112
Mark S. Boyce
Catch-Limit Algorithm
To formulate a new CLA for the RMP, the Scientific Committee of the IWC
solicited harvesting algorithms from a number of scientists. Because whales are
long-lived and growth rates are slow, empirical validation of a CLA may not be
feasible. Instead, competing models were evaluated by using extensive simulation
trials of other more detailed models that included various forms of complexity to
see how well the CLA performed. Although the models had to meet each of the
three objectives established by the IWC, the principal criterion in the selection of
a CLA was that harvests would be conservative under the algorithm and afford
security of persistence for the stocks. The selected algorithm was one formulated
by Justin Cooke.
Model Structure
Cooke’s CLA is essentially an ad hoc statistical device that uses historical time
series of harvests and estimates of abundance to calculate an allowable current
harvest. The model underlying the CLA has no age structure and assumes that the
population was at equilibrium prior to exploitation,
N t+1 = N t − C t + rN t [1 − (N t /N 0 )
2
]
( 1 )
where N t = population size in year t, C t = catch in year t, and N 0 is the population
size prior to exploitation in year 0. In practice, N 0 = N T /D T such that stock
depletion, D T , is the ratio of the population size at the beginning of the catch quota
period, T (0 Յ t Յ T).
At low population density, the potential growth rate for the population, r =
1.4184µ, where µ is a productivity parameter and 1.4184 is a constant assigned to
whale productivity by the IWC for arcane historical reasons (because µ can be
adjusted, the 1.4184 is of no real consequence). The density-dependent response
that permits sustainable harvests is labeled “sustainable yield” in Figure 8.1. The
maximum sustained yield rate (MSYR) is 0.9456µ. Faithful application of the
CLA should eventually result in stock sizes no less than about 75% of preexploitation levels.
One of the most difficult problems associated with application of the CLA, and
a key criterion used in selection of a CLA, is how to deal with uncertainty in
parameter estimates. In general, fitting ecological models to data is difficult
because when sufficient ecological structure is included in the model, data are
seldom sufficient to estimate all parameters reliably. The IWC has taken the
approach of keeping the structural model as simple as possible, so that few
parameters need to be estimated.
The model is fitted by using a joint likelihood function similar to a Bayesian
procedure, but the CLA does not “learn” quickly (Anon. 1993) (i.e., catch limits
do not respond quickly to new data on stock estimates). The model is governed by
prior distributions for parameters, and the underlying population model is used to
Mark S. Boyce
Catch-Limit Algorithm
To formulate a new CLA for the RMP, the Scientific Committee of the IWC
solicited harvesting algorithms from a number of scientists. Because whales are
long-lived and growth rates are slow, empirical validation of a CLA may not be
feasible. Instead, competing models were evaluated by using extensive simulation
trials of other more detailed models that included various forms of complexity to
see how well the CLA performed. Although the models had to meet each of the
three objectives established by the IWC, the principal criterion in the selection of
a CLA was that harvests would be conservative under the algorithm and afford
security of persistence for the stocks. The selected algorithm was one formulated
by Justin Cooke.
Model Structure
Cooke’s CLA is essentially an ad hoc statistical device that uses historical time
series of harvests and estimates of abundance to calculate an allowable current
harvest. The model underlying the CLA has no age structure and assumes that the
population was at equilibrium prior to exploitation,
N t+1 = N t − C t + rN t [1 − (N t /N 0 )
2
]
( 1 )
where N t = population size in year t, C t = catch in year t, and N 0 is the population
size prior to exploitation in year 0. In practice, N 0 = N T /D T such that stock
depletion, D T , is the ratio of the population size at the beginning of the catch quota
period, T (0 Յ t Յ T).
At low population density, the potential growth rate for the population, r =
1.4184µ, where µ is a productivity parameter and 1.4184 is a constant assigned to
whale productivity by the IWC for arcane historical reasons (because µ can be
adjusted, the 1.4184 is of no real consequence). The density-dependent response
that permits sustainable harvests is labeled “sustainable yield” in Figure 8.1. The
maximum sustained yield rate (MSYR) is 0.9456µ. Faithful application of the
CLA should eventually result in stock sizes no less than about 75% of preexploitation levels.
One of the most difficult problems associated with application of the CLA, and
a key criterion used in selection of a CLA, is how to deal with uncertainty in
parameter estimates. In general, fitting ecological models to data is difficult
because when sufficient ecological structure is included in the model, data are
seldom sufficient to estimate all parameters reliably. The IWC has taken the
approach of keeping the structural model as simple as possible, so that few
parameters need to be estimated.
The model is fitted by using a joint likelihood function similar to a Bayesian
procedure, but the CLA does not “learn” quickly (Anon. 1993) (i.e., catch limits
do not respond quickly to new data on stock estimates). The model is governed by
prior distributions for parameters, and the underlying population model is used to