Although the seeds of a source–sink model had been planted earlier, Pulliam is often recognized as the first to present a fully developed source–sink model. He defined source and sink patches in terms of their demographic parameters, or
BIDE rates (
birth,
immigration,
death, and
emigration rates). In the source patch, birth rates were greater than death rates, causing the population to grow. The excess individuals were expected to leave the patch, so that emigration rates were greater than immigration rates. In other words, sources were a net exporter of individuals. In contrast, in a sink patch, death rates were greater than birth rates, resulting in a population decline toward extinction unless enough individuals emigrated from the source patch. Immigration rates were expected to be greater than emigration rates, so that sinks were a net importer of individuals. As a result, there would be a net flow of individuals from the source to the sink
(see Table 1). Pulliam's work was followed by many others who developed and tested the source–sink model. Watkinson and Sutherland presented a phenomenon in which high immigration rates could cause a patch to appear to be a sink by raising the patch's population above its
carrying capacity (the number of individuals it can support). However, in the absence of immigration, the patches are able to support a smaller population. Since true sinks cannot support any population, the authors called these patches "pseudo-sinks". Definitively distinguishing between true sinks and pseudo-sinks requires cutting off immigration to the patch in question and determining whether the patch is still able to maintain a population. Thomas et al. were able to do just that, taking advantage of an unseasonable frost that killed off the host plants for a source population of
Edith's checkerspot butterfly (
Euphydryas editha). Without the host plants, the supply of immigrants to other nearby patches was cut off. Although these patches had appeared to be sinks, they did not become extinct without the constant supply of immigrants. They were capable of sustaining a smaller population, suggesting that they were in fact pseudo-sinks. Watkinson and Sutherland's who argued that differentiating between sources and sinks themselves may be difficult. She asserted that a long-term study of the demographic parameters of the populations in each patch is necessary. Otherwise, temporary variations in those parameters, perhaps due to climate fluctuations or natural disasters, may result in a misclassification of the patches. For example, Johnson described periodic flooding of a river in
Costa Rica which completely inundated patches of the host plant for a rolled-leaf beetle (
Cephaloleia fenestrata). During the floods, these patches became sinks, but at other times they were no different from other patches. If researchers had not considered what happened during the floods, they would not have understood the full complexity of the system. Dias described a source—pseudo-sink inversion in butterfly populations of
E. editha. who examined
wood thrush (
Hylocichla mustelina) survey data for evidence of source and sink populations on a large scale. The authors reasoned that emigrants from sources would likely be the juveniles produced in one year dispersing to reproduce in sinks in the next year, producing a one-year time lag between population changes in the source and in the sink. Using data from the
Breeding Bird Survey, an annual survey of North American birds, they looked for relationships between survey sites showing such a one-year time lag. They found several pairs of sites showing significant relationships 60–80 km apart. Several appeared to be sources to more than one sink, and several sinks appeared to receive individuals from more than one source. In addition, some sites appeared to be a sink to one site and a source to another (see Figure 1). The authors concluded that source–sink dynamics may occur on continental scales. One of the more confusing issues involves identifying sources and sinks in the field. Runge et al. and ecological statistics in order to differentiate sources and sinks. ==Modes of dispersal==