Lec.8
Habitat Specific Demography
Intro
Traditional thinking
Much of the history of wildlife management has dealt with habitat. We were
interested in habitat not for its own sake, but because we assumed that knowing
something about habitat (which is easily measured) would tell us something about species
population dynamics (which is not easily measured). We really care about how many of
a commercial or game species are present or how close to extinction were species in
trouble.
We made two critical assumptions.
1. Habitat suitability = species abundance=fitness.
2. That population processes are homogeneous in space.
The second is that when we do examine actual population dynamics it is ok to so
without consideration of space. Since a population is defined as occupying a specific
geographic area, we assumed that demographic rates were constant across this area and
that individuals mixed freely within the population.
birth
death
Population size
immigration
emigration
Hence, pop size=(N)(B+I-D-E). We ignore I and E, pop size= (b-d)N or =rN.
(exponential)
Or with logistic to predict the population size at some time in the future. dN/dt=rN(KN/K). Where K is carrying capacity.
New Thinking
We have come to realize that habitats are patchy and consequently that rates of
birth, death, and dispersal vary from place to place within the range of a population.
Consequently, abundance of a population within a habitat may not be a good measure of
fitness. A species may be abundant in the habitat not because fitness is high, but because
rates of immigration are high. These realizations have spawned a flourish of new
thinking on habitat specific demography. Challenges have been to develop habitatspecific models, to get field data to parameterize these models, to understand the
consequences of spatial and temporal heterogeneity for population dynamics and to
1
incorporate this knowledge into management and conservation. This thinking is young
and we have much to learn.
Today
Metapopulation dynamics
Source/sink dynamics
Application to protected areas
Current state
Metapopulation Concept
Some of the original thinking on this was by Levins (1969, 1970) who coined the
term metapopulation, "a population of populations" or a collection of subpopulations,
each occupying a suitable patch of habitat in a landscape of otherwise unsuitable habitat.
suitable
suitable and
occupied
Time 1
Time 2
Time 3
The fraction of suitable habitats occupied is a function of the rate at which patches go
extinct vs the rate that new patches are colonized.
Percent suitable habitat occupied = f(extinction rate, colonization rate)
Extinction reflects population size and chance events.
Colonization reflects dispersal ability of the organisms and the location of suitable
habitats in the landscape.
Now small subpopulations are prone to extinction, but they can be rescued from
extinction by immigrants from other subpopulations. Hence, Levins showed that
partially isolated subpopulations could lead to overall stability of the
metapopulation even though the subpopulations showed nonequilibrium behavior.
Years later conservation biologists seized on this theory to describe populations
scattered across isolated habitats and are in trouble. What subpopulations, habitat
patches, or links among patches are critical to maintaining a viable population? Several
good case studies emerged that demonstrated that this approach could help understand
real world dynamics of some species.
Could do acorn woodpecker example if time allows.
Generalizations were quickly drawn, e.g., that maintaining connectivity between
fragmented habitats was critical to population persistence, hence corridors are needed.
Also, big patches are better than small patches.
2
Source/sink theory
Sometimes some of the occupied habitats are much better than others allowing
high rates of survival and reproduction. These source habitats produce excess individuals
that move to the lower quality habitats. If reproduction does not offset mortality here,
these are sink habitats that would go extinct without immigrants from sources.
Implications: A small proportion of the population may be in source habitats and
maintain the rest of the population. Pulliam showed as few as 10 % could be in source
and maintain the population. So it is no longer sufficient to designate for conservation
places of high species abundance, we must instead identify source areas.
+
-
+
+
-
3
Mathematics of source/sink
Consider a seasonal population that breeds in summer.
(1) nT = number of individuals at the end of winter (T is time one or year 1)
(2) b = per adult birth rate
if no adults die in the breeding season and each adult produces b offspring then:
population size at the end of breeding = nT + bnT
(3) if PA = probability of adult survival in the non breeding season, and
PJ = probability of juvenile survival in the non breeding season, then
the expected number of individuals alive at the end oof the winter and just before
spring dispersal is given by:
nT+1 = PAnT + PJbnT
(4) Manipulating the equation, we get: nT+1 = PAnT + PJbnT = nT(PA + PJb)
Let  = (PA + PJb)
 is the finite rate of increase for the population, it gives the number
of individuals at the beginning of the year T + 1, per individual at the
beginning of the year T.
nT+1 = nT
if nT = 100 and
 = 1.0
 = 0.8
 = 1.2
then nT+1 = 100
then nT+1 = 80
then nT+1 = 120
4
(5) Birth and death in a habitat vary from year to year so:
 is the mean of  over several years
if   1 the population grows
if  < 1 the population shrinks
(6) Birth and death also vary by habitat so we need habitat-specific .
Source habitats are where   1 .
Sink habitats are where  < 1.
(7) Metapopulation dynamics reflects the weighted averages of the subpopulations.
Consider the case of 2 habitats (1 source, 1 sink) with dispersal among them.
1  1
2 < 1
Contributions from source to sink
Assume in source, the subpopulation grows at  1 until all breeding areas
are saturated and it reaches the maximum population size where all
breeding sites are occupied (n1*).
n1* = maximum population size in habitat 1
The remaining n1*(1-1) must go from the source to the sink.
If n1* = 100 and 1 = 1.2 then 100(1.2 – 1) = 20, 20 individuals go from
source to sink.
Size of sink population
If immigration from the source is sufficient to offset death in the sink, then
the subpopulation in the sink will persist.
n2* = the equilibrium population size in the sink
n2*= n1*(1-1) / (1-2)
n2* = per capita increase in the source/ per capita deficit in the sink.
5
If the per capita increase in the source is much bigger than the deficit in the sink,
the sink can have a larger population than the source.
If n1* = 100 and 1 = 1.2, then n2* =
n2*= n1*(1-1) / (1-2)
= 100(1.2-1) / (1-.7)
= 100(.2) / (.3)
= 100(.66) = 66
2 = .7
n2* =66
2 = .8
n2* =100
2 = .9
n2* =200
2/3 of the population is in the sink.
Thus, the sink can have a greater population size than the source.
Main Messages
Abundance in a habitat is not necessarily a good index of habitat quality.
A metapopulation may be lost if the source area is destroyed.
Community composition may reflect not so much local resources and
conditions, but also those across the region, thus, “landscape” studies are
needed.
Unifying Conceptual Model (omit this, simply point out the x axis)
As metapopulation theory was applied to increasing numbers of species, purists
were quick to point out that many of the applications were not to classic metapopulations.
Classic model assumes each suitable patch is of similar quality and dispersal is just
moderate. Here is a more complete model.
Both habitat heterogeneity and species-specific dispersal abilities influence population
dynamics (Fig 5.8). The more patchy the environment, the more animal survival,
reproduction, and abundance will differ among patches, leading to habitat specific
demography among subpopulations. If a species can disperse well among habitat patches
(patchy populations), then rescue effects are likely among subpopulations and risk of
extinction is reduced. Here source/sink models best apply (they assume good dispersal).
As dispersal ability decreases relative to habitat peachiness and the likelihood of
movement of individuals among subpopulations decreases (classic metapopulations),
then chance of local extinction increases, hence metapopulations can wink in and out.
Where dispersal is very poor and subpopulations do not exchange individuals (nonequilibrium metapopulations), extinction of individual subpopulations and, consequently,
the overall metapopulation is more likely. As we come to realize the high level of spatial
heterogeneity that abiotic factors impose on organism survival and reproduction, it
becomes apparent that such metapopulation dynamics are more common in nature than
previously appreciated. Thus, no need to get hung up on if a pop is a classic metapop.
The real question is are spatially explicit model of pop dyn needed to understand a
population.
6
Source sink
Implications for conservation: protected areas
Current state of application of spatial models to conservation and management
Mangers face biodiversity dilemma. Want to know pop dynamics and pop
viability, but can usually can only afford to get data on habitat. Thus tremendous interest
in using spatially-explicit approaches and increasing number of case studies. Some use
source/sink mathematics, others model individuals in a population (e.g., SPOW). But
because of data and knowledge limits, we still deal with habitat for most species.
Tremendous opportunity to link landscape ecology and population dynamics now.
Supporting literature
Pulliam, H.R. 1988. Sources, sinks, and population regulation. The American Naturalist
132:652-661.
Pulliam, H.R. Sources and sinks: Empirical evidence and population consequences. Pages
45-56, 63-69 in O.E. Rhodes, R.K. Chesser, and M.H. Smith, eds. Population
Dynamics in Ecological Space and Time. The University of Chicago Press,
Chicago, Ill.
7