A sample of fish is collected and then a known number of tagged/marked fish are released.

N=TC/R

N=stock size estimate

T=tagged

C=second total catch

R=recaptured tagged fish

The 95% confidence interval about the population estimate is obtained by multiplying the standard error by the z score of 1.96 (for 99% z score is 2.58) to generate the upper and lower estimate limits

therefore N= +/- (1.96*SE)

ASSUMPTIONS

1)Negligible mortality during the sampling period

2)Complete mixing/integration of released marked individuals amont the unmarked ones

3)Negligible population migration

4)no change in catchability

5)No tag loss

For small sample sizes, we use a t-value to obtain the confidence interval.

N=+/-(t*SE)

-t value is found  in the t-table for appropriate degrees of freedom 

Sample sizes should be at least 20-30 to use Z value, otherwise use t

CHAPMAN's ESTIMATOR

In cases where T+C is greater than or equal to N, Chapman's unbiased estimator of N should be ued

N=[(t+1)(C+1)/(R+1)] -1

A trawl net is used to estimate the mean catch at a numbre of stations in a fish stock, and the mean catch per area swept by the trawl (Cw) is multiplied by the stock area (A) to estimate the stock size or total stock weight/biomass.

Bestimate = Cw*A

Since the trawl net is not totally efficient, the Cw obtained during the tow is usually less than the actual weight of fish in the path of the towed net. The proportion of fish in the path of the net which are retained are termed the vulnerability (v). The weight or biomass of fish in the path of the trawl is therefore Cw/v. An estimate of the total stock biomass (B) is obtained by multiplying the biomass of the fish in the path of the trawl by the ratio of the stock area (A) to the trawled area (a)

B=(Cw/v)*(A/a)

A towed trawl net samples fish in an area (a) that is equivalent to a long rectangular sampling unit estimated as:

a=W*TV*D

The standard error of the mean for Cw is calculated asthe sample variance divided by the number of observations or as sample standard deviation divided by the square root of the number of observations

SE = SQRT((S^2)/n) = s/sqrt(n)

Using the SE, upper/lower estimates of the stock area can be estimated by calculating Cw limits at the 95% confidence interval (z score 1.96) and the nentering the limits into the stock biomass equation

Cw_(interval) = Cw+/- 1.96*SE

Blower is minus, Bupper is plus.

F=hx

F=fishing effort

h=# of possible hours of fishing in the period

x=average number of anglers fishing based on sample count data during the period (usually calculated per day)

RATE OF SUCCESS

r=(sum(Ci/ti))/n

r=fish/hour/angler

Ci= # of fish caught be the ith individual angler interviewed

ti= the number of ours fished by that individual

n=total number of anglers interviewed

CATCH-HARVEST-YIELD (C-H-Y)

Catch = harvest plus catch and release

harvest = fish kept (by # or weight)

yield = catch plus other benefits

C=rF and H=rF

F=fishing effort

r=rish/hour/angler

When sample estimators are used to infer attributes of the whole population the results are subject to uncertainty (due to the inductive process used); this uncertainty is stated in terms of probability - the basis of statistical inference

Important properties of estimators are:

1)Consistency (the estimator should get closer and closer to the true parameter value as the sample size increases)

2)Unbiasedness (the average or expected value over many hypothetical repetitions of the study should be the true parameter value

3)Variance (the variance of an estimator is the average or expected value of the squared deviations of the estimator from its expected value. The smaller the variance, the better)

4)Standard Deviation (the square root of the estimator's variance... smaller the better)

5)Precision (when variance/SD is small (how well the data clusters))

6)Accuracy (implies that there is little or no bias)

1)Simple Random Sampling w/o replacement

- Best applies where the fisher and the anglers are homogenous (not often the case)

2)Stratified Random

-A heterogeneous population (fishery and anglers) is divided into homogeneous sun-populations (strata) that are then subject to simple random sampling.

-purpose is to reduce variability

Common strata include:

-geographic location

-habitat types

-months or seasons of the year

-fishing methods (bank vs boat)

-weekday/wekend/holiday/etc

3)Systematic Random Sampling

used where it is easier to draw a systematic sample than a random.

4)Stratified Two-stage (cluster) probability sampling

-Random methods may be unsuitable due to time, cost, or loistic constraints

-Solution is to divide each SU (ie fishing day) into secondary or subsampling units

1)Sampling error

2)Reponse Errors

3)Non-response errors

OFFSITE

-mail surveys

-telephone surveys

-door to door

ONSITE

-questionnaire boxes/catch cards

-angler diaries/logbooks/tournament directories

-access point surveys

-Roving Crels Surveys

-Aerial Surveys

-Complemented/combination

Objective Types:

1)Ecological/Biological

2)Sociological

3)Informationsal

TYPES OF REGULATIONS

1)Licenses and Permits (annual, special, short-term, scientific collection permit)

2)Creel/Bag Limit

-posession limit

-commercial fisheries have quotas

3)Size Limits (Min, Max, Slot limit, combination)

4)Catch and release regulation

5)Closed Season (during spawning, for safety of users, closed hours)

6)Closed Areas (generally to protect users and environment)

7)Reporting (data collection)

8)Gear Restrictions

9)Regulation on Commercial Venture

10)Regulation Evaluation

The common name for the symptoms caused by the infection of salmonids by.....

Originated in Europe around 1900, entered US around 1956 from Denmark processed fish

First in Pennsylvania, then California, then New York

Now reported in wild fish in 11 states (pacific NW)

Presence in Montana, but not AB

AB has whirling disease task force, and a wild salmonid surveillance progra

State to state transition always due to hatchery fish

Drainage to drainage due to stocking or moving (legal or illegal)

Fish eating birds can spread the parasite

Potential of spreading through mud

Spores can be viable for 30 years!

SYMPTOMS

-deformities in spine, cartilage destruction, blackening of tail

-penetrates head and spinal cartilage of fingerling trot where it multiplies very rapidly, putting pressure on the organ or equilibrium. This causes the fish to swim erratically.

Life stages: 1) fish, 2)worm host (Tubifex)

Worm ingests spore, and is not harmed

Rainbow and Brown trout are particularly sensitive.