Ehrhardt and Deleveaux: Fishing capacity in a trap fishery for Panulirus argus 
187 
address the fishermen’s concerns regarding the TCP, 
the Florida Fish and Wildlife Conservation Commission 
(FWC) implemented a project to assess the status of the 
TCP under the existing conditions of the spiny lobster 
stocks and costs of the fishery. A comprehensive cost 
and social survey analysis was conducted in 2004 with 
FWC support. An assessment of the financial impact 
of different levels of stock abundance on the TCP was 
performed. As a corollary, one of the first tasks for the 
project was to test the hypothesis that the seasonal 
trap catchability should have been positively affected 
by the TCP. In this article we present the results of 
the research on the effects of the TCP on trap catch ef- 
ficiency, at both a fishery-wide and regional scale, and 
its financial impacts. 
Methods and Materials 
Evaluation of trap catch efficiency under the TCP 
A quantitative model was developed to estimate the 
seasonal catchability coefficient, q, and to study the 
resulting trends as the trap reduction schedules were 
implemented. A seasonal depletion model similar to 
those used in the scientific literature concerning fish- 
ery assessments (Chien and Condrey, 1985; Sanders, 
1988; Rosemberg et ah, 1990) was adopted using Pope’s 
(1972) approximation to Baranov’s catch equation. This 
approximation assumes that the total catch (C t ) real- 
ized in a given month (t) will be taken instantaneously 
at the middle of the month. Such an approximation 
generates unbiased estimates of population abundance 
at the beginning (N t ) and end (N l+1 ) of the time units 
given that the natural mortality rate (M) is not greater 
than 0.3/yr and fishing mortality rates are not greater 
than 1.2/yr. Hence, the basic population equation is 
expressed as 
N f _ 
N -< -C 
Ml 2 '-'t 
JW72 
( 1 ) 
and the average population abundance is expressed as 
( 2 ) 
Also, the relative stock abundance expressed as the 
catch in numbers per unit of effort (CPUE) in the time 
period t is assumed directly proportional to the average 
abundance. Hence, 
CPUE t = q, * N t , 
and therefore, 
Qi = 
CPUE t 
** t 
(3) 
Application of Equation 1 to express seasonal depletion 
in the spiny lobster fishery requires that N t varies with 
monthly fishing and natural mortality. However, at 
the beginning of the fishing season (August) the stock 
abundance is composed of the remainder of the previ- 
ous season’s stock abundance that escaped natural and 
fishing mortality (N t ), plus the new recruits (R t+I ) that 
accumulated during the closed season (April-July). In 
this manner, the abundance at the start of the season 
(August t+ 1) is expressed as 
N t + 1 - ^ 4 If + Rt+i- ( 5 ) 
The seasonal depletion model expressed by Equations 
1 and 5 was fitted to the monthly catch in numbers per 
unit of effort data for the period including the 1991-92 
through the 2002-03 fishing seasons, i.e., from the 
season previous to the base year for implementation 
of the TCP to the last fishing season when no further 
trap reductions were implemented. For this purpose the 
FWC provided landings and effort data for the commer- 
cial fishery extracted from the Marine Fisheries Infor- 
mation System. This system consists of all wholesale 
seafood dealers receipts of salt-water product purchases 
(trip tickets). Trip tickets show landings, fishing effort, 
gear, location, and date of landings per trip. The infor- 
mation used in this research is limited to the Florida 
Keys where most of the spiny lobster landings occur. 
Counts of the total number of traps deployed during 
the 1991-92 and 1992-93 fishing seasons were obtained 
from the National Marine Fisheries Service. Trap num- 
bers for subsequent seasons were obtained from the trap 
certificates issued by the State of Florida according to 
the TCP. Numbers of commercial trips per season were 
obtained from the trip ticket system for those records 
containing lobster landings. Numbers of recreational 
spiny lobster landings were obtained from the FWC. 
The FWC transforms the weight of commercial landings 
into numbers using sex and size frequency samples col- 
lected by the FWC and the National Marine Fisheries 
Service. The number of undersized lobsters used as at- 
tractants in the trap fishery was provided by the FWC 
from their observer program established in 1993. This 
program measures the total catch on selected commer- 
cial lobster fishing trips. 
The catchability coefficient was assumed to vary 
among the seasons following a random walk model of 
the type: 
<7, = q^z 1 , (6) 
where the £ t are annualized, and normally distributed 
with mean zero and variance o\. The model was fitted by 
minimizing the negative log-likelihood objective function 
using the Solver minimization tool in Excel (Microsoft 
Corp., Redmond, WA): 
§X(ln<V,)-ln<£7,)f 
t 
(4) 
(7) 
