sw a ves. * *** *** * * •=º ºr s ** • * ºn • * * *** * * * * * *** * * * * * * - • * * * gº ** * * * * ***** * * * * * * * * * * * * * * * *** * * * * as-p sº are sº • * * * * A tº * **** * * * *** - * * * * * * * * * * * r *s º **q → ſ** *** * * * * * * * * * * * *** *** * * * * **** ** as sº sers - sº * * * * * * * * * * * ^* * ºr saraw-, z - ºr - * * *.* * * * * *7 ***-aww.sts tº gº-rº vesses res-ºs." * * * * * *S - - wº"& ** ****** ******* **** ***** ** Fºrº a tºrcase rºº rºº º gº or ºvere we’re-saw” ºr sº tº a we as seaſe º MP ºr a vºwsºe ºr ºs ºr . . . . … • * * º “s * * * * * * * * * * * * * * vs. º are sºarer as saw sº * * * * *** *sº ****** * *** * * * *** ** snares -ºs.ºrs." -- ***** ******* *** *** * * * * * * * * ºr are ºw-ºrazºr-arºe sº - * * ****** *.*.*.* * * * * * ****** were easy---º-º-º-ºs---a-vºº-wºº ºve sº assº we sº re ºr ***** gº sº...sº sº wº 's - º º - : ºw tº tº * - I sº * * * * * * *S*** * * * * * * * * * * * * Sº *** * * * * * * * * * - *** * ***** * *** *** * * * * *** ***** **u." “ss ******* *** we “” is “º we's --- * ºw ºn Pººwº *** ºf “º r **** * º d * *** - ºr cº-ºws * * * * * * * * * * * * * = ... a are se - a sº tº - º reasºn wress: * * * * sº sºvº ºsº D ºrrºw D. ^ - *** ********** ******A reviºus-ºss; ºº g *A* ºrº" ºr * * * * sº wrºtawººdwºssºssºvernºw wºre tº *** *** ***** tº fºr eº- tº ºr *-***** º º ** * * * * * * * * * * * * : w O º * * is . e. i - ºr * : * * : * * * : * * * * * * * * * * * * * * * * * * * * * * * * U º * * * * * * * * * * * * * : **.*.* a - F. º º º sº wº º º Sº tºº º dº sº "" Rººse- - **************** wº ºf law -º sº." ~. ****** exº~ººks l ºf tº -** * * * * * ºw * : ** ºw sº º D I dº º 'º º sº ºw wºw a "p" aſ a wº ºr sº a rººf ºverse ºr saw - * * * * * * * * * - - - - - - w º º ºr ºr " - at tº * * * * * [V] ſº * * * - - sººts age "º tºº e = * * * *** * * * * - d d - ° N - º º-r ſº ºf ºn - * * * * * * * ~ * ºf “º “ wº *** * * * * * * * * w tº " iſ - t * -º a º º º ear tº: * * * * * ***** ***** *** attrº's º * * * * *, * * * * * arº wrºv ºss -- wºrs, a pºst- - a - as wear-e- ºr ew Gºwra- ºr . ºr, " *** * * sº º *** * * * * ſº tº Tºº º - a tº a was sºº" sº º' gº ºn " \g a sºn w varine sº was * * * * * * * * * * * * * ſº ** G º ſº *** * * * * * * * * º º Fº ** *... dº º ºvº a & * suº wºº is ºwwºwaº º • sº º ºr tº era e ºs • * gº tº ſº C a sºns-wne anaev awºrºw dºw sº ba ********* ‘ºw tº sº sº us tº ºw" ºr twº ***** *** ******** * **** ********* *** Sºrsºººººº. sa ºr sº yº * * * * * saº rºse was rºse's re-rººdºº wavestºw tºº ºr ºsteº sº tº tº . sº * * • * * ***'s swºrºwº gº ºvere” & ºw R & rºwwºw ºstex ºr and sº sº ºvºsºrºrºººººººº-º-º-º-º: a new sº win entiºn a variº, nºw outwº a Pºssrºasiºns **ºqa. *** * * * **, we expºs we ºwºtew ºn tº reasºvº pºrºsº Nº a sile as as * as It “iº as "is - ºr sº." sº ºwes cº-ºwº isºl JP we'rºº * ***.* tº sº, tº ºr tº sº see ºr wººwº. º. ºº is “tºwº tº º esa was sº-c = new we surº *** *wº-vºwtiº wºrris º * * * * stº wºº tº wa ” Fºº “º iw' . *gº ºr **** * * * * ***** º M gº *** * * * ** * * * * * * * *ºw ai º ºr ºf "tº a º - Sººn tº ºr nº Yºkºpº"gº vºyº rºstrº gº wrºsº | ºr tº it º º º' Mº " tºº Nºt tºº was sº was ºr ºver-wºº tºº `eº heºsºvº Nºwrºº ºr ºsewºº * * * *** * * * * **** * Rºs tº ºr .* ºr s. v . . . tº º ** "p tº ºn "w (" " is ºn , sº sº tº * ºap a ºn v tº sº assº º º - saa meet - *** * v- “ * * * * *** ******** ***** * * **** & & - J. : *i; } tº cº-º-º-º-º-º- ºr- ºr twº vºw: ******* ************* *-* * * * * * *s . fº tº ºne ºvºvºrºus ºw-tºº-ºººº vº' ºr ...As tº - ~ Wr ºw - - * * * * * * * we wº º A ſy" - As ºl trºute tºº wº ºarns ºr sºutpºuw wºw Mºrvº view ºv.ºrº wºº *** * * **** ºur wºrts ºvºvºr- ºur ºwners issuess sº º is: G sº * * * * * * * * * * * * * * *zarº rºst tº wº ºvºvº º ºsºvº sº we * * * * * * * * ***** ** *** * * * * * * * *** * * *-ºs tºº ºf * * * ww.rsºns: º sº ºur air is wºrlussº wº º * * * * * * * * * * * * * º twº sº , was sººn º r:rig tº *******º-ºº: sº * : * * * * * * * * * * * *** *** * * * * ºr lºss *Sºº-ºººººº- º law wº * * * * * * * * * * * * * * * * * * * º º Nº. 4 * * * * * * * * * ** - ************ º aw.arºº wer" tº §º : *" sºvºsºkº sº w Arºrapºva's sºrº ºusºvº Nºt º'ºrº" ºr wºupe was sº tºº * wz º. & º w was a tº tº wº tº w wºrs, waſ … sº sessiº: ºn tº ** savºr ºur ºwn as ºustº wºrkers swww.sºsseºwº ** º ºg - tº is ºr a vºw º'e' ºs-ºsº ºr ºvernºvº as "r “w * ****jº . A sº sº. º - so, sº sºrrºs & tºurº is ºwnstºwº-rººves tº ºr rºtºtº sº F & 3" & " " sº ºr " Ü tº wºrsº, ºn-sºº ºn tº ºs ºs tº ºr sºººººº-ººrºº • * * 2 * ºr ºn º tº wº wºt, wavºu" ºne ºf sºvº.ºtºvu ºvºvºvº • **** * * ****** * * * * * * * * ***, *.* tº ºr ris Hº re' ºr - wº- were wºrrier strºws-tº-wearer ºrwºw tº in a twº tº 3 we "...ºr w a “tº gº ºr ºuts tº is ºwn sº wºn tº twº www.º.wºwo ºr ºver tºur we nºw aw" wº ** * * * * * * * * * * *** wº, sº ºf wº up"º wº, º ºsºvº º ºx º' ºr ºr tº serºwº ºw wºx w w = ** a ºr a º º *** **** º *** **tº tº & a lºw, ºr "tºp ºf - wºs º ºx at was ºx * * * * * * ***** * * Swavº • ‘Nº. stºriº w wºnt sº Misº warrasnºsºvº 2 tº 33 ºvº as twº twº ºr tº: - ºvº's ºve" tº sarºese ***** Sirºvskºvºussº- a tº ºs w a lºw ºt - twº sº sº ºrv, ºn shºw Nºwºssºv-vºtºsysºsºsºsºrºrº º tº sº wºe swººs ºu'vºsauşºsswººdºº º “s ºvºv tºº tºur ºwn, usiºn ºvsisyrºs - * * * * * * * * As A tº-ºrº ºr 9 ºxws ºver-trusteriºusº ºustºstº" * * * * * * * * * * tº “a lº & ** * * * * * * * * * * * * * *** * * * * * * * ºn isºtrº wagºsº aws ess sº is ºwn ºver a vases tº v is a trus aws ten * * Sust's Nºt tº hºsts. g tº “ . . . , tº sº. 5 - a tºº “** **is wºvºsº intº tº saw wres sº twº ºrgskºwº-wº v wt vºs tº in ºvº-ºº-ºº vastº ºvºvºrºsiºts * Ifº ITTº tº run ºxº~ ºn rº * * * * * .. ** * * * * * we c º . s w tº ... • * * * * * * * * * * • * * * * * * -wºº. sº wºº wºº tº wºrsº * > * * ºf “r a "4: - «» sº * * * * * * * * * * * m . . tºº [w Mº' rú -º u º ºn tº w was ºw * * * * * * * * º s sº gº ºn “º nº us vo" ºr tº **** * * sº tº gº ºr gº *- —T- Pir O P E R T Y O 9 | ſh ſūló.gº * A : TE sº Scº Nºt I. A v ERITA’s , -ºgnºre . *xe--i ... -a-.…”-e-ºr-ºw. -- rººr rºy’ > * > *-** DYNAMICS OF LIGHTLY EXPLOITED POPULATIONS OF THE LAKE WHITEFISH, ISLE ROYALE VICINITY, LAKE SUPERIOR by Ann M. Koziol A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Fisheries School of Natural Resources The University of Michigan 1982 Committee members: Dr. Karl F. Lagler Chairman Dr. W. Carl Latta ACKNOWLEDGMENTS This research was supported by the Institute for Fisheries Research of the Michigan Department of Natural Resources. All data were graciously procured from the Michigan Department of Natural Resources by Gerald P. Rakoczy and Richard R. Schorfhaar who also provided useful information of Lake Superior whitefish. I am indebted to Richard D. Clark, Jr., who gave invaluable advice and assistance during this endeavor. I would like to thank Drs. Karl F. Lagler and W. Carl Latta for their advice throughout the project and review of the manuscript. My appreciation is extended to Grace M. Zurek for typing the final draft and Alan D. Sutton for drafting the figures. Special thanks go to my family, especially Dorothy and Walter Koziol, whose encouragement and support helped me through this study. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iV LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V LIST OF APPENDIX TABLES ....................................... Vi ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vii. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 MATERIALS AND METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 GROWTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Age-Length Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Length-Weight Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 MORTALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 YIELD PER RECRUIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 iii LIST OF TABLES Table 1. Estimated mean lengths (mm) at age (years) for the whitefish stock in northern area . . . . . . . . . . . . . . . . . . . . 2. Estimated mean lengths (mm) at age (years) for the whitefish stock in Southern area . . . . . . . . . . . . . . . . . . . . 3. Mean ages in years of the annual whitefish catches of the northern and southern Isle Royale, Keweenaw, and Whitefish Point stocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Mean weights (kg) at age (years) for the north and South areas calculated with the length-weight regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . tº 5. Number of fish remaining at age (years), potential egg number (millions) and yield per 1,000 age- 4.42 recruits (Y /R) with varying instantaneous fishing mortality (F) and size limit (x,) in millimeters for whitefish of northern Isle Royāle © tº º e º 'º e º 'º e o 'º e º e o e º e º e º & 6. Number of fish remaining at age (years), potential egg number (millions) and yield per 1,000 age- 3.88 recruits (Y/R) with varying instantaneous fishing mortality (F) and size limit (xe) in millimeters for Whitefish of Southern Isle Royāle . . . . . . . . . . . . . . . . . . . . . . . iV Figure LIST OF FIGURES Isle Royale, Lake Superior, showing the north and South study regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fitted von Bertalanffy curve and empirical mean length-age relationship with 95% confidence limits for northern and southern Isle Royale whitefish from 1978 through 1981 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Catch curve for northern Isle Royale whitefish collected With gill nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Catch curve for southern Isle Royale whitefish Collected with gill nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yield in grams per 1,000 age-4.42 recruits as a function of age at entry (xc) and instantaneous fishing mortality (F) for whitefish of the northern area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yield in grams per 1,000 age- 3.88 recruits as a function of age at entry (Xe) and instantaneous fishing mortality (F) for whitefish of the southern area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 15 16 19 20 Appendix A. LIST OF APPENDIX TABLES Back calculated lengths (mm) at age (years) for lake whitefish of southern Isle Royale for the Spring of 1978 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Back calculated lengths (mm) at age (years) for lake whitefish of southern Isle Royale for the Spring of 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Back calculated lengths (mm) at age (years) for lake whitefish of southern Isle Royale for the Spring of 1980 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Back calculated lengths (mm) at age (years) for lake whitefish of southern Isle Royale for the Spring of 1981 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Back calculated lengths (mm) at age (years) for lake whitefish of northern Isle Royale for the Spring of 1978 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Back calculated lengths (mm) at age (years) for lake whitefish of northern Isle Royale for the Spring of 1979 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Back calculated lengths (mm) at age (years) for lake whitefish of northern Isle Royale for the Spring of 1980 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Back calculated lengths (mm) at age (years) for lake whitefish of northern Isle Royale for the Spring of 1981 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 27 28 29 30 31 32 33 34 ABSTRACT Two lightly exploited Stocks of lake whitefish (Coregonus clupeaformis) near Isle Royale, Lake Superior, were compared in terms of growth, mortality rates, and yield per recruit. The stocks are Separated geographically to the north and south of the island. The ages of 501 lake whitefish from both stocks were deter- mined. Length at age was estimated by conventional back calculation methods. The whitefish from the northern and southern areas were judged to be of different stocks. The southern stock averaged 50 mm longer at a given age than the northern stock. Total mortality rates were calculated for both stocks but they appeared to be high due to gear selectivity. The Beverton and Holt dynamic pool model was applied to the stocks. Maximum yield per recruit for both stocks was attained at a fishing rate of 2.0 and a size limit of 482 mm (19 inches). The impli- cations of this increase in fishing pressure were viewed in terms of remaining reproductive potential. Potential egg numbers were compared for the stocks at the fishing rate of 2.0 and a fishing rate of 0.7, which approximates that found in northern Lake Michigan. At the 0.7 fishing rate, there were 108% more potential eggs for the southern stock and 46% more for the northern stock than at the higher fishing rate of 2.0. The increase in yield per recruit at the 2.0 fishing rate, however, was only 9% and 7% for the northern and southern stocks, respectively. The present size limit (432 mm or 17 inches) of the Isle Royale whitefish was hypothetically increased to 482 mm (19 inches) along with the instantaneous fishing mortality to 0.7. With a raised size limit of 482 mm, the decrease in yield per recruit was only 0.001% for the southern stock and 0.04% for the northern stock. The increase in residual egg potential was substantial, however, with 58% more potential eggs for the northern region and 59% for the southern region. viii INTRODUCTION Lake whitefish (Coregonus clupeaformis), a schooling fish of the subfamily Coregoninae are classified with salmon and trout, in the family Salmonidae. According to the Michigan Department of Natural Resources, lake whitefish are the most sought after of all Lake Superior commercial species, and their production in recent years has increased (Rakoczy 1982). Their growth is rapid in all of the Great Lakes except Lake Superior (Carlander 1950). However, the largest individual of record was caught in Lake Superior off Isle Royale (Van Oosten 1946). - The purpose of this study was to assess two lightly exploited stocks of lake whitefish in the vicinity of Isle Royale, Lake Superior, in terms of growth, mortality, and potential yield per recruit. Growth and mortality data for these stocks were used to predict yields. Hopefully with these figures in hand, a fishery biologist can regulate the exploitation of a fishery to achieve the goal of sustaining the population while maximizing the yield. Isle Royale parallels the northwestern shores of Lake Superior (Fig. 1) in the MS-1 statistical district of the State of Michigan waters of the upper Great Lakes (Hile 1962). Approximately 45 miles long and 9 miles wide at maximum, the island is a National Park and provides various fish habitats such as open and sheltered shores with variously steep or gently sloping bottoms (Lagler 1982). The commercial fishery of the surrounding waters depends primarily on several members of the whitefish subfamily and on the lake trout (Salvelinus namaycush). ONTARIO Fort William ___NORTH AREA f- | | | | | . LAKE | SUPERIOR | "south AREA N Copper YHarbor Keweenqv Penninsula Ontonagon 0 10 20 'L'Anse |-H STATUTE MILES M|CHIGAN Figure 1. -- Isle Royale, Lake Superior, showing the north and South study areas. The populations of these fishes are monitored by the Michigan Department of Natural Resources to record the natural dynamics of fish stocks. This is accomplished through the issuing of research fishing permits only to the three remaining traditional commercial fishermen. Each permit assigns the areas to be fished, and limits of the catch, and requires the taking of annual assessment data on various species of fishes. In this study, two areas were considered. A northern area with many small islands and protected irregular shoreline but, primarily, neighboring Lake Superior; and a Southern area with mainly the large Siskiwit Bay and adjacent waters. Both stocks are considered very lightly exploited, yielding on the average 2,067 kilograms per year from the northern area and 1,159 kilograms from the southern area (Andrew Nuhfer, Michigan Department of Natural Resources, personal communication). These yields are ex- tremely small compared to other Lake Superior stocks such as Keweenaw with 6,925 kilograms per year and Whitefish Point with 65,176 kilograms per year averaged Over the same years and approximately the same size area. The Keweenaw Stock is regarded as lightly exploited and Whitefish Point stock as heavily exploited (Rakoczy 1982). MATERIALS AND METHODS All data reviewed were collected for the Michigan Department of Natural Resources by commercial fishermen as a requirement of the research fishing permit. For the two sample regions, gill nets with mesh sizes ranging from 114 mm to 140 mm (stretched) were used to catch fish. The biological data and scale samples were taken from 100 whitefish from each fisherman's total catch each spring from 1978 through 1981. Data included catch per effort, total length, and occasionally, the weights of the fish. A total of 205 scales (about 52 per year) were aged from the northern site and a total of 284 scales (about 71 per year) were aged from the southern site. Of each avail- able inch group (fish 15.0-15.9 inches, 16. 0-16.9 inches, etc.), 10 scale samples were subsampled for age assessment. Scales were mounted in water between two microscope slides and examined on a microprojector with 48 mm magnification. Growth fields were measured to the nearest millimeter from the focus through the anterior portion of the scale. Aging was often difficult due to the condition of the scales, the closeness of circuli of the older fish caused by slow growth, small number of scales taken from each fish, and the possibility of the fisher- men not taking the scales from the correct anatomical place on the side of the fish. - The criteria for annulus dermination, as set by Van Oosten (1923) and ranked by Bell et al. (1977) were rigorously applied as follows: (1) cutting over of circuli into the lateral fields; (2) a break in the pattern of circuli indicated by discontinuity; and (3) spacing of the annuli. Because the samples were taken in the Spring, the margin of the scale was taken to represent the most recently laid down annulus. GROWTH Age-Length Relationship Average length at age and annual growth increments were calculated with a FORTRAN program which follows the standard back calculation formula (Lagler 1956). L_ = S_ (L_- a) + a Il Il C S C Where : Pn = length of fish when annulus n was formed Po = length of fish at capture Sn = radius of annulus n a = intercept from regression of body length on radius So = total scale radius It was decided not to use the calculated intercept of the body: scale regression (2.0 mm for both the north and south sampling regions). As stressed by Carlander (1981), a calculated intercept can be a misrepre- sentation due to the gear selectivity of gill nets and subsequent insufficient sample size of the smaller and larger fish. Although the difference from the calculated value was small and probably insignificant a recorded Lake Superior intercept value of 1.0 mm (Carlander 1950) was used. The lengths at age were estimated for each year (Appendix A-H) and the mean lengths at age for the four years were used in further calculations (Tables 1 and 2). Scale samples from both study sites came from fish ranging from 5 to 14 years of age. The lengths of the southern fish averaged 50 mm longer than the northern fish in the same age class. Taking into account the 95% confidence limits, the mean lengths overlapped through age 3 but proved to be significantly different for fish older than age 3 (Fig. 2). Table 1. --Estimated mean lengths (mm) at age (years) for the whitefish stock in northern area. The 95% confidence limits are in parenthesis. Year Age in years 1 2 3 4 5 6 7 8 9 10 11 12 13 1978 104 198 279 351 421 478 525 563 594 613 621 644 668 (4) (8) (10) (11) (11) (11) (10) (11) (16) (32) (54) (84) (74) 1979 102 198 278 354 420 473 520 555 584 614 608 623 635 (6) (11) (14) (19) (19) (20) (21) (23) (35) (56) (24) (23) (38) 1980 103 189 270 345 416 470 512 541 573 597 627 649 695 (6) (8) (10) (10) (12) (11) (11) (11) (13) (16) (21) (25) (12) 1981 111 190 263 332 397 457 507 543 564 602 252 (9) (10) (12) (13) (14) (14) (15) (16) (16) (17) (26) Mean 105 194 272 345 413 471 516 550 579 607 627 638 666 (6) (9) (12) (13) (12) (12) (13) (15) (21) (31) (31) (44) (38) Table 2. --Estimated mean lengths (mm) at age (years) for the whitefish stock in Southern area. The 95% confidence limits are in parenthesis. Year Age in years 1 2 3 4 5 6. 7 8 9 10 11 12 13 1978 100 198 2.91 381 467 530 577 616 645 666 691 718 (3) (7) (11) (13) (13) (12) (11) (12) (12) (12) (18) (27) 1979 96 202 298 388 469 537 586 622 647 671 704 727 756 (4) (7) (11) (13) (13) (12) (11) (13) (13) (14) (16) (19) (24) 1980 97 192 2.76 352 4.24 492 549 590 621 642 664 690 706 (5) (8) (13) (13) (14) (12) (12) (11) (11) (14) (17) (22) (27) 1981 102 214 312 404 483 549 593 628 651 679 696 717 (5) (8) (12) (14) (14) (13) (14) (15) (18) (33) (9) (34) Mean 99 201 294 381 460 527 576 614 641 664 689 713 731 (5) (8) (12) (13) (14) (12) (12) (13) (14) (18) (22) (26) (26) 7OOr 6OOH 500- 4OOH o = North Area / L=8061-EXPſ-O15(x-OO6)] 3OOH - / • = SOUth Area 200H / L=820ſ-EXPſ-O17(x-O3O]] I | | | | 1 1 | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 Age in Years (x) Figure 2. --Fitted von Bertalanffy curve and empirical mean length-age relationship with 95% confidence limits for northern and southern Isle Royale whitefish from 1978 through 1981. Different size gill nets were used when collecting data, possibly causing the difference in the northern and southern whitefish mean lengths. The southern whitefish were obtained with 114-mm mesh gill nets in 1978 and 140-mm mesh from 1979 through 1981, while gill nets of 133-mm mesh size were used all 4 years in the northern area. Although the greatest dissimilarity in mesh size occurred between the 1978 and remaining southern whitefish data, no difference in their mean lengths was observed (Table 2). Therefore, it was assumed the variation in the mean lengths of the north and South study areas was not due to mesh size difference. In the back calculated lengths for both the north and South areas, positive Lee's phenomenon was present. The younger the age group of fish used for the back calculations, the greater the mean length for the earlier years of life. Lee's phenomenon is often caused by the size selective mortality of the faster-growing fish which become vulnerable to the fishing gear first and are removed from the year class. In these lightly exploited stocks, however, this selective mortality should not be a major problem. Bias in the sampling of gill nets, which resulted in little representation of the smaller individuals of the younger age groups and the larger individuals of the older age groups, is more likely the major basis for the Lee's phenomenon in this case. The catch curve considered in the mortality estimates below re- flected the same selectivity. Using mean lengths at age undoubtedly offsets any effects of Lee's phenomenon on growth. Rakoczy (1982) suggested that for satisfactory population maintenance, the mean age of a Lake Superior Whitefish catch should be at least 6.5 years. This allows the fish to spawn 1.5 times before 10 death, which has been reported to be necessary for a stable whitefish population (Christie and Regier 1973). Both the north and south stocks had mean ages of catch over 8 years as might be expected from very lightly exploited stocks. The mean ages were slightly higher than the lightly exploited Keweenaw stock but almost double the heavily exploited Whitefish Point stock (Table 3). The mean back calculated lengths were utilized in a FORTRAN program of the following von Bertalanffy growth equation (Rafail 1973) : 1, = L. (1 - exp [-k (x - xo)] } where: *x length at age L. = theoretical asymtotic length in millimeters k = growth coefficient xo = theoretical time when length is zero The result for the two stocks of whitefish were as follows, with the 95% confidence limits in parenthesis: L k X OO sº O North 806 0.15 0.06 (0.63) - (0.07) (0.05) South 820 0.17 0.30 (0.10) (0.01) (0.30) The 95% confidence limits of k and *o overlapped, while those for L. did not. The difference in the L. parameters means the von Bertalanffy growth curves are statistically different. This provides further support that the northern and southern whitefish are indeed separate stocks. The predicted growth curves and the observed mean lengths are very close with the northern fish showing more variation in the higher ages (Fig. 2). 11 Table 3. --Mean ages in years of the annual whitefish catches for the northern and southern Isle Royale, Keweenaw, and Whitefish Point Stocks. Area Years 1978 1979 1980 1981 North 8. 6 9. 0 8.2 8.8 South 8.4 8. 3 9.4 8. 8 Keweenaw 8.4 6.2 7. 3 not (Rakoczy 1982) available Whitefish Point 4.5 5.2 5. 1 not (Rakoczy 1982) available 12 Length-Weight Relationship Individual weights were only available for the southern whitefish population. Least squares regression was used to describe the length-weight relationship as expressed in the conventional equation: W = al.” where: W = weight L = length a and b = constants For the southern Isle Royale whitefish, this relationship was : 1n W = -18. 7020 + 3.0497 1n D. The southern Whitefish were heavier at a given length than the northern whitefish (Table 4. ). 13 Table 4. --Mean weights at age for the north and south areas calculated with the length-weight regression. South - NOrth Mean . Mean Age length Weight length Weight (mm) (kg) (mm) (kg) 1 99 0.01 105 0.01 2 201 0.08 192 0. 07 3 2.94 0.30 272 0.20 4 381 0. 60 345 0.40 5 460 0.99 413 0. 70 6 527 1.50 471 1. 10 7 576 2. 00 - 516 1. 40 8 614 2. 40 550 1. 70 9 641 2. 71 579 2.00 10 664 3.05 607 2. 32 11 689 3.41 627 2. 60 12 713 *3. 79. 638 2. 70 13 731 4. 19 666 3. 10 MORTALITY Total mortality rate (Z) is the sum of the instantaneous natural (M) and fishing (F) mortality rates. The total mortality rate of a very lightly exploited stock should approximate the natural rate. Relatively high mortalities Were calculated, however, in both the northern (Z = 0.81) and the Southern (Z = 0.71) stocks. These estimates were derived through the regression of the natural logarithm of the catch per effort (catch per 1,000 feet of gill net per day) on age (Figs. 3 and 4). Total mortality (Z) is depicted by the slope of this regression line, but the line can be misleading if the young and old fish are not represented in the catch according to their abundance. It seems probable that my estimates for total mortality are high due to selectivity of gill nets (Healey 1975). Gill nets of a constant mesh size catch the larger fish in the younger age groups and the smaller fish in the older age groups. The former problem was eliminated by considering in the regression only fish over age 7 for the southern area and age 8 for the northern area; but the latter problem probably exaggerated the steep- ness of the slope and, thus, overestimated total mortality (Z). Using trap nets to catch whitefish gives a more realistic view of age classes. The more exploited stocks of Keweenaw and Whitefish Point were found to have total mortality rates of 0.43 and 0.59, respectively (Rakoczy 1982). Therefore, an instantaneous natural mortality (M = 0.3) recorded for an unexploited whitefish stock of Grand Traverse Bay (Patriarche 1977) was used in the yield calculations. A covariance test was conducted for the north and south regressions. No significant difference was found between the regression lines at the 95% level suggesting mortality is probably the same in both areas. 14 6T- 3S 5 5H. I § 4H O -C S § 3F O Ln(y) = a-0.8x O 2 R* = O.97 e 2h O —l E 1H Inj º 2 1 | | | -l 6 7 8 9 1O 11 Age in Years (x) Figure 3.--Catch curve for northern Isle Royale whitefish collected with gill nets. Ln(y) = a-O.7x 2H- R* = O.94 3 f |- 1. | | | - | | 1 5 6 7 8 9 1O 11 12 Age in Years (x) Figure 4.--Catch curve for southern Isle Royale whitefish collected with gill nets. YIELD PER RECRUIT The Model The dynamic pool model weighs the parameters of growth against the instantaneous natural and fishing mortality rates for the purpose of predicting the best level of exploitation for fish stocks. Although there is often difficulty in estimating these parameters confidently with avail- able data, this management model is intuitively more appealing to biologists than others such as the surplus production model. The parameters and structure of the dynamic pool model can also be more meaningful in a biological sense. A FORTRAN program of the Beverton and Holt (1957) model available at the Institute for Fisheries Research, Michigan Department Of Natural Resources, was used to make yield computations. This program is slightly changed from the standard Beverton and Holt model in at least three ways. First, it uses the von Bertalanffy parameters of growth in length rather than growth in weight, and it converts length to weight for yield computations by using the length-weight regression coefficients. Second, it uses the Baranov catch function to compute catch in numbers by age. And third, it calculates the number of fish by age remaining in the population. All these changes were suggested by Tyler and Gallucci (1980) and are described in more detail in their paper. The standard procedure of computing the isopleths of yield, as they vary with age of entry (size limit) and fishing mortality rate, was followed. The additional information provided by the program on number of fish at age in the population was used to compare relative egg pro- duction potential for selected size limits and fishing rates. 17 18 The smallest fish vulnerable to the gill nets of both sample areas was 381 mm (15 inches). Therefore, computations were based on 1,000 recruits of age 3.88 years (381 mm) for the southern stock and age 4.42 years (381 mm) for the northern stock. Results and Discussion The results of repetitive model applications with varying instantaneous fishing mortality (F) and age at entry (size limit) are presented in isopleth diagrams (Figs. 5 and 6). The isopleths show yield increasing assymptotically with fishing mortality rate (F) and a maximum yield per recruit is attained at the fishing rate of 2.0 and a size limit of about 482 mm (19 inches) for both stocks. The natural mortality rate used was 0.3. The actual fishing pressure of the Isle Royale populations is unknown, but if similar to the rates recorded for the lightly exploited Keweenaw area (0.14) or even the heavily exploited Whitefish Point (0. 30), a substantial increase in exploitation could be sustained by these populations. It seems unlikely, however, that they could sustain a fishing rate of 2.0 with no ill effects on recruitment. The isopleth diagrams were useful in establishing the maximum yield per recruit and the variations caused by changing size limit or fishing pressure. More information is needed, however, for proper yield predictions as the isopleths ignore the possible impact of fishing on recruitment. Constant recruitment was assumed by the model. Using for comparison a fishing rate of 0.7, which approximates that reported for northern Lake Michigan whitefish (Patriarche 1977), the effects of raising the fishing rate to 2.0 were viewed in terms of residual reproductive potential. Assuming a 1:1 sex ratio, that 56% of Lake Superior whitefish females are mature by age 5 (Rakoczy 1982), 19 14 r. – 200 –686 Tº 12H >< 92 H 309 E – 635 § 10|- O º pme +584 LL 8}- ºf -1533 g, ſ --|482 <ſ 6H- Wºme –432 | 4. | | l ! | ! | | | OOO O4O O.80 1.2O 1.60 2.00 Instantaneous Fishing Mortality (F) Figure 5. --Yield in kilograms per 1,000 age-4.42 recruits as function of age at entry (xe) and instantaneous fishing mortality (F) for whitefish of northern area. ZU 15 T- H. OO 13H 2 3 F 309 # 11 H. 686 G. L AOQ -168 CU O º, 9 H. 635 iT L & 584 g’ſ * * * * * ºn " ******** *** * * * * A "*- sº a “*** **** * * * * * * * * º wº ºr * * * * * * * , 5 * * * * * * * **** * * * * * * * * * * * * , sº t e º is a “ sº D - a," -- a º e º 'º & º' tº - ** **** ***** **** ***** º *** **wºres ºf a - *** * * * * * * * - º ºw ºw ºr ºf t”. “ººk “º * * * * º |-D **ºn. - - w tº e i s we a * * * * * * * * * * 4 * ºwawº-wºrsº ºrº tºº st *** * * *wu's *...** tº a º tiº ~ * * is ºr ºr w w is u tº... tº * v- * * * * * * * * *.* *** ****wº-ººººw' ********wo as ºn v.v. * **** sº an ºr tº sº. * - as ºwn ºn ºr ºn tº a tº as ~ 3 - 8. , : * * a *-* - *** **** **wa.ºr º ºgº * * * **** * * * * * wº º tº º tu º • * * * - see ea ºn as a as - ºut was as wººl, ºr sº sº. - ea tº a * * * * * dº sº. - Mº sº º [*** s º a e º is a 2, W. " ' º * * * u, Aºi ſ㺠su" wi •aw & "Nº ºxes "A tº 4 ºn "sº sº , «s si tsu as "... " d * * * * *s is ****** *s * * * * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * *** * * * * º a sure ºf sº ºw w is sº sºws sº ºracºw. - a - º ºs º carº º R -e "tº a s ************** - ºr ºrº º - * * * * * * ****, * * * * * * ****** ºw 4 ºf sº º a 'Pa * * * * * * * * * * ºxv ºr 4. ‘a’ - 4ººrºº's º ºr rººs. & º ** ** * * ~ * * * v- ºr 2, 4, assº...wº * * * * * * ******* ***.*, *, * ºr a ºn.'s "sº kº ". *** *** * * *gº º ſº *** **** tº as “a a. * * * * * * * ******************* **ºtºq" ºr ºvº, S A.º. r ºr w tº ******wº rºs.-- " wºº sº tºº-sº ºr ****** was sº x-wºº's ºw-º-º-º: ºr sº wºº arº º'º "" is “ sº.” ". -wºº's sºlºsº º º sº sº sº us...wºw.'s.” < *** * **** ** - ********* - º u º ****************** º s & º º- sº ºr w tºº At ºt,” & t * **** * * * * * * º, U. sº a ºs tº * * * * * * * sº a *Irºtºrºiº iſ \" ºlº ſº º ºx tº * ***"All tº º º º a ºr " Pºw - P." t º tº as ºr - *, º: * ºf , ºr tº ºf .*, * * ******** ºut sº, . wº lº & ºr a v ºr a . s tº º is a 4 m º " - tºº sº. ºº & "A" & A. ºr * tº s. sº wº's * ..." W’ºw a tº * * * * * * * * * * * * * * * * * * * * * * * * - * * * *. " " º wi." - ºn was sº º * * * * * **, * "... • * * M * * * * * * * * * rºººººººw'-sººk sº sº. º, ºr a wº ******** *** ***.***** * * * * sº a º tº º ºrs & ºr sº w *tº ºak ge: # * * * ww. ****** **** a ºlºtºkº.º. ººrrºsºsº.º.º.º. ºr sº a snºw, ſº *** * * * * * *** * * **** º **ºniº's sººººººººººººººwº an is sy-4 wººd ºf £ tº sº"; sº º 'º wºº tº w - - º tº ºr ºxºsiº rºw ºvºr ºr * * Sº ºases ººgº tº si si < *.******** * * * * tº **, * * * *"º º ºxcº, º ºs. ºr “s tº * * * ******** * * * * * * **** * * ********s, *.* tº re- sº. 4 as an at *** **** ******** **** *********** **** * ******, *.*.*.*.*.*, *, * * it we “ºur sº º's ºr ****, *, *, *ra; ºr Fºxsº a rººs ººººº º ºr tº sº tº sº º-º. “iº.º. º. ºf "nº Tº º ********wººººººººw'-s' ºtºl’sº at ºr ºf w. a s tº we v ºr *4 strºyº ºvº º Fº Fº *** **** * * wº ºr a ºustºsº tº º tº. wºwº º is aſ tº a jºiº ſº. 4's ºr a º ºrs "a is *** * : * * * * * site: “ ºf * * * * * * , ºf "Tº s tº dº º ºs t º º, ºl’s a sº **ºw a wº & “” & Kºº “º ºn tº ** * * * * * * * º ºw tºº. º - - ** ***, *, * * * v -ºº ºl º ... º.º. ºf Mºsuº º 'º -- tº Đ *iº ºxº sºººººººº- Pºº sº sººris tºº.º.º. º *#443 tº * * * * * * * * * * * * * * * **, *, * * * * * * a º 'º a º a. * * * a di e = * . . . . . . . . * * ** U = s. º * * * * * tº ſº * * ſº * * * * * * * * * * * * . . . . . . a * * * * * * * º **** * * * * * * * * * * - tº es e ea tº a w º 0 ° à * **us & 4 * - a * * * * * * * '.' s : a a