by/par
J.E. Thorpe
Freshwater Fisheries Laboratory, Pitlochry, Scotland
U.K./R.-U.
ABSTRACT
Information on stock density was obtained for brown trout in Loch Leven by mark- recapture methods. The advantages of this method are that it is reasonably accurate (95 percent confidence limits of 25–65 percent of the estimates) but the disadvantages are that it can only be applied for a relatively brief period of the year, it is laborious, and the results are not available until at least six months after the date to which they refer. Catches per standard seine haul were compared with the population estimates from the mark-recapture experiments but, as an index measure, appear to be usable only above a total fish population exceeding 100 000. This limitation is probably related to the summer feeding and territorial behaviour of the fish.
RESUME
On a obtenu des renseignements sur la densité du stock de truite de rivière du Loch Leven au moyen de la méthode de marque-recapture. L'avantage de cette méthode est dans sa quasi-précision (limites de confiance de 95 pour cent sur 25 à 65 pour cent des dénombrements), mais les inconvénients en sont: limite d'application à une brève période de l'année, elle est laborieuse et les résultats ne sont disponibles que six mois plus tard. Les prises par senne hissée-type ont été comparées aux évaluations de population des expérimentations marque-recapture, mais il appert que cet indice de mesure n'est utilisable que pour une population totale au-dessus de 100 000 poissons. Cette limite est probablement liée à l'alimentation estivale et au comportement territorial du poisson.
CONTENTS
1. INTRODUCTION
2. MATERIALS AND METHODS
3. RESULTS
4. DISCUSSION
REFERENCES
Information on fish stock density is often needed quickly for management decisions and prompt action. In this context a series of mark-recapture experiments on a brown trout population (Salmo trutta L.) are considered, and their results also used to examine the validity of some index measurements of density.
The production of brown trout (Salmo trutta L.) was estimated annually from 1968–72 as a part of a general productivity study of Loch Leven, Kinross, under the auspices of the International Biological Programme. To calculate production by the Allen (1950) or Ricker (Chapman, 1971) methods it is necessary to have estimates of population densities at the beginning and end of the production interval. An account of the method of estimation used has been published recently (Thorpe, 1974), and is also summarized below. Loch Leven covers an area of 1 331 ha, with a mean depth of 3.9 m, and is situated in a glacial kettle-hole in east-central Scotland. The fish species of prime social importance is brown trout for which there has been a flourishing angling fishery for the last 125 years, and a net fishery for several centuries before that (Thorpe, 1974a). A minimum size limit of 23 cm is imposed on the angling fishery which has meant that, during the period of study, the youngest group which is fully recruited to the fishery is that which is beginning its third year in the loch at the start of the angling season in April.
The estimation of the population (
) was made using Bailey's modification of the
Petersen mark-recapture method (Petersen, 1896; Bailey, 1951) namely:
where m is number of tagged fish released, c is number of fish examined for tags and r is number of tagged fish recaptured. Seine-caught trout were tagged at eight shore sites using numbered plastic discs (6 mm diameter) attached with silver wire through the musculature around the leading ray of the dorsal fin, and were released at the capture site. Samples to determine the proportion of tagged fish in the stock, byage groups, were obtained from the angling catch which is controlled and recorded at Kinross harbour. The age of the fish, and particularly the period spent in the loch, was determined by scale-reading. Potential errors arising from failure to meet the structures of the Petersen model were checked with respect to randomization, loss of tags, incomplete reporting of recaptures, and short-and long-term differential mortality of tagged and untagged fish.
Random sampling by angling: No statistical differences existed in the rates of recovery of tagged fish released at the eight main sites and thus, sampling was assumed to be at random with respect to the fish population.
Tag losses: From 600 trout which were double marked, the gross loss of tags over one angling season was estimated as 2.15 percent.
Reporting rate of tag recaptures: From regular samples of the angling catch the reporting rate was estimated as 56 percent of tags recaptured in 1968, 43 percent in 1969, and 71–60 percent in 1970.
Short-term differential mortality: Handling losses were found to be correlated with water temperature above 10°C, reaching 2.7 percent at temperatures over 20°C. Since all the April experiments reported on here were carried out at temperatures below 10°C, this source of error was ignored.
Long-term differential mortality: Systematic decrease in the recovery rate of tagged
fish was estimated by regression of 
on time. No such trend could be demonstrated,
except for a single age group in the 1971 experiment.
Recruitment: The experiment was restricted to groups already wholly recruited to the
angling fishery at the time of release of tagged fish, i.e., to groups whose minimum body
length was greater than the fishery limit of 23.0 cm. However, the plots of 
against
time revealed incomplete vulnerability of the whole stock before June, and after August.
The recapture period for population estimates was therefore restricted to June-August each
year.
Distribution of values: The observed values of 
over the stable period June-August
were assumed to be normally distributed, and their means and the variances of these were
calculated by age groups.
Mortality: The initial values of m were adjusted to allow for recaptures in the interval between release and the stable recovery period.
Estimate of population: The total population of trout in their third year or more in the loch fell from 126 665 in April 1968 to 48 800 in April 1972.
Confidence limits: The 95 percent confidence limits of the estimates ranged from -65.2 to +66.6 percent of those estimates at the worst to -24.9 to +40.2 percent at the best.
The method gives moderately accurate results for this particular trout stock of 50 000
to 125 000 fish over 3 years old in a 1 300 ha lake. Trout were caught, tagged and released
in April. Average catches in standard seine hauls increased while those from trawl hauls
off-shore decreased, from March to June each year, indicating movement of trout from deeper
water on to the littoral during spring and early summer. Consequently, the proportion of
tagged fish in the population on the littoral was progressively diluted during the early
summer and concomitantly, the recapture ratio 
declined. Once movement on to the
littoral had apparently ceased in June, the recapture ratio became stable and remained so
until August. Thus, the experiments revealed that, associated with movements of fish within
the system, the population was incompletely vulnerable to fly-fishing except during a
restricted period of 2–3 months during the summer. It is laborious, involving up to 80 man/
days field work catching and marking fish, 20–40 man/days for sampling the angling catch
during the subsequent five months, and 50–60 man/days for laboratory analysis of the material
and computation of the estimaten. The information on population size is retrospective,
applying to the population at the time of release of tagged fish, so that in the present case
the delay before the information was available was at least 6 months. Such a long delay
may be acceptable in long-term biological studies but is usually quite unacceptable for
fishery management where decisions on regulatory measures may depend on information on stock
sizes. It is, however, difficult to achieve statistically reliable estimates without great
sampling effort in this situation but, having obtained a series of totals by a thorough
method, it may be possible to correlate this with a series of index measurements obtained
in the same interval by much quicker and simpler means, and so evaluate the suitability of
that index. Catch statistics from the angling fishery are an obvious choice. Whole season
catches are only a small improvement as, although clearly correlated with population density
(see Figure 1), they too provide retrospective information. On some of the days when the
angling catch at Loch Leven was sampled for estimation of its age composition, the catch
per angler was also calculated but this varied so widely from day to day that a full sampling
programme would be required to evaluate the sources of variation in angling success. Seine
netting was carried out intermittently during the summer seasons and, since this was according
to a standard rectangular pattern, the catch per haul can be regarded as a valid effort
statistic, for any given netting site. Since seine catches at particular sites vary from
month to month, the data for use as index values must be taken from a “stable” period; in
this case June-July, during which little movement of individual trout within the loch was
observed (Thorpe, 1974 and 1974b). Site C provides the most extensive data on average catch
per haul and this has been plotted against estimated values of April stock density in
Figure 2. The two variables are correlated (r = 0.765) but not in a simple rectilinear
fashion. The average net catch increases steeply with increasing density above an April
minimum of about 100 000 fish; below this value of density the mean catch per haul is low
and almost constant. For the uppermost three pairs of readings the linear regression of c
(mean net catch) on (April population estimate) intercepts the mean value of c for the
lowermost three readings at = 103 900. The average standard seine catch at site C in
June-July might therefore be a useful index of stock size, but only if that stock was more
than 103 900 trout in April. Comparable but rather less adequate data are available for
4 other netting sites, B, D, K and E, during this period, also shown in Figures 2 and 3.
The simplest relationship between c and at these sites would be a first order regression
but, with the prior knowledge that at site C, where the data were more complete, such a
direct relationship is inadequate; the data for sites B, D, K and E were treated as those
at C. The intercept values are given in Table I. The mean value of at these intercepts
is 107 450, with 95 percent confidence limits of 103 120 to 111 780. The intercept value
at site C does not therefore differ from those for these other four sites so that it is
probable that whatever determines this particular relationship between c and is generally
applicable over all the littoral area. The implication of a constant value of mean catch
at any given seine site over a wide range of stock sizes is that these areas have a fixed
carrying capacity from which excess fish are excluded except at very high densities. It
has been shown elsewhere (Thorpe, 1974 and 1974b) that the trout move from deeper water on
to the littoral areas, particularly those with a stony substrate, in the spring and individual
fish remain there throughout the summer feeding period, and also “home” to these same
areas in successive summers. Since the Loch Leven trout are primarily benthos feeders, the
advantages of the littoral areas to these fish must be associated with the substrate itself,
and once this area has been occupied by resident trout in the summer there will be no room
for additional fish, unless there is a sufficiently deep water column above the loch bed to
accommodate them. In the cases of sites B, C, D and K, in the area swept by the net the
loch bed slopes very gently down and is nowhere deeper than 2 m; however, at site E, the
shoreline is steeper and, at its outermost range, the net sweeps through about 7 m depth to
the bed. It will be seen from Figure 3 that at site E the values of c at lower values of
are not constant and the relationship between the variables here may be represented by a
linear regression with more justification (0.1>p>0.05 for its slope). In September,
shortly before the spawning migration, individual fishes become more mobile, less restricted
to a particular home area in the loch, and the restriction of numbers on the littoral is
less evident. The data for site C in September (Figure 4) show a good correlation between
c and (r = 0.97) but although this is indirect evidence for some form of territorial
restriction in the previous months, an index based on average net catches in the final month
of the fishing season is not very valuable for management.
The same values of c for September are less well correlated with -values for the
following April (r = 0.67), probably because of wide variations in winter mortality due to
epidemic disease among the spawners (Thorpe and Roberts, 1972). A prospective index based
on September catches would also only predict the stock size of older fish at the beginning
of the following angling season. An additional method would be needed to predict recruitment
to the exploitable stock but that is outside the scope of the present paper.
| Site | Intercept | |
| c | |
| B | 102 400 | 5.1 |
| D | 113 100 | 2.4 |
| E | 107 800 | 9.9 |
| K | 106 500 | 2.0 |
Standard error = 4 330
Figure 1 Angling catch and estimated April stock
Figure 2 Average catch per standard seine haul c,
at range of
Figure 3 Average catch per standard seine haul c,
at range of
Figure 4 Average catch per standard seine haul (c) in September,
at a range of April population estimates ()
