Wainwnght et al.: Effects of dredging on a crab population 



173 



Figure 2 



Historical landings in the Washington coastal Dungeness crab 

 fishery. Sources: 1920-47, Cleaver (1949); 1948-50, Wash. 

 Dep. Fish. (1951); 1951-87, Pac. Mar. Fish. Comm. (1989); 

 1988-91 are preliminary estimates (S. Barry, Wash. Dep. 

 Fish., Olympia, pers. commun.). 



as density stratified by age, season, and location. 

 Dredging is described as the volume dredged by a par- 

 ticular gear in a location during a given season. Unad- 

 justed loss figures are converted to equivalent adult 

 loss by multiplying by the expected survival of crab 

 from a certain age-class and season to adulthood. This 

 approach is shown schematically in Figure 3, and 

 described in detail below. Because we could not resolve 

 older age-classes within our survey data, a crab was 

 considered to reach adulthood in winter of its age 2 + 

 year (i.e., approaching the end of its third year post- 

 settlement). 



Calculating losses in this manner requires an underly- 

 ing concept of population dynamics and several simpli- 

 fying assumptions. Creating a detailed model of local 

 dynamics for a mobile benthic animal is difficult; there 

 is continuous mortality and migration among habitats, 

 the rates of which may vary with season, age, and 

 locality. This may be summarized by the usual mass- 

 balance equation for change in the population in a local 

 area over a discrete time period: 



N(ti) = N(to) + R-M-E-HI, 



(1) 



where N is population abundance, to and tj are two 

 times, R is recruitment to the population (settlement), 

 M is mortality, E is emigration, and I is immigration. 

 Mortality and migration rates are rarely known ac- 

 curately (certainly not in our problem), so we have 

 taken an empirical approach to defining population 



Volume Dredged 

 (gear, season, location] 



Unadjusted Loss 



E 



Natural MortaJity 

 (age. season) 





Equrvaleni Adurt Loss 



Figure 3 



Flowchart of Dungeness crab adult loss model, showing main 

 variables and structural categories (in parentheses). 



abundance. The approach is similar to, but simpler 

 than, that taken by Boreman et al. (1981) for power 

 plant entrainment in an estuary. The model is a discrete 

 time, discrete age-population model with discrete 

 habitat structure. To allow for seasonal changes in 

 abundance or population structure, the year is sub- 

 divided into four seasons. Thus the population can be 

 described as the numbers in various age-classes pres- 

 ent in various habitat areas during particular seasons. 

 In our model, abundance of any age-class in an area 

 during a single time-step is taken to be the average 

 abundance estimated from field surveys. We assume 

 that all changes in abundance (i.e., mortality or migra- 

 tion) occur between time-steps, so that populations are 

 constant throughout a step. This assumption introduces 

 little error if the change during a step is small Oess than 

 about 10%), which will be true if time steps are relative- 

 ly short and rates of change are relatively low. To meet 

 this assumption in our application, we defined variable- 

 length seasons of relatively constant population struc- 

 ture (see Data and Estimation section below). 



The starting point for our calculations is estimated 

 total crab density (D) for locations (1) and seasons (s), 

 combined with age-class proportions (P). (Variables are 

 fully defined in Table 1.) The second set of informa- 

 tion needed for the calculation is the dredging schedule, 

 expressed as volume dredged (V) by a specific gear type 

 (g) in a specific location and season. For planning 



