Habitat Specific Demography

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(K- N/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 habitat- specific 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)

4 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

 = 1.0 then nT+1 = 100 if nT = 100 and  = 0.8 then nT+1 = 80

 = 1.2 then nT+1 = 120

5 (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.

6 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.

7 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.