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Source-Sink Dynamics

Source-Sink Dynamics. 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. Source-Sink Dynamics.

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Source-Sink Dynamics

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  1. Source-Sink Dynamics

  2. 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

  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: 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

  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 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

  8. Source-Sink Dynamics • 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

  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

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