Models of the effects of varying fishing mortality on the slope of size spectra
have focused on the various processes that lead to changes in slope, specifically:
(1) the differential reduction in the abundance of larger species that are more
vulnerable to a given rate of mortality, (2) within-population changes in mean
body size and life history due to the direct effects of fishing on the population,
(3) genetic changes in life history and (4) predator–prey relationships in the
community that result in proliferation of small species and individuals that are
better able to tolerate a given rate of fishing mortality and benefit from deple-
tion of their predators. Responses (1) and (2) are governed by the links between
body size, life histories and response to mortality that we considered above.
Existing theoretical models that describe the structure of size spectra and their
response to fishing have principally focused on (1), (2) and (4) (e.g. Boudreau
et al., 1991; Dickie, Kerr & Boudreau,1987b; Kerr,1974; Thiebaux & Dickie,
1993 ). Response (3) is arguably as important as the others in the medium- to
long-term and there is a developing body of theory and empirical observation at
the population level that would allow genetic effects to be addressed (Law,2000;
Law & Stokes, 2000 ; Heino & Godo,2002). Some recently published modelling
results suggest that the effects may not be intuitive due to the interplay between
the selection caused by fishing and changes in predation pressure on different
size classes (Thygesenet al., 2005; Persson & De Roos, this volume).
In models of fishing effects on community size structure, the capacity to
partition the direct and indirect effects of fishing and to understand how they
interact is critical in providing insight into the effects of fishing. Gislason and
Rice (1998) used a combination of existing length-based fishery models and
multispecies models to predict the slopes and intercepts of size spectra for a
community consisting of 11 fish species that account for much of the fisheries
production in the North Sea. Fishing mortality increased the slope of the size
spectrum. Building on this approach, Popeet al.(2006) generalized the model for
a community of species defined by their maximum body sizes (asymptotic
length L 1 as defined in the von Bertalanffy growth model, in 10 cm length
classes from 10 cm to 130cm). We discuss this model in a little detail, as it gives
important insights into the links between size-based population and commun-
ity responses to fishing and could provide a basis for predicting and managing
the impacts of fishing on size-based communities.
For each species (S), the number (N) surviving from one length class (L) to the
next, where successive length classes are denoted 1 and 2 was given as:
NL 2 ;S¼NL 1 ;S L^1 ðSÞL^2
L 1 ðSÞL 1
ZðkLð^1 S;ÞSÞ
( 14 : 5 )based on the fisheries assessment method of length cohort analysis (Jones,
1974 ), whereZ(L1,S) is the total mortality rate (y^1 ) at lengthL1 for the species
andkis the Brody growth parameter from the von Bertalanffy growth model
BODY SIZE AND EXPLOITATION 277