Harvest Levels for Commercially Exploited Stocks of Lake Whitefish in Michigan Waters of Lake Superior

Transcription

1 Harvest Levels for Commercially Exploited Stocks of Lake Whitefish in Michigan Waters of Lake Superior Gerald P. Rakoczy Fisheries Research Report No September 7, 1983

2 MICHIGAN DEPARTMENT OF NATURAL RESOURCES FISHERIES DIVISION Fisheries Research Report No September 7, 1983 HARVEST LEVELS FOR COMMERCIALLY EXPLOITED STOCKS OF LAKE WHITEFISH IN MICHIGAN WATERS OF LAKE SUPERIOR Gerald P. Rakoczy

3 2 Abstract Harvest levels ere calculated for six stocks of Lake Superior lake hitefish using data collected over a 4-year period ( ). Groth rates beteen stocks did not differ hen confidence limits ere taken into account. Mean age of the harvested portion of the stocks fluctuated yearly. The only stocks to exhibit a mean age of 1.5 to 2. years greater than the mean age of first maturity ere in the Keeena and Marquette areas. The mean age of first maturity as found to be 5.2 years for all stocks. Total instantaneous mortality rates ranged from.37 in the Marquette stock to.84 in the Brimley stock. Estimates of optimum yield ere made for all stocks utilizing a modified Beverton and Holt model. An optimum instantaneous fishing rate of.23 as recommended for all Lake Superior hitefish stocks. Commercial production of hitefish has averaged over 725, pounds during the last 6 years from these stocks. The recommended harvest level for all stocks combined as 573, pounds. Decreases in exploitation rates ere recommended for the Munising, Whitefish Point, and Brimley stocks hile increases ere recommended for the Keeena, Marquette, and Grand Marais stocks.

4 3 Introduction Lake hitefish (Coregonus clupeaformis) are the most valuable and most sought after commercial species in the upper Great Lakes. This species is not only one of the most sensitive to exploitation but has the reputation of being one of the most resilient after depletion (Smith 1972). Gill nets, trap nets, and pound nets have all been used extensively to harvest hitefish in the past. Today the bulk of hitefish landings from Michigan aters of Lake Superior come from large mesh trap nets, except in the Whitefish Bay area here an active Indian Treaty fishery utilizes large mesh gill nets. The objective of this study as to estimate population and fishery statistics for six stocks of Lake Superior hitefish and to use these estimates to develop harvest levels for the individual stocks. Data collected over a 4- year period ( ) on each of six stocks studied ere used to calculate the harvest levels. Methods Over 7,5 legal-size (17 inches or larger) hitefish from six commercial trap-net locations at Keeena, Marquette, Munising, Grand Marais, Whitefish Point, and Brimley ere sampled during (Fig. 1). In 1977 and 1978, total length and scale samples ere obtained for 2 fish in the spring and 2 fish in the fall at each location. Also, during 1978 sex and maturity data ere obtained from each fish. In 1979 and 198 sampling as done by commercial fishermen during to periods, spring through early summer and fall. During each period, at each location, a maximum of 5 net-run fish ere scale sampled and all fish ere measured from five eekly trap net lifts. In 1981, graded mesh (1.5- to 6-inch stretch} gill net as used by the Marquette Great Lakes Station cre at

5 4 Whitefish Point and Munising to sample age groups not recruited to the trap net fishery. A total of 112 hitefish, ranging in age from one to four, ere measured and scale sampled. All scales collected ere aged. Commercial production Results and Discussion Commercial landings of hitefish in Michigan aters of Lake Superior over the last 6 years ( ) have averaged over 725, pounds. Historical records shoed that landings averaged 364, pounds from Michigan aters of Lake Superior during the period before heavy lamprey infestation ( ). During the past decade, Michigan's licensed commercial fishermen (non-treaty fishermen) have landed an average of 452, pounds each year from Lake Superior. Yield has steadily increased hen recent and historical catches are compared. Most lake hitefish stocks in Lake Superior become fully vulnerable to the trap net fishery (4.5- to 4.7-inch stretch mesh) at age five at a mean total length of 19.8 inches. Eshenroder (198) found that hitefish in northern Lake Huron ere fully vulnerable to the trap net fishery at a length of 19.3 inches. Catch statistics from the various hitefish stocks studied on Lake Superior are presented in Table 1. Catches have generally increased through the 6-year period on all stocks, except at Marquette hich has been fairly stable and at Munising here a decline has taken place. Negative trends in catch per unit of effort (CPE) through time (Table 2) ere noted for the Marquette, Munising, Whitefish Point, and Brimley stocks, but only the trends at Marquette and Munising ere significant (P <.5). A positive trend in effort through time as noted for Marquette (P <.5) hile effort has remained at a relatively constant level at Munising. The fact that CPE

6 5 has declined in recent years at Munising hile effort has remained stable indicates that abundance has declined. At Marquette, CPE has declined and effort has increased. Therefore, from these data, it is not clear hether stock abundance in the Marquette area is declining or remaining stable. From 1975 through 198, CPE generally increased at the Keeena. This probably does not reflect an increase in abundance but only that a ne fisherman is becoming knoledgeable about his area and more efficient in using his gear. As fishermen enter into a ne fishery, such as the trap net fishery, it may take several years for them to become proficient in using the ne gear and to locate productive netting sites. Experience has shon that a ne fisherman's CPE ill increase for a number of years and then level off. The CPE data from the Keeena stock are a good example of this. Catch per unit effort for the Grand Marais stock increased rapidly from 1977 to 1979 then declined through Part of the increase can be attributed to a ne fisherman in a ne fishery. Hoever, suspected inaccuracies in daily catch reports for 1979 and 198 make any conclusions about stock abundance here questionable. Groth Mean size at age varied slightly among hitefish collected from trap nets at the six locations (Table 3). Spring data ere used to calculate groth at all areas except Munising and Brimley. At these areas some spring samples ere not obtained, so fall data ere used. Some unknon amount of disparity is created then by comparing mean size at age calculations beteen areas. When confidence limits are taken into account, there is little difference beteen stocks in mean size at age for the fully vulnerable age groups.

7 6 Mean length at age data for pre-recruited age groups of lake hitefish are presented in Table 4. These fish ere collected from the Munising and Whitefish Point stocks. Due to the small sample size, the data ere combined and a eighted mean length as calculated. Since differences in groth beteen stocks ere slight, eighted lakeide mean lengths for each age group ere calculated (Table 3). These mean lengths at age, along ith those noted for the pre-recruits, ere utilized in a FORTRAN program of the folloing von Bertalanffy groth equation (Rafail 1973): L = L [1. - e -k(x-xo)) here: L = length at age L = theoretical asymptotic length in inches k = groth coefficient x = theoretical age hen length is zero x = age The predicted groth curve and the observed mean lengths are very similar for fully vulnerable age groups (Fig. 2). Somehat larger variation beteen the predicted and observed occurs ith age groups one through four. This variation can probably be attributed to the small sample size of the pre-recruits. Healey (1975) summarized hitefish groth rates from various exploited and unexploited populations. He found that the rate of groth increased ith increased intensity of exploitation. Although some Lake Superior stocks are fished much heavier than others, for example, five times the fishing effort is expended on the Whitefish Point stock than on the Keeena stock (Table 2), differences in mean size at age are slight. These slight differences in groth rates could be attributed to other factors such as the availability of suitable habitat for each stock. Dryer (1963) studied hitefish from the Marquette, Whitefish Point, and Brimley areas during the mid to late 195's. Differences in mean size at age ere slight hen

8 7 Dryer's data ere compared to this study's data for Marquette and Whitefish Point. At Brimley, Dryer's fish ere shorter 1n total length. In addition, Dryer reported that groth rates from the Brimley stock ere sloer than those at Marquette or Whitefish Point. Dryer did not report confidence limits for his data and therefore these differences may be only apparent. Mean age and maturity Mean age of the catch varied by sampling year and stock, ranging from 4.5 to 8.4 years (Table 5). Mean age as calculated by the formula A= (a 1 k 1 + a 2 k2 +.. ai ki)/n. Where A is the mean age, a 1. ai are the ages of fish in the catch, k 1.. ki are the numbers of fish in each respective age group and "n" is the total number of fish in the sample. The mean age of the catch generally decreased from est (Keeena) to east ith the younger ages found in the Whitefish Bay stocks (Whitefish Point and Brimley). Maturity data ere collected during 1978 from all six stocks and ere combined into a lakeide sample (Table 6). No beteen stock analysis as conducted. Sex ratio of the lakeide sample as 49% male and 51% female. The mean age of first maturity for the sexes combined as 5.2 years. This as calculated utilizing the formula M = (a 1 m 1 +a 2 m2 +.. ai mi)/1. Where Mis the mean age of first maturity, a 1... ai are the ages of fish in the catch and m 1.. mi are the percentages of nely mature fish in each respective age group. Maccallum (198) investigated lake hitefish populations in eastern Lake Superior. He found the mean age of maturity to be 5 years. In addition, Maccallum reported the mean ages of the commercial catch ere 5.6 for males and 5.5 for females in 1978 samples taken near Gros Cap, Whitefish Bay. The lo mean ages of the Whitefish Point and Brimley stocks are not surprising hen one considers that

9 8 yields have been over 3, pounds annually from these areas since As catch increases, mean ages decrease. This again is probably hy mean ages generally decrease from est to east, since catch and effort generally increase in that direction. Abrosov (1969) investigated the relationship beteen yields, mean age of first maturity, and mean age of the catch. His analysis of several populations of hitefish suggested that a difference of 1.5 to 2. years beteen the to mean ages ould be optimal. Cristie and Regier (1972) supported this idea and suggested that lake hitefish be alloed to span 1.5 times in order for the population to maintain itself. When Abrosov's (1969) theory is applied to Lake Superior hitefish stocks, the mean age of the catch should range from 6.7 to 7.2 years. Only the Keeena and Marquette stocks fall into this range (Table 5). Although mean ages of the catch are somehat lo for the Munising and Grand Marais stocks, they rebounded during 198. Hoever, the lo mean age statistics for the Whitefish Point and Brimley stocks are cause for concern. Mortality Total instantaneous mortality rates (Z) ere calculated for the six stocks of lake hitefish from catch curves in hich the geometric means of percentage age frequency (y) ere related to age (x) (Ricker 1975). A semi-logarithmic relationship as used such that ln (y) =a+ bx. The slope (b) represents the total instantaneous mortality (Z) of the fully vulnerable portion of the stock. These instantaneous rates can be converted to annual or seasonal total mortality (A) according to Ricker (1975). Individual mortality relationships for each stock are contained in the Appendix, Figures 1 through 6. Instantaneous total mortality, annual total mortality rates,

10 9 and coefficients of determination for the regression for each stock are presented in Table 7. Annual total mortality for the fully vulnerable portion of the stocks ranged from 31% at Marquette to 57% at Brimley. These rates correspond ell ith the catch statistics presented in Table 1; here catches are large, the corresponding survival rates are lo, and total mortality is high. Once the total mortality has been determined for a stock, the question arises as to hat portion of total annual mortality is due to natural causes and hat portion can be attributed to fishing. Conclusive information about natural mortality rates of Lake Superior hitefish does not exist. Rybicki (198) reported a 36% natural mortality rate for an unexploited stock of lake hitefish in Grand Traverse Bay, Lake Michigan. He used fish obtained from graded mesh gill net samples hich ranged in age from six to thirteen. Cucin and Regier (1965) reported a natural mortality rate of 25.4%, in the absence of fishing, for Lake Huron hitefish ranging in age from four through eight. These same authors felt a natural mortality rate of 34% as a more realistic value for Lake Huron hitefish. The loest total mortality rate for the Lake Superior stocks studied as noted at Marquette. This rate of 31% total mortality is loer than the 34% or 36% natural mortality rates reported for lakes Huron or Michigan hitefish. The natural mortality rate for the fully vulnerable stocks (age 5 and greater) of Lake Superior hitefish is probably around 2 to 25%. The fact that groth rates are much sloer in Lake Superior than Huron or Michigan also lends credence to the belief that natural mortality rates are loer in Lake Superior stocks. Ricker (1949) reported a mean natural mortality rate of 18% for a slo-groing unexploited population of hitefish in Shakespear Island Lake, Ontario.

11 1 Estimates of optimum yield Estimates of optimum yield ere made for all stocks utilizing a FORTRAN program of the Beverton and Holt (1957) model. This dynamic pool model eighs the parameters of groth against the instantaneous natural and fishing mortality rates for the purpose of predicting the best level of exploitation. The model has been slightly modified from the standard Beverton and Holt model in three ays. First, it uses the von Bertalanffy parameters (Fig. 2) of groth in length rather than groth in eight and it converts length to eight for yield computations by using the length-eight regression coefficients. The length-eight relationship reported by Dryer (1963) of: ln(w) = ln (L) as used for all stocks. 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. These changes ere suggested by Tyler and Gallucci (198) and are described in detail in Clark and Huang (1983). It as assumed that all hitefish over 17 inches in total length ere equally recruited to the fishery. This corresponds to an age of entry of 4.1 years. The combined data of the von Bertalanffy groth curve (Fig. 2) ere used as model input because no groth differences ere found beteen the stocks. Since precise natural mortality rates of Lake Superior hitefish populations are not knon, yield estimates ere made for three alternative rates. These ere rates of 2, 22, and 25% natural mortality. In this ay, three alternative yield estimates for each individual stock could be compared ith other data, such as historical catches, and recommended harvest levels could be decided upon.

12 1 1 Yield-per-recruit analyses for each of the three alternative natural mortality rates ere used to ascertain optimum fishing rates. This as accomplished by plotting yield-per-recruit against the corresponding instantaneous rate of fishing (F). From this, the optimum rate of fishing mortality (Fopt) and the maximum rate of fishing mortality (Fmax) ere determined. Fmax is the rate of F hich corresponds to the peak of the yield-per-recruit curve (Fig. 3). Fopt is the rate of F hich corresponds to one-tenth of the slope of the yieldper-recruit curve here F equals zero (Fig. 3). This method of determining an optimum fishing rate has been idely used as a target fishing mortality rate for major commercial fisheries of the North Atlantic (Sissenine 1981, Gulland and Boerema 1973). There is an economic basis for maintaining the fishing mortality rate belo (Fmax). Fishing mortality corresponds to fishing effort and revenue is related to catch so the additional units of fishing effort hen F is near Fmax produce only very slight increases in revenue. Clearly, from any practical viepoint, it ould be undesirable to increase the amount of fishing beyond the level at hich the value of the marginal yield is small compared ith the costs of the extra units of effort required to produce that yield (Gulland and Boerema 1973). Yield-per-recruit curves for the three natural mortality rates are presented in Figures 4 through 6. The resulting optimum instantaneous rates of fishing ere.23 for the 2 and 22% natural mortality rates and.33 for the 25% natural mortality rate (Table 8). Fopt as solved for by approximating the tangents to the yield-per-recruit curve (Fig. 3) at F and F 1 using linear regression. To sets of coordinates near F ere arbitrarily chosen and the slope of the line through those points as determined. Then, by trial and error, a tangent to the curve as found that had a slope one-tenth of the slope found at F. The point at

13 12 hich that line on tangent (F 1) intercepts the yield-perrecruit curve is equal to Fopt Biomass and optimum yield estimates ere made utilizing the optimum fishing rates for each stock at each alternative natural mortality rate (Table 9). Average annual biomass (B) is equal to Yc/F (Rybicki 198) here Ye is the average commercial yield for and Fis the instantaneous fishing rate determined by the relation Z = M + F (Ricker 1975). Optimum yield (Yopt) estimates ere determined by substituting Fopt for Fin the biomass equation. Optimum yield estimates for all stocks combined ranged from 56,76 pounds for the 2% natural mortality rate (M=.22) to 1,87,788 pounds for the 25% natural mortality rate (M=.3) (Table 8). Historical catch records indicate that landings averaged 364, pounds from Michigan aters of Lake Superior from , the period before heavy lamprey infestation. Since 1929, hen a catch reporting system as introduced for Michigan licensed commercial fishermen, annual catches only exceeded 6, pounds on one occasion. Therefore, the yield estimate of over one million pounds for the 25% natural mortality rate seems unreasonably high. Very little insight is gained by analyzing historical catches by individual stock. Some stocks, such as those at the Keeena, Marquette, and Grand Marais areas, have never been heavily fished consistently. Only the stocks in the Whitefish Bay (Whitefish Point and Brimley stocks) fit this criterion. The historical record indicates that landings for these stocks average 178, pounds annually from This figure is very similar to the optimum yield estimate of 176,69 pounds for the Whitefish Point and Brimley stocks utilizing the 22% natural mortality rate.

14 13 Management recommendations The estimates of optimum yield for the 2 and 22% natural mortality rates are very similar. The yield estimates for the 22% natural mortality alternative are judged to be the most satisfactory. Recommended harvest levels for the six stocks of hitefish studied are presented in Table 1. Increases in exploitation rates are recommended for the Keeena, Marquette, and Grand Marais stocks. Decreases in exploitation are recommended for the Munising, Whitefish Point, and Brimley stocks. The recommended harvest (Yr) levels developed from the optimum yields (Yopt) in Table 9 are for the short term. As the average biomass (B) of the stocks change so ill the corresponding optimum yields. Theoretically, ith constant rates of fishing and natural mortality, the biomass of each stock ill gradually change along ith the corresponding optimum yield for that stock until some optimum biomass is reached, assuming constant recruitment. Taking this into account, the optimum yields or recommended harvest levels over the long term ill gradually decrease for the Keeena, Marquette, and Grand Marais stocks if Fopt is maintained. This ill occur because the average biomass of each stock ill decrease due to the increase in exploitation. The opposite ill occur over the long term ith the Munising, Whitefish Point, and Brimley stocks. Optimum yields for these stocks should increase gradually over time if Fopt is maintained. The average biomass of these stocks ill increase due to the decrease in exploitation. Particular attention should be paid to the Whitefish Bay stocks at Brimley and Whitefish Point. The recommended harvest level for the entire bay is 177, pounds--91, pounds from the Whitefish Point stock and 86, pounds from the Brimley stock. These recommended yields are

15 14 substantially loer than recent harvest levels. Historical catch records indicate that the recommended harvest levels are in line ith past yields. Mean age of the commercial catches are depressed in these stocks (Table 5). In addition, data reported by Maccallum (198) from the Brimley stock, hich is thought to be mutually shared by Michigan and Canada, indicates heavy overexploitation. Therefore, all of the evidence indicates that the large recommended reduction in harvest levels in Whitefish Bay, especially in the Brimley stock, is arranted. The harvest estimates presented in this paper could be refined further if a precise natural mortality rate as determined for Lake Superior hitefish populations. Therefore, it is recommended that further study on Lake Superior be targeted in this area. Acknoledgements The folloing commercial fishermen helped collect data for this study: Tom Bron, Jr., Willard (Sully) Kauppi, Gerald Moore, Ronald and Ted Thill, Jerome J. VanLandschoot, and Ralph Wilcox. Richard Clark gave valuable assistance on modeling and Richard Schorfhaar lent his support and encouragement for the project.

16 15 Table l. Landings in pounds of lake hitefish from state-licensed and treaty fisheries, Lake Superior, Area and fishery Average Keeena State 38,17 34,39 19,23 27,424 55, ,623 Treaty a 3,5 4,2 8,4 3,3 4, 8,745 Marguette State 62,68 6, ,236 55,268 64,164 7,634 Treaty 4,314 59,19 Munising State 233, ,115 23,999 26, ,675 18,86 228,925 Treaty 43,7 35,6 36, 43,8 27,394 64,6 Grand Marais State 1, 341 2,17 3,44 5, , ,31 Treaty 4,5 4, 4, 4,4 48,358 55,7 46,733 Whitefish Pt. State 42,939 21, ,3 52,81 89, , ,81 Treaty 79, 16 4,4 71,4 12,6 78,636 74,2 Brimle~ State 113,555 79,8 7,34 15,456 17,153 46,463 22,845 Treaty 118,74 6,6 17, 1 153,9 117, ,8 a Treaty catches for are estimates based on state holesale reports; catches for are from U.S. Department of Interior (1981).

17 16 Table 2. Catch per unit of effort (pounds per lift) and effort (number of lifts) for lake hitefish caught in trap nets, Lake Superior, Area Keeena Catch/effort Effort Marquette Catch/effort Effort Munising Catch/effort Effort Grand Marais Catch/effort Effort Whitefish Pt. Catch/effort Effort Brimley Catch/effort Effort

18 17 Table 3, Mean total length in inches (ith 95% confidence I imits in parentheses) and number in sample by age group for lake hitefish collected from trap nets in Lake Superior. (S = spring-summer and F = fa 11). Area Age Keeena (S) Mean total length 19, (. 17) (. 15) (. 13) (. 21) (. 21) (. 29) (. 49) Number Marguette (S) Mean total length , (. 15) (. 16) (.16) (. 25) (. 24) (.27) (. 38) Number Munising (F) Mean total length (. 15) (. 3) (. 59) (1. 11) ( 1 34) (. 45) (. 59) Number Grand Marais (S) Mean total length (. 11) (. 2 2) (. 39) (. 3 7) (. 29) (. 35) (. 7 3) Number ]16 Whitefish Pt. (S) Mean total length , (. 3) (.57) (. 88) ( 1 2) (1. 78) (. 96) (. ) Number Brimle~ (F) Mean total length (. 35) (. 48) (. 57) (. 69) ( 1 4) (.66) (. 14) Number l Combined Mean total length (. 19) (. 2 7) (. 35) (. 39) (. 3 7) (. 36) (.37) Number l, 52 1,192 1,169 1,

19 18 Table 4. Mean total length in inches (ith 95% confidence limits in parentheses) and number in sample by age group for lake hitefish collected ith graded mesh gill nets in Lake Superior, June 1981 Age Mean total length 5. 1 (.43) 9. 1 ( 1 ) 13. (. 32) Number (.62) 83 Table 5. Mean age of the commercial catch of lake hitefish, Lake Superior, Area Year Average Keeena Marquette Munising Grand Marais Whitefish Pt Brimley a a From Williamson, Liston, and Bohr (1981).

20 19 Table 6. Percentage of mature lake hitefish by age group, Lake Superior, Sexes Age Male Females combined _ Table 7. Instantaneous total mortality (Z), annual total mortality (A) as a percent and coefficients of determination (R 2 ) for catch curve analysis of six stocks of lake hitefish, Lake Superior, Area z A R2 Keeena Marquette Munising Grand Marais Whitefish Pt Brimley

21 2 Table 8. Corresponding natural mortality (m) as a percent and instantaneous rates of natural mortality (M), optimum fishing (Fopt) and maximum fishing (Fmax> for lake hitefish populations in Lake Superior. m M Fmax

22 21 Table 9. Optimum yield estimates at three levels of natural mortality for lake hitefish stocks in Lake Superior. (Y = average catch in pounds , Z = total instantaneou~ mortality, M = instantaneous natural mortality, F = instantaneous fishing mortality, B = average biomass in pounds, F t = optimum instantaneous fishing mortality and Y t = op optimum yield in pounds.) op Area z M F B F opt y opt Natural mortality (m) = 2% Keeena 4, Marquette 59,19.37 Munising 228, Grand Marais 46, Whitefish Pt. 133,81.59 Brimley 22,845 o O , ,46 654,71 245, , , , 153 9,495 15,436 56,571 83,179 81,926 Total 56,76 Natural mortality (m) = 22% Keeena 4, Marquette 59,19.37 Munising 228, Grand Marais 46, Whitefish Pt. 133,81.59 Brimley 22,845 o , , ,39 292,81 393, , , , ,539 67,178 9,518 86,91 Total 572,957 Natural mortality (m) = 25% Keeena 4, Marquette 59,19.37 Munising 228, Grand Marais 46, Whitefish Pt. 133,81.59 Brimley 22, ,17 843, ,87 424, ,413 48, , , ,797 14, , ,96 Total l, 87, 788

23 22 Table 1. Recommended harvest (Yr) in pounds and current (Uc) and optimum (Uopt) exploitation rates in percent for lake hitefish stocks in Lake Superior. Area Yr Uc opt Percent change Keeena 52, Marquette 113, Munising 165, Grand Marais 67, Whitefish Pt. 91, Brimley 86,

24 23 \ Keeena ~- Grand /1(orois 2 V ' ';...-: )! ~ Whilef~ Poir,t / Marque! te 1. Brirr:!ey Munising Figure 1.---Lake hitefish sampling areas in Lake Supedor.

25 _J en 25 I () z z 2 :c I- (!) z 15 _J _J <( ro r- I- z <( 5 :2E L = 32.3 [ 1. - e ( X ~ II AGE (x) Figure 2.--Fitted von Bertalanffy curve and empirical mean length-age relationship ith 95% confidence limits for lake hitefish, Lake Superior,

26 25 I => :: (.) :: F O._.:._I ---:---- :: a.. _J >- FISHING MORTALITY Figure 3.--Example of a yield-per-recruit curve: F is a line tangent to the yield curve at a fishing rate of O and F. 1 is a line tangent to the curve here the slope is.1 at the line F The tangent point of line F. 1 indicates optimum yield and rate of fishing Fopt indicates maximum yield. Fmax

27 26 - i:, "' C ::, a. -en 1- ::J : (.) : ::: a F. 1 F.1 _J > ~ INSTANTANEOUS RATE OF FISHING Figure 4.--Yield-per-recruit curve for a lake hitefish population in Lake Superior having a 2% natural mortality rate (M=.23).

28 27 -(/) "O 5 C ::, Q. - F. Cl).._ 4.. ::, ::: (.) ::: ' ::: a.. 1 C) Fopt _J > INSTANTANEOUS RATE OF FISHING Fmax Figure 5.--Yield-per-recruit curve for a lake hitefish population in Lake Superior having a 22% natural mortality rate (M=.25).

29 28,:, 5 C ::, c.. -Cl) 4... :::> :: (.) a::: O 3 a::: a Fo. ~-1... Cl _J -, Fopt >- o o~ , ~-----~r--j L-----r '- INSTANTANEOUS RATE OF FISHING Figure 6.--Yield-per-recruit curve for a lake hitefish population in Lake Superior having a 25% natural mortality rate (M=.3).

30 29 Literature Cited Abrosov, u. N Determination of commercial turnover time in natural bodies of ater. Journal of Ichthyology 9: Beverton, R. J. H., and S. J. Holt On the dynamics of exploited fish populations. United Kingdom Ministry Agriculture Fisheries. Fisheries Investigations (ser. 2) 19. Clark, R. D., Jr., and B. Huang The dynamics of competition beteen sport and commercial fishing: Effects on rehabilitation of lake trout in Lake Michigan. Michigan Department of Natural Resources, Fisheries Research Report 199. Ann Arbor, Michigan, USA. Cristie,. M., and H. A. Regier Temperature as a major factor influencing reproductive success of fish--to examples. In B.B. Parris (ed.) International Symposium on--gtock and Recruitment. Cucin, D., and H. A. Regier Dynamics and exploitation of lake hitefish in southern Georgian Bay. Journal of the Fisheries Research Board of Canada 23: Dryer,. R Age and groth of the hitefish in Lake Superior. Fishery Bulletin 63: Eshenroder, R. L Selectivity of deep trap nets for lake hitefish, Coregonus clupeaformis. Michigan Department of Natural Resources, CFRD Project No R. Gulland, J. A., and L. K. Boerema Scientific advice on catch levels. Fishery Bulletin 71: Healey, M. C Dynamics of exploited hitefish populations and their management ith special reference to the Northest Territories. Journal of the Fisheries Research Board of Canada. 32: Maccallum, W A revie of the eastern Lake Superior hitefish populations (unpublished manuscript). Rafail, s. z A simple fitting a von Bertalanffy Biology 19: and precise method for groth curve. Marine

31 3 Ricker,. E Mortality rates in some exploited populations of fresh-ater Transactions of the American Fisheries 77: littlefishes. Society Ricker,. E Computation and interpretation of biological statistics of fish populations. Bulletins of the Fisheries Research Board of Canada Bulletin 191. Rybicki, R Assessment of lake hitefish populations in northern Lake Michigan. Michigan Department of Natural Resources. Final Program Report for CFRD (PL 88-39). Sissenine, M. P An fish stock assessment. overvie of some methods of Fisheries 6: Smith, S. H Factors of ecological succession in oligotrophic fish communities of the Laurentian Great Lakes. Journal of the Fisheries Research Board of Canada 29: Tyler, A. v., and v. F. Gallucci Dynamics of fished stocks. Pages in R. T. Lackey and L.A. Neilsen, editors. Fisheries Management. John Wiley and Sons, Ne York, Ne York, USA. U. S. Department of Interior Status of the fishery resource A report by the Tripartite Technical Working Group on the assessment of major fish stocks in the treaty - ceded aters of the Upper Great Lakes: State of Michigan, September 3, Willaimson, R. P., C.R. Liston, and J. Bohr Age, length, and catch per effort of lake hitefish (Coregonus clupeaformis) from commercial trap nets in Whitefish Bay, Lake Superior. Michigan State University. (unpublished manuscript). Report approved by W. C. Latta Typed by G. M. Zurek

32 31 APPENDIX

33 > I- z 2.5 LLJ (.) a:: LLJ a.. 2. Q) (!)...J Log 8 (y) = ( x) r2 = o II AGE (x) 12 Figure 1.--Natural logarithm of percent age composition of lake hitefish (17 inches or larger) in trap nets at Keeena, Each point is a geometric mean of to observations.

34 ~ ~ 2.5 z (.) o:: 2. a.. (!)O) 1.5 _J 1. Loge(y) = (x) r 2 = AGE (x) 12 Figure 2.--Natural logarithm of percent age composition of lake hitefish (17 inches or larger) in trap nets at Marquette, Each point is a geometric mean of three observations.

35 I- 1.5 z (.) :: 1. Cl. Q.>.5 (!)..J Log (y)= (x) -.5 r2 = o AGE ( X ) 12 Figure 3.--Natural logarithm of percent age composition of lake hitefish (17 inches or larger) in trap nets at Munising, Each point is a geometric mean of three observations.

36 ~ I- 2.5 z (.) a: 2. a.. Q) 1.5 (.!) _J 1. Loge(y)= (x).5 r2 = o , ,------, r ,.-----q AGE (x) Figure 4.--Natural logarithm of percent age composition of hitefish (17 inches or larger) in trap nets at Grand Marais, Each point is a geometric mean of three observations.

37 O ~ 2. z (.) a::: 1.5 a.. Q) 1. (!) _J.5 Log 9 (y) = (x) r 2 =.96 -o.5..._...-,---r----., ,-----, II AGE (x) 12 Figure 5.--Natural logarithm of percent age composition of lake hitefish (17 inches or larger) in trap nets at Whitefish Point, Each point is a geometric mean of four observations.

38 >. t- z IJ.I a: IJ.I a.. Cl) (!) _J Log 8 ( y) = ( x) -1.5 r 2 = o r-----r-----r-----,,-----,---~ j~ II AGE (x) Figure 6.--Natural logarithm of percent age composition of lake hitefish (17 inches or larger) in trap nets at Brimley, Each point is a geometric mean of four observations. The 1979 and 198 data are from Williamson, Liston, and Bohr (1981).