1. Source-Sink Dynamics

2. 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

3. Source-Sink Dynamics 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.

4. Source-Sink Dynamics Why would individuals leave an area of higher quality? We get spatial dynamics of individuals dispersing from sources to sinks r > 0

5. Source-Sink Dynamics Remember from our population growth models: N t = B t –D t + I t –E t 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 N t+1 = N t + (b – d + i –e )N t

6. Source-Sink Dynamics 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

7. Source-Sink Dynamics Let’s examine the source Birth rate b t = B t /N t and B t = b t N t Immigration rate i t = I t /N t and I t = i t N t Death rate d t = D t /N t and D t = d t N t Emigration rate e t = E t /N t and E t = e t N t If you assume constant per capita rates, we can lose all the “t’s” on rates N t+1 = N t + (b – d + e – I )N t

8. Source-Sink Dynamics Remember R = b + i - d – e So N t+1 = N t +RN t ΔN t = RN t ΔN t /N t = R (per capita rate of change) N t+1 = (1 + R)N t (impact of R at time t) N t+1 = λN t When λ=1, the population remains constant

9. Source-Sink Dynamics 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

10. Source-Sink Dynamics 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’…

11. Source-Sink Dynamics 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

12. Source-Sink Dynamics 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

13. Source-Sink Dynamics 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