Vulnerability to exploitation of the yellownose skate (Dipturus chilensis) off southern Chile

Fisheries Research 109 (2011) 225–233

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Vulnerability to exploitation of the yellownose skate (Dipturus chilensis) off southern Chile JC Quiroz a,∗ , Rodrigo Wiff a , Luis A. Cubillos b , Mauricio A. Barrientos c a b c

División de Investigación Pesquera, Instituto de Fomento Pesquero (IFOP), Blanco 839, Valparaíso, Chile COPAS Sur-Austral, Departamento de Oceanografía, Universidad de Concepción, Casilla 160-C, Concepción, Chile Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile

a r t i c l e

i n f o

Article history: Received 27 April 2010 Received in revised form 13 December 2010 Accepted 11 January 2011 Keywords: Demography Population dynamics Leslie matrix Skate fisheries Management

a b s t r a c t The yellownose skate (Dipturus chilensis) is one of the most important component of the commercial elasmobranch fishery off Chile with an extensive distribution range from 36◦ 44 S − 55◦ 13 S. Nevertheless, fishery management for this species does not extend beyond the central zone off Chile (36◦ 44 − 41◦ 28 S), leaving the southern zone (41◦ 28 S − 55◦ 13 S) without a proper fishing effort regulation. As a result, fishing pressure has increased dramatically in the southern zone, with unknown potential consequences for this elasmobranch population. In the absence of rigorous fishery-biological data, we used a matrix population model to assess yellownose skate demographic traits under different fishing mortality levels. A Leslie matrix model was implemented, where changes in age classes are defined in terms of of life history parameters. Uncertainty was incorporated by applying a Monte Carlo method to survival, age at maturity, and fecundity. Three scenarios were evaluated based on different assumptions about survival, fishing mortality rates, and age at 50% of vulnerability. These scenarios showed a slow growth rate for population abundance (3–15% per year) with no fishing exploitation. The population reaches equilibrium at low mortality levels (0.31 yr−1 ), which is consistent with estimates reported for other rajidae skates. The elasticity analysis indicates that juvenile survival contributes the most to variations in the population growth rate. The sustainable mortality rate has a positive, non-linear relationship with age at 50% of vulnerability. Projections using different selectivity patterns showed that the population abundance is stable only when age-dependent fishing mortality removes individuals of older ages. We concluded that yellownose skate is extremely vulnerable to fishing exploitation and it is remarkably sensitive to juvenile and early life stages survival, implying that management actions are needed to ensure a sustainable exploitation. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The yellownose skate (Dipturus chilensis) is one of the most important species of the commercial elasmobranch fishery off Chile, where it is fished from the central zone (36◦ 44 S) to the far limit of the southern zone (55◦ 13 S) at depths of 100–500 m (Quiroz et al., 2008). In spite of this extensive fishing area (Fig. 1), before 2005 the government fisheries management only issued total allowable catch (TAC) for the central zone (36◦ 44 S − 41◦ 28 S), leaving the southern zone (41◦ 28 S − 55◦ 13 S) without a proper fishing effort regulations (Quiroz and Wiff, 2005a). This situation facilitated a remarkable rise in total effort, mostly in the southern zone where landings increased from 780 to 5200 tons between 1999 and 2003. As a response to this fishing pressure, the management authorities established arbitrary fishing quotas

∗ Corresponding author. Tel.: +56 32 2151418. E-mail address: [email protected] (JC Quiroz). 0165-7836/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fishres.2011.01.006

to the southern zone regardless of any scientific advice.The species comprising the Rajidae family show persistent reductions in abundance even at low exploitation levels (Dulvy et al., 2000; Dulvy and Reynolds, 2002; Frisk et al., 2002). These investigations suggest that skates are presumably the most vulnerable elasmobranch species, with a high need for conservation. Special attention has been paid to the genus Dipturus, whose species are highly vulnerable to exploitation due to their demographic traits, namely, large sizes, late maturity and low fecundity (Frisk et al., 2001,2005). Given the species’ demographic traits and the high increase in fishing efforts and landings in the unregulated southern zone, it is likely that this population is currently overfished. In terms of conservation, different modelling approaches can be used to evaluate exploitation status depending on the quantity and quality of the available data. Comprehensive fishery models might be able to capture the spatial-temporal stock dynamics, but their implementation requires detailed information about length/age structure which is, generally, not available for skates. On the other hand, unstructured models such as surplus production, requires

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JC Quiroz et al. / Fisheries Research 109 (2011) 225–233 Table 1 Notation and description of parameters and variables used in simulation framework and scenarios performed for evaluate Dipturus chilensis vulnerability.

Fig. 1. Principal fishing area of Dipturus chilensis in the eastern austral-south pacific. Latitudinal line (dotted line) divide the central and southern zone.

Parameter/variable

Units

Notation

Age Time Age-structured population Leslie matrix Leslie matrix entries Longevity Mean age at maturity Mean age at selectivity Length at 50% maturity von Betalanffy growth parameters Growth parameter of VBGF Asymptotic length parameter of VBGF Maximum length Length at zero age parameter of VBGF Fecundity Age-specific survival Age-specific vulnerability Fishing mortality rate Population growth rate Intrinsic population growth rate Stable age distribution Reproductive age distribution Elasticity matrix Elasticity matrix entries Elasticity at age Condition number

year year – – – age age age cm – year−1 cm cm cm eggs years−1 year−1 % year−1 year−1 – % % – – – –

n t N A ai,j nmax a50% s50% l50% VBGF K L∞ lmax t0 fec Sn n F  r w v e ei,j Ei K

matrix is defined as:

⎡

little data but they do not allow exploration of the age structure nor density-dependent process. The Leslie matrix approach is a good compromise between life history tables and other more detailed fishery models, providing a framework for incorporating density-dependence and stochastic dynamics in age-structured populations (Caswell, 2001; Getz and Haight, 1989). Since rigorous fisheries-biological data are lacking for this species, an agestructured demographic model seems to be the most parsimonious approach for assessing the exploitation status of yellownose skates off Chile. The principal objective of this article is to evaluate the population growth rates and depletion risks of yellownose skates under several exploitation scenarios. These scenarios include a variety of selectivity patterns, natural mortality rates and changes in survival in the early life stages and were evaluated in a stochastic model framework. Uncertainty for the model outputs were computed by applying the Monte Carlo method to survival, age at maturity and fecundity. With this stochastic framework we were able to assess the risk associated with changes in fishery mortality together with demographic characteristic of the skate’s population.

2. Methods 2.1. Demographic model The population dynamic was modelled using an age-structured matrix model considering females only and covering an age range (n) between 0 and nmax . The basic equation yielding population dynamics at any time t is given by: Nt = At × N0

(1)

where Nt is a vector representing the population age-structure and A is the Leslie matrix with entries ai,j (Caswell, 2001). The Leslie

f1 ⎢ S1

A=⎢

⎣0

0

f2 0 .. 0

.

⎤

··· 0

fn 0 ⎥

0 Sn−1

0 0

⎥ ⎦

where the top row shows the age-specific fertility (fn ) and the sub-diagonal entries give the age-specific survival (Sn ), the others entries have zero values. The notation for parameters and variables are given in Table 1. In this model, all surviving females in a given annual age class are moved to the next age class. Following the fisheries notation, Sn = e−F·n −M , where F is the instantaneous fishing mortality rate, n is the relative vulnerability to exploitation (i.e. gear selectivity pattern) in age class n and M is the natural mortality rate. The age-specific vulnerability was assumed to be invariant over time. fn was calculated as the product of Sn and fecundity (fec), while the sex ratio was assumed to be 1:1 for all ages. The solution of Eq. (1) was obtained from the general matrix model A w = w, where  is the population growth rate and w represents the stable age distribution (Caswell, 2001).  was computed numerically as the dominant eigenvalue of matrix A, whereas the vector w was obtained as the right eigenvectors associated with the dominant eigenvalue of the Leslie matrix. The dominant eigenvalue–eigenvector pair summarizes the population growth behaviour for different mortality sources. The condition  < 1 implies a declining population. The population reaches a stable distribution with an intrinsic population growth rate of (r) determined as r = log(). Another important demographic trait is the reproductive age distribution (v), which was calculated as the left eigenvectors associated with the dominant eigenvalue of the Leslie matrix, according to vAT = v. The proportional changes in  according to changes in vital rates, were calculated from the Leslie matrix elements and v–w pair vectors, as: e=

ai,j vi wj ai,j ∂ =  ∂ai,j  w, v

(2)

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Fig. 2. Probability distribution considered by the Monte Carlo simulation framework and scenarios performed for evaluate Dipturus chilensis vulnerability. (a) Distribution of the fecundity in number of eggs per female (b) Distribution of the age at 50% of maturity (c) Distribution of natural mortality and (d) Selectivity functions implemented for different mean age at selectivity (s50% ).

where e is the elasticity matrix, w,v is the scalar product of the two eigenvectors and, w and v are elements of the w and v, respectively. The elasticity matrix  elements (ei,j ) were used to determine the age elasticity as E = i i ei,j . Elasticities are additive, therefore  i j ei,j = 1, such that the sum of elasticities in Eq. (2) for each age class defines the proportional contribution of ai,j to the overall . See Table 1 for details about parameters notation and abbreviations. A sensitivity analysis was carried out to determinate the stability of the solution of the system Nt = At × N0 . How numerically well-conditioned the problem is can be defined by the condition number, where K(A) = ||A||||A−1 ||. A matrix with a low condition number is said to be well-conditioned, while a matrix with a high condition number is said to be ill-conditioned. In our case K(A) = 1.3129e + 003 which indicates the matrix model applied is not stable. In other words, for matrices with high condition numbers we will expect major changes in A under small changes on their elements. Although the matrix applied may be ill-conditioned it is common for matrices of the dimension used here. This condition may be caused by a combination of the mathematical structure and coefficients of the matrix model applied. Coefficients are determined mostly by starting parameters such as fecundity, maturity and age-dependent survival. Thus, a more stable solution may be found by tuning such processes until we get a matrix with better behaviour in terms of conditioning. This type of analysis is outside the main scope of this article. 2.2. Life history parameters M was calculated by four empirical methods selected according to the quality and availability of life history parameters. The selected methods were: (1) Pauly (1980), (2) Jensen (1996), (3) Frisk et al. (2001), and (4) Chen and Watanabe (1989). The first method estimates M using the von Bertalanffy growth parameters

(VBGF) and the annual average water temperature of the habitat (we used 10 ◦ C according to Bustos et al. (2007)). Jensen’s method is based on Beverton and Holt’s life history theory (Beverton and Holt, 1959) and it incorporates mean age at maturity (a50% ) as a survival indicator, whereas Frisk’s method is an extension of Beverton and Holt’s life history theory in which the ratio between M and K (growth parameter of VBGF) is evaluated for elasmobranches. Finally, Chen and Watanabe’s method provides a model based on two different functions: one predicting age-specific estimates of M for early life phases and the second producing an average estimated M for middles and senescent stages. The age and growth parameters for yellownose skates were obtained from Licandeo et al. (2006), who assigned ages using calcium ring counts in vertebrae of individuals collected off central Chile (37◦ − 41◦ S). These parameters provide the most reliable published estimates (for male: L∞ = 107.8 cm ; K = 0.134 yr−1 ; t0 = −0.862 yr; for female: L∞ = 128.3 cm; K = 0.112 yr−1 ; t0 = −0.514 yr), which are consistent with those reported by (Quiroz et al., 2010) for individuals sampled off southern Chile. The reproductive parameters of yellownose skates in the southern zone were taken from Quiroz et al. (2009). These authors reported that a50% is approximately 14 yr old (CI: 13–15 yr) which corresponds to a mean length at maturity (l50% ) of 103.9 cm (CI: 101.7–105.8 cm). They also showed that fec is positively correlated with female length. However, no model is proposed and Quiroz et al. (2009) suggest that the average number of eggs (48.2; s.d. = 10.65) is the most reliable estimate of fecundity in mature females. Lifespan for yellownose skates tends to be higher than the maximum ages observed (Licandeo et al., 2006) and the maximum lengths observed are frequently larger than L∞ (Quiroz et al., 2009; Quiroz et al., 2008). Thus, nmax was estimated as the age corresponding to the maximum length (lmax ), which was estimated as log(L∞ ) = 0.044 + 0.9841 · log(lmax ) according to Froese and Binohlan (2000).

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2.3. Uncertainty and scenarios The uncertainty for the life history parameters was computed using a Monte Carlo method as follows: we used a normal distribution for fecundity (mean = 24.1; s.d. = 5.33 eggs, Fig. 2a), a discrete triangular distribution for age at maturity (mean = 14; s.d. = 1 yr, Fig. 2b) and a uniform distribution for M (mean = 0.158 yr−1 ; s.d. = 0.025 yr−1 , Fig. 2c) which covers the wide range for values of M estimated in Section 3.1. According to Quiroz et al. (2010), the 95% confidence interval of M for D. chilensis computed by five empirical methods (Alverson and Carney, 1975; Frisk et al., 2001; Hoenig, 1983; Jensen, 1996; Pauly, 1980) were 0.10–0.18 yr−1 for females and from 0.11 to 0.22 yr−1 for males. The range of M values for combined genders overlaps closely to what was used here in the Monte Carlo methods (see Fig. 2c), allowing us to capture the variability of M estimates across methods. Uncertainty for a50% in females was computed using a discrete triangular distribution, assigning maturity probabilities of 0.6 to age 14 and 0.2 to ages 13 and 15. These maturity probabilities by age match the confidence intervals for l50% presented by Quiroz et al. (2009). The narrow age range of this distribution represents the quick maturation process that occurs in this species (Quiroz et al., 2009). The species’ longevity was assumed to have no error because uncertainty in this parameter generates unrealistic scenarios that might be inconsistent with the life history parameters reported for skates (Cortés, 2000; Denney et al., 2002; Frisk et al., 2001). The simulation process was based on 10.000 trials, where r values and w–v pair vectors were obtained in each combination of life history parameters, while 95% confidence intervals for these quantities were computed using the percentile method (Efron and Tibshirani, 1993). The described simulation framework was used to evaluate three scenarios, where we assessed  under certain parameter conditions described as follows:

1. Scenario A: This scenario evaluates progressive increments in F. For each increase, the Sn was calculated assuming an ageinvariant M value and a n representative for the southern Chilean zone. The n was obtained by make use of both an age-atlength key and a length-specific selectivity pattern taken from Quiroz et al. (2009) The shape of n reflects an intense exploitation (Quiroz et al., 2009; Quiroz et al., 2008) that is characterized by a mean age at selectivity (s50% ) of 5.6 yr, which means a large proportion of individuals younger (Fig. 2d). Scenario A can be seen as the baseline because all the following scenarios are modifications with added complexity. 2. Scenario B: This scenario modified scenario A to assess changes in the proportion of selected fish-at-age by modifying the logistic selectivity curve. The n was displaced along the age axis maintaining the slope of the selectivity curve (Fig. 2d). In this form, the s50% was displaced in intervals of 2 yr from 7.6 to 11.6 yr. Thus, a total of four selectivity curves were implemented getting with s50% = 5.6 to n , and where s50% takes values of 7.6 (s1 ), 9.6 (s2 ) and 11.6 yr (s3 ). Concurrently, progressive increments in F were then applied to each implemented logistic selectivity curve. 3. Scenario C: This scenario evaluates the hypothesis of agedependant variation in M. In this way, survival of the early life stages were modified by changes in M consistent with Chen and Watanabe’s method (see Section 3.1). This method assigns higher M (low survival) to capsular and juvenile ages which seems to be consistent with the skates’ life history (Frisk et al., 2002). Therefore, Sn was modified for ages 0–3 to take values of 0.4, 0.5, 0.6 and 0.7, respectively, whereas Sn for ages 4+ was constant and consistent with scenario A.

In each scenario, we calculated the steady-state fishing mortality rate (Fs ), defined as the fishing mortality value required to attain an intrinsic growth rate equal to zero (r = 0). Likewise, variations in Ei , w and v were evaluated for the case with no fishing mortality (F = 0). Age-dependent survival elasticity was computed for each case described in scenario C (see Table 2) in order to determine whether or not changes in Sn for the early stage will add information to the elasticity patterns. 2.4. Projections and depletion risk The population abundance was projected for 25 yr starting with a stable age distribution calculated with no fishing mortality. An arbitrary initial population abundance of 100 individuals was assumed at time 0. Projections included three values for fishing mortality (0.22, 0.35 and 0.50 yr−1 ) and four different logistic selectivity curve according to scenario B (n and s1 to s3 ). A total of 12 projection scenarios were evaluated which correspond to the pairwise combinations between the assumed level of fishing mortality and selectivity pattern. For each projection we calculate the median, 95% confidence intervals of the population abundance and its probability of decrease (known as depletion risk). This probability was calculated as the proportion of the 10,000 trials to the last year projected, that was bellow the initial abundance. 3. Results 3.1. Natural mortality rate The M fluctuated from 0.115 yr−1 (Jensen’s method) to 0.20 yr−1 (Frisk’s method). Pauly’s method yielded slightly lower values (0.176 yr−1 ) than those computed by Frisk’s method. These estimates are very close to those reported by Quiroz et al. (2010). Alternatively, Chen and Watanabe’s method provides two agedependent ranges of natural mortality rates: (i) 0.718–0.144 yr−1 for ages 0–13 and (ii) a mortality rate of 0.139 yr−1 that remains almost constant for ages 14+ (Fig. 3). lmax was estimated to be 123.2 cm for a nmax of 33 yr. 3.2. Scenarios According to scenario A, the Fs was 0.218 yr−1 (Fig. 4a), the maximum sustainable mortality rate (Zs = Fs + M) was 0.376 yr−1 and r with no fishing mortality was 0.142 yr−1 (95% CI: 0.087–0.198 yr−1 ). For the scenario B, when selectivity function is displacement towards older individuals (Fig. 2d), the estimates of Fs increased

Fig. 3. Estimates of natural mortality rate (M) in Dipturus chilensis for the four different methods applied.

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Table 2 Results of the scenario C in which survival for ages 0–3 is assumed to be different to the adult survival in Dipturus chilensis. M is the natural mortality rate corresponding to the levels of survival applied to ages 0–3. r is the population growth rate and Fs and Zs are the levels of fishing and total mortality needed to maintain the steady-state (r = 0). Survival ages 0–3

M (yr−1 )

r (yr−1 )

95% C.I. of r

Fs (yr−1 )

Zs = Fs + M (yr−1 )

0.4 0.5 0.6 0.7

0.92 0.69 0.51 0.35

0.03 0.07 0.10 0.12

(−0.01–0.08) (0.02–0.12) (0.05–0.15) (0.07–0.18)

0.05 0.09 0.13 0.17

0.19 0.23 0.27 0.31

Fig. 4. Relationships between intrinsic population growth rate and fishing mortality for different mean age at selectivity (s50% ) in Dipturus chilensis described for scenario A and B. Solid line indicates the median value and the shaded area the 95% confidence intervals. Circles in each plot represent the fishing mortality (Fs ) to maintain the population at equilibrium (r = 0).

from 0.26 to 0.51 yr−1 (Fig. 4b–d), highlighting the influence that the selectivity has on Sn . Likewise, when we plot s50% versus F it is clear that r has a non-linear behaviour (Fig. 5), this is specially noticeable of F greater than 0.3 yr−1 when r becomes highly sensitive to variations in s50% . In addition, when the exploitation removes an important proportion of immature individuals, the sustainable limit of fishing mortality (F to achieve r = 0) becomes smaller. In contrast, when exploitation is focused on mature individuals

(s50% > 9 yr), the range of F that produces sustainable population growth rates (r > 0) became larger (Fig. 5). A similar result is found in the analysis of the elasticity to survival (Fig. 6a), where immature individuals show a very large elasticity which decreases exponentially across ages. According to scenario C, when M of the capsular and juvenile stages increases, r decrease from 12 to 3% per year (Table 2). This fact highlights the importance of Sn in the early life stages. In fact, for each Sn case described in scenario C, the age-survival elasticity of immature individuals remains constant and higher than that of mature individuals (Fig. 6b). Survival elasticity in adults is only important when Sn for the early stages decreases significantly (Fig. 6b). Nevertheless, the main result suggests that enhancing egg and juvenile survival will provide greater benefit to the population conservation in comparison with increasing survival in adults. 3.3. Projections and depletion risk

Fig. 5. Contour lines for the population growth rate (r) under variations of the mean age at selectivity (s50% ) and fishing mortality rate (F) in Dipturus chilensis.

The first F used in the projections corresponds to the value required to reach an intrinsic growth rate equal to zero (Fs = 0.22 yr−1 ). Thus, in Fig. 7 (upper row) it can be seen that the population maintains its abundance across projected period, independent of the chosen value of s50% . The situation is different when the fishing mortality is increased. For F = 0.35 yr−1 (Fig. 6, middle row) when s50% is 5.6 and 7.6 yr, the projected abundance decreases across time. However, for the same fishing mortality but using vulnerability functions including s50% = 9.6 yr and s50% = 11.6 yr, the abundance across projected years fluctuated around the equilib-

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Fig. 6. Survival elasticity of  to changes in the elements of A. (a) For the scenario A when F = 0. (b) For the scenario C, when survival is age-dependent.

Fig. 7. Abundance estimates for the projection analysis considering different mean age at selectivity (S50% ) and three levels for fishing mortality rate applied for Dipturus chilensis. Solid line indicates the median value and the dotted line indicates the 95% confidence intervals.

rium. When fishing mortality is high (F = 0.50 yr−1 , see lower row in Fig. 7) abundance decreases even when s50% = 9.6 yr and it is only maintained when fishing starts removing individuals at relatively older ages (s50% = 11.6 yr). A similar behaviour between F and s50% is observed when depletion risk is analysed at the end of the projected period (Fig. 8). Probability of depletion increases faster according to the fishing mortality when s50% is low. In other words, when younger individual are fished, the probability of depletion increases faster in narrow range of fishing mortality. In this sense, the 10% probability of depletion is potentially an adequate threshold to quantify the risk of depletion.

4. Discussion For most elasmobranchs living off the coast of South America, fundamental fishery-biological information is fragmentary and usually unavailable. Thus, implementation of age-structured stock assessment models may not be feasible for those elasmobranch species. Age-structured models may give accurate estimations of processes such as recruitment and age-dependent fishing mortality upon which management decisions can be based. They also allow a sophisticated treatment of uncertainty by Bayesian analysis

Fig. 8. Probability profiles for the depletion risk in Dipturus chilensis derived from the projection analysis for different mean age at selectivity (s50% ) and fishing mortality levels (F). Probability of depletion was calculated to the last year of projection. Shaded area indicates the probability between 0.1 and 0.2 of depletion risk.

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(Quinn and Deriso, 1999). However, age-structured models require lengthy time series of abundance indexes and catch-at-age data, which usually are only available from rigorous fishery monitoring programs. Therefore, alternative modelling approaches generally need to be applied on elasmobranch species to assess exploitation vulnerability. The most basic approach comes from a meta-analysis of the life history parameters for different elasmobranch families to determine the existence of an empirical relationship between a relatively easy-to-obtain demographic attributes (i.e. maximum size), and the potential vulnerability under different levels of exploitation (Frisk et al., 2001). Nevertheless, accuracy of such empirical methods depends on the variability among the species for which the empirical relationship has been constructed and how well the demographic traits have been estimated for the stock of interest (Hewitt et al., 2007). Other option is to use unstructured model of biomass dynamic, but these kind of model do not allow the incorporation of age-related processes affecting population functioning. In this context, demographic analysis such as the one presented here, appears to be a good compromise between highly data-consuming age-structured models and empirical methods to determine exploitation vulnerability. The Leslie matrix approach provides a comprehensive framework for assessing the current status and vulnerability issues in data-poor or data-limited situations. Demographic data can be translated into matrix form once the life stages or age classes are delineated, and projections allow the comparison of population growth rates and the importance of certain life history parameters. Compared to many models used to determine population trends and vulnerability to exploitation, matrix models require less data and can be generalized for populations with a wide variety of life-history traits. This framework also allows the incorporation of uncertainty around the life history parameters which at the end, is transferred to the state variables (i.e. abundance, biomass). This is particularly important in conservation because it permits the risk of exploitation to be evaluated in a probabilistic framework. The analysis presented here shows that population growth rate (r) has non-linear behaviour when variations in age at 50% vulnerability (S50% ) and fishing mortality are assessed (Fig. 5). This means that there is a range of fishing mortality Fs that can maintain a stock in equilibrium (when r = 0). Particular values for Fs depend on at what age individuals start getting selected by the fishing gear. In our analysis, Fs take values between 0.22 yr−1 and 0.5 yr−1 when S50% is 5.6 and 11.6 yr, respectively. This behaviour of the population growth rate drives the way abundance is projected under fishing exploitation scenarios. When most individual are fished at relatively older ages (S50% = 11.6 yr), the median of projected abundance is maintained around the equilibrium, even when the population experiences high fishing mortality (F = 0.5 yr−1 , Fig. 7). On the other hand, when fishermen start removing animals at younger ages (S50% = 5.6 yr), fishing mortalities between 0.35 and 0.5 yr−1 make the population reach extinction at the end of the projected period (Fig. 7). In a similar manner, probability of depletion is highly affected by the chosen values of (S50% ). When individuals are removed at younger ages (S50% = 5.6 yr) the probability of depletion increases faster at small changes in F, whereas when S50% is high, the probability of depletion increases slowly according to F (Fig. 8). In other words, when S50% is incremented, the population is able to withstand a higher fishing pressure range for the same risk of depletion as in shown in the shaded are of Fig. 8. This fact underscores the importance S50% has on the conservation of yellownose skate off southern Chile. The natural mortality rate (M) is one of the key parameters defining the dynamics of any wild population. In spite of its importance, it is the least well-estimated parameter in fishery models (Hewitt and Hoenig, 2005), and the elasmobrach species are no exception (Quiroz et al., 2010). In data-limited situations, M is

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estimated from empirical relationships that try to account for the existing trade-off between this rate and other life history parameters. Several empirical methods have been proposed to estimate M, which usually differ in the functional form and/or the parameters needed to implement them. The application of those methods provides a point estimate of M, where each method produces different results and there are no clear criteria for determining which is the most credible. This is probably the reason why demographic analysis are usually implemented by considering a unique estimate of M. Here, we deal with this issue by considering M estimates with different empirical methods. We cope with uncertainty in M estimates by accounting for the range of M values across methods, between M = 0.115 yr−1 (Jensen’s method) and M = 0.2 yr−1 (Frisk et al.’s method). This allows the propagation of the intrinsic error of M due the method used, into the vulnerability to exploitation. For all empirical methods applied to estimate M, Chen and Watanabe’s is the only one that allows age-dependent variations in M. Although Chen and Watanabe give estimates of M for adult ages that were comparable with those produced by other empirical methods (Fig. 3), the introduction of a differential M for early stages (egg capsules and juveniles) produces profound variations on the population growth rate (r) (scenario C, Table 2). When a high mortality rate (low survival) is applied to early stages, population growth rate is close to zero whereas when M in early stages is closer to that of adults, population growth rate is higher and closer to those scenarios assuming constant mortality across ages (Table 2). Elasticity analysis of a Leslie matrix model compares the effect of changes in survival, individual growth, reproduction or fishing selectivity of particular life stages to population growth rate (r). The effect that each parameter has on r has been used as an index for evaluating the “importance” of certain life stages or demographic rates for management and research. In addition, r is a measure of fitness (Charnov, 1993), and elasticities of vital rates quantify their contributions to fitness, revealing important links between lifehistory evolution and demography. Thus, the elasticity concept has been applied in fish ecology in topics such as comparative demography, life history evolution and conservation and management of fished populations. Mortality in early stages has been found to be the most important factor contributing to the elasticity in elasmobranchs (Cortés, 2002). Our work on yellownose skate agreed with previous research because egg capsules and juvenile survival was the main factor contributing to the population growth rate variations. Here, elasticity to survival was tested by changing the mortality of early life stages in two different manners. By modelling a selectivity function that considers different proportions of immature fish (scenario B), or by considering a different M estimates for early stages, by applying Chen and Watanabe’s method (scenario C). Both scenarios indicate the importance of early survival in r. When age at 50% of vulnerability changed between 5.6 and 11.6 yr old, the fishing mortality rate needed to maintain the population at equilibrium (r = 0) changes from 0.22 to 0.50 yr−1 (Figs. 4 and 5). On the other hand, when M in early life stages changes from 0.35 to 0.92 yr−1 , r changes from a value near 0 to a population growth rate of 0.12 yr−1 . Elasticity to survival of early stages in yellownose skate seem to be caused by the particular reproductive strategy of this specie. According to Quiroz et al. (2009), yellownose skate exhibits low fecundity associated with an observed average of 48.2 egg capsules per female (both ovaries showed approximately the same number of eggs) assuming one reproductive event per year, maturity occurs at large size in females (l50% = 103.9 cm of total length) and the maturity function has a steep slope, indicating that individuals reach maturity in a narrow size range. Low fecundity will produce low recruitment and late maturity indicates that individuals should spend long time in the vegetative fraction of the population before they contribute to the renewal process. Even when individuals reach maturity, their contribution to popula-

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tion renewal will be low because of the low fecundity. Therefore, any factor affecting survival of juveniles will produces profound variations in population growth rate and thus the fitness of the population. Hence, conservation actions should be focused on the regulations of juvenile fishing mortality for yellownose skate. The optimal age at first capture that minimizes the risk of exploitation can be easily computed from demographic models as we have shown here. When r = 0 the population is at the steady-state, because all renewal is compensated by mortality. According to life history parameters observed in yellownose skate, Fs = 0.218 yr−1 is needed to match the steady-state condition. A simplistic approach to determine exploitation status indicates that a stock is being fully exploited when F = M (Pauly, 1996). Our results match this simple rule, because average value of M across methods is close the F needed to maintain the steady state. With no fishing mortality (when F = 0), population growth rate in yellownose skate is 0.142 yr−1 . Furthermore, total mortality (Z = F + M) that will not decrease the stock must be lower than 0.376 yr−1 . Independent estimates for Z for this species in the southern area indicate that total mortality rate is bigger than the value estimated to maintain a stock in equilibrium (Quiroz and Wiff, 2005b). Therefore, symptoms of overfishing are occurring in yellownose skate. The model proposed here for analysing the exploitation vulnerability assumes density independence (no compensation processes are considered) and it provides an instantaneous value of r for a specified set of life history traits that correspond to a specific population size. Gedamke et al. (2007) pointed out that values of r derived from such models may be biased, because at least some life history parameters should show plasticity and be able to respond to changes in population size. These authors added that r values may only be unbiased in the special cases where a severely depleted population is modelled, and where life history parameters were estimated under such conditions. The current exploitation state of yellownose skate off southern Chile is considered to be as severely depleted as the current level of spawning biomass has decreased to 19% of its unexploited condition (Contreras and Quiroz, 2010). On the other hand, life history parameters for this species are fairly recent and correspond to data coming from a depleted stock. In this context, we believe the estimate of r provided here can be considered as unbiased. Overfishing of this specie can be understood in light of capture and management history. Landings of yellownose skate have been reported since the late 1970s from the central and southern zone. Since 1993, landings have increased dramatically. The first period (1993–1998) was characterized by an increase in fishing effort of the industrial longline fleet operating exclusively in the central and southern zones. After 1998, the industrial fleet stopped its fishing operations and the small-scale longline fleet became important. Nowadays, landings fluctuate around 4000 tons per year, coming exclusively from small-scale vessels operating in the southernaustral zone, without any proper fishing effort regulation. High increase in fishing effort regardless of conservation attributes can have dramatic consequences in skates. Life history characteristics for skates include late maturity, low growth rate, low fecundity and large sizes make them one of the most vulnerable elasmobrach groups (Dulvy et al., 2000; Dulvy and Reynolds, 2002). This paper makes a contribution in generating a base-line analysis upon which management procedures can be implemented to ensure the conservation and sustainability of yellownose skate in Chile.

Acknowledgments We would like to thank Dr. Leslie New (University of St. Andrews) and two anonymous reviewers who suggested

major improvements. This work was supported by the grant “Investigación evaluación de stock y CTP raya volantín regiones VIII-X, 2006” from the Instituto de Fomento Pesquero (IFOP-Chile).

References Alverson, D.L., Carney, M.J., 1975. A graphic review of the growth and decay of population cohorts. J. Cons. Int. Explor. Mer. 36, 133–143. Beverton, R.J.H., Holt, S.J., 1959. A review of the lifespans and mortality rates of fish in nature and the relation to growth and other physiological characteristics. In: Ciba Foundation Colloquia in Ageing. V. The Lifespans of Animals. Churchill, London, pp. 142–177. Bustos, C., Balbontin, F., Landaeta, M., 2007. Spawning of the southern hake Merluccius australis (Pisces: Merlucciidae) in Chilean fjords. Fish. Res. 83, 23–32. Caswell, H., 2001. Matrix Population Models: Construction, Analysis and Interpretation. Sinauer Associates, Massachusetts. Charnov, E.L., 1993. Life History Invariants. Oxford University Press, London. Chen, S., Watanabe, S., 1989. Age dependence of natural mortality coefficient in fish population dynamics. Nippon Suisan Gakkai Shi 55, 205–208. Contreras, F., Quiroz, J.C., 2010. Investigación del estatus y evaluación de estrategias de explotación sustentables 2011, de las principales pesquerías Chilenas, Raya Volantín. Instituto de Fomento Pesquero-Subsecretaría de Pesca, Valparaíso (request a copy at: http://www.subpesca.cl. (in Spanish)). Cortés, E., 2000. Life history patterns and correlations in sharks. Rev. Fish. Sci. 8, 299–344. Cortés, E., 2002. Incorporating uncertainty into demographic modeling: application to shark populations and their conservation. Conserv. Biol. 16, 1048– 1062. Denney, N.H., Jennings, S., Reynolds, J.D., 2002. Life-history correlates of maximum population growth rates in marine fishes. Proc. R. Soc. B: Biol. Sci. 269, 2229–2237. Dulvy, N.K., Metcalfe, D.J., Glanville, J., Pawson, G.M., Reynolds, J.D., 2000. Fishery stability, local extinctions, and shifts in community structure in skates. Conserv. Biol. 14, 283–293. Dulvy, N.K., Reynolds, J.D., 2002. Predicting extinction vulnerability in skates. Conserv. Biol. 16, 440–450. Efron, B., Tibshirani, R.J., 1993. An Introduction to the Bootstrap. Chapman & Hall, New York, USA. Frisk, M.G., Miller, T.J., Fogarty, M.J., 2001. Estimation and analysis of biological parameters in elasmobranch fishes: a comparative life history study. Can. J. Fish. Aquat. Sci. 58, 969–981. Frisk, M.G., Miller, T.J., Fogarty, M.J., 2002. The population dynamics of little skate Leucoraja erinacea, winter skate Leucoraja ocellata, and barndoor skate Dipturus laevis: predicting exploitation limits using matrix analysis. ICES J. Mar. Sci. 59, 576–586. Frisk, M.G., Miller, T.J., Dulvy, N.K., 2005. Life histories and vulnerability to exploitation of elasmobranchs: inferences from elasticity, perturbation and phylogenetic analyses. J. Northwest Atl. Fish. Sci. 35, 27–45. Froese, R., Binohlan, C., 2000. Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency. J. Fish Biol. 56, 578– 773. Gedamke, T., Hoenig, J.M., Musick, J.A., DuPaul, W.D., Gruber, S.H., 2007. Using demographic models to determine intrinsic rate of increase and sustainable fishing for elasmobranchs: pitfalls, advances and applications. N. Am. J. Fish. Manag. 27, 605–618. Getz, W.M., Haight, R.G., 1989. Population Harvesting: Demographic Model of Fish, Forest and Animal Resources. Princeton University Press, New Jersey, USA. Hewitt, D.A., Lambert, D.M., Hoenig, J.M., Lipcius, R.N., Bunnell, D.B., Miller, T.J., 2007. Direct and indirect estimates of natural mortality for Chesapeake Bay blue crab. Trans. Am. Fish Soc. 136, 1030–1040. Hewitt, D.A., Hoenig, J.M., 2005. Comparison of two approaches for estimating natural mortality based on longevity. Fish. Bull. 103, 433–437. Hoenig, J.M., 1983. Empirical use of lengevity data to estimate mortality rates. Fish. Bull. 82, 898–902. Jensen, A.L., 1996. Beverton and Holt life history invariants result from optimal tradeoff of reproduction and survival. Can. J. Fish. Aquat. Sci. 53, 820–822. Licandeo, R., Lamilla, J.G., Rubilar, P.G., Vega, R.M., 2006. Age,growth, and sexual maturity of the yellownose skate Dipturus chilensis in the south-eastern pacific. J. Fish Biol. 68, 488–506. Pauly, D., 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. CIEM 39, 175–192. Pauly, D., 1996. One hundred million tonnes of fish, and fisheries research. Fish. Res. 25, 25–38. Quinn, I.I., Deriso, T.R., 1999. Quantitative Fish Dynamics. Oxford University Press, New York. Quiroz, J.C., Wiff, R., 2005a. Demographic analysis and explotation vulnerability of beaked skate (Dipturus chilensis) off the Chilean austral zone. Aberdeen, UK. ICES CM/N:19.

JC Quiroz et al. / Fisheries Research 109 (2011) 225–233 Quiroz, J.C., Wiff, R., 2005b. Investigación Evaluación de Stock y CTP Raya Volantín VIII a X Regiones, 2006. Report No. BIP 20068605-0, Instituto de Fomento Pesquero-Subsecretaría de Pesca, Valparaíso (request a copy at: http://www.subpesca.cl. (in Spanish)). Quiroz, J.C., Wiff, R., Caneco, B., 2010. Incorporating uncertainty into empirical estimations of natural mortality for two species of Rajidae fished in Chile. Fish. Res. 102, 297–304.

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Quiroz, J.C., Wiff, R., Céspedes, R., 2009. Reproduction and population aspects of the yellownose skate, Dipturus chilensis (Pisces, Elasmobranchii: Rajidae), from southern Chile. J. Appl. Ichthyol. 25, 72–77. Quiroz, J.C., Wiff, R., Gatica, C., Leal, E., 2008. Species composition, catch rates, and size structures of fishes caught in the small-scale longline skate fshery off southern Chile. Lat. Am. J. Aquat. Res. 36, 15–24.