by/par
Kj. W. Jensen
Freshwater Fishery Laboratory, P.O. Box 63, Vollebekk
Norway/Norvège
ABSTRACT
In a small Norwegian lake the spawning population of stunted perch was estimated by Schnabel's method of multiple census. The perch were caught in wiremesh traps and marked by cutting off the second dorsal. A later Petersen estimate after rotenone poisoning was in good agreement with the Schnabel estimates. The figures indicate that in localities where the spawning period of the perch is short (a couple of weeks) rough estimates of the total number of spawning perch can be obtained by multiple census.
RESUME
Dans un petit lac norvégien, la population de reproducteurs de perches de taille réduite fut estimée selon la méthode de recensement multiple de Schnabel. Les perches furent capturées aux nasses de grillage métallique et marquées en coupant la deuxième nageoire dorsale. Une estimation Petersen faite ensuite par empoisonnement au roténone se comparait favorablement aux estimations Schnabel. Les chiffres indiquent que dans les localités où la période de ponte est brève (environ deux semaines) des estimations approximatives peuvent être obtenues par le recensement multiple.
One of the first authors to estimate the size of stunted perch populations by means of marking and subsequent recaptures (the Petersen method) was Alm (1946).
In lakes with stunted perch populations great numbers of spawning perch can easily be caught in simple unbaited wiremesh traps, be marked by fin-cutting and released unharmed. Continued marking and recapture can be used to obtain estimates of the numbers of spawning perch by means of Schnabel's method of multiple census (Schnabel, 1938; Richer, 1958). However, estimates obtained in this way could be expected to be seriously biased by day-to-day changes in the spawning population through the season, and by differences in catchability between females and males.
A small lake (34 400 m2; 257 200 m3) in a forest area in southeast Norway harboured a stunted population of perch, vast amounts of small bream (Abramis brama L.) and a small population of trout (Salmo trutta L.). In 1952 it was decided to wipe out the fish population with rotenone and restock with trout only. The perch spawns in this area in the beginning of May, and trap-fishing and marking for a Schnabel census took place 5–17 May, 1952. Marking was done by cutting away the second dorsal fin with a small scissor.
In Table I, c is the number of perch caught on each day, m is the number of marked
perch present in the lake in the beginning of the day, r is the accumulated number of recaptures
and B is the accumulated number of perch that had been killed until the morning of the
day. 
s is the Schnabel estimate according to the formula (formula 3.12 in Ricker, 1958):
As a small part (magnitude 10 percent) of the population was killed during the fishing, estimates were also computed according to Robson and Regier (1971) as:
As seen from Table I the differences between the two kinds of estimates are not important.
The last column in Table I gives the 95 percent confidence intervals for s. They are
computed by treating r as a Poisson variable. The 95 percent intervals for r are taken from
Pearson and Hartley (1969).
Care was taken to avoid killing fish which were marked. Among the early spawners the proportion of marked fish was probably higher than among the later arrivals. This may explain the increase in the estimates in the last days of the experiment when the perch marked in the beginning of the season have finished spawning and lose interest in the traps. The estimates made on 13, 15 and 17 May are therefore probably too high, and the estimate on the first day (5 May) obviously too low. The rest of the figures in the table indicate a spawning perch population of magnitude 12 000–19 000 individuals; 1 662 specimens were killed during the trap fishery.
We might with good reason believe that this estimate is probably too small, because during the spawning period continuous recruitment takes place to the spawning population, and continuously spent individuals are leaving the spawning shoals and are not attracted by the traps any longer. If this is so, we shall grossly underestimate the number of spawners.
No fishing of any consequence took place until 15 August 1952 when all fish in the lake were killed by rotenone treatment. During and after the rotenone treatment care was taken to secure as many of the dying and dead perch as possible, but most of the fish sunk to the bottom in deep water. Altogether 1 303 perch were collected.
As usual in stunted populations of perch the size of the fish was extremely uniform (13–18 cm) and young year-classes were obviously missing. Probably all, or nearly all, perch in existence on 15 August had spawned the last spring.
As the natural mortality is low in stunted perch populations (Alm, 1952) the natural mortality between May and 15 August, 1952 cannot be expected to have caused any significant change in the population size. We can therefore use a population estimate based on the rotenone sample as a check on the more dubious May estimates of the spawning population.
Of marked perch from the May fishery, 1 004 specimens were not killed during the fishing. As 97 of the 1 303 perch secured in August had been marked, a Petersen estimate (with Bailey's correction) gives:
with approximate 95 percent confidence interval 12 199–14 830. If we add the 1 662 perch that were killed in May, the population at the beginning of the May fishing was 15 022 perch with 95 percent interval 13 861–16 492. This is in good agreement with the Schnabel estimates from May.
Apparently the Schnabel estimates have not been much biased by emigration from the stock of spawners during the experiment. This may be due to the short spawning period - about two weeks only. In locations where the spawning period lasts longer and spent perch leave the spawning areas or lose their interest in the traps before the late spawners arrive, multiple census will probably underestimate the number of spawning perch.
| Date | c | m | r | B | s | s* | 95% int. for s |
| 4.5.1952 | 29 | 0 | 0 | 0 | |||
| 5.5 | 365 | 29 | 2 | 0 | 5 293 | 5 293 | 1 500–43 700 |
| 6.5 | 320 | 197 | 5 | 195 | 14 725 | 14 890 | 6 300–45 400 |
| 7.5 | 70 | 264 | 10 | 445 | 9 211 | 9 429 | 5 000–19 200 |
| 8.5 | 405 | 309 | 19 | 465 | 11 434 | 11 786 | 7 300–19 000 |
| 9.5 | 590 | 460 | 31 | 710 | 15 763 | 16 300 | 11 400–24 100 |
| 10.5 | 170 | 708 | 32 | 1 040 | 19 032 | 19 662 | 13 500–27 800 |
| 11.5 | 120 | 757 | 38 | 1 150 | 18 417 | 18 565 | 13 400–26 000 |
| 13.5 | 389 | 871 | 48 | 1 150 | 21 639 | 22 465 | 16 300–29 300 |
| 15.5 | 203 | 966 | 51 | 1 434 | 24 211 | 25 126 | 18 700–32 500 |
| 17.5 | 75 | 1 013 | 54 | 1 587 | 24 273 | 25 222 | 19 000–32 000 |
