Mark-recapture on Atlantic cod (Gadus morhua) off Eastern and Southern Newfoundland: Estimation of Exploitation rate and Measuring Growth
Table of Contents
Acknowledgements
Thanks to John Brattey of the Department of Fisheries and Oceans for providing the data. Please address queries to John Brattey at Fisheries and Oceans or Karla Fox at Statistics Canada.
The Questions of Interest
Exploitation
Growth
What happens over time?
Background
As can be seen from the map, data are collected off the Eastern and Southern Coast of Newfoundland using a Capture- recapture survey.
Fig 1. Cod stock management boundaries (red=2J3KL, orange=3NO, green=3Ps, blue=4RS3Pn).
Note : for mark- recapture analyses the variable reg_rel and reg_ret values correspond to the following areas: 3K_IN=3Ka, 3Kd, 3Kh, 3Ki;
3L_INN=3La, 3Lb;
These are essentially "open populations" but the stock management boundaries we use define where they live and emigration is not thought to be a major issue. There is a lot of sub-structure within the population (resident inshore cod and migrant offshore cod within the same management area) and the student may want to consider what assumptions are being made when modeling or estimating. The time span of the database is from 1997-2010. There was approximately 124,000 cod tagged. The researchers record location (management zone, local area), fish length (cm), date, depth of capture, capture gear type and other variables. Within the dataset you may notice that there are a few specific sites where the researchers have tagged a lot of fish each year (>500) for several years (ie area 3Lb in Fig.2).
Fish are tagged externally with a Floy t-bar anchor tag. Each tag has a unique number, return address, and reward value printed on it. Commercial and recreational fishers as well as fish-plant workers return the tags and the tagging program is well advertised within Newfoundland. In the past the researchers double-tagged many fish as well – to try and estimate tag loss rates by looking at how the proportion of double tagged fish with only one tag remaining at recapture increases with time at liberty. Additionally, rewards for returning tagged fish are given and are $10 (standard) or $100 (high- reward). It is assumed 100% of the high reward tags are returned and about 20% of the fish are released with these high-reward tags. The ratios of standard to high reward returns can be used to estimate the reporting rate of standard tags.
On the dataset the minimum size of tagged fish is 45 cm and maximum is >100 cm when released, most of the fish tagged are in the 45-70 cm range. There are about 21,400 recaptures. Most recaptures come in within the first 3 yrs at liberty. Recapture data include date, location, length, fishing gear type, depth (note that some or all of these values can be missing), but the most complete variables tend to be date and location.
Objectives
Primary objective
The primary objective is to understand capture-recapture surveys, what assumptions this type of survey has and what its potential uses are.
Secondary objectives
It is also of interest to learn the following:
- How to estimate recapture population size using mark-recapture data.
- How to estimate growth using mark-recapture data.
Capture-Recapture Estimation
Capture-recapture surveys were first used in biology and ecology to estimate the size of animal populations. And although this case-study is on estimating cod populations, we note to the student that capture-recapture surveys and their associated models apply in a much wider range of domains, such as for:
estimating at risk populations (e.g., homeless people, prostitutes, illegal migrants, drug addicts, etc.);
measuring delicate or rare subcategories (as in the U.S. census undercount procedure and the new French census);
measuring consumer habits;
estimating defaulting companies;
measuring fraud detection;
software debugging.
Population estimates are needed for both monitoring of and control over of fish populations. It is impossible to enumerate and measure all members of a fish population, so statisticians use Capture-Recapture surveys to estimate population sizes. In the case of capture-recapture surveys, any single individual is observed either once or several times and the repeated observations are used to draw inference on the population size and other dynamic characteristics (like growth).
There are two important ideas or assumptions we wish to discuss. First, that a population is either a closed or an open population. A closed population is one where the total number of individuals is not changing through births, deaths, immigration or emigration. If any of these elements are changing we consider the population open. However, if the interval between sampling times is short, then these changes over the time period may be small enough to assume that we have a closed population. Next, we want to note to the student that some mathematical models assume that all the individuals have the same capture probabilities, while others do not.
Recapture Population Size – the exploitation rate
The exploitation rate or, fraction of the population that is captured each year, can be estimated from the ratio of tag returns (adjusted by reporting rate and tag loss) to numbers of tagged fish available to be captured. You will have to take into account the natural mortality rate for the tagged fish into your calculation. Note that for fish such as cod we typically assume that about 18% of the population dies each year through natural mortality (instantaneous rate of 0.2 per yr). So we should see that the number of tagged fish available is diminishing over time. This exploitation rate is usually expressed either as a percentage or as an instantaneous rate per year.
Growth Curves
As growth curves are an important part of stock assessment of fish populations, there has been considerable effort devoted to determining age using growth models. Fish, like other animals, can experience seasonal variations in growth. This is from the direct impact of water temperature, metabolic rates and food (Krohn et al., 1997). They are also influenced indirectly by reproduction, feeding and prey availability (Schwalme & Chouinard, 1999).
Growth modeling is applicable to data where individuals are measured repeatedly over a period of time. Much research has been devoted to modeling growth processes, and there are many ways of doing this: parametric, non-parametric, time series or even differential equation models can be used. In general, growth‑curve models are generalized multivariate analysis‑of‑variance models used to model data in a longitudinal study. Within these parametric models there are linear, polynomial, non-linear and factor analytic or latent growth curve (LGC) models. Additionally there are Bayesian methods that can be used to deal with unknown parameters. Finally, several methods have been developed using linear differential equations, stochastic differential equations and power transformations.
The Data
Data File NLcod.csv
- Observations (number of cod tagged): 124,630 (first row of data set is variable names).
- Observations with recapture information: 21,406.
- Variables: 19.
Alphabetic List of Variables and Attributes.
Var # Variable Type & nbsp; Length ; Description.
| Var # | Variable | Type | Length | Description |
|---|---|---|---|---|
| 14 | area_rel | Char | 4 | Geographic area of release (e.g. 3KH, 3LA, 3PSC). |
| 2 | area_ret | Char | 4 | Geographi c area of recapture (e.g. 3KH, 3LA, 3PSC). |
| 1 | exp | Num | 8 | Experiment number (unique identifier for a group of fish tagged at approx same time/place, e.g., 1998001, 2010003). |
| 6 | gear | Char | 9 | Recapture gear type (e.g. gillnet, linetrawl, trap, handline, etc.). |
| 8 | id | Char | 9 | Unique tag number that identifies each fish (e.g. H45312, K64257, CT10246). |
| 16 | reg_rel | Char | 6 | Geogra phic area defining region of release of cod (e.g. 3K_IN, 3L_INN, 3Ps_BB; see footnote to Fig 2). |
| 15 | reg_ret | Char | 6 | Geographic area defining region of return (recapture) (e.g. 3K_IN, 3L_INN, 3Ps_BB). |
| 18 | rel_d | Num | 8 | Release day of month (e.g., 1, 2, 3, 4, ..., 31). |
| 7 | rel_len | Num | 8 | Release length of cod (in cm). |
| 17 | rel_m | Num | 8 | Release month (e.g. 1-12, where 1=January, 2=February, etc). |
| 5 | ret_d | Num | 8 | Return day of month (e.g. 1, 2, 3, 4, ..., 31). |
| 9 | ret_len | Num | 8 | Recapture length of cod (in cm). |
| 4 | ret_m | Num | 8 | Recapture month (e.g. 1-12, where 1=January, 2=February, etc). |
| 3 | ret_y | Num | 8 | Recapture year (e.g. 1997, 1998, 1999, ..., 2010). |
| 13 | t | Num | 8 | Recapture week of tagged cod (relative to 1 January 1997). |
| 10 | tag_pos | Num | 8 | Tag position (1=front, 2=back) for double tagged fish only. |
| 19 | tagtype | Char | 6 | Tag type. Single (low reward), Double (two tags, both low reward), or Single High- reward. |
| 12 | tx | Num | 8 | Release week of tagged cod (relative to 1 January 1997). |
| 11 | type | Num | 8 | Type of return (1=single return from single low-reward release, 2=single return from double release, 3=double return from double release, 4=single return from single high-reward release). |
References
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Brattey, J., Canada. Dept. of Fisheries and Oceans.Science & Canadian Science Advisory Secretariat 2009, Assessment of the cod (Gadus morhua) stock in NAFO Divisions 2J+3KL in 2009: Évaluation du stock de morue (Gadus morhua) dans les divisions 2J+3KL de l'OPANO en 2009, Fisheries and Oceans Canada, Science, Ottawa.
Brattey, J., Canadian Science Advisory Secretariat & Canada. Dept. of Fisheries and Oceans.Science 2009, Assessments of the cod (Gadus morhua) stock in NAFO divisions 2J3KL (April 2007 and April 2008): Évaluation du stock de morue (Gadus morhua) dans les divisions 2J3KL de l'OPANO (avril 2007 et avril 2008), Fisheries and Oceans Canada, Science, Ottawa?.
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