Cooper and Mangel: Metapopulation structure in the conservation of salmonlds 



215 



not cover the complete metapopulation. First, if man- 

 agers are looking strictly at the abundance of indi- 

 viduals, they could be lulled into a false sense of se- 

 curity. The size of the demes in the source and sink 

 habitats could be relatively constant despite the fact 

 that, without the demes in the source, the demes in 

 the sink would become extinct. Brawn and Robinson 

 (1996) uncovered this very scenario with Neotropi- 

 cal migrant birds in Illinois. 



The second problem is even more insidious. If deme 

 abundance is no longer a good indicator of habitat 

 quality, managers could be led into conserving the 

 wrong type of habitat (van Home, 1983; Pulliam, 

 1988). Gowan and Fausch ( 1996) demonstrated how 

 this could occur regarding the effects of habitat 

 changes on the demography of a variety of trout spe- 

 cies in Colorado, although they did not discuss their 

 results in terms of metapopulations. Over an eight- 

 year period (four generations of trout), Gowan and 

 Fausch ( 1996) discovered that the addition of woody 

 debris in treatment areas significantly increased the 

 number of individuals and the total trout biomass in 

 treatment areas in relation to the control areas. How- 

 ever, with the aid of fin marks (clipped fins) and in- 

 dividual tags, they discovered that survival, indi- 

 vidual growth, and recruitment rates in the treat- 

 ment areas were not significantly different from those 

 in the control areas. Immigration from outside the 

 study area to the treatment sites was solely respon- 

 sible for the increase in abundance and total biom- 

 ass. If Gowan and Fausch (1996) had not been able 

 to account for immigration to the site, they would 

 likely not have been able to discern the true effects 

 of the addition of woody debris and would have likely 

 mistaken increased density for increased habitat 

 productivity (cf Hunter, 1991 ). Although source-sink 

 metapopulation structure was not the cause of these 

 results, such an example demonstrates how reliance 

 on abundance or density estimates can lead manag- 

 ers astray when immigration or emigration is not 

 taken into consideration. 



Those faced with the responsibility of managing 

 salmonid populations may encounter these very prob- 

 lems and issues. In the remainder of this paper, we 

 develop a model to help focus ideas about the poten- 

 tial dangers of undetected metapopulation structure 

 for salmonid conservation. 



Materials and methods 



The model 



The model is simple, and the form of the model was 

 chosen for ease of comprehension. We found that even 



such a simple model was adequate to illustrate the 

 possible consequences of ignoring metapopulation 

 structure. 



We considered a group of generic salmonid demes 

 that reside in streams that are distributed evenly 

 along some waterway but that are close enough so 

 that straying between any of the two groups is pos- 

 sible (though not necessarily with equal probability). 

 The scale was completely generic. The streams could 

 be tributaries to a single river, rivers within a wa- 

 tershed, or even separate watersheds. Next, we num- 

 bered these streams consecutively along this water- 

 way. Each deme was then indexed by the number 

 associated with the stream in which it resides (e.g. 

 deme 4 resides between deme 3 and deme 5 along 

 this waterway). For computational purposes, we con- 

 sidered 10 streams, which is equivalent to a 

 metapopulation consisting of 10 demes spread over 

 10 patches. Assuming that density-dependent effects 

 could be ignored (which, except for AUee effects, 

 would be the case for any recovering population), the 

 fundamental variables are 



N{i,t) = the deme abundance in stream ( in year t; 

 r{i,t) = the per-capita reproduction in stream / in 



year t; 

 s(J,i,t) = thenumber offish that stray from their na- 

 tal streamy to stream / in year t; and 

 f = the fraction of fish that stray from their na- 

 tal stream (assumed equal for all demes). 



For simplicity's sake, we assumed that strays have 

 the same reproductive potential as nonstrays in a 

 given stream. This assumption decreases the param- 

 eter space but does not affect overall dynamics of the 

 model. It does, however, limit the direct applicabil- 

 ity of our specific examples to streams that are rela- 

 tively close in proximity, yet, as will be explained, 

 does not diminish the danger for management at the 

 watershed, basin, or even ESU level. By incorporat- 

 ing an additional parameter to account for the dif- 

 ferential reproductive potential, some of the dynam- 

 ics would simply have been dampened, making them 

 more difficult to perceive. Therefore, the population 

 dynamics for a deme are 



NiiJ + 1} = r(i,t)\N{i,t)a- f) + ^s(j,i,tn . (1) 



As with differential reproduction, the assumption 

 that there are more complicated population dynam- 

 ics (e.g. Ricker stock-recruitment relationships) 

 would not change the basic message of our paper but 

 would make it harder to perceive. In a more compli- 



