Checkerspot on the news

Patrick Foley patfoley at csus.edu
Mon May 8 16:59:24 EDT 2000


Leppers,

    Ron Pulliam's idea for sources and sinks defines sink populations as
those in deterministically disadvantageous patches (Expected r < 0) (Pulliam
1988. American Naturalist 132:652-661). Susan Harrison's patches are not
sinks in that sense. They go extinct due to environmental stochasticity
(weather related mostly) (Foley 1994. Conservation Biology). They do belong
to a metapopulation (in the broad sense) in which as John Shuey states large
patches act as the main sources of colonists. Narrow sense metapopulations
(in Levins' original model) depend on all the patches for persistence.
    While my criticism of the term "source-sink metapopulation" for use in
the case of the bay checkerspot is semantic (definitional), it is important
to avoid confusing the already confusing language of metapopulations. Ilkka
Hanski 1999, Metapopulation Ecology covers this ground on p. 50. Ilkka
argues that even source-sink metapopulations (in the deterministic-sink
sense) may get some persistence from their sinks.Susan's metapopulation may
get even more help from the transient patches Nonetheless it is true that in
metapopulations with varying patch size, the smaller patches are most
dispensable.
    Incidentally, the persistence of metapopulations has only been modeled
effectively for the simplest cases, such as the Levins' metapopulation with
no correlated extinctions between patches. Russ Lande has done some work on
this as have I.

Patrick Foley
patfoley at csus.edu

John Shuey wrote:

> Neil at NWJONES.DEMON.CO.UK wrote:
>
> > Well the developer's argument about the species' absence has little
> weight
> > when the known mathematical models of the species population dynamics
> are
> > taken into account.
> > It actually matters little whether the butterfly is present in any
> period
> > rather whether the site is suitable and reasonably close to an
> occupied one.
> >
> > As I have said before checkerspot populations exist in
> metapopulations.
> > These are linked groups of colonies where individual colonies become
> extinct
> > to be eventually colonised from their neighbours. The classical model
> of
> > metapopulation
> > dynamics postulates that  the number of occupied patches P at a given
> time
> > t is given by dP/dt=cP(1-p)-eP where c and e are colonisation and
> > extinction rates.
> >
> > What can be clearly seen from the mathematics is that EMPTY habitat is
> a
> > fundamentally inherant component of the system. So suitable but
> unoccupied
> > habitat in the vicinity of occupied habitat must be conserved.
> >
> > In fact if the mathematics is expanded on and worked up then the most
> modern
> > experssion of it is the Incidence Function Model developed by
> Professor
> > Ilkka Hanski at Helsinki. I know at least one of his team is
> subscribed
> > so if I get it wrong I will be corrected.
> > The model is far too complex to state in an email but it can be
> simplified
> > to an approximation that states that 3 times the Square root of the
> habitat
> > patches need to be occupied in order for the system to be stable.
> > It can be seen from this that there could be an awful lot of empty but
>
> > necessary habitat in the system.
> >
>
> Unfortunately, this is a simplification based on traditional
> metapopulation models, applied
> to an animal that doesn't fit the traditional model.
>
> As I remember, most folks think that Bay Checkerspots are structured as
> a Source-Sink
> metapopulation as opposed to the traditional (albeit very rare) true
> (extinction-recolonization) metapopulation.  The persistence of a
> source-sink metapopulation,
> for example, depends on the viability of the source population.  The
> smaller, occasionally occupied sinks contribute little, if anything, to
> the long-term
> persistence of the metapopulation (Susan Harrison 1991). Thus, only the
> factors influencing the viability of the source population (e.g., patch
> area and population
> densities) are of management concern.  The Bay Checkerspot is usually
> heralded as the stereotypical source-sink metapopulation animal in the
> US (and Harrison
> originated the concept after working with the species as part of
> Ehrlich's
> group).
>
> Conversely, in an extinction-recolonization structure, all local
> populations are vulnerable
> to extinction, and thus, influential in the persistence of the
> metapopulation.  In this type of structure, the factors controlling
> extinction and
> recolonization rates  (e.g., number of occupied and unoccupied patches,
> patch
> size, patch population densities, arrangement of patches and corridor
> availability) (Harrison
> 1991, Neve et al. 1996) are of management concern. In the US, the
> Karner Blue is the poster child for this type of population structure.
>
> The implications are severe from a conservation standpoint.  With a
> source-sink model it is
> fairly easy to argue that small "sink" populations are not important
> for survival.  In this case, the source population (associated with a
> landfill and managed
> for the butterfly) is supposedly secure.  Because other occupied or
> unoccupied habitat patches presumably do not influence population
> persistence at the source,
> they may be deemed non-vital for the conservation of this animal.
>
> I'm not endorsing this approach (in part because I think that there are
> other, genetic
> implications to population persistence in a dispersal friendly world),
> but
> it is an easy one to argue based on the math.
>
> --
> John Shuey
> Director of Conservation Science
> Indiana Office of The Nature Conservancy
>
> phone:  317-923-7547
> fax:  317-923-7582
> email:  Jshuey at tnc.org


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