Estimating survival and exploitation rates from a tagging study on juvenile Atlantic halibut

Department of Statistics and Actuarial Science

Simon Fraser University

8888 University Drive

Burnaby, BC, V5A 1S6

cschwarz@stat.sfu.ca
2007-10-10

Abstract
Tags have been applied to juvenile halibut since 1995 with about 4000 tags applied between 1995 and 2001. Recoveries have occurred from these releases from 1995 to 2007. The Hoenig et al (1998) model M(*) F(t) was used to estimate a uniform (over years) natural mortality rate and year-specific fishing mortality rates. The estimated instantaneous natural mortality is .084 (SE .03). Instantaneous exploitation rates were about .03-.05 (SE .01) in the late 1990s, but declined to less than .01 by 2007. These exploitation rates make a strong, untestable, assumption that the product of initial tagging mortality and tag retention is 1. Reward studies initiated in 2006 have very few recoveries to date, but suggest that the tag reporting rate may be substantially less than 1 implying that estimated exploitation rates from this study may be seriously negatively biased.

1. Introduction

2. Data Screening

Extensive data screen was performed on the supplied records. Full listing of “problem” records available on request from the author.

2.1 Release records

This database contains just over 8700 records for each tag issued in the program.

Some basic data screening was performed to check for data coding errors or omissions.
Obvious errors were corrected and coding in some fields was made consistent such as:

• 
  Depths of greater than 1400 m;
  
• 
  Gear codes of “Location approximate” were set to missing;
  

About 1600 (19%) of the release records did not have a date of release (not even to the year level), nor a release location (lat/long). For the majority of the records, it is unknown if the tags corresponding to these records were ever actually placed on the halibut. For some records, the comment field indicated the tag was lost when a vessel sank. Some of the these undated records were recovered indicating that at least some of the tags were placed on fish, but the date of tagging was not recorded.

For approximately 25 release records (0.3%) the actual tag number is unknown or can only be partially read.

2.2 Recapture records

This database contains just under 740 records.
Basic data screening was performed to check for data coding error or omissions.
Obvious errors where corrected such as:

• 
  Invalid dates (29-Feb-2001 (sic) when this is not a leap year). For this recapture, the corresponding release record didn’t have a release date so it wasn’t clear how this should be corrected (i.e. change to 28 Feb 2001 or 29 Feb 2000 or 29 Feb 2004).
  
• 
  Latitude/longitude recorded incorrectly (e.g. as 4414.52 rather than 44 Deg and the appropriate minutes
  

Approximately 45 records (0.6%) had no date of recapture available.

2.3. Matching releases and recaptures

The recapture records were matched against the release records. Twenty five (3%) of the recapture records could not be matched against a corresponding release record for a variety of reasons.

3. Model development and fitting

3.1 Introduction

The Brownie band-recovery model (Brownie et al., 1985) is a standard model used to analyze recoveries from exploited populations. These models provide estimates of survival and tag-recovery rates. The latter are a composite of tag retention, exploitation, tag-induced mortality, and tag-reporting rates.
The Brownie models (also known as tag recovery models) are suitable when there is a fixed tagging point followed by a harvest of indeterminate length (up to a year after the tagging event). Animals that are harvested may have their tags reported.
Conceptually, following Brownie et al (1985), the fates of an animal can be diagrammed in Figure 1.Unfortunately, without further information is impossible to separate the parameters K, c, and -- only their product can be estimated. The earlier fate diagram can be simplified as shown in Figure 2.
The sampling protocol for the Brownie et al (1985) models requires that a number of animals are tagged and released each year (). Recoveries occur in subsequent years with representing the number of animals released in year i and recovered and reported between year j and j+1 (where the start of the year commences at the tagging point). For example, would be the number of animals tagged in 2005 that are recovered between the tagging occasions in 2007 and 2008.
The recovery data may be arranged in an array as shown in Table 1 and the expected number of fish in each of these cells is presented in Table 2. For example, the expected number of fish released in year 1 and recovered in year 2 is found as the product of the number of fish released () probability that a fish survives from the release time in year 1 a full year to the release time in year 2 () the probability that the fish is harvested, its tag retrieved, and its tag reported (). The expected number of fish tagged but never recovered nor reported after release is found by subtraction.
Brownie et al (1985) presented the statistical theory behind fitting these models. Briefly, each row of recoveries from a release (including those animals never seen) follows a multinomial distribution. The overall likelihood is the product of the individual multinomial distributions. Standard numerical methods can be used to find the maximum likelihood estimators and their associated standard errors. Simpler models can be fit, such as assuming that survival rates are constant over time and/or recovery and reporting rates are constant over time.
Hoenig et al. (1988) reparameterized the Brownie model. Survival rates were reparameterized in terms of instantaneous natural and fishing rates (M and F). Tag-recovery rates were reparameterized in terms of initial tag-shedding and/or tag-induced mortality (), the exploitation rate (the probability that an animal present at the beginning of year i is harvested during the year) (), and the tag reporting rate (the probability that the tag will be reported given that the animal is harvested in the year) ().
Hoenig et al. (1988) also showed that the timing of when the fishery takes place relative to the tag releases (e.g. soon after releases or throughout the year) affects the expected number of tag recovered. For example, when fishing takes place continuously, the expected number of recoveries in Table 2 (the Brownie model) is displayed in Table 3.
Consider the expected number of fish released in year 1 and recovered in year 2. This is found as the product of the number of fish released ()probability that the fish survives the initial tagging event and retains the tag ()the probability does not die from natural causes nor is harvested between release in 1 and the timing of releases in year 2 the fish is harvested between year 2 and year 3 the tag is retrieved and reported ()
Model where instantaneous natural mortality () are constant over time have similar expressions. The expected number of recoveries under different patterns of fishing effort between releases are found in Hoenig et al (1998).

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Halibut -> Atlantic Halibut fishing mortality estimated from tagging on the Scotian Shelf and the southern Grand Banks

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