Spatial Model for the Population Dynamics and Exploitation of the ...

ation Dynamics and Exp oitation of Rock Lobster, Panulirus cygnus

the Weste

Carl ). Walters Resource Ecology, University of British Columbia, Vancouver, BC 1/6P 1 &V5,Canada

and Norm Hall, Rhys Brown, and Chris Chubb Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Peking University on 05/28/13 For personal use only.

Western Australia Marine Research Laboratories, P.O. Box 20, North Beach, %VesternAustralia 6020

Walters, C.]., N, Hall, R. Brown, and C. Chubb. '1 993. Spatial model for the population dynamics and exploitation of the Western Australian rock lobster, Panulirus cygnus. Can. 1. Fish. Aquat. Sci. 50: 1 650-1 662. There is concern about whether long-standing regulatory measures (size and effort limits) are adequate to protect spawning stocks of the Western Australian rock lobster, h n u l i r u s cygnus, and assure the highest average yields. Virtual population analysis and tagging studies indicate that exploitation rates are extremely high (possibly exceeding 70%/yr) on younger, mainly immature lobsters. To predict the efficacy of alternative regulatory schemes, it has been necessary to explicitly model the spatial and temporal dynamics of lobster abundance and fishing effort. 0 areas, and at 3-5 yr of age in most Puerulus settlement (at age 9-1 1 mo) is mainly into shallow-water ( ~ 4 m) areas, there is a migration into deeper water where the animals mature after a further 1-2 yr. The size at migration (70-90 mm-8carapace (ength) ensures that at least some animals w i l l have a chance to reach the breeding grounds offshore, where fishing effort has historically been lower than inshore, before they reach the minimum legal size (76 m m carapace length). By explicitly modelling the effort distribution as well as lobster movement and stock distribution, we hope to anticipate some consequences of changes in management policy that could not he predicted from biological assessments alone. O n s'inquiete pour la protection des stocks de geniteurs de la langouste d'Australie, Panulirus eygnus, par les vieilles mesures de reglementation (limites quant A la taille et A I'effort de capture). O n se demande aussi si ces mesures peuvent maximiser les rendements moyens. Selon I'analyse des populations virtueiles et les ktudes de rnarquage, les taux d'exploitation des jeunes langaustes, immatures surtout, sont extremement eleves (ils pourraient meme depasser 70 %/an). Pour pr6dire I'efficacit6 des rGgIements projetes comme solutions de rechange, i l a fallu moddiser explicitement la dynamique spatio-temporelle de I'abondance et de l'effort de peche de la [angouste. Les puerulus s'etablissent (A 9-1 '1 mo) en eau peu profonde principalement ( ~ 4 m) 0 et, 2 3-5 ans, dans la plupart des endroits oh ils se sont ktablis, ils rnigrent vers les eaux plus profondes oir les langoustes srrivent A maturitk apres un d d a i d'encore 1 ou 2 ans. La taille A la migration (longueur de carapace de 70 A 90 mm) fait en sorte qu'au moins certains anirna~rxauront une chance d'atteindre les zones de reproduction du large, oh ['effort de peche a toujours 6te inferieur 2 l'effort en eaux cdtieres, avant d'atteindre la taille minimaie de capture autorisee (longueur de carapace de 76 mm). En modelisant explicitement la repartition de I'effort de meme que le deplacernent et /a repartition des stocks de ia langouste, nous esperons pritvoir certaines consequences d'un changernent dans la politique d'amenagement, qui pourraient ne pas &re predites uniquement 2 partir des seules 6valuations biologiques. Received March 3 1, 7 992 Accepted March 5, 1993 j.JB4.55)

s Australia's largest single-species fishery, the western rock lobster, Panukir~scJygaux, has been the focus sf intensive research and management analyses over the past three decades. Ira 1963, it was one of the first major fisheries in the world to have a liimited-entry policy for effort control (Bowen 19'71; ?dorgan 1980; Hancock 1981). Since 1907, catches have been relatively stable at a o m d 10 000 t, with an annual landed value of AUS$120-200 million. The main regulatory measures to avoid biological overfishing and promote economic efficiency have been the establishment of a minimum size limit ('76 rn carapace length), the requirement to return ovigerous females to the sea, the setting of limits on the total number of lobster pots, a d a seasonal closure from I July to 14 November. There have also been regulatory measures to avoid waste, including escape gaps that dlow undersize lobsters to 1650

Re~B ue 3 7 mars 1 992 Accept4 /e 5 mars 7993

leave the pots, and delayed season openings in the Abrolhos Islands regulatol zone to avoid problems of handling newly moulted animals during the hot midsumer period. Fishers are dlowed to fish in each of three regulatory zones (A, B, and C) along the Western Australian (WA) coast (Fig. 1). The key policy issues at this time are whether the existing regulatory system will remain adequate to prevent overfishing in the face of increasing gear efficiency and fishing expertise and whether average yields and overall efficiency might be increased by altering key regulations such as the minimum size limit. TO make credible assessments or predictions about these issues, careful examination of the spatial and temporal dynamics of both the stock and the fishing effort is required. There are four key stages in the life cycle of the western rock lobster: (1) the 9- to I 1-mo planktonic larval period, where larvae from all along the Can. J. Fish. Aqunb. Sci., Vul. $0, 19993

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ability to fishing; and (4) maturation 1-2 yr after migration to contribute to the offshore spawning stock (Morgan et al. 1982). An exception to this pattern occurs in the Abrolhos Islmd area, where animals mature in shallow and deep areas at 40-70 mm carapace length, a year or two before becoming vulnerable to fishing. At present, fishing is mainly concentrated on juvenile lobsters in the shallow-water areas and on whites migrating into deeper water. Less effort occurs in deeper water (where the spawning stock is concentrated), apparently due to the various returns, costs, risks, and discomfort of fishing further offshore. Fishers generally go out from port each day (or every few days when fishing is poor) to remove catches and redistribute pots. Lobsters are landed alive within a few hours after removal from the pots. Changes in fishing technology and/or regulations could substantially alter the fishers' incentives for targeting on shallow versus deep water, and hence, on exploitation patterns in relation to lobster size and maturity. This paper describes a simulation model we have developed to help evaluate the possible consequences of altering size and effort limits and fishing season times. The model explicitly represents the spatial and temporal dynamics sf the stock and of fishing effort by predicting abundance and effort distribution over a grid of spatial cells off the WA coast. We have tuned the parameters of the model to fit historical catch and effort data as closely as possible, m d we compare policy alternatives by doing b i g h t have" rather than "what if" c o m p ~ s o n sWe . also ask the model to predict what might have happened in the past, given historical patterns of disturbances such as oceanographic effects on larval settlement, if alternative policies had been followed. We believe that this is a safer and more credible use of the model, as compared with, for example, demanding that it make outright forecasts of future changes in the fishery. The model is programmed for a personal computer such that it hcilitates rapid comparison of policy alternatives and testing of the sensitivity of its predictions to various uncertain parameters.

Model Structures and Assumptig~ns

FIG.1. Coast of Western Australia showing major ports and fishing zones fos western rock lobster. The two different grid cell sizes used in the model (fast and slow versions) are shown on the 30's latitude. Small cells are 16 x 16 km and larger cells are approximately 100 x 50 b.

coast are mixed and transported over large distances in the Indian Ocean (Phillips 1981); (2) puerulus settlement that occurs mainly in shallow waters, followed by 3-5 yr of inshore residence and growth (the majority of animals reach the 76-mrn size limit during this period (Morgan et al. 1982)); (3) an offshore migration by 70-90 lrarrn immature animals in a pale ("white") colsur phase, taking place over a short period (2 mo) following a November-December moult, and involving very high vulnerCan. J. Fish. Aquat* Sci., Vol. 5OV1993

The simulation model consists of a series s f submodels for updating population stmcture and the distribution of fishing effort over "fortnightly" (15-d) time steps, for up to 45 yr. The baseline starting simulation year is taken to be H 944 (1944- 1945 fishing season), when catch and effort first began to increase rapidly. The simulation year commences in nid-November, when the annual rock lobster fishing season opens. The fortnightly time step is used for most calculations within each simulation year, rather than simpler equations integrating changes over an annual time step, in order to capture the seasonality of growth (moulting), recruitment, migration, closed fishing seasons, and redistribution of fishing effort in response to migration and seasonal depletion of more accessible (inshore) lobster concentrations. The lobster population structure is represented as a size distribution (numbers by 4 - m length class, 60-100 + nun carapace length) in each of a series of rectangular spatial cells extending along the WA coast and offshore, from Shark Bay in the north to Augusta in the south (Fig. 1). The model can be run with various cell sizes (spatial resolutions), ranging from a detailed 250-cell version (16 x 16 h cells, Fig. 1) to a much simpler "fast9' version with 12 cells each representing 1" latitude and 0.5" longitude (roughly 100 x 50 h, Fig. I). Most of our


parameter estimation and gaming has keen with the fast version, which requires only about 2 s of computing time for each simulation year (24 biweekly steps) on a personal computer with 20-MHz 88386 processor and 80387 math coprocessor. We have only used the detailed version to check the fast model results because the detailed calculations require about 12 s of computing time per ye= For each simulation yea, the submodel calculations are organized to reflect the natural annual cycle of changes beginning in the spring (September-November). First, a spawning1 recmitment submodel calculates aggregate egg production over the spatial grid (over the whole stock), and predicted total recmitment (to the 6 0 - m and larger size structure) 3 yr hence. Next, a set of submodels perfoms the following calculations for each of 24 fortnights within the year: (1) moult animals (grow them) into larger length classes; (2) apply natural mortality to d l length classes; (3) add new recruits moulting into the 60-63 rnm size class; (4) move some animals into a separate white (migrant) size structure, and revert postmigrant animals to the normal (red-sedentary) type; (5) predict total fishing effort for each regulatory zone and distribute this effort among the cells in the zone; (6) predict and remove catches and release mortalities (of undersize) from the length distributions (red and white); and (7) move white animals m o n g cells to represent the offshore migration. Finally, the results of the fortnightly calculations (e.g., cumulative catches, efforts) are summarized for graphical display as the simulation proceeds. The following sections describe the various submodels in more detail,

The stock and recruitment calculations involve three steps: (1) sumation of annual egg production; (2) prediction of average recmitment (to 60 m carapace length, at age 3) as a function of egg production (stock-recruitment relationship); and (3) adjustment for the deviation from the average recruitment using a time series of estimates of relative puerulus settlement, available for the period 1868-88. Steps (1) and (2) are typical of dynamic pool models in fisheries assessment; step (3) allows the model to reproduce historical stock dynamics more realistically and precisely, making the "might have9' policy compksons more credible. The contribution of each spatial cell to egg production is estimated from the length distribution of lobsters in a cell by assuming that mean fecundity (proportion mature females times eggs per mature female times proportion female) is linearly related to body length above a threshold length at maturity (Morgan 1972; Chubb et al. 1989). There are Iage differences in the length at maturity between the Abrolhos Islands and K a l b d (north coast) weas (60-70 m)compared with more southerly areas (80 m)(Chubb et al. 1989;Chubb 1993). These differences are represented by assigning each spatial cell to a "growth zone" where each zone is assigned a unique size at maturity and slope for the fecundity versus length relationship. Given total egg production E(t) for a year, recruitment of $ 0 - m lobsters in year t + 3, R(t + 3), is predicted using the product of a Beverton-Holt stock-recruitment prediction SsEI(1 + sEIR*) m d an "environmental effect" P(t)d to produce a modified Beverton-Holt recruitn~entequation of the form

where S is the survival rate from puerulus settlement to age 3, s is the maximum number of puemlus settling per egg E(P),R* is the maximum average recruitment rate of puen~lussettling when E(t) is large, P(t) is an index of relative puen~lussettle ment based on historical measurements, and d is a "density dependence" parameter measuring the strength of the regression relationship between historical puemlus settlement and subsequent recmitment to 60 n m carapace length. The index P(f) is adjusted to have a mean of 1.0 over the historical data period (1968-88); d values below 1.8 imply that recmitment ends up being more than proportional to P(t) for low settlement years (P(t) below 1.O) and less than proportional for high settlement years, i.e., low settlements underestimate recruitment, while high settlements overestimate it. The R* and d parameters were estimated by "tuning" the model to historical data, in coujunction with the estimation of catchability (see Parmeter estimation: Tuning the Model to Historical Data below). We took S to be exp(-3M), where M = 0.23 is the instantaneous annual natural mortality rate assumed for older animals (Morgan 1977 ; see next section). Ht is likely the natural mortality rate is higher for age 1-3 lobsters (Soll 19841, but we had no way to estimate that rate directly. However, this is not a critical issue because the key requirement is to estimate recruitment to age 3 when the animals first become vulnerable to pots. Provided s is sufficiently large, recruitment to age 3 will on average be equal to SR*; when lower S values are assumed, the model-tuning procedure will simply assign higher values to R* so as to ensure that the final recruitment is high enough to explain observed catches. The really critical uncertainty in the recruitment calculation is about s. This parmeter determines the risk of recmitment overfishing because sS represents the slope of the stock-reeruitment relationship for low spawning stock sizes. There is no evidence in the historical puerulus settlement or catch data that there has been recruitment overfishing (Morgan 1977; Morgan et al. 1982). Environmental effects, in particular, water currents, probably play a major role in the level of puemlus settlement and hence recmitment to the fishery (Peace and Phillips 1988; Caputi and Brown 1989; Peace 1989). However, management measures, such as improved enforcement to prevent the sale of undersize lobsters and pot modifications to provide more escape gaps for small lobsters (Brown and Caputi 1986), could also be responsible for a modest increase in recruitment to the fishery over the past 20 yr. Lacking any evidence of overfishing, we chose to set s = 0.0001 (1 puerulus per 10 080 eggs). This is an optimistic assumption about the egg-puerulus survival rate; s would have to be an order of magnitude lower for the model to predict significant recruitment overfishing (50% reduction in recruitment, or greater) given our best estimates of historical stock size and exploitation rates. Vdlues of s below about 0.5 times the assumed value would predict recruitment overfishing for policies that result in a decline of 50% or more in the spawning stock from its present level, which is not an unrealistic future scenario based on the current high exploitation estimate.

Ccm. 9.Fish. Aquaf. Sci'i., Voi.50, I993

TABLE1. Assumed gmportions of rock lobsters moulting by season (indexed by month), size, and coastal region. Region Southern


Length (mm)

No%:

Female length at maturity Slope fecundity versus length (1000 eggdmm)

May

Feb.

Abrolhos Aug.

No&:

Feb.

May

Dsngaa Aug.

Nov.

Feb.

May

Aug.

80 10.00

Gradh and Natural MsMity Fortnightly growth and survival are modelled using the equations

whereA(L i,j) is the number of lobsters in length class L in spatial cell k,j after fishing in any fortnight, N(L9iJ ) is the number in the lengtwcell before fishing for the next fortnight, m&w) is the proportion moulting from length class E to L + 1 in fortnight w, SIV = exp 6-Mi24) is the fortnightly natural sunrival rate, and R(w,i,j) is the recruitment to length class 1 (60-63 m carapace length) for cell iJj in fortnight w. The key assumption in this representation of growth is that animals either remain in a length class or moult into the next larger class. The average moult increment for western rock lobsters of 60-100 m carapace length is around 4 nun in most areas (Chittleborough 1974,1975, 1976; Chittleborsugh and Phillips 1975; Morgan 1977; Phillips et d . 1977, 1983; Joll 1984; Joll and Phillips 1984), so moving up two length classes per moult is unlikely (this is why we chose as the length class width). In the Abrolhos Islands, mature females usually only grow about 2-3 mn per moult (Morgan %977),which was represented by reducing the probability m(E,w) of moulting to the next larger class for those cells i9j representing the Abrolhos area. Our growth "model" is essentially the matrix rn(L,w) representing the probability of moulting (and moving up, on average, 4 n m in size) for animals of different sizes (L) in different fortnights (w). We constructed m( L,w) tables (Table 1) by examining reported growth patterns based on laboratory and tagging studies (Chittleborough 1975, 1976; Chittleborough and Phillips 1975; Morgan 1977; Phillips et al. 1977,1983; Joll1984; Joll and Phillips 1984). For lobsters 60 m and larger, moulting Can. J. Fish. Aqucdt. Sci., Vol. 50. 1993

is concentrated in four periods, in the months of November, March, June, and August-September; to save corn puter storage, we assumed that rn(L,w) = O for all w except the four fortnights corresponding to the middle of these periods. Most animals except for breeding females are assumed to moult in the November period, and lager animals are assumed to m i s s more of the autumn and winter moults. The overall effect of the assumed moulting pattern is to produce a length-age pattern that looks much like a von Be~talanffygrowth curve, with distributions of lengths at age around the curve that are roughly noma%(unless grossly distorted by fishing) with coefficients of variation that are about 10% of the mean lengths at age. The fortnightly recruitment rate R(w7i9j)for cell i,j is c d culated from the predicted total recruitment rate for the year, R(t) (see above), by apportioning R(d) among cells and fortnights as R(w,i,j) = r(w)c(ij)R(t). Here, r(w) is the proportion of recruits reaching 60 mrn carapace length in fortnight w of their third year after settlement, and c(i,j) is the proportion sf the recruits that are assumed to have settled (and grown to 60 m)in cell i,j. We assume that 0.4 of the reemits reach 60 m in mid-Noven~ber and 8.1 in each of mid-Febmaq, early March, early May, rnidMay, ewly August, and mid-August, corresponding to the moulting times documented by Morgan (2977). Based on puemlus settlement rates on collectors scattered dong the coast (Phillips and Hall 1978), we used two key assumptions to construct the assumed spatial distribution matrix, c(i9j).First, we assume that c (i,j) is nomdly distributed in the north-south direction, with a peak near the centre sf the fishery (at Geraldton). Second, we assume that c(iQ) decreases exponentially in the offshore (east-west) direction, except in the Abrolhos Islands area, so that 90% of the settlement will occur in the coastal and Abrolhos Islands cells. Based on tagging data and size (grade) composition sf catches, Morgan (1977) estimated the annual natural mortality rate M to be 0.23. We used this estimate without correction for size- and season-related (moulting, predation) variations that are likely present but cannot be estimated with any precision given the available data. In exmining the sensitivity of the model, a higher 1653

estimate of M (=0.5) was also tested.


White Moulting And Migration The white migration (George 1958) involves a synchronous moult in late November (first simulated fortnight of the annual fishing season), by inshore animals mainly in the 70-90 nun size rmge (Fig. 2). While the duration of the subsequent white colour phase and migratory behaviour may differ considerably among individuals, the typical white is thought to be migratory and highly vulnerable to fishing for about 8 wk (four simulation fortnights). In the simulation, we assume that all whites appear in the first simulation fortnight and then revert to the redsedentary type at the end of the fourth fortnight. The number of whites of length L created in the first fortnight for cell i,j is taken to be W(L, i,j) = w(L)N(L,i,j) for coastal cells i,j only (whites may be generated offshore, but are impossible to distinguish from the much larger pool of migrants coming from inshore). Crude estimates of the moulting proportions w(L) by length were obtained in two steps. First, we did a length-based virtual population analysis (see Catch and Undersize Mortality) to estimate average total abundance by size for two representative fishing seasons (1983-84 and 1985-86). Second, we estimated the total number of whites initially present by size as the white catch (Fig. 2) divided by an assumed exploitation rate of 0.6 because fishing is intense and concentrated on the highly vulnerable whites (Hancock 1981; Bowen m d Hancock 1989; Phillips and Brown 1989). w(L) was then taken to be the number of whites initially present divided by the estimated total abundance less the number estimated to have turned white at smaller sizes. The results of this calculation we as follows: Length (L) w(L)

68-71 0.02

72-75 0.2

76-79 0.4

80-$4 0-6

84-87 1.4

Thus, according to the method, it would appear that virtually all of the 84 + WI animals undergo the white moult; having more than 100% of the animals in the 84-87 m class appear to moult is likely to be due to a significant proportion of larger animals undergoing a second white moult (George 1958). However, it may dso be due to overestimation of the number of whites produced (assumed exploitation rate too low) or to underestimation of the number of lager animals present. Lacking better estimates of white moult rates from tagging data, we elected to assume h a t d l inshore animals in the 84-87 nun category undergo the white moult. For each of the four fortnights while whites are present, we assume that a proportion of the whites in each cell will move to adjacent cells to the west and to the north. The total proportion moving out of m y cell depends on the cell size; for the detailed model (16 x 16 kin cells), we took this proportion to be 0.8. For the larger, one-half-degree block cell size, the proportion was assumed to be 0.3. Of the proportion that move, we assume (from tagging studies) that 80% will go west and 20% north for smdl grid cells or 95, and 5%, respectively for the large cells (Phillips 1983). Based on tagging data. the averrtge movement speed of migrating whites is about 1 M d (14 ladfortnight).

Fishing EEod Lobster licenses are issued to fish in two coastal zones and the Abrolhos Islands. Under current management regulations, there

Length (mm)

FIG.2. Size distribution of white (migrant) phase rock lobsters estimated from catch monitoring samples for the 1986-88 fishing seasons.

is a limited transfer of pots between zones; therefore, we assume that the number of pots allowed to fish in each zone is set as a model policy variable. The Abrolhos (A) zone fishers are also allowed to fish in the adjacent coastal (B) zones from the coastal zone opening fortnight until the Abrolhos opening in mid-March. Prediction of fishing effort (pot lifts) for any fortnight for the cells within each zone is done in two steps: (1) the total number of pot lifts for the zone is predicted from the overall average catch rate (kilograms per pot lift); and (2) the proportion of these lifts occuning in each cell is predicted from the relative catch rate and distance offshore of the cell. The number of pot lifts L(z) for zone z in a fortnight is assumed to be L(z) = P(z)LdB(z) where P(z) is the number of pots licensed for zone z, Lrn is the maximum number of days fishing per pot per fortnight, and D(z) is the mean number of days between pot lifts for the zone in that fortnight. Based on historical effort data for early season (peak) fishing times, Lm is taken to be 11 d (i.e., 22 dims). D(z) is predicted from the expected catch rate ce(z) using the simple inverse relationship B(z) = dYce(z) where dl = 1.0 is the average catch rate needed to induce the average fisheman to lift his pots daily. This rela tionship predicts that fishers will lift their pots progressively less often as the expected catch rate drops below dl. D(z) is further constrained to be 1.$ or larger (i.e., no multiple pot lifts per day). This model for L(z) results in the modelled fishery exerting wound 60-70% of its maximum possible number of pot lifts in typical fishing yeas, with the maximum possible number of lifts per fortnight occk~aringonly in the first few fortnights when catch rates we highest. The expected catch rate for the zone ce(z) is taken to be the simple average of the expected catch rates for the cells in the zone, where the expected rate for each cell for any fortnight is updated each year using the exponential averaging fomula (new mean) = m (old mean) + (I - m) (catch rate for the fortnight this year) where the weighting factor m (a measure sf fisherman memory) is assumed to be 0.5. Note that this averaging fomula does not assume that fishers predict their catch rates from previous fortnights within the same fishing season. We trust the fishers to have the sophistication to look across years so as to correct for seasonal effects associated with typical depletion dynamics, moulting, and migration. Effort for each zone, E(z) is then distributed m o n g cells using a simple gravity model similar to that used by Caddy (1975): E (i J)

+

E (z)a(ij)/sum A (ij) h.9.Fish. Aquaf. Sci., bd.50, 1993

TABLE2. Distribution of fishing effort and CPUE by depth for the WA rock lobster fishery, 1986-88 seasoms.


Depth range (fathoms)

Fishing effort (million pot lifts)

% total effort

where E(i5j)is the effort in cell i,j5a(i,j) is an attractiveness index for cell k,j, and sum A(i& is the sum of the attractiveness indices over the cells in the zone. The attractiveness index for each cell where ce(ij) is the expected catch is calculated as (ce(i,j)l~(ij))~, rate for the cell (see preceding paragraph), s(i5j)is an index of the offshore distance of the cell (1.0 for coastal cells, 1.0 plus the number of cells away from coast times cell width in kilometres for offshore cells), and k is a 66concentrationparameter." High vdues of k (>>I .O) will cause effort to be concentrated in zones with the highest catch rate per distance travelled (measured by ce(i,j)/o(ij)). For large values of k (>5.0) the n~odelwill approach the effort distribution pre dicted by the sequential effort allocation method of Hilborn and Walters (1987), i.e., for each fortnight the effort will all be placed in whichever cell has the highest attractiveness. For intermediate k vdues (1.0-5.0) the model will 66smea"effort more broadly than the sequential method, thus recognizing variation among fishers in objectives, costs of operation in different cells, and infomation. Logbook data do not permit detailed analysis of the effort distribution on a cell-by-cell basis except for our largest cell sizes, but there is good information on the depth distribution sf effort (Table 2). For recent yeas, around 75% of the effort has been 0 generally within concentrated in shallow water ( ~ 2 Fathoms, model cells bordering the coast) where juveniles are abundant. About half of Qe effort in deeper waters (generally offshore) has been exerted during the white migration. We found by trial m d enor mns with the overall model that k = 3.O-5.0 would produce this general depth distribution; too much effort is distributed offshore after the white migration for k < 3.0, and too little effort is distributed offshore for much higher values of k. The decision processes leading to onshore-offshore distribution of fishing effort are not well understood and represent a major area of uncertainty for the future of the fishergr. Sf we have underestimated the extent of offshore movement of effort in response to declines in relative catch rates inshore (or improvements in technology for working offshore), we will in turn have underestimated the risk of overfishing on the spawning stock, which is largely concentrated in deep water (>20 fathoms) (Morgan et al. 1982). Another possible weakness in our effort model is in the use of pot lifts as the unit of effort, rather than pot days or total so& time. We chose to use the pot lift measure because trapping efficiency is thought to decline rapidly after the first day in mulitple day sets in shallow water (420 fathoms), so that the pot is fishing mainly on the first day of m y set (or one day per lift). In experiments with single versus multiple day sets, N. Caputi and R. Brown (personal comunication) found that only about 20% more lobsters are caught on the second and subsequent days of soaking in shallow water, due apparently to locd depletion of residentid lobsters in the neighbsurhood of pots and to deterioration of baits. Can. J. Fish. Aqlaat. Sci., %)I. 50, 6993

Catch CPUE Million kg kg11ift

Catch and Undersize M s a i t y Catch of length L lobsters in cell i,j for any fortnight is predicted from the explsitdtion equation c@,i4) = N(e,kj) [ 1 - exp ( -qv(l)E(ij) )] where C(Lyi,j)is the catch, N(L9i,j)is abundance (or W(L,i,j) for whites when they are present), g is the overall catchability coefficient, v(L) is a relative vulnerability for length L lobsters (whites of d l lengths are assumed to have a single vulnerability vw), and E(i,jj) is predicted effort in the cell. This equation accounts for exploitation competition due to overlapping areas swept by pots when effort is high and differs from the standard fisheries catch equation only by ignoring natural mortality during the fortnight (accounted for in growth-survival equations; see above). For undersize lobsters, only a fraction (um) of C(L, i,j) is removed from the simulated stock, representing postrelease mortality. urn is assumed to depend on the number of escape gaps required per pot, g, as urn = 0.213 x exp (-0.347 g); prior to I987 regulations (g = I), this relationship results in um = 0.15 (Brown and Caputi 1986). The catchability coefficient q is interpreted as the fraction of the fully vulnerable stock taken by one unit of fishing effort. where the fully vulnerable stock is defined as the size-colour groups with relative vulnerability v(L)= 1.0. We estimated q in conjunction with the recruitment parameters W* and d by fitting the overall simulation model to time series of historical catch and catch per unit effort (CPUE) data. Physically, q can be defined as the area of detection by lobsters of a pot, times the proportion of lobsters in the detection area that will enter and remain in the pot, divided by the total area over which the lobsters are distributed within a cell. W i l e the area of detection and probability of reaction could be assessed by localized tagging and behavioral studies, the total area over which lobsters are distributed would remain a gross udmown. Lobsters use only a small proportion of the ocean bottom (except duiing the white migration), concentrating on rocky bottom and reef areas that afford protection; although fishers may k11ow most of these areas quite well, it would be difficult and expensive to map the areas with any precision. Thus, we had little choice but to estimate q directly from overall catch and effort data. The relative vulnerabilities v(L) were estimated by doing a length-based cohe~rtanalysis (Jones 1984) on lengwfrequency data for the total catch from two typical (average) fishing seasons, 1983-84 and 1985-86. The cohort analysis provides estimates of the annual number of lobsters entering each length class and the fishing mortality rate suffered by the class, given the length distribution of the catch, an estimate of the natural mortality rate, and estimates of the average time spent in each class (i.e., the growth rate). It is based on the catch equation


where C(L) is the catch of the length class, F(E) is the fishing rate suffered by animals while passing through it, N(L) is the number entering the class, and N(L + 1) is given by

where t(L) is the average time spent in the class. Because F(L) can be expressed as F(L) = -log (hrg L + 1) / RrgL))l t(L) - M? the catch equation can be rewritten to express N(L) as a transcendental function of C(L), N(L + I), M9 and t(L). The cohort analysis proceeds by assigning a terminal population estimate N(LL) to some large length class LL (we used the simple assumption that N(LL) = C(LL) / 0.5 for the 140-1 43 nun length class). Then, N(LL - 1) is found by numerically solving the transcendental equation for it given NLL), using NewtonRaphson iteration. This procedure is repeated for N(LL - 2) given hrQLL - I), and so forth, until the abundance of the smallest length lobsters caught is estimated. For our analysis. we aggregated the length / frequency data intc~4 - r n "moult intervals9' as used in the simulation (see Growth and Natural Mortality above). assumed M = 0.23, and estimated t(L) from published data on the average number of moults per year for lobsters of different sizes (Chittleborough 1974, 1975, 19'76; Morgan 197'7; Phillips et d. 197'7, 1983; Joll1984; Joll and Phillips 1 984). We calculated the average time per moult as t(L) = I/m(L), where nm(L) is the average number of moults per year*From the published growth and moulting data, we found that it is reasonable to assume that nm(L) = 461 - L*/148) where L* is calculated from the length class index L by L* = 62 + 4(L - 1). Here, L = 1,2, . . . is d e h e d as follows: L = 1 corresponds to the 60-63 mm length class, L = 2 corresponds to 64-67 m,and so forth. The cohort analysis results (Fig. 3) indicate a striking pattern where the fishing rate is highest for animals in the 70-80 m size range (but note that 70-75 mm animals are released, so that only a fraction will actually die). Smaller animals either do not enter, or escape from the pots though escape gaps (and between the pot battens or cane and sticks of other pots for very smdl animals). Larger animals may be subject to lower fishing rates for three reasons: (1) fishing effort is lower in the deeper waters where most sf the lager animals are resident; (2) larger animals may be less active (feed less, be less prone to enter traps in search of food); andor (3) larger animals may be distributed over a larger area of deepwater habitat, so that the proportion taken by (vulnerable to, exposed to, able t s detect) any one pot lift is lower. There is anecdotal evidence that (3) is not the case and that there is in fact much less good habitat in deep water than in shallow water. The simplest explanation, and the one we assume in the simulation, is a combination of (1) and (2): larger animals are now subject to low fishing rates partly because fishing is concentrated elsewhere, and these large animals are also somewhat less vulnerable than smaller ones to effort placed in the depths (model cells) where they are concentrated. Ordinarily the relative vulnerabilities v(L) would be calculated from the cohort analysis results by taking ratios of F(L) to the largest F (e.g .,F for 72-75 nun in Fig. 3). Unfortunately this procedure does not provide a complete assessment for the rock lobster, since it does not provide a distinct estimate for the relative vulnerability (vw) of whites. Whites (pale-shelled migratory animals) make up 15% or more of the total catch, even though

60

80

400

12Q

140

160

140

160

Length (mm)

0.0

60

80

900 120 Length (mm)

FIG.3. (a) Size distribution of the 1986-88 rwk lobster catch; (b) results of length-based cohort analysis to estimate numbers reaching each size interval per ye=; (c) average numbers at each size interval through the year (i.e., numbers reaching the size adjusted for the time to grow through the size interval and for total mortality during that period); (d) annual fishing rates by size interval.

they are present for only 8-10 wk sf the fishing season. Further, fishers deliberately target them during their offshore migration, setting pots across presumed migration paths. Thus, there is reason to suspect that vw may be twice or more the peak v(L) for nonmigratory red lobsters. Industry estimates of the "whites catch" (i.e., migrating animals) are often far higher than the 159% that is typical for monitoring data; this is because the industry classifies d l lobsters caught over the main migration period, whether migrating or not, as white; using the industry estimates would result in even higher relative vulnerability estimates for the whites. Lacking any direct way of estimating the ratio vw/v(L), we proceeded by assuming that the exploitation rate for whites is CCIPI. J. Fish. Aquat. Sci., VtL 50, I993

around 0.5 (Brown and Caputi 1983), implying that the number of whites initially present for each size class is about two times the measured catch and that the annual fishing mortality rate ( F ) for whites is around 5.0. When compared with the annual fishing


Length class v(&)

60-63 0.03

64-47 0.06

68-71 0.13

72-75 0.40

Here, the estimates for 60-7 1 nun animals are likely to be quite accurate. The 0.4 values for 72-79 m animals are purely a result of the assumed exploitation rate for whites. The values of 8.2 for larger animals are again somewhat speculative, being about half sf what we would assume if the depth distribution of large and smdl animals were csmpletely disjointed so that fishing rate differences could be ascribed solely to differences in effort (the fishing rate for older animals is about one quarter of the fishing rate for smaller ones, and about one quarter of the effort occurs offshore). Assuming h a t fishing rate F is proportional to effort, we woutd conclude that large and smdl animals are equally vulnerable to the effort directed at them.

Policy Optiom and Model User Intedace The simulation model is programmed to allow users to access several policy variables, and most of the population dynamics and effort parameters, through a user interface that presents the values in a spreadsheet format for easy editing and revision. A disk file system allows easy storage and retrieval of policy and parameter combinations, so that alternative scenarios can be constructed by adding new files or selecting among existing ones. A "script" file containing details of historical policy changes provides a simple method of incorporating these changes. Policy variables accessible though the user interface are 41) minimum and (optionally) maximum size limits (by 4-rnm carapace length increments); (2) required number of escape gaps; (3) a map defining the regulatory zone to which each cell is assigned; (4) the number of pots licensed to fish in each zone: and (5) a table of proportions of maximum effort allowed by fortnight in each zone (e.g, 8.8 represents having the zone closed for the fortnight, 1.0 represents having it open to fishing). Closed areas can be created by assigning cells to a new zone and setting the number of pots licensed to fish in this zone to 8.0. Some other policy changes can be simulated by estimating (outside the model) the effects sf these changes on population dynamics and effort- parameters that are accessible through the user interface. For instance, changes in escape gap sizes can be simulated by changing the relative vulnerabilities v(&). Policies that increase or decrease the cost of fishing (subsidies, taxes) can be represented through ateir effects on the dl parameter that defines the catch rate needed to induce fishers to make daily pot lifts. The user interface is progr d so that policy and pxameter changes can be introduced in any simulated fishing season (as well as before a simulation begins), simply by watching the simulation results as they appear graphically on the screen and touching h e microcomputer keyboard when desired times for changes are reached. This allows the user to build up a complex scenario of changes, for example, progressive growth or decrease in the number of licensed pots over time. These changes may represent either a multiyear policy plan or uncontrolled Can. 9.Fish. Aquat~Sci., Kd. 50, 1993

rates for the remaining animals, and assumitng that low fishing rates for larger animals are due partly to low effort in offshore waters, this assumption about the whites results in the following approximate relative vulnerability schedule: 76-79 0.40

79-81 0.30

82-85 0.20

$69 0.28

Whites 1.00

dynamics that we have not thought to (or did not h o w how to) include in the original model. The user interface also allows a number of options for graphical display of simulation results. As each simulation proceeds, the program displays cmde maps of yearly changes in "juvenile" m d 'bdult" abundance (coded by colour or grey scale intensity for each modelled spatial cell). Dynamic changes within each fishing season are displayed on similar maps showing fishing effort, CPUE, and catch for every fortnight. Besides the mapped infomation, the user can choose to display various graph ""panes," where each pane shows a graph over y e a s of one or a few key variables such as total catch, catch by processor grade, total fishing effort, and landedexport values of the catch. A few of these panes also display historical information (catch by processor grade, effort, CPUE) for comparison with simulated vdues.

Parameter Esthation: mning the M d e l to Historied Data The user interface provides two options for tuning the model so as to provide parameter estimates that better fit the historical data. First, the user can simply run the model repeatedly with different parmeter values entered through the spreadsheet displays and make visual comparisons between simulated and historical catches, efforts, and CPUEs. Second, the user interface provides access to a simple nonlinear estimation scheme for finding better estimates of a few aggregate (over d l spatial areas) parameters (R*, d9 M , q). Generally we used trial and emor simulations to obtain reasonable f"as to the data and then used the nonlinear estimation t s "fine tune" the estimates. The following section describes the nonlinear estimation scheme in more detail and presents general results of applying it to the model.

Estimation Procedures Any dynamic model represents a mapping from a set of parameters (including initid values of variables) onto a set s f predicted values, whether or not the mode%can be expressed as a simple equation reminiscent of some statistical regression formula. As noted by J. Schnute (personal communication), we may view any detailed simulation as a "stew" of calculations from which observable quantities (e.g., time series of catches) percolate to the surface for comparison with historical data. In this view, what nonlinear estimation does is to adjust one or more parameters of the stew so as to maximize (or minimize) some criterion for goodness sf fit between the modelled oksewables and available data. Further, we need not regard a11 sf the parmeters in this stew as equally ianpsrtant or uncertain; like the model equation structure, some parameters may be treated as well determined by independent sources of infomation and argument (e.g., vulnerabilities v(L),fixed from length composition data), so that ate estimation algorithm can concentrate


on finding better values of a few key pwmeters sf overall importance to model pedomance. We choose to tune the model to the coastwide annual catches by processor grade (A, B, C+) and CPUE (kilograms per pot lift) for the fishing seasons 1974-77 to 1988-89. Processor grade A lobsters are mainly 76-78 rn carapace length (new recruits), grade B lobsters are 79-86 m, and grade C and higher (Cs) lobsters are mainly mature animals exceeding 87 m m carapace length. The catch grade data are thought to c q considerable information about the sizelage composition of the stock, and hence about overall mortality rates. We used the data for recent fishing seasons only, so as to provide the best possible fit to current conditions and also to see whether the fitted model could accurately estimate earlier catches and catch rates. Simple weighted least squares was used as the estimation criterion:

SSBV = sum over i [l/var(i)

1 [yobs(i)

@

-

Otasewed Simulated

- yhat(i) l2

where yobsfi) is the ith observation (catch or CPUE), yhat(i) is its predicted vdue from the simulation, and 1lva-f6) is a weight defined by assigning a prior estimate of the relative variance var(i) expected for observations of type i, Expressing catches in millions of kilograms and CPUE in kilograms per pot lift resulted in most of the observed values being scaled to within the range 1.0-3.0, and we felt that there was no reason to assume heterogeneity of variance within this range; therefore for most estimation trials, we assumed v&i) = 1.0 for all 6. We found that changing the weights had no noticeable (>I%) effect on the estimates. Various algorithms can be used to minimize SSW. We have used the Simplex method recommended by Schnute (19821, the Fletcher-Powell algorithm (Press et al. 1986), and a Gauss method with step size corrections (Bxd 1974, p. 111). By far the best choice has been the simple Gauss method. This method requires derivatives (sensitivities) sf the predicted values with respect to the ?a parameters. These derivatives are easily obtained numerically by doing n + 1 simulations for each iteration in the nonlinear search; the first simulation provides base predictions, and for each of the other n simulations, one parameter is perturbed slightly (adding 0.000 1) and the derivatives are calculated as the changes in predicted values divided by the perturbation. The step size correction procedure requires one to three additional simulations per iteration, to test for an "optimum" step length. We usually found that the Gauss iteration converged (parameters changing less than 0.001 per iteration) within 5-10 iterations, typically requiring a total of 30-40 simulations for three-parameter cases md about 1.5 h of microcomputer time. Two-parameter searches generally required less than 0.5 h. In contrast, the Simplex and Hetcher-Powell dgo9ithnns typically require 100-200 simulations (function evaluations) to satisfy the same convergence criterion.

Estimation Resdts The reduced model (50 x 100 h grid cells) was able to reproduce recent historical catch and CPUE trends with considerable precision after only minor parmeter tuning (Fig. 4). When the parameter estimates were substituted into the detailed (16 x 16 Ian grid) model, essentially the same fits were obtained except that predicted catch and CPUE were higher for early years.

Year

as

-

Observed Simulated

PIG.4. Simulated versus observed fishing: (a) effort; (b) catch by processors category A(76-78 mm carapace length), B (79-84 mrn carapace length), and C and higher (C+); (c) CPTE for the WA rock lobster fishery.

The power parmeter d (for incorporating historical puemlus settlement variation into the predictions) was estimated to be 66.42, suggesting that puerulus settlement underestimates subsequent recmitxnent in poor settlement years and overestimates recmitment after good settlement years. For d = 0.42, the best estimates of the recauitrnent and catchability parameters were R* = 76.1 and q = 64.9. However, we found that a higher d value (0.8) appears to result in a better visual fit to the data (model tracks strong changes in the 1980s better), although it results in a somewhat higher SSW (40.4 versus 25.91, We believe that the higher d value should be used for policy analysis because it is conservative in exaggerating recmitment variation and the possible management risks associated with that variation. Ford = 0.8, the best fitting estimate of average recruitment R* was 76.9 million puemlus settling per year, or around 39 million recruits to the 6 0 s m stock. This estimate is shabstcintially higher than Morgan's (1977) estimate of 23 million annual Can. Jo Fish. Ayraut. Sci, Vol. 50, 1993


recruits to legal size but compares favourably with our estimate from the length-based virtual population malysis (VPA) of 34 million recruits to 60 m. The best estimate of q of 47.3 per million pot lifts (for d = 0.8) is also reasonable. This corresponds to a radius of attraction for each pot of around 274 m for white lobsters (173 m for 76-49 n m nonmigratory animals), if these lobsters were distributed over the entire area of each model grid cell (50 x 180 km) and every individual within the radius entered the trap. The estimated radius of attraction would be much less if we assume hat only a small fraction of the area is actually used and fished (e.g., the radius would be 8'7 rn if 10% of the area is suitable). These apparent attraction distances are well within the range observed or inferred from tagging studies and direct population estimates (Morgan 1977; Jemakoff 1987; Jen~akoff and Phillips 1988). Fishing effort calculated by the model for recent y e a s underestimates the observed effort. Examination of logbook data suggests that the assumption of 22 &mo of fishing is no longer valid. Ira recent yeas this has risen to 26 &mo. Whether this is a response to increased competition among fishers or the implementation of new management strategies is uncertain. The excellent agreement between model and recent catch data (Fig. 4) should not be interpreted as evidence that the model is structurally correct or that the parameter estimates are very accurate. Although some parameters may be treated as well determined from other sources, in reality, it is impossible to distinguish among a range of hypotheses about recruitment, catchability, natural mortality, and vulnerability of large lobsters. As the SSW values in the following table show, almost equally good fits are obtained when SSW is minimized over R* and g (holding d = 64.8) for a range of assumptions about the relative vulnerability v(E) of 84 + rnlobsters: Best fitting estimates Assumed vulnerability

R*

4

SSW

8.1 8.2 (nominal) 8.4

103.1 76.9 71.9

30.7 47.3 54.9

39.0 40.4 46.2

Here the 0.4 case corresponds to assuming that all lobsters above the legd size limit are equally vulnerable. Note that there is a trade-off between R* m d q in this table: at one extreme (0.1 case), the stock may be quite large, be subject to relatively low fishing rates, and have relatively low adult vulnerability; at the other (0.4 case), the stock may be considerably smaller, be subject to very high fishing rates, and have low catches of grade C+ animals simply because very few animals survive to large sizes and there is little effort in deep water where they are concentrated. We can see no way to distinguish among these hypotheses with the data available. The uncertainty would not be resolved by fitting the model to much more detailed data (catch by cell/season) using a multiparmeter estimation scheme that included the v(L) and white mdting/movement rates as unknowns because the same basic arguments about trade-offs among the parameter estimates would hold at any scale of analysis. When the stock assessment steps (VPA, vulnerability assessment, parameter estimation) were repeated with natural msrtality rate A4 = 0.5 (rather than Morgan's (1977) M = 0.23), we Can. 9.Fish. Aquat. Sct., Vol. 50>I993

obtained essentially as good a fit to the data as for the base line case. This higher M value is supported for early juveniles only by results in Joll(1984). Using the higher but still possible M has at least three major implications for the estimates and management predictions: (1) much higher estimates of average recruitment rate (over 300 million recruits to 60 im carapace length per year9which appears unlikely) m d lower estimates of catchability ( q 20); (2) MSY estimated to be at least 58% higher than the recent average yield; and (3) much higher estimates of the rates of current to unfished spawning stock size (i.e., much less effect of the historical fishery on the spawning stock). For a further explanation sf why implications (2) and (3) generally follow from increasing M in the assessment process, see Walters (1986, chap. 4). W i l e uncertainty concerning M implies that there is a scenario that suggests an opportunity to substantially increase the yield from the fishery, we feel that it should be viewed instead as evidence that a key research priority should be to imprcsve estimates of M and/or q though methods such as tagging studies. With best fitting parameter estimates for recent years, the model generates higher CPUE and catch estimates for early y e a s of the fishery than were actually observed (Fig. 4). The discrepancy can be interpreted as a "prediction" that modem fishers would be roughly 50% more successful than the early fishers (due to better boats and gear and howledge of lobster distribution, for example) should a few modem fishers encounter the unfished abundance and lack of exploitation competition that fishers experienced in the 1940s. This difference in efficiency appears quite reasonable, in view of changes that have occurred in the distribution of fishing, vessel capabilities, pot hauling and handling methods, fish-finding equipment, and fishing knowledge. However, two other possibilities exist: (1) we may have overestimated the current catchability and exploitation rate, so that the stock available may not have declined as much as we have estimated (lower q and less decline relative to the unfished stock size would jointly contribute to make the model fit earlier years better); and (2) the natural mortality rate may have been higher (or recruitment rate lower), due to density dependence in the natural mortality rate under unfjshed conditions, so that the unfished stock was not so much larger thm the present stock as the model predicts using Beverton-Holt type (essentially constant) recruitment and constant mortality rate.

The Model as a Management Game The 45-yr simulations (fishing seasons from 1944-45 to 1988-89) require only about 2-3 min of microcomputer time for the reduced (50 x 1064 km grid) model arad about 12-15 f i n for the detailed model. A simulatiora is simple to intempt at any time to alter policy variables and parmeters, The graphics interface is programmed so that results from previous simulations can be left on the screen or restored from disk files and new results are n ong then added as csverlays permitting easy visual c o m p ~ s s m scenarios (Fig. 5). These combined features make the model easy to use as a game, where many management policies can be quickly tested and the results from each used to help decide what to try next. As promising options are uncovered, additional simulations can be easily made to check how robust the results are to uncertainties about various model parameters (e.g., a different size limnit may initially lock good, but this result may depend on the particular proportions assumed for white moulting/migration in relation to size).

" H i s t o r i c a l data -----Current s t r a t e g y Alternate strategy

Historical

a

data

-C u r r e ~ st t r a t e g y


.----.A l t e r n a t e strategy

2

-

l data -HG ius rt roerni ct astrategy

5

$

Alternate strategy

c s 0 *

\-

Current strategy

-...---. Alternate strategy

2

s;

19468

4 960

1 980

FIG.5. Output from the most recent version of the model, comparing the current management strategy with an alternative strategy comprising a 1-30 June closure, a 10%reduction in the number of pots used, and a maximum carapace length of I16 mm for female rock lobsters. The alternative management strategy for this exercise was introduced in the 1992-93 season. Environmental variability for seasons after 1992-93 has been held eoasstant.

The usefulness of the model and the gaming approach to assessing management policy changes has been tested in work shop sessions attended by both scientists, fishery managers, and fishing industry representatives with the practical experience of operating in the fishery. For example, we presented the model to the Western Australian Rock Lobster Industry Advisory Comn&tee, a group of fishers (commercial and recreational), processors, and government fisheries officials who meet reguarly to review and recommend management policies. Members of the group suggested a variety of policy scenarios, which were then exmined in the model. The predicted outcomes from the policy changes were judged by the fishers to represent the responses to the proposed management chmges and likely catch outcomes. We had feared that the fishers would either be completely hostile towards the computer or uncritically accept its results. Instead we foarnd them to be quite sophisticated in their appraisal sf the model structure, and they carefully considered whether the possible weaknesses they had identified would affect the comparisons of the relative performance of alternative policy options. A useful outcome of the workshop testing of the model was that the rapid availability of the results helped to stimulate a highly focussed and productive debate among the committee members and a call for the continued development of the gaming approach. The remainder of this section reviews some general conclusions that have emerged from gaming sessions to date about the efficacy of various changes in fishing regulations. Our general 1660

-

conclusion (using our best estimate of M 0.23) has been that the fishery is now producing at near its maximum level in terns sf both catch and export value of the catch, so that most policy changes would have a deleterious short-term effect, although they might reduce the risk of long-tern1 difficulties such as reckaitment overfishing. There has been debate over the years about the size limit of '76 mm carapace length*This linit has been in place since the turn of the century, when it was introduced to satisfy marketing demands (Hancock 1 98 1 ). It is too low to prevent the capture of immature lobsters (except in the Abrolhos, where it gives significant protection) and perhaps too high to fetch the maximum possible price per kilogram. Small lobsters are preferred in the key Japanese market. On average, over the various export markets for 1988-89, the small grade A lobsters (350-460 g whole weight) fetched around $25kg, while the larger C grades (970-690 g whole weight) brought only $2Okg (Monaghan 1989). Industry estimates that lobsters in the 72-76 rnm size range (currently not legal) would sell for about $32kg. Thus, it might be worthwhile to either increase the size limit so as to better protect breeders or reduce it to increase econonic value. The model supports this view, but indicates that the current size limit may in fact be about the best bdmce between conservation of spawning stock m d economic return. It predicts that an increased size limit (to 80 mm) would result in a slight decrease (5%) in average CPUE and catch (due to allowing growth to larger sizes), as much as a 22% increase in spawning (annual egg Can. .I P.i~;h. . Aqraa~Sci., KJZ. 50, I993


prduction), but a decrease in landed (6%) and export (I I%) values of the catch. A reduced size limit (to 72 m)would result in slightly (1%)reduced CPUE and catch (due to taking more small lobsters, foregoing growth), as much as a 13% decrease in annual egg production, and an increase in export value (7%) which would be greater during y e a s when very strong year classes enter the fishery. Thus, while changes in the size limit could generate substantial changes in the spawning stock, it is likely that there would be smaller (but significant) changes in economic value, acting in the opposite direction. The model predicts that combining a reduced size limit (72 m) with an upper size limit of around 96 m (perhaps by reducing the size of the pot entry port) would reverse the deleterious effect on the spawning stock of the size limit reduction (resulting in approximately 25% spawning increase). This '6sslot" size policy would result in the total catch being about 13% lower than at present in terns of weight and 4% lower in export value, unless the 72-76 m lobsters could be sold at very high prices (>$40kg). It is an interesting option for providing increased protection for the spawning stock while offering the fishers something in return (lower size limit) but does not address continuing increases in fishing efficiency that might erode any increase in spawning stock obtained initially. Another key issue in recent y e a s has been effort reduction by reducing the number of pots licensed to fish. The model predicts that pot reductions of 10% would be sufficient to cause noticeable (5% or more) decreases in annual fishing effort. With fewer pots fishing early in the season (when catch rates we high and all pots are lifted as often as possible), there would be a reduction in the exploitation rate of whites, and hence potentially an increase in the offshore spawning stock. However, lower effort early would mean more lobsters surviving to keep catch rates high later in the season, hence encouraging fishers to fish harder (continue making daily pot lifts) until later in the season and perhaps moving further offshore to deeper water to take the whites after h e y have reverted to the red type. Thus, a reduction in pot quota will result in only a modest reduction in catch or effort, which will be redistributed seasonally and spatially. The model estimates that the spawning stock would increase by approximately 7%, catch and export value would be reduced by about only 3947, and the effort by 7%, if the pot quota were reduced by 10%. It has been suggested that recruitment to the offshore spawning stock might be improved and protected by opening the season later or by having a closure during the peak of the white migration. We found that a simulated closure for the month of December would indeed reduce the white catch greatly and result eventually in s o m increase (30%) in spawning. However, the main effects predicted for the policy would be to attract more fishing pressure to offshore areas during Jmuv-March m d to shift the catch more to larger (less econornaically valuable) animals. Despite increased fishing effort later in the season, reduced vulnerability of the nonmigratory lobsters would t 9 ' resulting in a decrease prevent full recovery of the ' 6 ~ s l ~catch, in catch of about 16% and a decrease in export value of 19%. Ht has been encouraging for model users to see the effects of alternative policy ideas, although often these ideas may result in negligible effects, or even the opposite effects than intended. But in each case, such model predictions have turned out to make good sense when the numerical m d functional reasons for them have been examined. If nothing else, the model will certainly provide a moderating influence for g o v e m e n t officials or Can. Je Fish. Aquat. Sci., Vol. 50, 1993

industry representatives who believe that modest "tinkering" with the regulations can be sf significant benefit.

Is the Rock Lobster Fishery in Danger? Perhaps the most important issue in WA rock lobster mmagement is whether current regulations are sufficient to ensure that the spawning stock size will remain high enough to produce adequate recmitment levels, given expected future improvements in efficiency of fishing. The modelling results (for M = 0.23) suggest that annual total egg production (combining spawner numbers and the sizeifecundity relationship) has already been reduced to only 25-3596 of its natural (unfished) level, and it would not be prudent to allow any further reduc tion. However, based on the possible (but less likely) modelling results for M = 0.5, the reduction in egg production is much less significant. Until this uncertainty associated with Morgan's (1977) best estimate of the parameter M is resolved, management decisions should be based on the more conservative and less risky assuanption that M = 0.23. The primary protection for the spawning stock now is apparently through the combined effect of four factors: (1) a significant percentage (33%) of the white migration consists of undersize lobsters that '6escape" to deep water before being subject to legal fishing (Fig. 2); (2) effort is largely concentrated in shallow water (Table 2); (3) females in the Abrolhos Islands subpopulation mature at well below the legal size; and (4) q is lower in deep water and for larger animals. Imnature lobsters reaching legal size in inshore waters are already subject to exploitation rates of at least 70% before moving offshore (Fig. 3), and increases in fishing effort or efficiency in inshore areas are unlikely to increase this rate dramatically (because of the exponential relationship between effort and exploitation rate, most additional effort would simply '"weep" areas already fished) unless the size limit is reduced. Thus, the main concern should be whether exploitation rates will increase on postmigrant immature and mature lobsters in deep water. This could occur due to I) an increase in pot siting efficiency (reduced proportion of pots set in poor habitats) by the fishers who currently work in deep water as more fishers l e m where and how to fish these deeper areas by using better Iocational aids (e.g., global positioning systems), andor (2) fishers encountering declining catch rates inshore due to poor recruitment y e a s or increased competition from other fishers and hence moving off shore. These mechanisms involve changes in catchability coefficients; such changes are not included in the model and are notoriously difficult to predict because they involve human learning and inventiveness. There are a number of possible management strategies for dealing with the possibility of increasing catchability ccsEicients and effort in deeper waters, assuming that these increases are not (even in principle) predictable in advance. One is a "passively adaptive" (Walters 1986) strategy of trying to msnitor deepwater abundance more closely (e.g. spawning abundance indices) and then applying additional fishing restrictions (e.g., pot quota reductions, maximum size limit) when and if necessary The second strategy is to implement a "I-obust" package of regulations that will protect the spawning stock no matter what happens to deepwater catchabilities; such a package might include cIosures to fishing in waters deeper than 20 fathoms, reducing pot neck (entry port) sizes so that 90- 1OO+ nun animals cannot enter pots, andor a simple maximum size limit. Note that


the robust policy would not include measures, such as a closure during the white migration, that might end up attracting more fishing effort offshore or otherwise simply redistribute the timing of effort movement. A third option not currently addressed by this model is the introduction of individual transferable quotas and a total allowable catch. Any robust policy for spawning stock protection will inevitably involve some immediate loss in catch m d fishing opportunity as the "price" to be paid for reducing the risk of long-term overfishing. This is without any guarantee whatsoever that the risk is even significant (it may even be that the spawning stock could be substantidly reduced without impairing recruitment). Therefore, it becomes a purely political decision about whether the price, which we estimate from the model would probably be around 10% sf the current lmded value of the catch, is worth paying.

We thmk our colleagues at the Western Australian Marine Research Laboratories for critically reading the manuscript and offering many helpful suggestions.

References BARD,Y. 1974. Nonlinear parameter estimatioaa. Academic Press, New York, N.Y. 341 p. BOWEN, B.K. 1971.Management of the western rock lobster ((PnnuEirus longipes cz1gnusGeorge). Proc. Indo-Pac. Fish Counc. 14(1I): 139-153. BOWEN, B.K., .WD D.A. HANCOCK. 1989. Effort limitation in the Australian rock lobster fisheries. p. 375-393. In J.F. Caddy [ed.] Marine invertebrate fisheries: their assessment and management. John PViley & Sons, Inc., New York, N.Y. BROWN, R.S., AND N. CAQUTI. 1983. Factors affecting the recapture of undersize western rock lobster PurzuEirus cygnus George returned by tishennen to the sea. Fish. Res. 2: 103-128. BROWN, W.S., AND N. CAPUTI.1986. Consenation of recruitment of the western rock lobster (Paraulirus csgnus) by improving survival and growth of undersize rock lobsters captured and returned by fishermen to the sea. Can. J. Fish. Aquat. Sci. 43: 2236-2242. CADDY, J.F. 1975. Spatial model for an exploited shellfish population, and its application to the Georges Brmk scallop fishery. J. Fish. Res. Board Can. 32: 1305-1328. CAPTITI, N., AND R.S. BROWN.1989. The effect of environmental factors and spawning stock on the puerulus settlement of the western rock lobster. In B.F. Phillips. led.] Workshop on Rock Lobster Ecology and Management. CSIRO Mar. Lab. Rep. 207: 29 p. CHITTLEBOROU~. R.G. 1974. Western rock lobster reared to maturity. Aust. J. Mar. Freshwater Wes. 25: 221-225. CHITTLEBOROUGM, R.G. 1975. Environmental factors affecting growth and survival of juvenile western rock lobsters Panulirus lorzgipes (MilneEdwards). Aust. J. Mar. Freshwater Res. 26: 177-196. CHITTLEB~OUGH. R.G. 1976. Growth of juvenile P~111~6liru.s longipes cygnus George on coastal reefs compared to those reared under optimal environmental conditions. Aust. J. Mar. Freshwater Wes. 27: 279-295. CHITTLEBOROUGH, W.G, AND B.F. PHILLIPS.1975. Fluctuations of year class strength and recruitment in the western rock lobster Punulirus 1ongipc.s (Milne-Edwards). Aust. J. hqar. Freshwater Res. 26: 317-328. CHUBB,C.F. 1993. A study of the spawning stock of the western rock lobster. International Workshop on Lobster Ecology and Fisheries, 12-15 June 1990, Havana, Cuba.

C H ~ BC.F., , C. DIBDEN, AND K. ELLARD. 1989. Studies on the breeding stsck sf the western rock lobster, PanuEirus cygnus, in relation to stsck and recruitment. FIRTA Project 85/57. Final Report. GEORGE, R.W. 1958. The status of the white crayfish in Western Australia. Aust. J. Mar. Freshwater Res. 9: 537-545. HANCBGK, D.A. 1981. Research for management sf the rock lobster fishery of Western Australia. Proc. Gulf Carihb. Fish. Inst. 33: 207-229. HILBORN, R., AND C.J. WALTERS. 1987. A generlal model for simulation of stock and fleet dynamics in spatially heterogeneous environments. Can. J. Fish. Aquat. Sci. 44: 1366-1369. JEKNAKOFF~ P. 1987. An electromagnetic tracking system for use in shallow water. J. Exp. Mar. Biol. Ecol. 113: 124-144. JEWNAKOFF, P., AND B.F. PHILLIPS.1988. Effect of a baited trap on the foraging movements of ~uvenilewestern rock lobsters. Aust. 9.Mar. Freshwater Res. 39: 185-192. JOLL,L.M. 1984. Natural diet and growth of juvenile western rock lobster, P~anulirus cygnus George. Ph.B. dissertation, University of Western Australia, Nedlmds, Western Australia. 194 p. JOLL,L.M., AND B.F. PHILLIPS. 1984. Natural diet md growth of juvenile western rock lobsters Panukir-us cygnus George. J . Exp. Biol. Ecol. 75: 145-169. JONES,R. 1984. Assessing the effects of changes in exploitation pattern using length con~positiondata (with notes on VPA and cohort analysis). F A 0 Fish. Tech. Pap. No. 256: 1 18 p. MONAGHAN, P.J. 1989. Distribution and marketing of Western Australian rock lobster. Fish. Bep. West. Austr. Manage. Rep. 29: 125 p. MORGAN, G.R. 1972. Fecundity in the western rock lobster Ba~ruliruslongipes cyg~zus(George) (Cmstacea: Decapda: Palinuridae). Aust. J. Mar. Fresh water Res. 23: 133-141. MORGAK, G.R. 1977. Aspects of the population dynamics of the western rock lobster and their role in management. Ph.B. thesis, University of Western Australia, Nedlands, Western Australia. 341 p. MORGAN, G.R. 1980. Population dynamics and management of the western rock lobster fishery. Mar. Policy 4: 5 2 4 0 . MORGAN, G.W., B.F. PHILLIPS,AND L.M. JOLL.1982. Stock and recruitment relationships in Panulirus cygnus, the commercial rock (spiny) lobster of Western Australia. Fish. Bull. 8063): 475486. PE.I\RCE, A.F. 1989. The keeuwin Current and the rock lobster. In B.F. Phillips led.] Workshop on Rock Lobster Ecology and Management. CSIWO Marine Laboratories Rep. 207: 29 p. PEARCE, A.F., AND B.F. PHILLIPS. 1988. ENSB events, the Leeuwin Current and larval recruitment of the western rock lobster. J. Cons. Int. Explor. Mer 45: 13-21. PHILLIPS, B.F. 1981. The circulation of the southeastern Indian Ocean and the planktonic life of the western rock lobster. Bceanogr. Mar. Biol. 19: 11-39. PHILLIPS, B.F. 1983. Migrations of pre-adult western rock lob$ters, Parzulirus cj7gnus.in Western Australia. Mar. Biol. 76: 31 1-318. PHILLIPS,B.F., AND R.S. BROWN.1989. The Western Australian rock lobster fishery: research for management, p. 159-1 81. In J.H. Caddy [ed.] Marine invertebrate fisheries: their assessment and management. John Wiley and Sons, Inc., New York, N.Y. PHILLPS,B.F., AND N.G. HALL.1978. Catches of puemlus larvae on collectors as a measure sf natural settlement of the western rock lobster Panukims cygnus George. CSIRB Rep. Div. Fish. Bceanogr. 98: 18 p. PHILLIPS, B.F., N.A. CAMPBELL, TI W.A. REA.1977. Laboratory growth of early juveniles of the western rock lobster Prsriulirus longipe.~cygnus. Mar. Biol. (Berg.) 39: 3 1-39. PHILLPS,B.F., L.M. JOLL,R.L. S A N D L ~AND D , D.W. WRIGHT.1983. Longivity, reproductive condition and growth of the western rock lobster Pr~nulirus cygnus reared in aquaria. Aust. J. Mar. Freshwater Wes. 34: 419- 429. PRESS,W.H., B.P. FLANNERY, S.A. TEUKBLSKY, AND W.T. V E ~ E R I N 1986. G. Numerical recipes, the art of scientific computing. Cambridge University Press. Cambridge, N.Y. 818 p. SCHMJTE, J . B 982. A manual for easy nonlinear parameter estimation in fishery research with interactive computer programs. Can. Tech. Rep. Fish. Aquat. Sci. 1140: 115 p. WALTERS, C.J. 1986. Adaptive management of renewable resources. Masmilan, New York, N.Y. 374 p.

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