5.1 . Three-Age-Cohort Model and Fishing
75
perature , availability of food, and age-specific predation, all of which exert an
influence on fish length throughout a fish's life history (Cushing 1968). The
length of any individual fish at any particular age is determined by these factors (Pitcher and Hart 1982) as well as by the fish's genetic make-up.
Fishing-the dominant anthropogenic factor in many marine systemsexerts selective pressure on specific groups of individuals within a population through the fisherman 's choice of specific mesh sizes and minimum
length requirements for landings. This selectivity varies among gear types.
For example, the meshes of mobile fishing gear, such as bottom and otter
trawls, and seine nets, will generally retain fish whose girth is greater than
the circumference of the opening. Winger et al. (999) found that the herding efficiency of bottom trawls for American plaice (Hippoglossoides platessoides) is highly dependent on fish size and water temperature, whereas the
gill nets will capture only those fish whose girth and shape allow them to
become entangled in the mesh. In contrast, hooks tend to select for smaller
fish, since larger fish are able to break free (Royce 1972). The selectivity of
each of these gear types will also vary due to day/night differences in behavior. For example, Korsbekke and Nakken (999) showed that catch of
Atlantic cod (Gadus morhua) and haddock (Melanogrammus aeglefinus) increases during daylight hours and declines at night.
Increased fishing pressure often disproportionally affects mortality of older
and larger fish. The remaining younger and shorter fish tend to produce offspring which are themselves short. Thus, fishing may not only remove older
and larger fish, but skew the average size of subsequent generations towards
smaller fishes. Let us develop a model that captures these dynamics.
Assume there are three age cohorts of fish: zero to one year old, one to
two years old, and two to three years old . Assume also that each age cohort
has members that are either short , medium or long. Thus , we need six state
variables to capture each individual group of fish within our population.
Begin by laying out the model for the three age cohorts of short fish as
shown in Figure 5.1.
Specify the initial stocks of the zero- to one-year-olds, one- to two-yearoIds, and two- to three-year-olds as 100, 76, and 67, respectively . Define the
deaths of short fish in the zero- to one-year-old cohort as
SHORT DEATHS 01 = SHORT MORTALITY 01 • SHORTYEAR 01
0)
and use an analogous definitions for the deaths of the one- to two-yearoids. If we assume there are only three age cohorts, then
SHORT DEATHS 2 3 = SHORTYEAR 2 3.
(2)
The individuals in the first two cohorts that do not die will move on to
become members in the next higher cohorts . For example:
SHORTAGE 01 =(I-SHORT MORTALITY 01) • SHORT YEAR 01.
(3)
75
perature , availability of food, and age-specific predation, all of which exert an
influence on fish length throughout a fish's life history (Cushing 1968). The
length of any individual fish at any particular age is determined by these factors (Pitcher and Hart 1982) as well as by the fish's genetic make-up.
Fishing-the dominant anthropogenic factor in many marine systemsexerts selective pressure on specific groups of individuals within a population through the fisherman 's choice of specific mesh sizes and minimum
length requirements for landings. This selectivity varies among gear types.
For example, the meshes of mobile fishing gear, such as bottom and otter
trawls, and seine nets, will generally retain fish whose girth is greater than
the circumference of the opening. Winger et al. (999) found that the herding efficiency of bottom trawls for American plaice (Hippoglossoides platessoides) is highly dependent on fish size and water temperature, whereas the
gill nets will capture only those fish whose girth and shape allow them to
become entangled in the mesh. In contrast, hooks tend to select for smaller
fish, since larger fish are able to break free (Royce 1972). The selectivity of
each of these gear types will also vary due to day/night differences in behavior. For example, Korsbekke and Nakken (999) showed that catch of
Atlantic cod (Gadus morhua) and haddock (Melanogrammus aeglefinus) increases during daylight hours and declines at night.
Increased fishing pressure often disproportionally affects mortality of older
and larger fish. The remaining younger and shorter fish tend to produce offspring which are themselves short. Thus, fishing may not only remove older
and larger fish, but skew the average size of subsequent generations towards
smaller fishes. Let us develop a model that captures these dynamics.
Assume there are three age cohorts of fish: zero to one year old, one to
two years old, and two to three years old . Assume also that each age cohort
has members that are either short , medium or long. Thus , we need six state
variables to capture each individual group of fish within our population.
Begin by laying out the model for the three age cohorts of short fish as
shown in Figure 5.1.
Specify the initial stocks of the zero- to one-year-olds, one- to two-yearoIds, and two- to three-year-olds as 100, 76, and 67, respectively . Define the
deaths of short fish in the zero- to one-year-old cohort as
SHORT DEATHS 01 = SHORT MORTALITY 01 • SHORTYEAR 01
0)
and use an analogous definitions for the deaths of the one- to two-yearoids. If we assume there are only three age cohorts, then
SHORT DEATHS 2 3 = SHORTYEAR 2 3.
(2)
The individuals in the first two cohorts that do not die will move on to
become members in the next higher cohorts . For example:
SHORTAGE 01 =(I-SHORT MORTALITY 01) • SHORT YEAR 01.
(3)