Combining density dependence and independence weather and ecological interactions

Seeking to dissect out the relative contributions of direct and delayed density dependences, however, could itself be seen as prejudging the determinants of abundance by focusing too much on density-dependent, as opposed to density-independent, processes. Other studies, then, have examined time series precisely with a view to understanding how density-dependent and -independent factors combine in generating particular patterns

Snowshoe hare


2 1

1 0







. display three and two dimensions, respectively multimammate rats in Tanzania

Hawk owl

Golden eagle

Great horned owl



Red fox

Small rodents

Red squirrel



Ground squirrel

Willow ptarmigan

Golden eagle

Great horned owl



Passerine birds



Passerine birds




Bog birch

Grey willow

Soapberry White spruce Balsam poplar


Figure 14.10 (continued) (b) The main species and groups of species in the boreal forest community of North America, with trophic interactions (who eats who) indicated by lines joining the species, and those affecting the lynx shown in bold. (c) The same community, but with the interactions of the snowshoe hare shown in bold. (After Stenseth et al., 1997.)

of abundance. Leirs et al. (1997), for example, have examined the dynamics of the multimammate rat, Mastomys natalensis, in Tanzania. Using one part of their data to construct a predictive model (Figure 14.11a) and a second part to test that model's success (Figure 14.11b), they found first, in model construction, that variations in survival and maturation were far better accounted for by using both densities and preceding rainfall as predictors than by using either of these alone. In particular (Figure 14.11c), subadult survival probabilities showed no clear trends with either rainfall or density (though they tended to be higher at higher densities), but maturation rates increased markedly with rainfall (and were lowest at high densities following wet months), while adult survival was consistently lower at higher densities.

Estimates of demographic parameters (survival, maturation) from the statistical model were then used to construct a matrix model of the type described in Section 14.3.2, which was used in turn to predict abundance in the second, separate data set (Figure 14.11b), using rainfall and density there to predict 1 month ahead. The correspondence between the observed and predicted values was not perfect but was certainly encouraging

(Figure 14.11d). Hence, we can see here how the density, mechanistic (rainfall) and demographic approaches combine to provide insights into the determination of the rats' abundance. This example also reminds us that a proper understanding of abundance patterns is likely to require the incorporation of both density-dependent, biotic, deterministic effects and the density-independent, often stochastic effects of the weather.

Of course, not all the effects of the weather are wholly stochastic in the sense of being entirely unpredictable. Apart from obvious seasonal variations, we saw in Section 2.4.1, for example, that there are a number of climatic patterns operating at large spatial scales and with at least some degree of temporal regularity, notably the El Nino-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO). Lima et al. (1999) examined the dynamics of another rodent species, the leaf-eared mouse, Phyllotis darwini, in Chile and followed a similar path to Leirs and his colleagues in combining the effects of ENSO-driven rainfall variability and delayed density dependence in accounting for the observed abundance patterns.

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