) determined?

• If there are many habitats, the population reaches equilibrium when the total surplus in all the source habitats equals the total deficit in all the sink habitats

• Some basic take points from Pulliam’s (1988) ‘source-sink model’…


• At equilibrium, the number of individuals in the overall, greater population is not changing

• Each source and sink subpop(n) can be characterized by its “strength”, depending on its intrinsic rate of growth and the number of individuals present

• Within-subpop(n) dynamics (b,i,d,e) are important in determining eh overall equilibrium population size, since the numbers of individuals on each patch and their growth rates are implicit in the model


• The source-sink status of a subpop(n) may have little to do with the size (number of individuals) within the subpop(n)

• Sinks can support a vast number of individuals and sources can be numerically very small

• However, sources must have enough individuals with a high enough per captia production to support sink populations


• Objectives:• Set up a population model of two

subpop(s) that interact through dispersal• Determine how b, d, and dispersal affects

population persistence• Determine how the initial distribution of

individuals affects population dynamics• Examine the conditions in which a source-

sink system is in equilibrium

source-sink dynamics. remember, all landscapes are heterogeneous at some scale consequently, patch...

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