Fisheries Research 125–126 (2012) 318–330

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Fisheries Research journal homepage: www.elsevier.com/locate/fishres

Estimating ﬁshery-scale rates of discard mortality using conditional reasoning Hugues P. Benoît a,b,∗ , Thomas Hurlbut a , Joël Chassé c , Ian D. Jonsen b a

Gulf Fisheries Centre, Fisheries and Oceans Canada, Moncton, NB E1C 9B6, Canada Department of Biology, Dalhousie University, Halifax, NS B3H 4J1, Canada c Institut Maurice Lamontagne, Fisheries and Oceans Canada, Mont-Joli, QC G5H 3Z4, Canada b

a r t i c l e

i n f o

Article history: Received 2 August 2011 Received in revised form 8 December 2011 Accepted 9 December 2011 Keywords: Discard mortality Survival modelling Mixture model Fisheries observers Error propagation

a b s t r a c t Obtaining a representative estimate of discard mortality for population and ecosystem assessments is very challenging. This can only rarely be done directly by recovering tagged discarded individuals. Instead, semi-quantitative measures of individual ﬁsh vitality or physical condition, obtained by onboard observers prior to discarding, can be used. Such vitality measures can be a good indicator of discard mortality, and by virtue of the data collection method, should also reﬂect the condition of discards throughout the ﬁshery. Furthermore, vitality can be predicted using covariates known to affect discard mortality, allowing for a more general assessment. We argue that a representative mortality rate can be estimated using the product of at least two probabilities: that of belonging to a particular vitality class, conditional on the factors experienced during capture and catch handling; and the probability of surviving the event, conditional on pre-release vitality. Here we estimate mortalities for ﬁve ﬁsh taxa captured in southern Gulf of St. Lawrence ﬁsheries. The conditional survival probabilities were obtained using survival analysis of data from experiments in which ﬁsh were captured using commercial ﬁshing methods and held to assess short-term mortality (2–3 days). The analysis included a mixture model with a fraction of unaffected individuals, which appears appropriate for data from bycatch mortality studies. Based on this study and the mechanistic interpretation of the mixture model, short-term monitoring of discard mortality may be sufﬁcient to characterize longer term impacts in a number of taxa. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved.

1. Introduction In many commercial ﬁsheries, discarded ﬁsh can represent a large and potentially species diverse proportion of total catch (Alverson, 1997; Harrington et al., 2005). Understanding the magnitude of incidental ﬁshing mortality for discarded species requires estimating the amounts that are discarded, as well as the fraction of those ﬁsh that die as a consequence of the capture and discarding process. In principle, data on catch composition collected via a well structured onboard observer or video monitoring program can be used to estimate discard amounts (e.g., Rochet and Trenkel, 2005; Stanley et al., 2009). However, estimating relevant discard mortality rates is considerably more problematic given the need to properly reﬂect the effects of the various factors that inﬂuence it and to assess the long-term fate of individuals (Muoneke and Childress, 1994; Davis, 2002; Suuronen, 2005; Broadhurst et al., 2006).

∗ Corresponding author at: Gulf Fisheries Centre, Fisheries and Oceans Canada, Moncton, NB E1C 9B6 Canada. Tel.: +1 506 851 3146; fax: +1 506 851 2620. E-mail address: [email protected] (H.P. Benoît).

The only direct manner of estimating discard mortality is by recovering ﬁsh tagged prior to release. With traditional tags, this requires that rates of natural and tagging mortality, tag loss and tag reporting be estimated (e.g., Hoag, 1975; Pollock et al., 1995; Cadigan and Brattey, 2006). This approach will therefore likely be limited to species for which there are high levels of catch, strong incentives for tag reporting and good population monitoring. The method would generally not be applicable to non-commercial species, including those for which bycatch mortality has contributed to an elevated extinction risk (Dulvy et al., 2003; Kappel, 2005). Data from satellite pop-up transmission tags have also been used to estimate discard mortality (Domeier et al., 2003; Kerstetter et al., 2003; Campana et al., 2009), though the cost (thousands of U.S. dollars) and size (tens of cm3 ) of these tags limit this approach to higher proﬁle megafauna. As an alternative to tagging, ﬁsh caught during commercial or simulated ﬁshing have been held in sea cages or tanks to assess eventual mortality (e.g., Olla et al., 1997; Davis and Olla, 2001). This approach is useful in isolating the effects of a limited set of factors affecting discard mortality. Estimating a discard mortality rate that is representative of a ﬁshery, where there are numerous factors contributing, will generally not be possible using holding

0165-7836/$ – see front matter Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ﬁshres.2011.12.004

H.P. Benoît et al. / Fisheries Research 125–126 (2012) 318–330

2. Methods 2.1. Background The taxa included in this study illustrate different cases that motivate discard mortality rate estimation. Discarding of American plaice, Atlantic cod and witch ﬂounder, was permitted in sGSL ﬁsheries up to 1993. Amounts discarded prior to that year were very large at times (Jean, 1963; Powles, 1969; Bousquet et al., 2010), and some illegal discarding has persisted since the ban (Allard and Chouinard, 1997). Incorporating estimates of this otherwise unaccounted ﬁshing mortality into population assessments is highly desirable (e.g., Casey, 1996; Punt et al., 2006). The skates of the sGSL are of conservation concern; winter skate, Leucoraja ocellata, has been designated as endangered (COSEWIC, 2005), and thorny skate, Amblyraja radiata, and smooth skate, Malacoraja senta, are

12 10

Number of holdings

8 6 4 2

114

102

90

78

66

54

42

30

18

0 6

experiments alone. However, it may be possible if these results are combined with additional data from the ﬁshery, as we present in this study. The condition or vitality of ﬁsh just prior to discarding (e.g., Table 1) has been shown to be a good predictor of mortality in both holding and tagging studies (e.g., Van Beek et al., 1990; Hueter and Manire, 1994; Richards et al., 1995). Vitality scores have in turn been shown to reﬂect the diverse conditions experienced by ﬁsh during the capture and discarding process (e.g., Richards et al., 1994; Benoît et al., 2010). A representative discard mortality rate could therefore be estimated using the product of at least two probabilities: the probability of belonging to a particular vitality class, conditional on the factors experienced during capture and handling; and the probability of surviving the event, conditional on pre-release vitality. This approach has at least two advantages. First, data on the pre-release vitality of ﬁsh can be collected easily and at little or no additional cost to existing onboard observer programs (e.g., Richards et al., 1994; Benoît et al., 2010). Second, because these programs are typically structured to provide data that are representative of their ﬁsheries, the data on discarded ﬁsh vitality, and in turn their mortality, should also be representative of the conditions experienced by discarded ﬁsh. The present study has four objectives. First, we analyze the results of experiments to quantify the vitality-dependent shortterm mortality of ﬁve southern Gulf of St. Lawrence (sGSL; Canada) ﬁsh taxa captured by a bottom trawl: Atlantic cod (Gadus morhua), American plaice (Hippoglossoides platessoides), skates (Rajidae Family), winter ﬂounder (Pseudopleuronectes americanus) and witch ﬂounder (Glyptocephalus cynoglossus). There are concerns regarding extirpation risk for the ﬁrst three of these taxa (COSEWIC, 2005, 2009, 2010), and discard mortality must be quantiﬁed for population assessment and recovery planning. Survival functions were ﬁtted to the data (e.g., Cox and Oakes, 1984; Ibrahim et al., 2001), including functions based on a mixture model containing a fraction of individuals whose survival probability is unaffected by capture and discarding (e.g., Farewell, 1982). Second, the selected survival functions were combined with information on ﬁsh prediscard vitality from commercial ﬁsheries (Benoît et al., 2010), to estimate relevant rates of short-term survival. This was done for two cases: one in which ﬁshery-speciﬁc data on vitality were available; and a second in which the distribution of vitality scores in the ﬁshery was predicted using the empirical model of Benoît et al. (2010). Third, we review existing literature on mortality trends in released ﬁsh, to assess the extent to which short-term mortality estimates can predict longer term impacts. Fourth, we discuss how the conditional reasoning used to estimate discard survival from observer and experimental data can be expanded to incorporate the effect of other processes known to affect discard mortality.

319

Holding duration (hr) Fig. 1. Frequency distribution of the duration of experimental holding periods for individual ﬁshing sets. At the end of each holding period, all live ﬁsh were returned to the sea and were considered as censored observations in the analyses.

considered priority candidates for conservation status assessment. Skates in the sGSL are typically discarded and estimates of associated mortality are necessary to determine the role of ﬁshing in population decline and recovery (e.g., Swain et al., 2009a). Finally, discarding of undersized winter ﬂounder (Pseudopleuronectes americanus) is permitted for conservation reasons. Mandatory live release policies may also be contemplated for endangered species, including the recently assessed sGSL cod and plaice (COSEWIC, 2009, 2010). Understanding discard mortality and the causal factors will help determine the efﬁcacy of such policies. 2.2. Discard mortality experiments Experiments were undertaken in 2005 and 2006 aboard the CCGS Opilio (an 18-m stern trawler), to correlate ‘pre-release’ vitality codes (Table 1) to short-term mortality in the ﬁve ﬁsh taxa of interest. Fish were caught using a conventional bottom trawl and following common commercial ﬁshing tow speed (2.75 knots) and set durations (1–2 h). Fish were handled as they would have been during commercial ﬁshing operations and sampled as the observers would do: measured for fork length (cm), vitality assessed and time spent on deck prior to holding (henceforth, deck time) noted (Benoît et al., 2010). Vitality was scored according to Table 1, based on a rapid (10 s) evaluation of each individual. Attempts were made to solicit a response from immobile ﬁsh by depressing their eye with a ﬁnger and by repositioning the ﬁsh on the measuring board. Fish that remained unresponsive were scored as vitality level 4 (moribund). Regardless of vitality, each ﬁsh was then individually tagged (t-bar streamer tags) and placed into onboard 1200-L holding tanks containing continuously exchanged refrigerated seawater. Tank temperatures were set to match the bottom temperatures where the ﬁsh were captured, as measured using trawl-mounted temperature loggers. Short-term mortality of individual ﬁsh was assessed by holding them for 14–110 h (Fig. 1), depending on available time and weather. During the ﬁrst 24 h of holding, the tanks were monitored approximately hourly for fatalities. Monitoring frequency was then progressively decreased to once every 2–4 h, as the frequency of fatalities declined. Death was mostly established by ﬂaring of the gills, rigor mortis and absence of ventilation during an approximately 2 min observation period. Fish that survived the holding period were returned to the sea.

320

H.P. Benoît et al. / Fisheries Research 125–126 (2012) 318–330

Table 1 Description of the codes used by onboard observers to score the pre-discarding vitality of individual ﬁsh (Benoît et al., 2010). Vitality

Code

Description

Excellent Good/Fair Poor Moribund

1 2 3 4

Vigorous body movement; no or minora external injuries only. Weak body movement; responds to touching/prodding; minora external injuries. No body movement, but ﬁsh can move operculum; minora or majorb external injuries. No body or opercular movements (no response to touching or prodding).

a b

Minor injuries were deﬁned as ‘minor bleeding, or minor tear of mouthparts or operculum (≤10% of the diameter), or moderate loss of scales (i.e. bare patch)’. Major injuries were deﬁned as ‘major bleeding, or major tearing of the mouthparts or operculum, or everted stomach, or bloated swim bladder’.

2.3. Analysis All analyses were undertaken separately by species, except for skates, which were treated together (family Rajidae) to achieve an adequate sample size. Because the ﬁsheries observers do not consistently or reliably identify skates below the family level (Benoît, 2006), the taxonomic resolution in the analysis of the experiments matches that from ﬁsheries sampling (Benoît et al., 2010). 2.3.1. Capture and handling survival probability Not all ﬁsh classiﬁed into vitality class 4 (moribund) were dead; some were in an unresponsive catatonic state (e.g., Richards et al., 1995; Laptikhovsky, 2004). Once placed in seawater, some of these ﬁsh resumed ventilating and may have even recovered. Fish classiﬁed as vitality class 4 that were determined to be dead within the ﬁrst hour of holding were considered to have died during capture or handling. As a ﬁrst step, the capture and handling survival probability for ﬁsh belonging to vitality class 4 was estimated for each taxon. This probability was modelled using a logistic regression (McCullagh and Nelder, 1989) of the ﬁsh state (i.e., dead or alive) as a function of deck time, given an expected inverse relationship: logit[] =

0

+

(1)

1d

where is a vector of individual pre-release survival probabilities, d is a vector of observed deck times, and 0 and 1 are model parameters. Note that by deﬁnition the capture and handling survival probability is 1 for individuals in vitality classes 1, 2 and 3 (Table 1). 2.3.2. Survival during captivity The next step was estimating the probability that individuals survived the tank-holding period, given that they had survived capture and handling. The data for each individual ﬁsh were their assessed pre-holding vitality score and the elapsed holding time before they were either assessed as dead or were returned to the sea. Individuals that survived the entire holding period are referred to as right-censored, in that true times of death are unknown. The data were analyzed using survival analysis (e.g., Cox and Oakes, 1984; Ibrahim et al., 2001), which models the survival probability as a function of time, and which can accommodate both uncensored and right-censored observations. The underlying model used in our analyses was a Weibull-type survival function, chosen for its ability to mimic common survival functions encountered in ecology (e.g., Deevey’s, 1947 Type I, II and III survival functions) and its use in other discard survival studies (Neilson et al., 1989; Campana et al., 2009). It is deﬁned as S(t) = exp[−(˛ · t) ]

(2)

where S(t) is a vector of the survival probability of individual ﬁsh to time t, and ˛ and are respectively the scale and shape parameters of the underlying Weibull distribution. The effect of covariates on survival are commonly included via ˛, such that S(t|X) = exp[−(exp(X ) · t) ]

(3)

where S(t|X) is a vector of the survival probability, conditional on the matrix of covariate observations X, and  is a vector of parameters for the effect of the covariates. The covariate observations in this study are the vitality classes, treated as a factor. The survival model in Eq. (3) assumes that, conditional on the covariates, the sample of ﬁsh is homogeneous, i.e. that all individuals in a common vitality class follow the same survival function. Furthermore, it assumes that S(t|X) is a continually declining function of t. The homogeneity assumption will be violated if only a portion of the captured ﬁsh were adversely affected by the associated events. These affected ﬁsh might be expected to die within hours or days of holding. In contrast, ﬁsh that were not adversely affected would be expected to die according to their normal life schedule (i.e., on the scale of years). For these latter individuals, the risk of dying during an experimental holding period is very close to nil. The overall observed survival trend for the whole sample of ﬁsh would then be a combination of a rapid decline in survival within the ﬁrst few hours or days of the study, followed by general stability in survivors, a pattern observed in numerous published studies (see Section 3.5). To account for this heterogeneity, a mixture of two survival models was applied to the data. The ﬁrst component models the survival of individuals adversely affected by the ﬁshing event, SA (t), and in the present case follows the Weibull model (Eq. (2)). The second component models survival for the proportion of individuals that were not adversely affected (i.e., immune individuals), SI (t). Mathematically, we have S (t) = SA (t) + (1 − )SI (t)

(4)

where S (t) is the overall survival function for the sample and is the proportion of individuals that were adversely affected by the capture/handling process. Both and the parameters dictating the form of SA (t) are estimated from the data, while we assumed that SI (t) = 1. The assumption for SI (t) enhances model identiﬁability, and is consistent with the assumed near zero probability of death by natural causes during the course of the holding period. The validity of this assumption clearly declines as the duration of the holding period increases, but is likely reasonable for holding periods on the time scale of days. Note that in Eq. (4) as t → ∞, S (t) → 1 − (i.e., constant survival rate). Furthermore, when = 1 (i.e., all individuals are adversely affected by the ﬁshing event), S (t) = SA (t). Models such as Eq. (4) have been used to analyze survival data from experiments in which applied treatments do not appear to affect all experimental subjects (e.g., Boag, 1949; Berkson and Gage, 1952; Farewell, 1982). To the best of our knowledge, such models have not previously been applied in ﬁsheries science. In medical clinical trials, these are termed cure rate mixture models (ch. 5, Ibrahim et al., 2001), but here we refer to them as survival mixture models (SMM). Replacing SA (t) in Eq. (4) with the function in Eq. (2), and dropping SI (t), we obtain the following general SSM: S (t) = · exp[−(˛ · t) ] + (1 − )

(5)

Given different assumptions for the parameters ˛ and , we deﬁned six competing models for our analysis (Table 2). We note the use

H.P. Benoît et al. / Fisheries Research 125–126 (2012) 318–330

321

Table 2 Assumptions for the parameters ˛ and of Eq. (5), used to deﬁne the six competing models for the analysis of the ﬁsh holding survival data. In the table, X is an indicator matrix of vitality classes for observations on individual ﬁsh, and , 1 , and 2 are vectors of parameters for the effect of each vitality class. The table entry ‘constant’ indicates instances where the value of ˛ and/or was estimated as part of the model ﬁtting. Model

˛

Interpretation

Weibull 1 (W1) Weibull 2 (W2) Mixture 1 (M1) Mixture 2 (M2)

Constant exp(−X ) Constant exp(−X )

1 1 Constant Constant

Mixture 3 (M3)

Constant

[1 + exp(−X )]−1

Mixture 4 (M4)

exp(−X 1 )

[1 + exp(−X 2 )]−1

Common survival function for all ﬁsh (i.e., Eq. (2)) Common survival function within each vitality class (i.e., Eq. (3)) Common survival function for a ﬁxed proportion of affected individuals Common survival function within each vitality class for a ﬁxed proportion of affected individuals Common survival function for affected individuals, with the proportion affected dependent on vitality class Common survival function within each vitality class, where the proportion of affected individuals also depends on vitality class

of the common logit-linear transform to link and vitality class in the mixture models M3 and M4 (e.g., Farewell, 1982). The ﬁsh holding data for each of the ﬁve taxa were ﬁt to each of the six models using maximum likelihood (details in Appendix A). For each taxon, the model ﬁts were compared using delta-values of Akaike’s Information Criterion corrected for small sample sizes (AICc; Burnham and Anderson, 2002). As a rule of thumb, AICc values 10 suggested that the competing model is very unlikely (Burnham and Anderson, 2002). Though all six models were compared, three of them were considered unlikely a priori. Previous studies (e.g., Van Beek et al., 1990; Richards et al., 1995; Benoît et al., 2010) have indicated a relationship between vitality and survival, making models W1 and M1 (Table 2) very unlikely a priori. Comparisons to these models do however indicate the importance of vitality as an explanatory variable. Model M2 (Table 2) was also considered unlikely a priori because we expected the proportion of affected individuals to increase with vitality class. The predicted survival function from the models was also plotted against the empirical Kaplan–Meier survival curve (ch. 2, Cox and Oakes, 1984) to assess model suitability. The Kaplan–Meier survival curve is a function of the data only, and in the absence of censored values, it follows the proportion of individuals alive at each time interval during the holding phase of the experiment. 2.3.3. Estimating ﬁshery-scale short-term survival using observations for vitality In the commercial groundﬁsh mobile-gear ﬁsheries of the sGSL, certiﬁed third-party observers are deployed on approximately 10% of ﬁshing trips as a condition of ﬁshing license (Kulka and Waldron, 1983; Benoît and Allard, 2009). During the 2005 and 2006 ﬁshing seasons, observers collected data on ﬁsh vitality from a subset of the observed ﬁshing sets (details in Benoît et al., 2010). Up to 25 individuals of a given ﬁsh taxon were sampled by the observer during a given ﬁshing set just prior to discarding, and the vitality of ﬁsh was assessed following the method in Section 2.2. Deck time for each ﬁsh was also noted. For those taxa for which discarding was not permitted in the ﬁsheries, sampling occurred at around the time that the discarded portion of the catch was released. The distribution of vitality scores observed in the ﬁshery was combined with the vitality-dependent survival rates estimated

m ¯ R(t) =

s=1

(1) and (5) (and making explicit the conditional dependence on ¯ covariates), the average survival to time t for a given taxon, R(t), was estimated as:

m

¯ R(t) =

ws · n−1 s ·

s=1

ns

(v = vi,s , d = di,s ) · S (t|v = vi,s )

m

s=1

ws

(6)

where ws is the catch weight of the taxon in set s of the m sets in which vitality observations were made, ns is the number of ﬁsh sampled for vitality in set s, (v = vi,s , di,s ) is the capture and handling survival probability for individual i in set s assessed at vitality level vi,s and having experienced a deck time of di,s , and S (t|v = vi,s ) is the vitality-dependent post-release survival probability to time t for the ﬁsh. The capture and handling survival probability was obtained from an inverse-logit transformation of Eq. (1), such that:

(v = vi,s , d = di,s ) =

1 [1 + exp(−

0

−

1 di,s )]

−1

for vi,s ∈ (1, 2, 3) for vi,s = 4

(7)

To keep predictions within the range of experimental holding period durations (Section 2.1), t was set at 72 h. A Monte Carlo simulation based on bootstrapping (Efron and ¯ Tibshirani, 1993) was used to estimate the error for R(t), taking into account error associated with each component of Eq. (6) (see Appendix B for details). 2.3.4. Estimating ﬁshery-scale short-term survival in the absence of vitality observations Benoît et al. (2010) presented a multinomial model that relates vitality scores to covariates, while accounting for inter-observer differences in vitality scoring using a random effect (details in Appendix C). With this model, and given information on ﬁshingset-speciﬁc discard amounts and values of relevant covariates, it is possible to estimate ﬁshery-scale discard mortality in the absence of observations of vitality. Here, as an example, we estimated the short-term survival rate of skates and cod discarded during the commercial mobile-gear ﬁshery in 1991 and 1992. These years were immediately prior to the collapse of the southern Gulf cod ﬁshery, a time when ﬁshing effort and catches were considerably greater than during the mid-2000 period considered in the analyses of Section 2.3.3 (e.g., Swain et al., 2009b; Dufour et al., 2010). Furthermore, prior to 1993, discarding of cod in the ﬁshery was legal and observers regularly reported the discarding of individuals falling mainly below the regulated size limit of 41 cm. Under this approach, a term for the expected probability that a ﬁsh is in vitality level vis , conditional on relevant covariates, is ¯ added to Eq. (6) to estimate R(t): ws · n−1 s ·

ns 4 i=1

r=1

P(vi,s = r|zi,s ) · (v = r, d = di,s ) · S (t|v = r)

m

s=1

using the methods in Sections 2.3.1 and 2.3.2 to estimate average short-term survival for ﬁsh discarded in the ﬁshery. Based on Eqs.

i=1

ws

(8)

where P(vi,s = r|zi,s ) is the probability that the vitality level for ﬁsh i in set s is equal to r, for r ∈ {1, . . ., 4}, conditional on the vector of relevant covariates found to affect vitality for the species in

322

H.P. Benoît et al. / Fisheries Research 125–126 (2012) 318–330

Table 3 Numbers of ﬁsh included in the study as a function of vitality class and taxon. Classes are further divided for ﬁsh that were initially alive but subsequently died during holding (ds ), that survived the holding period and were therefore treated as censored observations in the analyses (c), and those that died during capture and handling (di ). Vitality code

1

Species

ds

c

ds

c

ds

c

di

ds

c

Cod American plaice Winter ﬂounder Skates Witch ﬂounder

19 15 0 0 1

41 114 19 58 0

44 24 2 0 5

29 62 23 31 3

56 29 7 9 11

11 30 12 16 3

441 565 36 22 89

60 76 3 8 6

9 23 8 16 0

2

3

4

question, zi,s , and a set-speciﬁc random effect used to account for inter-observer differences in vitality scoring and for the clustered nature of vitality sampling, us (Appendix C; Benoît et al., 2010). The relevant covariates for skates were catch (kg), the sea surface temperature (SST, ◦ C) and the deck time, d. For cod, the covariates were ﬁsh length (cm), SST and d (see Appendix B). The value for P(vi,s = r|zi,s ) was obtained from an inverse-logit transformation of the multinomial cumulative-logit model (Eq. (C.1)) such that,

Table 4 Parameter estimates (standard error, SE) for each ﬁsh taxon for the logistic regression relating the probability that a ﬁsh assessed as vitality level 4 actually survived to the time of holding. Species Cod American plaice Winter ﬂounder Skates Witch ﬂounder

2.3.5. Prognosis for long-term discard survival: indications from the literature To assess the generality of the shape of the survival functions we observed, and to determine whether short-term discard mortality can predict longer term fatalities, we assembled survival functions from published studies concerning discarded ﬁsh or ﬁsh escaping through net meshes. Criteria for inclusion were: (1) the period of observation for mortality was ≥72 h, (2) at least three data-points along the survival curve were presented, including a point at ∼24 h following the experimental treatment, and (3) some fatalities were observed. Nineteen studies covering 22 species were retained, including holding studies and studies in which the survival function was inferred using data from pop-up archival satellite tags (Table D.1). An average survival curve was calculated for studies that presented replicate survival curves from an experimental treatment, or similarly shaped relative curves from different treatments. The empirical survival curves from the various studies were plotted together to compare their shapes. Survival was calculated relative to the number of live ﬁsh remaining 24 h after capture, to make the curves clear and more comparable and because much of the post-treatment mortality in these studies occurred in the ﬁrst 24 h.

1

0.8266 0.0048 0.0060 0.1135 0.5067

(SE)

P

−0.085 (0.015) −0.065 (0.008) −0.220 (0.067) −0.032 (0.016) −0.118 (0.039)

Contents lists available at SciVerse ScienceDirect

Fisheries Research journal homepage: www.elsevier.com/locate/fishres

Estimating ﬁshery-scale rates of discard mortality using conditional reasoning Hugues P. Benoît a,b,∗ , Thomas Hurlbut a , Joël Chassé c , Ian D. Jonsen b a

Gulf Fisheries Centre, Fisheries and Oceans Canada, Moncton, NB E1C 9B6, Canada Department of Biology, Dalhousie University, Halifax, NS B3H 4J1, Canada c Institut Maurice Lamontagne, Fisheries and Oceans Canada, Mont-Joli, QC G5H 3Z4, Canada b

a r t i c l e

i n f o

Article history: Received 2 August 2011 Received in revised form 8 December 2011 Accepted 9 December 2011 Keywords: Discard mortality Survival modelling Mixture model Fisheries observers Error propagation

a b s t r a c t Obtaining a representative estimate of discard mortality for population and ecosystem assessments is very challenging. This can only rarely be done directly by recovering tagged discarded individuals. Instead, semi-quantitative measures of individual ﬁsh vitality or physical condition, obtained by onboard observers prior to discarding, can be used. Such vitality measures can be a good indicator of discard mortality, and by virtue of the data collection method, should also reﬂect the condition of discards throughout the ﬁshery. Furthermore, vitality can be predicted using covariates known to affect discard mortality, allowing for a more general assessment. We argue that a representative mortality rate can be estimated using the product of at least two probabilities: that of belonging to a particular vitality class, conditional on the factors experienced during capture and catch handling; and the probability of surviving the event, conditional on pre-release vitality. Here we estimate mortalities for ﬁve ﬁsh taxa captured in southern Gulf of St. Lawrence ﬁsheries. The conditional survival probabilities were obtained using survival analysis of data from experiments in which ﬁsh were captured using commercial ﬁshing methods and held to assess short-term mortality (2–3 days). The analysis included a mixture model with a fraction of unaffected individuals, which appears appropriate for data from bycatch mortality studies. Based on this study and the mechanistic interpretation of the mixture model, short-term monitoring of discard mortality may be sufﬁcient to characterize longer term impacts in a number of taxa. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved.

1. Introduction In many commercial ﬁsheries, discarded ﬁsh can represent a large and potentially species diverse proportion of total catch (Alverson, 1997; Harrington et al., 2005). Understanding the magnitude of incidental ﬁshing mortality for discarded species requires estimating the amounts that are discarded, as well as the fraction of those ﬁsh that die as a consequence of the capture and discarding process. In principle, data on catch composition collected via a well structured onboard observer or video monitoring program can be used to estimate discard amounts (e.g., Rochet and Trenkel, 2005; Stanley et al., 2009). However, estimating relevant discard mortality rates is considerably more problematic given the need to properly reﬂect the effects of the various factors that inﬂuence it and to assess the long-term fate of individuals (Muoneke and Childress, 1994; Davis, 2002; Suuronen, 2005; Broadhurst et al., 2006).

∗ Corresponding author at: Gulf Fisheries Centre, Fisheries and Oceans Canada, Moncton, NB E1C 9B6 Canada. Tel.: +1 506 851 3146; fax: +1 506 851 2620. E-mail address: [email protected] (H.P. Benoît).

The only direct manner of estimating discard mortality is by recovering ﬁsh tagged prior to release. With traditional tags, this requires that rates of natural and tagging mortality, tag loss and tag reporting be estimated (e.g., Hoag, 1975; Pollock et al., 1995; Cadigan and Brattey, 2006). This approach will therefore likely be limited to species for which there are high levels of catch, strong incentives for tag reporting and good population monitoring. The method would generally not be applicable to non-commercial species, including those for which bycatch mortality has contributed to an elevated extinction risk (Dulvy et al., 2003; Kappel, 2005). Data from satellite pop-up transmission tags have also been used to estimate discard mortality (Domeier et al., 2003; Kerstetter et al., 2003; Campana et al., 2009), though the cost (thousands of U.S. dollars) and size (tens of cm3 ) of these tags limit this approach to higher proﬁle megafauna. As an alternative to tagging, ﬁsh caught during commercial or simulated ﬁshing have been held in sea cages or tanks to assess eventual mortality (e.g., Olla et al., 1997; Davis and Olla, 2001). This approach is useful in isolating the effects of a limited set of factors affecting discard mortality. Estimating a discard mortality rate that is representative of a ﬁshery, where there are numerous factors contributing, will generally not be possible using holding

0165-7836/$ – see front matter Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ﬁshres.2011.12.004

H.P. Benoît et al. / Fisheries Research 125–126 (2012) 318–330

2. Methods 2.1. Background The taxa included in this study illustrate different cases that motivate discard mortality rate estimation. Discarding of American plaice, Atlantic cod and witch ﬂounder, was permitted in sGSL ﬁsheries up to 1993. Amounts discarded prior to that year were very large at times (Jean, 1963; Powles, 1969; Bousquet et al., 2010), and some illegal discarding has persisted since the ban (Allard and Chouinard, 1997). Incorporating estimates of this otherwise unaccounted ﬁshing mortality into population assessments is highly desirable (e.g., Casey, 1996; Punt et al., 2006). The skates of the sGSL are of conservation concern; winter skate, Leucoraja ocellata, has been designated as endangered (COSEWIC, 2005), and thorny skate, Amblyraja radiata, and smooth skate, Malacoraja senta, are

12 10

Number of holdings

8 6 4 2

114

102

90

78

66

54

42

30

18

0 6

experiments alone. However, it may be possible if these results are combined with additional data from the ﬁshery, as we present in this study. The condition or vitality of ﬁsh just prior to discarding (e.g., Table 1) has been shown to be a good predictor of mortality in both holding and tagging studies (e.g., Van Beek et al., 1990; Hueter and Manire, 1994; Richards et al., 1995). Vitality scores have in turn been shown to reﬂect the diverse conditions experienced by ﬁsh during the capture and discarding process (e.g., Richards et al., 1994; Benoît et al., 2010). A representative discard mortality rate could therefore be estimated using the product of at least two probabilities: the probability of belonging to a particular vitality class, conditional on the factors experienced during capture and handling; and the probability of surviving the event, conditional on pre-release vitality. This approach has at least two advantages. First, data on the pre-release vitality of ﬁsh can be collected easily and at little or no additional cost to existing onboard observer programs (e.g., Richards et al., 1994; Benoît et al., 2010). Second, because these programs are typically structured to provide data that are representative of their ﬁsheries, the data on discarded ﬁsh vitality, and in turn their mortality, should also be representative of the conditions experienced by discarded ﬁsh. The present study has four objectives. First, we analyze the results of experiments to quantify the vitality-dependent shortterm mortality of ﬁve southern Gulf of St. Lawrence (sGSL; Canada) ﬁsh taxa captured by a bottom trawl: Atlantic cod (Gadus morhua), American plaice (Hippoglossoides platessoides), skates (Rajidae Family), winter ﬂounder (Pseudopleuronectes americanus) and witch ﬂounder (Glyptocephalus cynoglossus). There are concerns regarding extirpation risk for the ﬁrst three of these taxa (COSEWIC, 2005, 2009, 2010), and discard mortality must be quantiﬁed for population assessment and recovery planning. Survival functions were ﬁtted to the data (e.g., Cox and Oakes, 1984; Ibrahim et al., 2001), including functions based on a mixture model containing a fraction of individuals whose survival probability is unaffected by capture and discarding (e.g., Farewell, 1982). Second, the selected survival functions were combined with information on ﬁsh prediscard vitality from commercial ﬁsheries (Benoît et al., 2010), to estimate relevant rates of short-term survival. This was done for two cases: one in which ﬁshery-speciﬁc data on vitality were available; and a second in which the distribution of vitality scores in the ﬁshery was predicted using the empirical model of Benoît et al. (2010). Third, we review existing literature on mortality trends in released ﬁsh, to assess the extent to which short-term mortality estimates can predict longer term impacts. Fourth, we discuss how the conditional reasoning used to estimate discard survival from observer and experimental data can be expanded to incorporate the effect of other processes known to affect discard mortality.

319

Holding duration (hr) Fig. 1. Frequency distribution of the duration of experimental holding periods for individual ﬁshing sets. At the end of each holding period, all live ﬁsh were returned to the sea and were considered as censored observations in the analyses.

considered priority candidates for conservation status assessment. Skates in the sGSL are typically discarded and estimates of associated mortality are necessary to determine the role of ﬁshing in population decline and recovery (e.g., Swain et al., 2009a). Finally, discarding of undersized winter ﬂounder (Pseudopleuronectes americanus) is permitted for conservation reasons. Mandatory live release policies may also be contemplated for endangered species, including the recently assessed sGSL cod and plaice (COSEWIC, 2009, 2010). Understanding discard mortality and the causal factors will help determine the efﬁcacy of such policies. 2.2. Discard mortality experiments Experiments were undertaken in 2005 and 2006 aboard the CCGS Opilio (an 18-m stern trawler), to correlate ‘pre-release’ vitality codes (Table 1) to short-term mortality in the ﬁve ﬁsh taxa of interest. Fish were caught using a conventional bottom trawl and following common commercial ﬁshing tow speed (2.75 knots) and set durations (1–2 h). Fish were handled as they would have been during commercial ﬁshing operations and sampled as the observers would do: measured for fork length (cm), vitality assessed and time spent on deck prior to holding (henceforth, deck time) noted (Benoît et al., 2010). Vitality was scored according to Table 1, based on a rapid (10 s) evaluation of each individual. Attempts were made to solicit a response from immobile ﬁsh by depressing their eye with a ﬁnger and by repositioning the ﬁsh on the measuring board. Fish that remained unresponsive were scored as vitality level 4 (moribund). Regardless of vitality, each ﬁsh was then individually tagged (t-bar streamer tags) and placed into onboard 1200-L holding tanks containing continuously exchanged refrigerated seawater. Tank temperatures were set to match the bottom temperatures where the ﬁsh were captured, as measured using trawl-mounted temperature loggers. Short-term mortality of individual ﬁsh was assessed by holding them for 14–110 h (Fig. 1), depending on available time and weather. During the ﬁrst 24 h of holding, the tanks were monitored approximately hourly for fatalities. Monitoring frequency was then progressively decreased to once every 2–4 h, as the frequency of fatalities declined. Death was mostly established by ﬂaring of the gills, rigor mortis and absence of ventilation during an approximately 2 min observation period. Fish that survived the holding period were returned to the sea.

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H.P. Benoît et al. / Fisheries Research 125–126 (2012) 318–330

Table 1 Description of the codes used by onboard observers to score the pre-discarding vitality of individual ﬁsh (Benoît et al., 2010). Vitality

Code

Description

Excellent Good/Fair Poor Moribund

1 2 3 4

Vigorous body movement; no or minora external injuries only. Weak body movement; responds to touching/prodding; minora external injuries. No body movement, but ﬁsh can move operculum; minora or majorb external injuries. No body or opercular movements (no response to touching or prodding).

a b

Minor injuries were deﬁned as ‘minor bleeding, or minor tear of mouthparts or operculum (≤10% of the diameter), or moderate loss of scales (i.e. bare patch)’. Major injuries were deﬁned as ‘major bleeding, or major tearing of the mouthparts or operculum, or everted stomach, or bloated swim bladder’.

2.3. Analysis All analyses were undertaken separately by species, except for skates, which were treated together (family Rajidae) to achieve an adequate sample size. Because the ﬁsheries observers do not consistently or reliably identify skates below the family level (Benoît, 2006), the taxonomic resolution in the analysis of the experiments matches that from ﬁsheries sampling (Benoît et al., 2010). 2.3.1. Capture and handling survival probability Not all ﬁsh classiﬁed into vitality class 4 (moribund) were dead; some were in an unresponsive catatonic state (e.g., Richards et al., 1995; Laptikhovsky, 2004). Once placed in seawater, some of these ﬁsh resumed ventilating and may have even recovered. Fish classiﬁed as vitality class 4 that were determined to be dead within the ﬁrst hour of holding were considered to have died during capture or handling. As a ﬁrst step, the capture and handling survival probability for ﬁsh belonging to vitality class 4 was estimated for each taxon. This probability was modelled using a logistic regression (McCullagh and Nelder, 1989) of the ﬁsh state (i.e., dead or alive) as a function of deck time, given an expected inverse relationship: logit[] =

0

+

(1)

1d

where is a vector of individual pre-release survival probabilities, d is a vector of observed deck times, and 0 and 1 are model parameters. Note that by deﬁnition the capture and handling survival probability is 1 for individuals in vitality classes 1, 2 and 3 (Table 1). 2.3.2. Survival during captivity The next step was estimating the probability that individuals survived the tank-holding period, given that they had survived capture and handling. The data for each individual ﬁsh were their assessed pre-holding vitality score and the elapsed holding time before they were either assessed as dead or were returned to the sea. Individuals that survived the entire holding period are referred to as right-censored, in that true times of death are unknown. The data were analyzed using survival analysis (e.g., Cox and Oakes, 1984; Ibrahim et al., 2001), which models the survival probability as a function of time, and which can accommodate both uncensored and right-censored observations. The underlying model used in our analyses was a Weibull-type survival function, chosen for its ability to mimic common survival functions encountered in ecology (e.g., Deevey’s, 1947 Type I, II and III survival functions) and its use in other discard survival studies (Neilson et al., 1989; Campana et al., 2009). It is deﬁned as S(t) = exp[−(˛ · t) ]

(2)

where S(t) is a vector of the survival probability of individual ﬁsh to time t, and ˛ and are respectively the scale and shape parameters of the underlying Weibull distribution. The effect of covariates on survival are commonly included via ˛, such that S(t|X) = exp[−(exp(X ) · t) ]

(3)

where S(t|X) is a vector of the survival probability, conditional on the matrix of covariate observations X, and  is a vector of parameters for the effect of the covariates. The covariate observations in this study are the vitality classes, treated as a factor. The survival model in Eq. (3) assumes that, conditional on the covariates, the sample of ﬁsh is homogeneous, i.e. that all individuals in a common vitality class follow the same survival function. Furthermore, it assumes that S(t|X) is a continually declining function of t. The homogeneity assumption will be violated if only a portion of the captured ﬁsh were adversely affected by the associated events. These affected ﬁsh might be expected to die within hours or days of holding. In contrast, ﬁsh that were not adversely affected would be expected to die according to their normal life schedule (i.e., on the scale of years). For these latter individuals, the risk of dying during an experimental holding period is very close to nil. The overall observed survival trend for the whole sample of ﬁsh would then be a combination of a rapid decline in survival within the ﬁrst few hours or days of the study, followed by general stability in survivors, a pattern observed in numerous published studies (see Section 3.5). To account for this heterogeneity, a mixture of two survival models was applied to the data. The ﬁrst component models the survival of individuals adversely affected by the ﬁshing event, SA (t), and in the present case follows the Weibull model (Eq. (2)). The second component models survival for the proportion of individuals that were not adversely affected (i.e., immune individuals), SI (t). Mathematically, we have S (t) = SA (t) + (1 − )SI (t)

(4)

where S (t) is the overall survival function for the sample and is the proportion of individuals that were adversely affected by the capture/handling process. Both and the parameters dictating the form of SA (t) are estimated from the data, while we assumed that SI (t) = 1. The assumption for SI (t) enhances model identiﬁability, and is consistent with the assumed near zero probability of death by natural causes during the course of the holding period. The validity of this assumption clearly declines as the duration of the holding period increases, but is likely reasonable for holding periods on the time scale of days. Note that in Eq. (4) as t → ∞, S (t) → 1 − (i.e., constant survival rate). Furthermore, when = 1 (i.e., all individuals are adversely affected by the ﬁshing event), S (t) = SA (t). Models such as Eq. (4) have been used to analyze survival data from experiments in which applied treatments do not appear to affect all experimental subjects (e.g., Boag, 1949; Berkson and Gage, 1952; Farewell, 1982). To the best of our knowledge, such models have not previously been applied in ﬁsheries science. In medical clinical trials, these are termed cure rate mixture models (ch. 5, Ibrahim et al., 2001), but here we refer to them as survival mixture models (SMM). Replacing SA (t) in Eq. (4) with the function in Eq. (2), and dropping SI (t), we obtain the following general SSM: S (t) = · exp[−(˛ · t) ] + (1 − )

(5)

Given different assumptions for the parameters ˛ and , we deﬁned six competing models for our analysis (Table 2). We note the use

H.P. Benoît et al. / Fisheries Research 125–126 (2012) 318–330

321

Table 2 Assumptions for the parameters ˛ and of Eq. (5), used to deﬁne the six competing models for the analysis of the ﬁsh holding survival data. In the table, X is an indicator matrix of vitality classes for observations on individual ﬁsh, and , 1 , and 2 are vectors of parameters for the effect of each vitality class. The table entry ‘constant’ indicates instances where the value of ˛ and/or was estimated as part of the model ﬁtting. Model

˛

Interpretation

Weibull 1 (W1) Weibull 2 (W2) Mixture 1 (M1) Mixture 2 (M2)

Constant exp(−X ) Constant exp(−X )

1 1 Constant Constant

Mixture 3 (M3)

Constant

[1 + exp(−X )]−1

Mixture 4 (M4)

exp(−X 1 )

[1 + exp(−X 2 )]−1

Common survival function for all ﬁsh (i.e., Eq. (2)) Common survival function within each vitality class (i.e., Eq. (3)) Common survival function for a ﬁxed proportion of affected individuals Common survival function within each vitality class for a ﬁxed proportion of affected individuals Common survival function for affected individuals, with the proportion affected dependent on vitality class Common survival function within each vitality class, where the proportion of affected individuals also depends on vitality class

of the common logit-linear transform to link and vitality class in the mixture models M3 and M4 (e.g., Farewell, 1982). The ﬁsh holding data for each of the ﬁve taxa were ﬁt to each of the six models using maximum likelihood (details in Appendix A). For each taxon, the model ﬁts were compared using delta-values of Akaike’s Information Criterion corrected for small sample sizes (AICc; Burnham and Anderson, 2002). As a rule of thumb, AICc values 10 suggested that the competing model is very unlikely (Burnham and Anderson, 2002). Though all six models were compared, three of them were considered unlikely a priori. Previous studies (e.g., Van Beek et al., 1990; Richards et al., 1995; Benoît et al., 2010) have indicated a relationship between vitality and survival, making models W1 and M1 (Table 2) very unlikely a priori. Comparisons to these models do however indicate the importance of vitality as an explanatory variable. Model M2 (Table 2) was also considered unlikely a priori because we expected the proportion of affected individuals to increase with vitality class. The predicted survival function from the models was also plotted against the empirical Kaplan–Meier survival curve (ch. 2, Cox and Oakes, 1984) to assess model suitability. The Kaplan–Meier survival curve is a function of the data only, and in the absence of censored values, it follows the proportion of individuals alive at each time interval during the holding phase of the experiment. 2.3.3. Estimating ﬁshery-scale short-term survival using observations for vitality In the commercial groundﬁsh mobile-gear ﬁsheries of the sGSL, certiﬁed third-party observers are deployed on approximately 10% of ﬁshing trips as a condition of ﬁshing license (Kulka and Waldron, 1983; Benoît and Allard, 2009). During the 2005 and 2006 ﬁshing seasons, observers collected data on ﬁsh vitality from a subset of the observed ﬁshing sets (details in Benoît et al., 2010). Up to 25 individuals of a given ﬁsh taxon were sampled by the observer during a given ﬁshing set just prior to discarding, and the vitality of ﬁsh was assessed following the method in Section 2.2. Deck time for each ﬁsh was also noted. For those taxa for which discarding was not permitted in the ﬁsheries, sampling occurred at around the time that the discarded portion of the catch was released. The distribution of vitality scores observed in the ﬁshery was combined with the vitality-dependent survival rates estimated

m ¯ R(t) =

s=1

(1) and (5) (and making explicit the conditional dependence on ¯ covariates), the average survival to time t for a given taxon, R(t), was estimated as:

m

¯ R(t) =

ws · n−1 s ·

s=1

ns

(v = vi,s , d = di,s ) · S (t|v = vi,s )

m

s=1

ws

(6)

where ws is the catch weight of the taxon in set s of the m sets in which vitality observations were made, ns is the number of ﬁsh sampled for vitality in set s, (v = vi,s , di,s ) is the capture and handling survival probability for individual i in set s assessed at vitality level vi,s and having experienced a deck time of di,s , and S (t|v = vi,s ) is the vitality-dependent post-release survival probability to time t for the ﬁsh. The capture and handling survival probability was obtained from an inverse-logit transformation of Eq. (1), such that:

(v = vi,s , d = di,s ) =

1 [1 + exp(−

0

−

1 di,s )]

−1

for vi,s ∈ (1, 2, 3) for vi,s = 4

(7)

To keep predictions within the range of experimental holding period durations (Section 2.1), t was set at 72 h. A Monte Carlo simulation based on bootstrapping (Efron and ¯ Tibshirani, 1993) was used to estimate the error for R(t), taking into account error associated with each component of Eq. (6) (see Appendix B for details). 2.3.4. Estimating ﬁshery-scale short-term survival in the absence of vitality observations Benoît et al. (2010) presented a multinomial model that relates vitality scores to covariates, while accounting for inter-observer differences in vitality scoring using a random effect (details in Appendix C). With this model, and given information on ﬁshingset-speciﬁc discard amounts and values of relevant covariates, it is possible to estimate ﬁshery-scale discard mortality in the absence of observations of vitality. Here, as an example, we estimated the short-term survival rate of skates and cod discarded during the commercial mobile-gear ﬁshery in 1991 and 1992. These years were immediately prior to the collapse of the southern Gulf cod ﬁshery, a time when ﬁshing effort and catches were considerably greater than during the mid-2000 period considered in the analyses of Section 2.3.3 (e.g., Swain et al., 2009b; Dufour et al., 2010). Furthermore, prior to 1993, discarding of cod in the ﬁshery was legal and observers regularly reported the discarding of individuals falling mainly below the regulated size limit of 41 cm. Under this approach, a term for the expected probability that a ﬁsh is in vitality level vis , conditional on relevant covariates, is ¯ added to Eq. (6) to estimate R(t): ws · n−1 s ·

ns 4 i=1

r=1

P(vi,s = r|zi,s ) · (v = r, d = di,s ) · S (t|v = r)

m

s=1

using the methods in Sections 2.3.1 and 2.3.2 to estimate average short-term survival for ﬁsh discarded in the ﬁshery. Based on Eqs.

i=1

ws

(8)

where P(vi,s = r|zi,s ) is the probability that the vitality level for ﬁsh i in set s is equal to r, for r ∈ {1, . . ., 4}, conditional on the vector of relevant covariates found to affect vitality for the species in

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Table 3 Numbers of ﬁsh included in the study as a function of vitality class and taxon. Classes are further divided for ﬁsh that were initially alive but subsequently died during holding (ds ), that survived the holding period and were therefore treated as censored observations in the analyses (c), and those that died during capture and handling (di ). Vitality code

1

Species

ds

c

ds

c

ds

c

di

ds

c

Cod American plaice Winter ﬂounder Skates Witch ﬂounder

19 15 0 0 1

41 114 19 58 0

44 24 2 0 5

29 62 23 31 3

56 29 7 9 11

11 30 12 16 3

441 565 36 22 89

60 76 3 8 6

9 23 8 16 0

2

3

4

question, zi,s , and a set-speciﬁc random effect used to account for inter-observer differences in vitality scoring and for the clustered nature of vitality sampling, us (Appendix C; Benoît et al., 2010). The relevant covariates for skates were catch (kg), the sea surface temperature (SST, ◦ C) and the deck time, d. For cod, the covariates were ﬁsh length (cm), SST and d (see Appendix B). The value for P(vi,s = r|zi,s ) was obtained from an inverse-logit transformation of the multinomial cumulative-logit model (Eq. (C.1)) such that,

Table 4 Parameter estimates (standard error, SE) for each ﬁsh taxon for the logistic regression relating the probability that a ﬁsh assessed as vitality level 4 actually survived to the time of holding. Species Cod American plaice Winter ﬂounder Skates Witch ﬂounder

2.3.5. Prognosis for long-term discard survival: indications from the literature To assess the generality of the shape of the survival functions we observed, and to determine whether short-term discard mortality can predict longer term fatalities, we assembled survival functions from published studies concerning discarded ﬁsh or ﬁsh escaping through net meshes. Criteria for inclusion were: (1) the period of observation for mortality was ≥72 h, (2) at least three data-points along the survival curve were presented, including a point at ∼24 h following the experimental treatment, and (3) some fatalities were observed. Nineteen studies covering 22 species were retained, including holding studies and studies in which the survival function was inferred using data from pop-up archival satellite tags (Table D.1). An average survival curve was calculated for studies that presented replicate survival curves from an experimental treatment, or similarly shaped relative curves from different treatments. The empirical survival curves from the various studies were plotted together to compare their shapes. Survival was calculated relative to the number of live ﬁsh remaining 24 h after capture, to make the curves clear and more comparable and because much of the post-treatment mortality in these studies occurred in the ﬁrst 24 h.

1

0.8266 0.0048 0.0060 0.1135 0.5067

(SE)

P

−0.085 (0.015) −0.065 (0.008) −0.220 (0.067) −0.032 (0.016) −0.118 (0.039)