Protecting old fish through spatial management: is there a benefit for sustainable exploitation?

Authors

  • Charles T. T. Edwards,

    Corresponding author
    1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
    2. Division of Biology, Imperial College London, Silwood Park, Ascot, SL5 7PY, United Kingdom
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  • Éva E. Plagányi

    1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
    2. CSIRO Marine and Atmospheric Research, PO Box 120, Cleveland, QLD 4163, Australia
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Correspondence author. E-mail: charles.edwards@imperial.ac.uk

Summary

1. Spatially defined restrictions on fishing activity are considered to be important for biodiversity conservation in marine ecosystems. However, it is uncertain whether such restrictions also benefit wider populations of exploited fish species, in terms of a reduced risk of overexploitation. Since fishing leads to contraction of the age structure, one potential benefit of protection is recovery of the highly fecund older age classes, potentially leading to higher recruitment levels. This investigation explores the benefits of protecting older fish and how spatial management can be used to adjust the age structure and improve the sustainability of the catch (productivity).

2. We use a non-spatial equilibrium model accounting for biomass growth, mortality and recruitment to describe the relationship between mean age of the population and productivity for the South African deepwater hake Merluccius paradoxus trawl fishery. Our results indicate that management measures capable of increasing the mean age at which fish are caught may be of benefit. Furthermore, although the contribution of older fish to recruitment is important, the biomass growth of individuals before they are caught is responsible for the most significant productivity benefit of an older population age structure.

3. Older M. paradoxus are found in deeper water, so that distinct age classes can be defined spatially using empirical data. We describe a non-equilibirum model to examine spatial management alternatives for adjusting the age structure by targetting these different age classes. We investigate the benefits of protecting either older or younger fish, with results suggesting that it is more important to limit fishing on the younger (shallow) sections of the population if productivity benefits are to be realized.

4.Synthesis and applications. We conclude that the age structure of a population can be modified through spatially managed targeting of different age classes, and that, contrary to previous assumptions for M. paradoxus, protecting older fish has a negative consequence for the age structure of the resource. Instead, younger sections of the population should be protected through limitations on fishing in shallower waters, if older age classes are to recover.

Introduction

Spatial managment measures, including the implementation of marine protected areas (MPAs) are widely considered to be essential components of effective marine resource management. MPAs are ‘no take zones’ where fishing of a particular species, or all species, is prohibited. There is evidence of ecosystem benefits associated with MPAs, including higher biodiversity, at least in coastal regions amenable to such studies (Halpern & Warner 2002; Halpern 2003). There is also evidence that fish populations within the boundary of an MPA benefit from protection (McClanahan & Arthur 2001; Willis et al. 2003). However, when considering exploitation of the wider resource, it is less clear that MPAs can improve prospects for long-term sustainability. This is because the benefits associated with protection are dependent on a restricted range of assumptions that may undermine their applicability in a given context (Hilborn et al. 2004). Primarily, if adult fish are too mobile, then the anticipated benefits of an MPA are negated (Polacheck 1990; Walters, Hilborn & Parrish 2007).

Protected areas are often promoted with good intent but inadequate empirical support (Willis et al. 2003). This is important, since the implementation of a poorly conceived MPA can have negative consequences for the resource it is supposed to protect (Parrish 1990; Dinmore et al. 2003; Hobday, Punt & Smith 2005), including undermining attempts to reliably estimate status of the stock (Field et al. 2006). Furthermore, it has been shown that by introducing an inefficiency into fishing practices, MPAs have an effect on yield similar to that achieved through a reduction in fishing capacity (Mangel 1998; Botsford, Kaplan & Hastings 2004), indicating that they may not be necessary if more traditional measures to limit effort can be imposed effectively.

Despite these concerns, MPAs still have a number of potential benefits for resource management. They may act as buffers against uncertainty in resource status (Roberts & Polunin 1993; Clark 1996; Botsford, Castilla & Peterson 1997; Lauck et al. 1998), mismanagement (Roberts 2000) and the evolutionary consequences of fishing. Fishing can lead to small size and early maturity (Ernande, Dieckmann & Heino 2003; Miethe et al. 2010) with associated increases in the variability of stock dynamics (Anderson et al. 2008). In particular it has been argued that MPAs provide refugia for the older more fecund members of the population (Berkeley et al. 2004).

The removal of old, large adults through fishing (Jackson et al. 2001; Berkeley et al. 2004; Yemane, Field & Leslie 2008) decreases the reproductive potential of a population and hence its ability to withstand and recover from overexploitation (Begg & Marteinsdottir 2003; Aubone 2004; Law 2007). This is because large females produce more eggs, that are also of better quality (Marteinsdottir & Steinarsson 1998; Vallin & Nissling 2000; Berkeley, Chapman & Sogard 2004; Carr & Kaufman 2009), so that their potential contribution to recruitment is higher. Such maternal recruitment effects mean that an older population will have a higher reproductive capacity than a younger population of equivalent biomass. Although there may be density-dependent limitations on recruitment at high population sizes (so that the presence of older individuals is not important), recruitment to heavily exploited populations may benefit if the biomass in older age classes could be recovered. MPAs may provide a means to do this, with proponents argueing for the protection of older individuals to allow these more fecund age classes to recover (Berkeley et al. 2004).

Sustainable exploitation is primarily dependent on recruitment and, due to the maternal recruitment effects described above, we might expect the age structure of a population to be an important correlate of the level of exploitation which it is able to sustain. However, there is an additional reason why this should be the case: allowing fish to grow increases the exploitable biomass available to fishing. If they are harvested too late many of the fish will have already died and optimal fishing practices must address this trade-off between biomass growth and natural mortality. This predicts an optimum mean age at which to catch fish (Quinn & Deriso 1999), and associated age structure for the population, at which the harvested biomass from each recruit is maximized. If the mean age of the population is below this optimum, then allowing the age structure to recover will increase the harvest level it is able to sustain. These yield-per-recruit (YPR) effects therefore act in a complementary manner to maternal recruitment effects, so that recovery in the age structure will increase the prospects for sustainable harvest.

Here, we investigate the role of spatial management in recovering the age structure of exploited marine populations. If different age classes of a population have a distinct spatial distribution that can be resolved by management, spatial allocation of fishing effort offers a means to modify the average age at which fish are caught. This change in fishing practices would be reflected in the age structure of the harvested population and could thus increase the productivity (defined here as the sustainable catch) of the fishery. This could improve the prospects for sustainability or initiate population recovery from a depleted state.

A case study for our investigation was provided by the South African hake fishery, which consists of trawl (both offshore and inshore), longline and handline fleets, and targets two species, the shallow-water Merluccius capensis and deepwater M. paradoxus hake. These species have a bathytrophic distribution with age, with older fish occupying deeper water (Payne 1989). They thus have an overlapping spatial distribution, with older M. capensis occupying a similar depth range to the younger M. paradoxus. The focus here was on the offshore trawl fleet only, which is responsible for c. 90% of the commercial catch and is focused on M. paradoxus.

We first investigated the relationship between mean age and productivity for the deepwater hake using a non-spatial equilibrium model (Model 1). We then developed a quasi-spatial, non-equilibrium, age-structured model (Model 2) to investigate the potential role for spatial management in adjusting the mean age of the population. This model assumes a single population, which can be exploited by spatially distinct fisheries, targetting different age classes of fish at different depths. It consists of a simple extension of standard age-structured models, and does not require any explicit assumptions about population movement – noting that poorly quantified movement patterns often undermine realistic attempts to model exploitation patterns in a spatial framework (Walters, Hilborn & Parrish 2007). Instead, the emprical catch at age profile for each fishery is used to estimate a static, spatially heterogeneous age distribution. We used Model 2 to investigate the benefits of protecting younger (shallow) or older (deep) sections of the population. For both models two Options (A and B) were considered. Only under Option B were maternal recruitment effects included. Thus, comparison of results with Option A allowed us to distinguish the contributions of maternal recruitment effects and underlying YPR effects to the relationships between age structure and productivity.

Materials and methods

Model 1: equilibrium model

The population age structure at unfished equilibrium is

image(eqn 1)

from which the spawning potential per recruit is obtained

image(eqn 2)

where Ma is the natural mortality at age a, a++ is the model plus group age, ua is the mass at age at the beginning of the year, ma is the maturity at age, and fa is the fecundity per unit mass at age. Fecundity per unit mass is a relative measure of the contribution to recruitment per unit mass by each age class, allowing eqn 2 to account for age dependent variation in batch fecundity and spawning frequency. If fa = 1 for all a, SPR0 is equal to the spawning biomass per recruit (Option A). If maternal recruitment effects are included (Option B) fa is assumed to increase with age.

Given the pristine spawning potential (K), recruitment to the unfished population (R0) can be estimated from the relationship

image(eqn 3)

Pristine recruitment is then used to parameterize the (Beverton-Holt) stock recruitment curve as a function of spawning potential for a particular year (By)

image(eqn 4)
image(eqn 5)
image(eqn 6)

where h is a proportion defined so that hR0 is the recruitment when = 0·2K. Under the assumption of constant fishing mortality Fa (i.e. Fa = Fay for all y) the age structure of the population PFa is given by replacing Ma in eqn 1 with Za = Ma + Fa. This can be used to calculate SPRF (see eqn 2). It follows that By = Ry-1SPRF (i.e. recruitment at the start of the previous year, multiplied by the spawning potential per recruit, will give the total spawning potential at the start of the current year), giving

image(eqn 7)

Under equilibrium fishing conditions (and ignoring environmentally driven fluctuations), recruitment will be constant across years. Eqn 7 can then be solved for a constant Ry, giving

image(eqn 8)

from which the numbers at age for this equilibrium population can be obtained

image(eqn 9)

Eqn 9 accomodates the influences of age structure, determined by Ma and Fa, and the stock recruitment relationship in predicting Na under equilibrium fishing conditions. The yield can then be estimated using the Baranov catch equation

image(eqn 10)

where va is the mass at age in the middle of the year. When estimating the maximum sustainable yield (MSY), FMSY is chosen under a constant selectivity Sa (where FaMSY = FMSYSa) to maximize Y.

Given life-history parameters for a population it is possible to estimate the equilibrium yield (Y) from eqn 10 as a function of Fa. Since Fa also contributes to the population age structure we were able to gain insight into the relationship between age structure and productivity through simulation.

Model 2: non-equilibrium model

Population dynamics (numbers at age Nya) are represented by standard equations for an age-structured fisheries population model (e.g. Fournier & Archibald 1982; Deriso, Quinn & Neal 1985):

image(eqn 11)

with recruitment given in eqn 4 and spawning potential biomass

image(eqn 12)

The catch is restricted to spatially disaggregated zones z, so that catch at age

image(eqn 13)
image(eqn 14)
image(eqn 15)

where Cb is the catch biomass and Bexp is the exploitable biomass. kza is the proportionate numbers in each zone by age group (inline image). It is assumed, for reasons of simplicity to be constant across years, and is estimated independently for ages a = {a,...,a+}. To prevent confounding of kza with selectivity Sza, and since gear is similar across the offshore fleet, we assume a constant selectivity across zones (Sza = Sa). Selectivity at age was given by the logistic function

image(eqn 16)

with estimated parameters acrit and δ.

For the survey, catches at age were given by

image(eqn 17)

again, assuming Szasurv = Sasurv. In this case selectivity was allowed to have a decreasing slope at higher ages, so that inline image for aslope. Thus, we also estimated s for the survey selectivity, with aslope assumed to be the youngest age at which Sasurv > 0·99.

Data

Commercial catch and effort (CPUE) data for the offshore M. paradoxus trawl fishery are reported for 20′ × 20′ rectangles (minutes of latitude and longitude) covering the South African EEZ, and were available from Marine and Coastal Management (MCM), South Africa, for the years 1978–2007. Total commercial trawl catches of M. paradoxus for the offshore fleet up to 2007, were obtained from MCM (Rademeyer, Butterworth & Plagányi 2008a,b) and distributed across grids using catch information in the CPUE data for these years.

Length frequency data per grid for M. paradoxus were available from observers placed on commercial vessels by Capricorn Fisheries Monitoring, South Africa, since 2002 (Edwards et al. 2009). Age length keys for M. paradoxus were obtained directly from MCM and were available from 1988 to 2000 (excluding 1989 and 1998). Since they were not available for the same years as the length frequency data, an average age length key was generated and applied to obtain spatially disaggregated catch at age data for the years 2002–2007.

After application of the age length key to obtain catches at age, proportionate catches at age per zone were obtained as follows: we first derived inline image by scaling catches at age so that the biomass sum across ages equals the total catch for that grid (g) and year; we then estimated the proportionate catch at age across zones

image(eqn 18)

where inline image. Thus, pzyl reflects not only the age distribution in a particular zone, but also the proportion of the total catch taken from that zone in a particular year. It is this use of the information contained in the spatial distribution of total catches that allows estimation of kza (eqns 13 and 17).

Information on the proportionate distribution at age is also contained in the survey catch at age data, provided per grid by MCM for the years 1983–2007. This is because survey catches at age are routinely scaled to reflect the total catch biomass for a particular survey trawl, which follows a random stratified spatial sampling protocol (T. Fairweather 2008, personal communication.). The survey proportions at age inline image were therefore derived in a similar manner to eqn 18. For simplicity, seasonally distinct surveys were combined and assumed to take place in the middle of the year.

Parameter estimation

All parameters were estimated within a maximum likelihood framework, assuming that the observed catches at age follow a multinomial distribution. Thus, the likelihood for the observed proportions at age (p, eqn 18) for a particular data series (survey or commericial) is given by

image(eqn 19)

where inline image is the effective sample size. The effective sample size is that which would be expected given a true multinomial distribution of the data. It was initialized at inline image = 100 for all years and re-estimated over two iterations of fitting using (McAllister & Ianelli 1997):

image(eqn 20)

Projections

As spatially disaggregated catch data were only available since 1983 (see above), the population model was initialized at this year using the results from Rademeyer, Butterworth & Plagányi (2008a). Estimated commercial selectivity was assumed to be constant between 1993 and 2007. For 1983 and 1984, commercial selectivity was taken from Rademeyer, Butterworth & Plagányi (2008a), with a linear interpolation used to represent changes in selectivity between 1984 and 1993. Only a single commercial selectivity was estimated, with spatial differences in the catch at age profile attributed to differences in the availability of fish (kza). Uncertainty was represented by Monte Carlo sampling of estimated parameters from a multivariate normal distribution with approximate covariance matrix obtained from the maximum likelihood fit.

Projections were then performed in which the total offshore catch was redistributed between two different zones. Changing spatial distributions of catches were simulated by increasing and decreasing the proportion of the total catch in Zone 1, relative to that recorded for 2007, by 10% increments. For each increment the population was projected 50 years into the future, keeping the distribution of catches constant throughout the projection period. Zone 2 represented all fished areas not in Zone 1, and encompassed the remaining catch, so that total catch across zones was held constant at 112885 tonnes (equal to that recorded for 2007) for all projections.

Management zones were chosen after visual inspection of the mean age of the catch per grid (Fig. 1a). Two scenarios were investigated (Fig. 1b). In the first Scenario, Zone 1 was identified from the survey data as a region containing a high proportion of young fish. In the second Scenario, Zone 1 was selected using the commercial catch at age data, and consisted of a smaller, deeper region that contains a high concentration of older fish. The empirical age distributions for each Scenario (averaged across years) are shown in Figs 2 and 3.

Figure 1.

 (a) Map of South Africa showing the relative mean age of fish per grid derived from survey and commercial catch data. Grids represent 20′ × 20′ rectangles (minutes of latitude and longitude) covering the South African EEZ. Darker grids indicate an older mean age. (b) Map of South Africa showing locations of Zone 1 for Scenarios 1 and 2 (Zone 2 is the area fished that is not in Zone 1).

Figure 2.

 Scenario 1. Mean proportions at age across zones (withinline imageand equal to the mean pzya across years, see eqn 18).

Figure 3.

 Scenario 2. Mean proportions at age across zones (withinline imageequal to the mean pzya across years, see eqn 18).

Projection results were described using the following summary statistics: (i) Δā: change in the mean age of the population; (ii) ΔBlrg: change in the biomass of large fish (defined here as fish older than 9 years of age); (iii) ΔB: change in the spawning potential biomass (eqn 12); (iv) ΔR: change in the recruitment; and (v) ΔBexp: change in the exploitable biomass (eqn 15). Change is represented by the difference between first and last years of the projection period, normalized so that the change associated with the status quo distribution of catches is zero. For example, Δā ā2058 − ā2008 − Δā0 where Δā0 refers to the change associated with the status quo distribution of catches. This allowed results from different projections to be compared relative to the underlying status quo biomass dynamic. Statistics (i) and (ii) represent changes in the age structure of the population; (iii) and (iv) changes in the reproductive capacity and output; and (v) the resultant changes in productivity (i.e. the catch that could be supported by the fishery – assuming that status quo catch levels are sustainable).

Results

Model parameters, specifically Ma, K, h, ma, ua and va were obtained from Rademeyer, Butterworth & Plagányi (2008a); Table 1). We assume a++ = 12. Under Option A: fa = 1 for all ages; under Option B: fa increases linearly from f1 = 0 to f12 = 1·535. Option B was based on assumptions made by Field et al. (2008) that spawning frequency is the primary determinant of maternal recruitment effects and increases by fourteen times from = 2 to = 15. Values of fa for Option B were rescaled so that SPR0 was the same for both options, allowing estimates of equilibrium yield to be compared directly. Estimates of SPRa0 for both options are shown in Fig. 4, illustrating the increased contribution to recruitment made by the older age classes for Option B.

Table 1.   List of parameters for M. paradoxus from Rademeyer, Butterworth & Plagányi (2008a) and Field et al. (2008)
ParameterValue
  1. K, carrying capacity (tonnes); h, steepness of the stock recruit relationship; Ma, natural mortality at age; ma, proportion mature at age; ua, weight at age at start of year (kilograms); va, weight at age in middle of year (kilograms); fa, fecundity per unit mass at age for Option B (for Option A fa = 1 for all a).

K1270940
h0·95
a0,…,a++0, 1,...,12
inline image0·531, 0·531, 0·531, 0·447, 0·396, 0·362, 0·362, 0·362, 0·362, 0·362, 0·362, 0·362, 0·362
inline image0·000, 0·000, 0·000, 0·000, 1·000, 1·000, 1·000, 1·000, 1·000, 1·000, 1·000, 1·000, 1·000
inline image0·006, 0·054, 0·180, 0·412, 0·766, 1·254, 1·880, 2·645, 3·545, 4·575, 5·726, 6·989, 8·354
inline image0·022, 0·105, 0·281, 0·573, 0·993, 1·550, 2·245, 3·079, 4·044, 5·136, 6·344, 7·659, 9·071
inline image0·000, 0·000, 0·140, 0·279, 0·419, 0·558, 0·698, 0·837, 0·977, 1·116, 1·256, 1·395, 1·535
Figure 4.

 Model 1 Options A and B. Spawning potential per recruit at age (SPRa0) at unfished equilibrium. Maxima for Options A and B occur at ages 6·1 and 9·0 years respectively.

Model 1: Mean age and productivity

Mean age of the equilibrium harvested population was controlled using the fishing mortality at age

image(eqn 21)

with 0 < ac < a++. We first estimated FMSY = 0·76 with ac = 4 – the first age at which the population is fully selected by the fishery (Rademeyer, Butterworth & Plagányi 2008a) – giving the mean F across all ages as inline image = 0·5. Keeping inline image constant across a range of ac values, we estimated the equilibrium catch (from eqn 10) as a function of mean age (Fig. 5, Right panel). For Options A and B there is a clear optimum mean age at which equilibrium yield is maximized. The shape of the yield curves illustrate the trade-off between biomass growth and natural mortality (YPR effects) in deciding the optimum age at which to harvest fish. From Rademeyer, Butterworth & Plagányi (2008a), mean age of the population is around 1·0 years (Fig. 6). Fig. 5 suggests that management measures capable of increasing the mean age will prove beneficial to population productivity, by increasing the sustainable catch. Specifically, if the age at which fish are first selected by the fishery can be increased (Fig. 5, Left panel), the sustainable yield will also benefit.

Figure 5.

 Model 1 Options A and B. Left panel: relationship between age of first selection by the fishery (acrit) and mean age of the population. Right panel: equilibrium yield as a function of mean population age. Estimated current age from Rademeyer, Butterworth & Plagányi (2008a) is shown. Maxima for Options A and B occur at a mean age of 1·71 and 1·74 respectively.

Figure 6.

 Mean age of South African hake M. paradoxus estimated by Rademeyer, Butterworth & Plagányi (2008a). Estimated current age (2006) is shown.

When interpreting the difference between Options A and B, it should be remembered that the stock recruitment relationship is asymptotic at high spawning potentials. Thus at higher mean ages of the population (represented by higher SPRF), equilibrium recruitment (eqn 8) is equivalent for each of the models (Fig. 7). At lower mean ages, recruitment drops off more rapidly for Option B, as illustrated by the drop in sustainable yield (Fig. 5, Right panel). This illustrates that maternal recruitment effects become increasingly important as the mean age of the population is reduced.

Figure 7.

 Model 1 Options A and B. Relationship between equilibrium recruitment (RF; eqn 8) and mean age of the population.

Model 2: spatial management

The analysis of Model 1 indicates that the mean age of the population can be adjusted by the age at which fish are first caught, and that this will have an influence on the equilibrium yield that can be sustained. Model 2 was used to explore management options that target spatially disaggregated age classes. This may allow the age structure of the population to be adjusted.

Two spatial management scenarios were investigated to examine their likely consquences for mean age and productivity of the population. For both scenarios, a 1 and kz(a = 0) kz(a = 1). For Scenario 1, a+ = 5, corresponding to the survey data plus group, with kz(a > 5) = 0. For Scenario 2, a+ = 7, corresponding to the commercial data plus group, with kz(a > 7) kz(a = 7). Convergence of the model fit was ensured in each case, with parameter estimates and associated coefficients of variation given in Table 2. Estimated commercial exploitable biomass at age for = 2007 (the last year for which catch data were available) is shown for Scenarios 1 and 2 in Figs 8 and 9 respectively. Since these estimates are similar for Options A and B (Table 2) only results from Option A are shown.

Table 2.   Parameter estimates from model fits
ParameterScenario 1Scenario 2
Option AOption BOption AOption B
  1. k1a is the proportion of the total numbers at age in Zone 1. acrit and δ describe the logistic selectivity function (eqn 16) with decreasing slope s for the survey selectivity. Coefficients of variation were estimated from the maximum likelihood fit and are given in brackets.

k110·791 (0·0003)0·788 (0·0004)0·031 (0·0016)0·030 (0·0021)
k120·333 (0·0007)0·340 (0·0010)0·099 (0·0011)0·105 (0·0014)
k130·079 (0·0031)0·066 (0·0032)0·106 (0·0019)0·137 (0·0028)
k140·119 (0·0127)0·070 (0·0187)0·090 (0·0035)0·134 (0·0057)
k150·056 (0·0300)0·073 (0·0405)0·141 (0·0059)0·193 (0·0079)
k160·175 (0·0100)0·222 (0·0108)
k170·126 (0·0175)0·186 (0·0194)
inline image2·240 (0·0014)2·031 (0·0018)2·432 (0·0012)2·20 (0·0006)
inline image1·044 (0·0015)1·027 (0·0017)1·061 (0·0013)1·042 (0·0017)
δcomm0·369 (0·0027)0·308 (0·0040)0·312 (0·0018)0·264 (0·0014)
δsurv0·348 (0·0007)0·351 (0·0008)0·331 (0·0007)0·333 (0·0009)
s0·842 (0·0095)1·0661 (0·0082)0·615 (0·0121)0·985 (0·0100)
Figure 8.

 Model 2 Scenario 1 Option A. Estimated commercially exploitable biomass for 2007. The proportionate Bexp describes the proportion of the biomass at age in each Zone.

Figure 9.

 Model 2 Scenario 2 Option A. Estimated commercially exploitable biomass for 2007. The proportionate Bexp describes the proportion of the biomass at age in each Zone.

It can be seen that for Scenario 1 (Fig. 8), Zone 1 is estimated to contain a high proportion of younger individuals, as expected from an intuitive interpretation of the data. Thus, increasing the catch in Zone 1 is predicted to lead, on average, to a reduction in the mean age of the catch (results not shown). The consequences of this changing catch distrubution are given in Table 3, with Δā and ΔBexp illustrated in Fig. 10. Both Options show that the mean age of the population decreases as the catches in Zone 1 increase. There is also a reduction in Blrg, B, R and ultimately the Bexp available for harvest.

Table 3.   Projection results showing summary statistcs under Scenarios 1 and 2, Options A and B, assuming a 100% decrease or increase in catches from Zone 1. A change in the catch of −100% represents a total closure of Zone 1 to all fishing. A change of +100% represents catches from Zone 1 of 171 and 45934 tonnes for Scenarios 1 and 2 respectively. Total catches remained constant at 112885 tonnes
Scenario and OptionChange in catchΔā (years)ΔBlrg (103 tonnes)ΔB (103 tonnes)ΔR (millions)ΔBexp (103 tonnes)
  1. Coefficients of variation are given in brackets.

1A−100%0·0004 (0·134)0·11 (0·133)0·44 (0·124)0·04 (0·145)0·47 (0·061)
+100%−0·0004 (0·134)−0·11 (0·133)−0·44 (0·124)−0·04 (0·145)−0·47 (0·061)
1B−100%0·0005 (0·161)0·15 (0·190)0·48 (0·158)0·09 (0·181)0·61 (0·156)
+100%−0·0005 (0·161)−0·15 (0·190)−0·48 (0·158)−0·09 (0·181)−0·61 (0·156)
2A−100%−0·0117 (1·012)−2·77 (1·385)−13·95 (1·054)−1·45 (1·06)−14·46 (1·037)
+100%0·0118 (0·908)2·94 (1·380)14·63 (0·969)1·4 (0·994)15·03 (0·961)
2B−100%−0·0185 (0·629)−4·89 (0·455)−17·41 (0·649)−3·79 (0·676)−23·50 (0·529)
+100%0·017 (0·604)4·57 (0·420)16·11 (0·628)3·16 (0·634)21·71 (0·521)
Figure 10.

 Model 2 Scenario 1. Select summary statistics illustrating predicted changes in the age structure (Δā) and productivity (ΔBexp) of the fishery as a consquence of proportionate changes in the Zone 1 catch.

For Scenario 2, Zone 1 is estimated to contain a high proportion of older fish (Fig. 9). Thus, increasing the catches in Zone 1 is predicted to lead to an increase in the overall mean age of the catch. The consequences are given in Table 3 and illustrated in Fig. 11. Results demonstrate an increase in the summary statistics as more catches are taken from Zone 1, indicating an increase in the overall productivity of the fishery.

Figure 11.

 Model 2 Scenario 2. Select summary statistics illustrating predicted changes in the age structure structure (Δā) and productivity (ΔBexp) of the fishery as a consquence of proportionate changes in the Zone 1 catch.

Fig. 5 demonstrates the productivity benefits of increasing the mean age of the population. Figs 10 and 11 confirm this conclusion, correlating an increased mean age with increased spawning potential and recruitment. As expected from Model 1, similar results for the two Options illustrate the overall importance of YPR effects in determining the productivity. Nevertheless, when maternal recruitment effects are included (Option B) there is an increased sensitivity of the system to changes in the mean age at which fish are caught, due to a more pronounced change in recruitment (Fig. 7). Furthermore, we can conclude from both Scenarios that the age structure of the population is increased by targeting the older sections of the population. Thus, a reduced fishing pressure on the younger age classes allows them to make a larger contribution to the mean age as they grow through the population, than that achieved by protecting the older individuals.

Discussion

The exploitation of marine populations is generally associated with a contraction of the age structure (e.g. Yemane, Field & Leslie 2008). This can have a negative impact on the ability of the population to withstand exploitation, through the loss of highly fecund older females (Berkeley et al. 2004). However, perhaps more importantly, it is also the case that a younger population can lead to lower yields because of the lost biomass growth that would otherwise be available to harvest. For both these reasons it is often desirable to change fishing practices so that the age structure of the population can recover (Froese et al. 2008). In this investigation we have examined how this can be achieved through spatial management.

The equilibrium analysis presented here (Model 1) demonstrates that an increase in the mean age of the population is desirable for M. paradoxus, as it will be likely to yield an increase in productivity. Comparison between Options A and B illustrates that this result stems largely from the additional biomass growth allowed when fish are caught at an older age (YPR effects), but that maternal recruitment effects may contribute to the magnitude of the associated benefit and the rate at which it is realized. This is despite a weak stock recruitment relationship (high h) that predicts high recruitment levels even at low B, so that the productivity benefit of older females in the population will be small.

The non-equilibrium model (Model 2) demonstrates that by shifting catches between different spatial zones, each of which is characterized by a distinct age-class structure, the proposed shift in mean age can be initiated. As expected from Model 1, considerations of maternal recruitment effects (Option B) lead to more pronounced changes in the productivity of the population as the age structure of the population is modified.

It is often the case that MPAs are proposed as a means of protecting older sections of the population (Birkeland & Dayton 2005). However, unless overall catches are reduced, the equivalent catch of older individuals would have to be taken from elsewhere. It is coincident with the original proposition that this catch will be taken from younger age classes. This additional fishing mortality will lead to a reduction in the number of younger fish growing through the population. This can have a greater effect on the age structure than reduced fishing mortality on the older age classes. We have shown this to be the case for M. paradoxus. Protecting older age classes (Scenario 2) leads to a lower mean population age and a reduction in overall biomass after a 50 year projection period. In contrast, protection for the younger age classes (Scenario 1) has the opposite effect, with the model suggesting that such a spatial management strategy would yield an improved level of population productivity. Although relative differences in the predicted final year biomass (across different catch redistribution scenarios) are small, this is simply due to the small proportion of the total catch taken from Zone 1 under this Scenario (Table 3). In this case increased (targetted) fishing of older M. paradoxus may be a more effective means by which recovery of the age structure can be initiated (Fig. 11).

Density dependence might influence our results and has not been considered in our analysis. It can take a variety of forms. One of the most important relates to cannibalism (intraspecific predation) and the predation of younger M. paradoxus by older M. capensis (interspecific predation) (Punt & Leslie 1995). These may lead to a density-dependent reduction in recruitment at high spawning potentials; an effect that may be expected to dampen the productivity benefits associated with population recovery. Inter and intraspecific predation may also be important for density-dependent effects on the spatial distribution of hake, predicted by MacCall’s basin hypothesis (MacCall 1990; Simpson & Walsh 2004). If the distribution of age classes is primarily determined by this predation, changes in population abundance are likely to have a less pronounced effect on the mean age of catches taken from a particular area. The final density-dependent consideration is that of growth. If individuals grow more slowly when densities are high, the benefits of catching older fish are weakened. However, the converse is also true. At the low population sizes exhibited by this (and many) fisheries, individual growth rates might be enhanced. This would mean the benefits of catching fish at a later age may be even greater than this investigation suggests.

The results and model framework presented here are relevant to fisheries subject to growth overfishing where individuals are currently caught below the size associated with optimal productivity. Fisheries within European waters provide noticeable examples (Froese et al. 2008). We propose that spatial management can be complementary to more traditional measures (e.g. mesh size) that may have so far failed to direct the required changes in mean age of the population. In cases where different age classes of fish can be spatially segregated (e.g. Southern bluefin tuna Thunnus maccoyiiHonda et al. 2010), spatial management initiatives may thus allow the the population age structure to be manipulated so as to improve the future sustainability and productivity of the resource.

Acknowledgements

Thanks to Doug Butterworth (University of Cape Town, South Africa), Richard Hillary and Trevor Hutton (CSIRO Marine and Atmospheric Research, Australia) for useful comments on the manuscript. Also thanks to Rebecca Rademeyer for assistance with development of the model. This work was funded by the National Research Foundation of South Africa and the DeepFishMan EU Framework 7 project.

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