Estimating the number of fish that return to spawn using capture-recapture methods.

Background

The Fraser River is the largest producer of sockeye salmon in the world, and contributes the majority of the salmon harvest for both commercial and native fisheries. The Fraser River Sockeye is a preferred commercial species of salmon because of its flavor and texture.

The commercial catch of millions of fish is worth tens of millions of dollars to the economy of British Columbia in the form of employment for fishermen, cannery workers and related industries. Commercial fisheries originating from both Canada and the United States exploit salmon returning to the Fraser River. The proportion of the estimated forecast of sockeye salmon, as well as other species of salmon (chum, pink, chinook and coho), harvested by the commercial sectors of each country are determined through the Pacific Salmon Treaty, which is negotiated between the United States and Canada. The size of the commercial harvest of sockeye, pink, and chum is closely monitored by each nation, and reported to the Pacific Salmon Commission (PSC) which publishes harvest information weekly.

Historically, the Sockeye salmon has been an important food source of the indigenous people of British Columbia. As the sockeye migrate upstream through the Fraser River, they are further exploited by a number of native fisheries. The number of salmon taken by each native fishery is determined prior to the start of the fishing season through bi-lateral negotiations between individual Indian Bands and the DFO. Native harvests of salmon are monitored by either Native Organizations or the DFO, depending upon the area of the Fraser River being surveyed. Once fishing begins, weekly summaries of native harvests of salmon are submitted to the DFO every week, until the end of the fishing season.

Life cycle

For an excellent synopsis of this species please visit the Alaska Department of Fish and Game Homepage
(http://www.state.ak.us/local/akpages/FISH.GAME/notebook/sockeye.htm).

The life cycle of a Fraser River Sockeye salmon is four years. Every spring the salmon eggs hatch in gravel beds of streams and rivers which feed into the Fraser River. The young fish, known as fry, hatch in such well-known B.C. rivers such as the Adams, Chilko and Stellako.

Typically, the fry mature in calm, nutrient-rich lakes for one to two years prior to proceeding to the Fraser River and then on to the salt water of the Pacific Ocean. Three large salmon fry rearing lakes are the Shuswap, Harrison and Stuart.

The Sockeye salmon spend the next two to three years in the North Pacific Ocean feeding (Figure 1). There they grow to sizes exceeding 20 kilograms.

Each fall, the mature salmon return from the open ocean and pool at the mouth of the Fraser River. The salmon will remain here for two to six weeks before ascending the river to spawn (or reproduce). Much of the commercial harvesting takes place at this point as the salmon are highly concentrated in this small area.

The salmon that escape this harvesting (the escapement) leave the salt water for the fresh water of the Fraser River. Incredibly, the adult salmon return to the tributaries of the Fraser from which they were hatched (Figure 2). In gravel-bed nests, called redds, the adult Sockeye salmon spawn in pairs. Each mating pair then defends its redd until it dies. The cycle is repeated by the young of each pair four years later.

Survey protocol

In order to set fishing quotas and to manage the stocks in a sustainable fashion, the Department of Fisheries and Oceans (DFO) estimate the number of salmon at various stages in their life cycle. These include:

an estimate of the number of eggs laid in the spawning grounds;
an estimate of the number of young fish that swim to the ocean;
an estimate of the total number of adult salmon that survive to breeding age and are eligible for harvesting;
and finally, an estimate of the number of fish that actually make it back to the spawning grounds (called the escapement).

This latter estimate is the most crucial, as the number of salmon that return to spawn determines the number of eggs laid and, to a great extent, the size of the next generation. The method commonly used to estimate the escapement is the focus of this workshop.

The escapement is often estimated using a technique called the Petersen method.

A number of fish are captured alive as they return to spawn in a section of river where the flow is restricted (Figure 3). A Petersen disk tag, a colored tag about 3 cm. in diameter, is applied to the fish for identification (Figure 4) and then the fish is released back into the water. The number of fish caught and released at this first time point is denoted as n₁.
Once the spawning season has finished (after about 7 to 14 days following the initial tagging), a team searches the spawning beds (Figure 3) for fish carcasses. The team records how many carcasses they found in their sample (denoted as n₂) and the number of carcasses they found that had Petersen disk tags (denoted as m₂).

The subscripts 1 and 2 refer to the timing of the samples, while the symbols n and m refer to the number of fish observed and those with marks respectively. This notation is the standard notation used by users and researchers in capture-recapture methods.

Example

Here is an example using actual 1994 data from the Chilko River in British Columbia.

n₁ =	2,213	number of fish marked with tags
n₂ =	59,665	number of carcasses examined
m₂ =	505	number of tags recovered from carcasses examined

How can this information be used?

The goal is to use information that is known from samples (statistics) to estimate unknown quantities (parameters). In this problem, the known statistics and unknown parameters are:

Known Statistics	Unknown Parameters
n₁ = number of fish initially tagged	p₁ = proportion of all fish that are tagged
n₂ = number of carcasses examined	p₂ = proportion of all carcasses that are searched
m₂ = number of tags recovered from carcasses examined	N = total number of fish returning to spawn (the escapement)

We wish to obtain an estimate of N, the total number of spawning fish, which we call .

Questions

Can you suggest potential problems associated with the Petersen method? For example, perhaps fish do not behave the same after being caught and tagged as compared to untagged fish?
Can you suggest a way to use the above information to estimate the escapement?

[PREV Module][NEXT Module][OVERVIEW Module]
[Background][Point estimate] [Sampling Bowl][Computer simulation]