SourceSink Dynamics

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 gt0)
• Sinks are areas where individuals are
  reproducing, but the net reproductive rate is lt0
  (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 gt 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

Nt1 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

• Lets 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 ts on rates

Nt1 Nt (b d e I )Nt
8
Source-Sink Dynamics

• Remember R b i - d e
• So Nt1 Nt RNt
• ?Nt RNt
• ?Nt /Nt R (per capita rate of change)
• Nt1 (1 R)Nt (impact of R at time t)
• Nt1 ?Nt
• When ?1, the population remains constant

9
Source-Sink Dynamics

• Without dispersal, a source can be defined as a
  subpopulation where ?gt1. this occurs only when
  bgtd.
• A sink can be defined as ?lt1, which occurs when
  bltd
• A source or sink population is in dynamic
  equilibrium when BI-D-E 0
• For a sink to be in equilibrium, egti

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 Pulliams (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