new perspectives in managing endangered species. When we are dealing with the habitat of a species, we believe that the species has found the best environmental conditions. Pulliam, working on sparrows, has demonstrated that species recognize the quality of a patch probably indirectly, when the survival of individuals is menaced by starvation or high risk of predation. The patchy nature of the habitats (in sensu stricto) was not fully considered before the Pulliam model. A gradient of quality for habitats is the rule and not the exception in nature and habitat-specific demography plays a relevant role in regulating natural populations.

According to the Pulliam demographic model (see Table 3.1), Lambda is the finite rate of increase for populations and appears positive in the source habitat and negative in the sink habitat.

The source-sink dynamic is de facto the confirmation that patchiness operates not only on vegetation patterns but also at the level of animal populations. Along a suitable period of time, it is possible to observe in the same habitat populations of source type and in other years populations with sink characteristics. In order to evaluate in a determined time lag if a habitat has a positive or negative demographic trend, Pulliam suggests the calculation of the geometric mean of all (X1X2X3.. At)1/i. If the mean of X on a long period is <1, the population declines; on the contrary, if X>1, the population has a net gain.

The model proposed has been further implemented by Watkinson and Sutherland (1995), who introduced the concept of pseudo-sink. According to this model, some populations considered sink can maintain a minimum population also in the absence of migration, and this is a further confirmation of the complex dynamics of populations in patchy habitats.

In many cases some patches are true ecological traps for species that are attracted by some factors like food, roosting availability, nesting suitability, but other factors like disturbance, predation, or competition can produce a negative balance in the

Table 3.1 Demographic source-sink model (from Pulliam 1988, 1996)

ut = Individuals at the end of winter B = Offspring ut+Put = Individuals alive at the end of the breeding season Pa = Adults that survive during the nonbreeding season Pj = Juvenile survival ut+1 = PaUt+PjPut=ut(Pa+PPj)=Aut Population at the beginning of the next year Lambda = (Pa+PPj) is the finite rate of increase for the population

In a heterogeneous environment habitats may sustain source or sink populations with different levels of A 1,2,3

If A1 > A2 then A1 is source and A2 is sink u1*= is the maximum size of a source population

A1u1* = Individual at the end of the nonbreeding season

A1-1 = per capita reproductive surplus in the source habitat

A2-1 = per capita deficit in the sink habitat u1*(A1-1) = Number of individuals that migrate in sink habitats u2*=u1*(A1-1)/(1-A2) Equilibrium in a population of type sink population. In this case, we can observe a denser population in such habitats that in reality is the result of immigration fluxes from other source habitats.

The source-sink model opens up new perspectives on the mosaic theory indicating that often the local density of a population is a misleading indicator of habitat quality. The seasonal variation in habitat quality for a species can determine characters of source in one season and of sink on another occasion. This source-sink patchiness allows better understanding of the dynamic of populations, especially over a long period. Some good habitats can be found empty while other habitats that are considered poor habitats can be found to be full of organisms. In conclusion the demography of populations is quite far from being understood in detail, and the role of patchiness could be more important than suspected in the past.

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