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T. . . “.va . . . , _ _o.v .. . . ...:... . ”r1.“ 2 ....., ....,.. . . . . . . . ... . ... . . r. .r. .. ......_. .... . ._......_. ... ...... .. ..._.....,........ _.._......_.L.........‘5” c.........1.~'m_......sa ... friarmfir, v.1.....fi.¢r~.~oa:mfl.zTr. .. $41 . ‘ nuuuu 11111111111 11/... 3291008084190 i LIBRARY [ Michigan State ,1: University ' ' ABSTRACT MULTIPLE REGRESSION ANALYSIS OF YELLOW PERCH YIELDS NEAR THE LUDINGTON PUMPED-STORAGE RESERVOIR BY David J. Lechel This investigation determined the parameters that affect the concentration and the activity patterns of adult, yellow perch. Yellow perch were collected by gill net at six sampling sites during 1973 in the inshore Lake Michigan waters near the Ludington Pumped-Storage Power Plant. The yield was examined by a step-wise deletion multiple regres— sion program that utilized climatic and water condition parameters and gonadal development. The independent climatic variables are barometric pressure, wind direction and velocity, and air temperature. Water condition parameters include water temperature, light penetration, and turbidity. Factors that affect gonadal develOpment and spawning, such as photOperiod and the gonad: body weight ratio, were also incorporated in the regressions. The results show that the independent variables explain 77 to 99 percent of the variation in yield of males, and 45 to 95 percent of the variation in yield of female yellow perch. 0% David J. Lechel The information reveals the importance of baro- “first. ( L0 metric pressure at the stations most affected by the power plant. The male and female yield response to barometric pressure was quite different. Complex climatic interre- lationships that influence activity were prevalent at all sampling sites. Photoperiod and water temperature are significant as they may affect seasonal migration patterns. Depth, although not an independent variable, is important. MULTIPLE REGRESSION ANALYSIS OF YELLOW PERCH YIELDS NEAR THE LUDINGTON PUMPED-STORAGE RESERVOIR BY David J: Lechel A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Fisheries and Wildlife 1974 ACKNOWLEDGMENTS I would like to thank the Department of Fisheries and Wildlife, Michigan State University, for providing the research project and Consumers Power Company for the funds with which to carry out this project. I also wish to thank Dr. Peter Tack, Dr. Eugene Roelofs, and Dr. Charles Liston for their efforts and guid- ance in preparing this thesis and in meeting the require- ments of the Master of Science degree. A special thanks is extended to Dr. John Gill for his advice and help with the statistical portion of this research. I am indebted to my fellow graduate students; John Armstrong, Walter Duffy, Fredrick Bauer and Gregory Olson, for their aid in collecting data and for their continual ability to help ease the burden of research in Ludington, Michigan. I am greatly appreciative of Richard W. and Kathrine E., without their existence, this would not have been possi— ble. ii TABLE OF CONTENTS Page LIST OF TABLES O O 0 O 0 O O O O O O 0 iv INTRODUCTION . . . . . . . . . . . . . 1 DESCRIPTION OF SAMPLING AREA . . . . . . . . 3 MATERIALS AND METHODS . . . . . . . . . . 8 RESULTS . . . . . . . . . . . . . . . 16 Males . . . . . . . . . . . . . 16 Females . . . . . . . . . . . . . 25 DISCUSSION . . . . . . . . . . . . . . 33 Males . . . . . . . . . . . . . 33 Station One . . . . . . . . . . . 33 Station Two . . . . . . . . . . . 34 Station Three . . . . . . . . . . 36 Station Four . . . . . . . . . . 37 Station Five . . . . . . . . . . 37 Station Six . . . . . . . . . . . 38 Females . . . . . . . . . . A. . . 40 Station One . . . . . . . . . . . 40 Station Two . . . . . . . . . . . 41 Station Three . . . . . . . . . . 41 Station Four . . . . . . . . . . 42 Stations Five and Six . . . . . . . 43 SUMMARY . . . . . . . . . . . . . . . 46 LITERATURE CITED . . . . . . . . . . . . 49 iii Table l. 10. 11. LIST OF TABLES Location of sampling sites, their depths and bottom sediment description . . . . . Parameters measured to compute regression equations . . . . . . . . . . . Variable names assigned to the recorded para- meters . O O O O O O O O O O O O The 1973 yield of male yellow perch at each of six stations . . . . . . . . . The proportion of variance explained by the best predictive equation (R2), for male yellow perch at each of six stations . . The significant variable names, the para- meters they represent, the regression coeffi- cients and their standard errors for each variable in the predictive equations for male yellow perch at six stations . . . . Predictive equations and the minimum stand- are error of the estimate for the yield of male yellow perch . . . . . . _. . . Results of t-tests for HzBA=BB . . . . . The 1973 yield of female yellow perch at each of six stations . . . . . . . . . . The proportion of variance explained by the best predictive equation (R2), for female yellow perch at each of six stations . . The significant variable names, the para- meters they represent, the regression coeffi- cients and their standard errors for each variable in the predictive equations for female perch at six stations . . . . . iv Page ll 17 18 19 24 26 27 28 29 Table Page 12. Predictive equations, the minimum standard error of the estimate for the yield of female yellow perch at six stations . . . . . . 32 INTRODUCTION The demand for electrical energy is accelerating. Coupled with this growing demand is a change from conven- tional fossil fuel generating plants to nuclear power plants and large pumped-storage reservoirs. Each new power gener— ating facility is required by the Federal government to conduct a pre and post-operational environmental impact study. Michigan State University, Department of Fisheries and Wildlife, contracted with Consumer Powers and Detroit Edison Companies in 1971 to evaluate the effects of the Ludington Pumped-Storage Power Plant on the fish, physical- chemical conditions, benthic and plankton pOpulations of an inshore area of Lake Michigan. Questions under study relating to local fish species include: 1. Do the currents produced by the power plant attract or repel or in some other fashion affect the concen- trations of fish species near the plant? 2. Do the pumping and generating modes physically harm individual fish through mechanical damage or pressure change? 3. What are the effects of fish entrainment in the reservoir? This research represents an attempt to answer questions about fish concentration and movement in Lake Michigan, by using multiple regression analysis. Use of multiple regression analysis by fisheries biologists has been minimal and of a limited nature. Gen- erally, few independent variables are chosen and these are linear variables only. Walburg (1972) used four independent variables to examine sauger year class strength. Lewis (1969) attempted to explain the number of trout per stream pool using seven independent variables. A more comprehen- sive study related amphipod numbers to ten linear variables and one quadratic variable (Alley, 1968). This investigation has utilized various climatic parameters, water condition variables and factors that affect gonadal deve10pment to explain the numbers of fish and their movements near the power plant. Yellow perch, Perca flavescens, (Mitchill) was chosen for study because of its importance as a sports fish and its localized abund- ance. The ultimate goal is to determine under what condi- tions yellow perch were most affected by the Ludington Pumped-Storage Reservoir. DESCRIPTION OF SAMPLING AREA The inshore sampling area of Lake Michigan was 6.4 km (4.0 mi) south of Ludington, Michigan, adjacent to the ‘pumped-storage hydro-electric plant (Figure 1). Station one was 4.8 km (3 mi) south of the breakwall (Table 1). Station one served as the control station as this site was considered to be unaffected by currents from the power plant. Station two was 1.6 km (1 mi) south-southeast of the south- ern jetty. Station three was .8 km (.5 mi) south of the breakwall. Station four was about 2.4 km (1.5 mi) west- southwest of the breakwall. Station five was .8 km (.5 mi) north-northwest of the breakwall. Station six was 1.6 km (1 mi) north of the northern jetty. Sampling station depths and bottom sediment composition are shown (Table 1). These stations were chosen so as to gauge the magni- tude of the effects of the currents created by the pumping and generating cycles of the power plant. Current velocities and directions were not obtained for 1973. Although current velocities were not measured, they have been calculated to be about .7m/sec (2.3 ft./sec) between the jetties when all six units are generating (Liston and Tack, 1973). The volume Figure l.--Map and location of sampling sites near the Consumers Power Pumped-Storage Reservoir. W/ ON’ PIrI Marquette Lao 00000 oooooo ccccccc nnnnnnn ooooooo 0000000 IIIIIIII oooooooo 000000000 ccccccccc IIIIIIIIII oooooooooo oooooooooo ooooooooooo nnnnnnnnnnn cccccccccccc llllllllllll nnnnnnnnnnnnn oooooooooooo 0000000000000 nnnnnnnnnnnn ooooooooooooo ‘- IIIIIIIIIIIII nnnnnnnnnnnnn IIII oooooooooooo cccccccccccccccc IIII ................... I II I 7". IIIIIIIIIII aaaaaaaaaaa nnnnnnnnnnn oooooooooo ooooooooooo nnnnnnnnnn oooooooooo ooooooooo 000000000 ......... oooooooo oooooooo ....... ooooooo cccccc ...... oooooo uuuuuu ccccc uuuuu III. I... IIII III III II II I. II I I. I .0 I I I I I I O I I I I I SAMPLING STATIONS Ludington Pumped Storage Project N L i 3 . Infles R ESE RVOIR A? h..\. '\ C D h E E G _ _ 2‘ Bass d Lake ..... l .whmd .COmHO mxoou .6:~m o =0H .sm 0mm =om .em .me e mxoou .Hm>mum .ocmm «H .mm .sm .mm =o~ .em .me .m uHHm Seaman can seem Sufism em =oo .mm .mm =om .mm .me e Hm>mum .eamm 4H =o~ .sm .mm =m .mm .ms m mama m =om .mm .mm .ms .Nm .me N scam NH =om .sm .om =oo .Hm one H «moms Ase gamma .maoq s .umq z coaumum .coflumflnommc usefiapmm Eouuon cam msumwt sawnu .mmuwm momeEmm mo coaumooqal.a mamas of water will be 75,960 cfs. A more detailed description of the power plant's facilities and the reservoir can be found in Liston and Tack (1973). Since the power plant is located on the eastern side of Lake Michigan, it is constantly exposed to winds from the southwest, west, and northwest. These onshore winds may affect the sampling areas through an increase in tur- bidity, and water column mixing. Also, high water levels eroding large sandy bluffs add large amounts of particulate matter to the water column. These prevailing winds also bring in new weather systems which affect these sampling sites. Prevailing winds are also partially responsible for water temperature change. Continual onshore winds that shift offshore suddenly, due to a passing weather system, push warm epilimnetic waters offshore forcing the cold hypolimnetic waters to the surface. MATERIALS AND METHODS Samples of adult yellow perch (age 3 and greater) were collected using experimental gill nets set on the bottom at each of six stations. Twenty-one 24-hour collec- tions were made between 25 April and 02 October, 1973, at stations 1, 2, 3, 5, and 6, and 20 collections at station 4. The nets were of 25.4 mm (1 in), 50.8 mm (2 in), 63.5 mm (2.5 in), 76.2 mm (3 in), 101.6 mm (4 in), 114.3 mm (4.5 in), 177.8 mm (7 in) stretched nylon mesh. Each mesh size was 50 feet (15.24 m) in length until 10 July. At that time each 50-foot panel was decreased to a 25-foot (7.62 m) panel because of manpower demands in the reservoir. All yields of perch after 10 July were doubled for direct comparison with earlier data. The parameters and units used to compute regression equations are given in Table 2. All parameters were meas- ured and recorded on the day the gill nets were set. Barometric pressure, wind direction and velocity were obtained from the Ludington Coast Guard Station approximately 6.4 km (4 mi) north-northeast of the breakwall. This infor- mation was recorded at 1000 hours for stations 4, 5, and 6 and at 1300 hours for stations 1, 2, and 3. Bottom water 8 TABLE 2.--Parameters measured to compute regression equa- tions. Parameter Units Atmospheric Pressure Inches of Mercury Wind Direction 22 Degree Intervals Wind Velocity Knots Bottom Water Temperature Degrees Celsius Air Temperature Degrees Celsius Photoperiod Hours From Sunrise to Sunset Light Penetration Secchi Disk (meters) Bottom Turbidity Formazon Turbidity Units GonadzBody Weight Ratio temperature was measured with a Yellow Springs Instruments thermistor. Light penetration was measured by a Secchi disk. Turbidity was determined by a Hach turbidimeter. Values for these three parameters were recorded at each station. There- fore, barometric pressure, wind direction, and velocity were constant for stations 4, 5, and 6 and for stations 1, 2, and 3, but water and air temperature, light penetration and turbidity varied from station to station. Sunrise and sunset was recorded for Muskegon, Michigan (430 10' NLat, 860 14' WLong) approximately 89 km (55 mi) south of the breakwall. For the gonad to body weight ratio, a random sample of ten yellow perch was selected from each station. Each fish was weighed, the.gonads were removed.and weighed,_and the 10 ratios were determined. A mean gonad to body weight ratio was then determined for each 24-hour gill net lift by sta- tion. Yields were also determined from this random sample of ten perch. The proportion of males to females was found and then compared to the total yield at that station. The above information was keypunched onto standard Hollerith computer cards and parameters were assigned vari- able names to be entered into the regression equations (Table 3). The parameters were chosen because of their possible effects on the inshore fisheries of this area. The values for similar parameters from 1972 data were graphed against the dependent variable, yellow perch yield, as a preliminary exercise (graphs not shown). In this way relationships con- cerning linearity were established between yield and these various parameters. Interactions were also graphically depicted. The climatic interactions were deemed important in that they influence inshore water temperature, current direction and velocity, turbidity, and food availability. The various gonad:body weight interactions involving water temperature and photoperiod were believed to be important because the inshore areas were used for Spawning by yellow perch (Liston and Tack, 1973). Temperature and daylength have been shown to be determinants of gonad maturation in 11 mx x mx x waumvx mx x Hvxuwwx mx x Avxumvx ox .xmx .a Nx N N V." X N .mxummx qummx hxnmmx mxflhmx Hxnmmx Nxflmmx mxnwmx HNHMNN unavxvumex «Amxvnmmx Nxmxvuamx mxnxvuomx Nxmxvumax mamxvumax Nxmxvuoax mxmxvumax mxaxvueax unmwmz upon "ungowuawx page» nonmm 3oHHmHumax muwoon> oswzumx muwcaauseumx conumuuoama pamequsx musumummsma deumx coaummouonmumx musumummEme umumzumx coauomuao ocazumx whammmnm Owuumfioummuax mfiuma coauomumugH wanes OHDMHUMDO memos Hmocwq .mumumfidumm vmpuoomu on» on cosmflmmm moan: manmwum>ll.m mqmda 12 many species of fishes (Hoover, 1937, Burger, 1939, Kaya and Hasler, 1972, and Burrows, 1958). On the basis of the preliminary graphs, a statisti- cal model was postulated. Preliminary attempts using the control station to utilize this regressional model were abandoned as relationships concerning the graphical linear- ity of the dependent to independent variables had apparently changed from 1972 to 1973. The regressions were calculated using a least squares stepwise deletion program from the Michigan State University Computer Center. In vector notation, the normal equations to be solved are: gfgfisgfy. Solving, one obtains the vector of regression coefficients §?(§T§)-;§'y. The matrix §'§ is symmetric of the form: n X.1 X.2 . . X.k 2 . . x.1 zxil zxélxlz . . . Exilxik X'2 XXilxiz Zx12 X. XX. X 2X2 k 11 ik ik where: n = number of observations X.k = sum of all observations of variable k zxik = sum of squares of independent variable k Exilxik = sum of cross-products of variable 1 and variable k 13 .gfly is a vector of the form: '— 7 where: y. = sum of all observations of the dependent variable zxikYi = sum of cross-product of independent varia- ble k and dependent variable i. By finding the inverse of gig, one can solve for the pre- dicted regression coefficients, fi (Searle,l971). In stepwise deletion regression, the initial least squares equation is obtained using all independent variables available. The least significant variable is deleted and the equation is recalculated. This is continued until cer- tain stOpping criteria are met. Possible criteria include the following: (1) largest significance probability; (2) smallest sequential test—statistic (Fbi); (3) smallest inde- pendent test—statistic (tbi); (4) smallest highest order partial correlation coefficient; (5) the variable that will reduce the square of the multiple correlation coefficient the least; or, (6) the variable that increases the error sum of squares the least (Ruble gt_al., 1969). A five percent significance level was chosen for all tests of significance 14 and as a stOpping criteron. A variable, therefore, was deleted if there was less than ninety-five percent confi- dence that the corresponding regression coefficient was non- zero. Before the equations were calculated the catch data were transformed to more closely approximate the normal dis- tribution. Yields from gill nets are not normally distribu- ted but are probably best represented by a negative binomial distribution (Moyle and Lound, 1960). The negative binomial is best explained by examining the assumptions of its close relative, the Poisson distribution. The Poisson assumes the following: (1) there is a low probability of any given point being occupied; (2) the number of individuals in a sampling unit must be very small compared to the maximum possible: (3) individuals act as a discrete unit; and, (4) the samples must be small compared to the present population (Elliott, 1971). The yields of this study violate assumption number three because yellow perch form schools and cannot be con- sidered a discrete unit (Hasler and Villemonte, 1953). Also, the variance is much greater than the mean and increases with the mean (Elliott, 1971). A transformation of the form, 109 (yield + 0.5) was thought to be adequate. The 0.5 was nec- essary due to zero yields on some dates. . Since thirty variables were being considered, and there were only twenty-one observations for stations 1, 2, 15 3, 5 and 6, and twenty at station 4, only certain variables were entered into deletion regression at a time. For the' first regression run, terms Xl...X3, x5...x9, X14...X16, X18...X22 were entered into the program for both males and females at each of six stations. The terms X23...X27, X29, X35 and X36 were added to the statistically significant variables (5%) for the second run. A third run was used to try to improve the multiple correlation coefficient (R) using all of the quadratic and cross-product terms and a few linear terms that were consistently significant. Variables X41...X45 were then added to the runs which explained the greatest amount of variance of the catch to determine the effect of the addition of the gonad:body weight ratio on the multiple correlation coefficient. The number of variables entered into each regression run was small enough so as not to "overload" the system (as the number of "entered variables" approaches the number of observations, the multiple correlation coefficient reflects this and moves towards unity). After examining the best regression equations, common variables were compared between stations that appeared to be highly similar. Certain stations were alike in depth, thermal stratification, proximity to the plant, sediment composition and yield. Therefore, a two-tailed t-test to compare regres- sion coefficients was performed for the male yellow perch between station pairs 3-5 and 2-6. RESULTS Males The yields of male yellow perch for each station are shown in Table 4. The proportions of variance that are explainable using the best predictive equations are shown in Table 5 as the squares of the multiple correlation coefficients. Sta- tion 1, the control, had the lowest R2, followed in order by stations 4, 6, 3, 5 and 2. The significant variables in each predictive equation and the parameters they represent are shown in Table 6. Table 6 indicates that some variables are common to all sta- tions, whether they are quadratically or linearly related to yield. Barometric pressure was significant at five stations. PhotOperiod, and air and water temperature are also common to some of the stations. The multiple occurrence of interaction terms (X24... X29, X35, X36) indicate the complexity of parameters that affect yield of yellow perch. Table 6 also lists the final significant variables in each predictive equation, their corresponding regression coefficients and standard errors, and the standardized 16 17 TABLE 4.--The 1973 yield of male yellow perch at each of six stations. Station Date 1 2 3 4 5 6 4-25 0 0 0 0 0 0 4-29 0 0 0 0 0 0 5-14 2 51 23 18 8 38 5-19 13 186 68 18 54 55 5-22 46 139 154 24 85 221 5-30 96 413 119 18 43 196 6-06 53 5 6 176 22 11 6-13 78 88 57 174 53 0 6-23 108 54 106 31 19 45 7-09 36 90 149 0 40 20 7-11 0 100 0 — 0 103 7-22 0 41 20 0 0 17 8-12 2 0 4 62 6 0 8-14 50 97 70 0 146 133 8-22 0 80 3 0 125 167 8-25 14 4 34 0 46 34 9-08 18 24 2 0~~ 50 83 9-17 0 60 48 0 17 10 9-26 0 18 74 0 0 10-01 2 0 127 ll 3 10-02 0 2 22 23 0 Total 518 1436 883 744 748 1136 18 TABLE 5.--The pr0portion of variance explained by the best predictive equation (R2), for male yellow perch at each of six stations. % Station 77 99 89 87 93 88 19 m H mm: vo. u Hm.ol oowummouonm x musumummemu Home: omx mm. « mh.ou Hooo. H oooo.ol wusumummfimu kum3 x cowuowuwp wsw3 mmx ma. s eo.H mo. H oo.o muflownusu x coflumuumsmm unqu mmx n.~ « n.ma mo. u oa.o wwsumswmfimu Ham x coHHmmouosm hmx m.m u h.HH| Ho. 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Hmooo.o musumummfimu HmHm3 x coHuomHHU UCHB mmx vH. H mm.o moo. H ma.o mHHUHQHsH x GOHHMHHmcmm uanA mmx o.H H m.m| moo. H vmo.ol musumummfiwu HHm x enammmum OHHHmEonm omx H.H H m.s moo. H mmo.o AoHHeHemseo mHsHmHmasmH HHa me m H me AH. H o~.H loHHmHemseo eoHHmaoHoam me mm H omm H.m H n.mm AOHHmnpwsqv OHDmmmHm OHHHmEonmm wax m H we: o.¢ H H.Nm| oOHHmmouonm mx mm H mom: H Hmmal musmmmum OHHHmEoumm Hx HsmHOHHHOOU HcmHOHmmmoo Hmumfimsmm mEmz UONHUHMUGMHm conmmHmmm mHanHm> m :oHHmHm .wwscHuaOUIl.m mamma 21 L m.H H ~.o No. H mo.o wOHHomouonm x mnsumnwmfimu Hmumz omx v.H H m.m booo. H mHoo.o musumummsmu Hmez x coHHomHHU ost mmx m. H o.Hu mH. H oo.ou HHHoHaHoH x coHHmHHmoma HamHH oNx H.H H o.m boo. H vmo.o OHDHMHOQEOH HHM x whammmum OHHHmEOHmm omx h.H H m.m| mooo. H mooo.o| wusumummfimu HHm x COHHOOHHo UGHB mmx m.H H N.HHI Ho. H no.0: musumummEmu HHm x musumnmmfimu kumz omx hm H No moo. H mNo.o coHHomHHo psH3 x wusmmmum OHHHmEoumm mmx m. H o.H mH. H so.o HoHHmHomseo HHHoHaHse HNx mm. H mn.o mo. H mo.o HOHHMHUMDOV enammmum OHHHmEOme «Hx om H on: em. H H>.o| COHHOOHHG UGHS Nx o cOHHmum h. H v.m| mooo. H vHoo.oa musumummamu Hmum3 x soHHomHHo UQHB mmx NH. H mm.ou so. H NH.o- HHHoHnHoH x coHHmHHmama HaoHH oNx v. H H.NI voo. H mmo.ou musumnmmsmu HHm x UOHHmmouoam ANN o. H m.N mooo. H mHoo.o mHsHmHmosmH HHm x aoHHomHHo ost me o. H m.~ moo. H mHo.o muoumnmmEmH HHm x musumquEwH HmeB vmx m. H o.m| boo. H vvo.o| HOHHmuomsqo >HHOOH¢> ocHB mmx o H NH oo. H Hm.o AoHHmHomseo ooHHmaouoam on mm H hhH o.m H >.m AOHHmuomsqo gnommmum UHHHmEoumm on m. H o.m NH. H H>.o >HHOOHO> UGHB ox o H NH- m.N H H.ou ooHHmmouoaa mx mm H oth H ohm: gunmmmnm UHHHmEoumm Hx HcmHOHmeoo HsmHOHmmmoo Hmumamumm mEmz omNHonccmHm sonmmHmmm mHanHm> m coHHmHm .GODCHHCOUII.© mamdfi 22 coefficients with their standard errors. Standardized coefficients are normalized or unitless regression coeffi- cients found by dividing each coefficient by the standard deviation of the corresponding independent variable (Ruble gt_gl., 1969). They can be used to determine the relative biological importance of each significant variable with respect to the other variables in the equation in propor- tion to their magnitude. Regression coefficients are used in the predictive equations, as they are in the units of the original observations. The standardized coefficients for station 1 indi- cate that the interaction of water temperature and air temperature (X24) was least important in explaining signifi- cant proportions of variation in yield, and the interaction between wind direction and air temperature (X25) was most important. The standardized coefficients at stations 2, 3 and 5 indicate the overriding significance of parameters concerned with barometric pressure (X1, X14). The signifi- cance of many interaction terms at these stations indicates the complexity of parameters that help govern yellow perch activity. Station 4 results include three interaction terms involving air temperature (X24, X26, X27) that are able to explain most of the variation in yield. Quadratic main effects (X14, X16, X18, X21, X22) are also significant. 23 Those indicate that barometric pressure, water temperature, photoperiod, turbidity, and wind velocity are related to yield in a curvilinear manner. Wind direction and the interaction between barometric pressure and wind direction are the major contributors to the explainable variance at station 6. Interactions of those factors (and water temperature) with air temperature (X24, X25, X26) add a portion to the explainable variance. Predictive equations are deve10ped from the signifi- cant regression coefficients (Table 7). The first term in the equation is a constant. This is commonly interpreted as the predicted yield when the independent variables have zero value. To the extent that zero values are not realis- tic, for some variables at least, the constant merely pro- vides a mathematical base. The minimum standard error of the estimate is also shown (Table 7). The minimum standard error is found by extracting the square root of the mean square error from the analysis of variance (Ruble §t_31., 1969). The standard error helps determine the reliability of the predictive ability of the equations. The minimum standard error applies when yield is predicted using aver— age values for all of the independent variables. A two-tailed t-test was used to test for signifi4 cant differences between regression coefficients of variables that were common to certain station pairs. The test-statistic, 24 TABLE 7.--Predictive equations and the minimum standard error of the estimate for the yield of male yellow perch. Minimum Standard Station Predictive Equation Error A * 1 Y = - 1.39 + .61X3 - .010X3X6 + .0015X2X6 .538 .018X1X6 + .022x5X6 - .0017X2X3 2 f = 17117 - 1158x1 + .59x2 + 3.71x3 .195 2 2 2 + 1.15X7 + 19.6X1 + .044X3 + .09X5 2 + .0026X9 - .20X1X2 .026X3X6 - .06X1X6 + .14X5X6 + .60x7X8 - .0004X2X3 - .31X3X5 3 i = 20313 - 1351x1 - 32.1x5 + 22.7xi .404 2 2 + 1.20X5 + .035X6 - .034xlx6 + .13X7X8 + .0009X2X3 - .024X3X5 A 2 2 2 2 4 Y = 22.7 - .04x + .025X + .04x + .06X .520 l 3 5 8 2 + .007X9 - .04X3X6 + .OSXlX6 - .09X5X6 + .04X3x5 H _ _ 2 5 Y - 8568 574x1 8.1x5 + .7lx9 + 9.7x1 .337 2 2 + .31X5 - .044X9 + .013X3X6 + .0013X2X6 - .023X5X6 - .12X7X8 - .0014x2X3 A _ _ _ 2 2 6 Y — 66.7 .71X2 + .05xl + .97X8 + .025X1X2 .494 — .07X3X6 - .0049X2X6 + .054xlX6 - .98X7X8 + .0019X2X3 + .08X3x5 *X X = X for coding purposes only (see Table 3). 3 6 24 25 t = bA-bB//§ (Lee, 1971), has a critical value (bA) + V(bB) of ta/Z, vA, v2, where a is the significance level and e v: and v: are degrees of freedom associated with the mean square error from analyses at stations A and B. The test was utilized for station pairs 2-6 and 3-5. These station pairs seemed to be most similar by depth, yield, thermal characteristics and distance from the power plant. The results of the t-test indicate that the regression coeffi- cients were significantly different (Table 8) Since the common variables had regression coefficients that were sig— nificantly different, neither of the station pairs were pooled to increase the number of yield observations and therefore sensitivity of measuring the regressions. Females The yields of female yellow perch for each station are shown in Table 9. The squared multiple correlation coefficient for female yellow perch indicates that the variance of the catch at station 3 was most explainable, followed by sta- tions 4, l, 2, 5 and 6 (Table 10). The significant variables and the parameters they represent are listed by station (Table 11). Station 1 results are similar to those of the male yellow perch at that station. Water temperature and various interaction 26 TABLE 8.--Results of t-tests for H:B =B A B' Station Pairs Station Pairs 2-6 3-5 Variable a Variable b (from Table 6) t-Value (from Table 6) t-Value x2 0.945 x1 3.562* x14 8.202** x5 4.551** x23 5.087** x14 3.557* x24 3.785* X18 4.523** X26 7.911** x29 0.213 x29 8.993** x35 7.647** x35 3.231* X36 9.856** a15 d.f. b20 d.f. * .01 level of significance. * .001 level of significance. 27 TABLE 9.--The 1973 yield of female yellow perch at each of six stations. Station Date 1 2 3 4 5 6 4-25 0 0 0 0 1 4‘29 0 0 l9 0 1 5-14 0 5 24 1 0 5-19 1 13 0 l4 0 0 5-22 0 0 8 6 16 5-30 0 0 8 0 0 6-06 6 10 10 20 51 12 6-13 9 132 14 0 22 133 6-23 162 216 26 8 78 67 7-09 28 22 19 0 30 6 7-11 0 66 4 - 0 103 7-22 0 95 14 0 0 7 8-12 4 8 0 4 0 8-14 22 225 30 0 36 89 8-22 0 34 13 0 31 251 8-25 10 2 2 20 50 9-08 12 6 0” 34 125 9-17 0 26 0 7 9-26 2 18 74 0 10-01 0 85 11 10-02 2 10 15 Total 254 853 171 272 346 868 28 TABLE 10.-—The proportion of variance explained by the best predictive equation (R2), for female yellow perch at each of six stations. % Station 61 59 95 91 59 45 terms again indicate the complex relationships that affect fish. Station 2 appears to be influenced primarily by photoperiod and air temperature. Stations 3 and 4 have in common several significant climatic interactions (X26, X27, X29, X35). Barometric pressure is important at station 3 alone. Stations 5 and 6 are unique in that variables directly related to spawning (gonad:body weight) are sig- nificant only at these stations. PhotOperiod, or an inter- action involving photoperiod, is important at all stations. The regression coefficients and standardized coef- ficients reveal the variability among stations and differ— ences between males and females (Table 11). The standardized coefficients at station 1 indicate the relatively equal importance of all four significant variables. Of the explain- able variance at station 2 (59%), air temperature and its interaction with photOperiod is most important. Station 3 is the only station in which barometric pressure is 29 h. H m.m moo. H Hmo.o ooHHmmouonm x mnsumummfimu Hmpwz omx m. H o.Hu Hooo. H mooo.ou 0H5H8H0msmu H0Hm3 x aoHuomHHo ocHz mmx m.~ H o.mH No. H mo.o wusumummsmu HHm x voHHmmouozm hmx o.~ H o.oHt Ho. H vo.ol mssumummeu HHm x whammmum OHHquonmm mmx m. H m.mn woo. H oHo.o: musumnmmfimu HHm x musumummawu kumz vmx ooH. H ooN.o Hooo. H oHoo.o AoHumHomsoo HHH00H0> oaHz NNx o. H N.ou mo. H sq.on HoHHmHomseo HHHoHnHBH HNx mm H moH- so.H H oH.on AoHumHomseo 0Hsmm0Hn 0HHH020Hmm on o. H N.H Hm. H oo.N _ HHHoHane ox o. H o.Nu so. H oo.Hn oOHHmmouoam mx oN. H Hm.H Noo. H oHo.o :OHHomuHo qu3 NH mm H mnH mm H mow musmmmum OHHHmEonmm Hx m coHHMHm m.m H o.m mo. H oH.o wusvmummfiwu HHm x ooHHmmouosm wmx ms. H ms.Hu No. H mo.o- AoHumHomseo UOHHwaoHoaa on N.m H o.ou ow. H om.Hn 0H5H8H0mswu HHH ox N ooHHmHm H.v H m.oH vo. H HH.o UOHHmQOHOQQ x musumquEmH Hmumz omx H.m H m.hl mo. H no.o| musumnmmfimu HHm x UOHHmmouozm hmx o.m H ¢.> Ho. H mo.o musumummfimu HHm x musmmwum OHHumEouwm omx o.H H o.mn mm. H oo.Hu 0HsHmH0m50H Hmumz mx ucmHOHHHmOU HcmHoHHHmoo Hmumfimumm mEmz GONHoHMUGMHm :onmemmm wHQMHHm> H cOHHmHm .mCOHHMHm me Hm comma 30HH0> mHmEmm How mcoHumsqm m>HHOH©me map CH OHQMHH0> some How mHOHHm oumocmpm HHwnu com musmHOHmmmoo COHmmmHmmH 03H .Hcmmmummn menu meHwEmumm may .mmEms mHQmHHm> HCMOHHHsmHm 039:1.HH mqmda 30 boo. H hHo. musumuomsmu Hmum3 x UOHHOQOHOSQ x HamHm3 moonuomcow mwx s. H H.N- mo. H mH.ou ooHHmoouoaa x Haonz Hoonuomaoo wwx o coHHmum o H oH oN. H os.o ooHH0o0Hoaa x HamHme Hooauomcoo oox o H oHI H.w H h.oH| HamHms moonuomcou wa m coHHmHm o.H H m.m| mooo. H mHoo.oI mHsumumemu Hmpm3 x coHpomHHo UQHB mmx o. H h.m MH. H om.o mHHcHQHsH x soHHmuumcmm HamHH mmx w.m H m.ml No. H mo.ol OHDHmumewu HHM x OOHHmmouonm hmx m.N H o.n Ho. H mo.o muoumummamu HHM x musmmmum OHHHoEOHmm omx m. H m.m mooo. H HHoo.o musumnmmamu HHm x coHuomHHo oon mmx o. H o.m- so. H mm.o: HoHumHomseo HHHoHaHse HNx oN. H oo.ou Ho. H mo.ou HoHHmHomsoo aoHHmHHmcma HamHH oNx w H NN oH. H om.o HoHumHoesoo ooHHmaOHoaa on o. H w.N woo. H hHo.o HOHHmsomsqo musumumemH Hmumz on w H oHu m.N H o.mHu ooHHmmouoaa mx HcmHOHmmmou usmHOHmmmoo kumsmumm oEmz UONHGHMUgmum sonmmHmmm OHQMHH8> w coHumum .UOSGHHCOUII.HH mqmfifi 31 overriddingly important. Again, climatic interaction terms are important (X24, X26, X27, X35). Station 4 reveals non- linear association of photOperiod with female yellow perch yield (X5, X18). The presence of complex interaction terms is also an important aspect of female perch catch. Gonadal develOpment as influenced by photoperiod and water tempera- ture are the only significant variables at stations 5 and 6. At each station neither of the two variables are dominant in explaining the variance. The predictive equations and minimum standard errors of the estimate are developed from the significant regres- sion coefficients for each station (Table 12). The first term of each equation is a constant. 32 TABLE 12.--Predictive equations, the minimum standard error of the estimate for the yield of female yellow perch at six stations. Minimum Standard Station Predictive Equation Error 1 Y - .55 - 1.4x3 + .03xlx6 - .07x5x6 .543 + .11x3x5 . 2 2 Y- 9.61 - 1.34x6 .05x5 + .10x5x6 .682 3 9 - 7271 + 489xl + .010x2 - 1.66x5 .248 2 2 + 2.86x8 - 8.19xl - .47x8 2 + .0019x9 - .016X3X6 .04xlx6 + .09x5x6 - .0005x2x3 + .031x3x5 4 2- 76.2 - 13.0x5 + .017x§ + .54x2 .358 2 2 - .05x7 - .33x8 + .0011x2x6 + '03X1X6 - .09x5x6 + .56X7X8 - .0019x2x3 5 Y 1.52 - 10.79x41 + .70x4lx5 .323 6 Y 1.30 - .15x4lx5 + .017x41x3x5 .603 DISCUSSION Males Station One Male yellow perch activity at this station is rela- ted to climate (Table 6). The most significant variables affecting yield are interaction terms in which interrelated parameters represent characteristics of a change in the weather pattern. The significance of five interaction terms (four of which involve air temperature) illustrates the complexity of factors which influence yellow perch activity. A positive linear term for water temperature indi- cates that a direct relationship exists between yield and temperature. As bottom water temperature begins to increase, yellow perch become more active and yield increases (Pearse and Achtenberg, 1917-1918). The increase in activity makes the yellow perch more vulnerable to gill nets (Scott, 1955). All of the variables are of relatively equal importance in explaining yield variability except for the interaction term, air temperature by water temperature (X24), which is least important. Since station 1 is unaffected by the power plants' operation, it is assumed that yellow perch 33 34 yield in other areas of like conditions would be explain- able by similar variables. Station Two The two most significant variables at station 2 are barometric pressure (X1, X14, Table 6). Significance of the linear parameter (X1), indicates that as the pressure decreases, activity increases and yield climbs on the aver- age. However, yield is related to pressure in a curvilinear manner (X14). Peterson (1972) found that spawning activity increases with a decline in barometric pressure. There may be several reasons why barometric pressure is highly signifi- cant. Generating and pumping may slightly alter water pres- sures, and in combination with atmospheric pressure fluctua- tions, barometric pressure becomes inordinately important. As barometric pressure falls, the weather generally becomes inclement. Wind velocity may increase and cloud cover reduces available light. Transmitted light is required for formation and maintenance of schools, feeding behavior and net avoidance (Clarke, 1936, Morrow, 1948, Blaxter, 1965, Hasler and Bardach, 1949, Hergengrader and Hasler, 1968, Whitney, 1969, and Scott, 1955). Other climatic variables support this theory. When wind velocity increases, yield increases curvilinearly (X22). Station 2 is shallow, (8 m) and contains silt from large 35 eroded bluffs and particulate matter created by currents from the plant. Therefore, a forceful wind will create a turbid situation which reduces available light. Reduced visibility results in greater gill net yields. Wind direction also is significant (X2). As the prevailing winds move south to west (directly onshore) and farther north, the water column and particulate matter become greatly mixed. Turbulence produced by changes in wind direction may cause fish to seek an area of less dis- turbance thereby resulting in a greater catch. One variable that directly contradicts this theory is light penetration, X7. Examination of the regression coefficient reveals that clearer water produced a greater yield. However, standardized coefficients indicate the very low importance of this variable relative to others that affect yield (Table 6). Water temperature has the same relationship to catch as at station 1. Wells, (1968) found that yellow perch move onshore with warmer water temperatures. These data support the concept of seasonal migration but also indicates the importance of photOperiod (x18). The inter- action of photoperiod and water temperature (X36) reveals that "extremes" of water temperature should be viewed in. relation to season, rather than absolutely. The biological significance of certain interaction and quadratic variables may become more apparent with the 36 addition of a time variable. The regressions were calcu- lated on a total season basis, ignoring any time element. Utilizing time on a seasonal basis may lead to a better understanding of the significance of certain variables, par- ticularly water temperature and photOperiod. Station Three Station 3 is similar to station 2 in that barometric pressure is by far the most important variable and has the same inverse relationship to catch (Table 6). Other signifi- cant climatic variables are similar to station 2 except for variables that can directly affect water currents. Because of strong currents produced by the power plant, environmental parameters that directly affect water currents have little affect at this station. Variables that might affect currents are wind direction and water temperature acting jointly. Significance of the interaction between them is probably due to winds affecting water temperatures and yellow perch responding to these changes by following preferred isotherms (Wells, 1968). As noted earlier, yellow perch migrate offshore with cooler weather and changing photoperiod (Wells, 1968). Sta- tion 3 (14 m depth) is approximately .8 km (.5 mi) offshore. As photoperiod decreases, catch increases. The interaction of photoperiod and water temperature is again significant, as at station 2. 37 Station Four Station 4 is similar to station 1 in that various climatic interaction terms have the most important influ- ences (X24, X26, X27, Table 6). Other related terms are quadratic variables representing water temperature, baro- metric pressure and turbidity. These terms probably reflect activity pattern change. As changes occur in the weather pattern, yellow perch may try to compensate for those changes by seeking a less affected area, possibly moving to areas of greater depth. This increase in activity results in a greater yield by making perch more vulnerable to gill nets. Water temperature and photOperiod are significantly related to yield in a non-linear manner. Since seasonal migration has been shown to be a function of water tempera- ture and possibly photOperiod, it seems reasonable to assume that the significant quadratic terms (X16, X18, Table 6) are reflecting these migratory trends. By examining the raw data, it can be seen that the yield at station 4 decreases at the first of June and abruptly increases during the last week in September (Table ‘4). Again the interaction between water temperature and photoperiod is important. Station Five Station 5 is very similar to station 3. Barometric pressure is the single most important variable and the 38 inverse relationship between barometric pressure and yield still exists (Table 6). As expected, climatic interaction terms are significant except for variables that directly affect water currents (X24, X25, X35). The only possible exception to this is the effect of wind velocity (X9, X22), in which their importance cannot be readily explained. Again, as at station 3, the interaction between wind direc- tion and water temperature is important. Wind direction influences temperature change, possibly through upwelling and this temperature shift probably induces yellow perch to try to remain in a preferred temperature. This movement with the shifting isotherms results in an increase in yield. PhotOperiod is significant as at station 3 (X5, X18). As photoperiod is decreasing at an increasing rate, catch increases. As earlier, this probably reflects the seasonal migration patterns of yellow perch. Station Six The two most important variables at station 6 involve wind direction (X2, X23, Table 6). Also, two other inter- action terms involving wind direction are significant (X25, X35). The main effect for wind direction (X2) indicates that, in general, as the prevailing wind shifts from west to south to east (decreasing degrees) the yield increases. There may be two reasons for this effect. Currents from the 39 power plant may be attracting fish and/or affecting their activity patterns. Also, since station 6 is north of the power plant, as the prevailing wind shifts toward the south, it may complement northward currents produced by the plant. When compared to station 2, the same affect occurs. As the prevailing wind moves toward the north, it begins to comple- ment southward currents produced by the plant and in general yield increases. Climatic variables seem to play a role, primarily as interaction terms (Table 6). Barometric pressure is signifi- cant as a quadratic term and in two other cross-product terms. As barometric pressure rises, yield increases curvil- inearly. This phenomenon is contrary to examples at stations 2 through 5, although it is relatively unimportant when com- pared to other significant variables at this station. The interaction term of water temperature by photo- period probably shows the affects of general seasonal onshore and offshore movements, although neither photOperiod nor water temperature are significant alone. Depth at all stations is probably an important factor. The basic similarities in common variables at sta- tions pairs 2-6 and 3-5 are offered as support. The common relationships of photOperiod and water temperature to yield at these station pairs and the importance of their inter- action support seasonal movements as reported by Wells (1968). 40 Photoperiod may also be significant as it affects the develOpment of sperm and the onset of spawning (Hoover, 1937, Burger, 1939, Matthews, 1939, and Kaya and Hasler, 1972). Male yellow perch store viable sperm during the late winter months until the onset of spawning (Turner, 1919). They arrive earlier and remain on the spawning beds longer than females (Scott and Crossman, 1973, and Pearse and Achtenberg, 1917-1918). The direct or inverse rela- tionship of photOperiod to yield that occurs at these sta- tions may help describe when spawning males are present and their migratory habits. Females Station One The importance of complex interactions that influ- ence activity can be seen at the control station. Of the four significant terms, three are interaction variables. The only significant climatic term is the interaction of barometric pressure and air temperature (X26). A logical explanation for the significance of this variable and the lack of significance of other climate-associated variables cannot be postulated at this time. Two variables (X36, X3) are slightly more important than the other two significant terms (Table 11). The linear term for water temperature indicates an inverse relationship 41 with yield. As bottom water temperatures decrease, catch increases. Photoperiod also plays a role in the interaction with water temperature. This may reflect seasonal migration of female yellow perch. Station Two There are three highly interrelated significant variables at station 2. Air temperature and the interaction term between photoperiod and air temperature are about equally important (Table 11). The linear term for air tem- perature, X6, is inversely proportional to yield. Photo- period, the least important term, is a negative quadratic that indicates an inverse non-linear relationship with yield. Photoperiod probably plays a role in on and offshore seasonal migration. It may also reflect gonad maturation and the subsequent migration onto spawning areas. The lack of significance of many climate related terms is difficult to explain.- At this station, female yellow perch appear to be unaffected by weather changes. Station Three As in stations 2, 3, 5 and 6 for the male yellow perch, barometric pressure is by far the most significant variable (X1, X14, Table 11). This variable is directly, but curvilinearly related to yield. As barometric pres- sure increases, catch increases, but at a decreasing rate. 42 The above weather pattern, and the complex relationships between its parameters are significant and affect catch (X24, X26, X27, X35, Table 11). The effect of wind direc- tion, X2, is directly related to yield. Since station 3 lies south of the plant, prevailing winds changing direc- tion to greater degrees probably acts as an additive effect with currents produced by the power plant, and yield increases. This same type of affect was found for the males at station 2 and 6, but not at station 3. The significant turbidity variable is directly related to yield. As turbidity increases, catch increases. This may be due to a lessened ability to avoid gill nets. Since vision plays an important role in feeding, school formation and maintenance, the activity associated with these behaviors must be altered for a continuation of these behaviors. A significant photoperiod term indicates that a decreased daylength leads to an increase in yield. When examining yields for station 3 (Table 9), the Opposite appears to be true. The significance of this linear term (X5) and the interaction of photoperiod and water tempera- ture has been attributed to seasonal migration. In this case such interpretation is difficult to make. Station Four The most important variables are photOperiod terms (X5, X18, Table 11). As daylength decreases, perch move 43 offshore and yield increases at an increasing rate at this offshore station. This seasonal migration has been attribu- ted to temperature (Wells, 1968), but photoperiod is proba- bly important. Water temperature is related to yield in a non- linear manner. As water temperature increases, yield increases curvilinearly. Light penetration and turbidity (X20, X21) are both inversely non-linearly related to yield. As light penetra- tion decreases, yields increase. This would be expected if vision were important in net avoidance at this depth. Turbid- ity when decreasing, results in an increase in yield (X21). Although turbidity is a curvilinearly related to yield, and more important than light penetration (X20, Table 11), a rational explanation of this affect is difficult to find. Climatic variables reflecting weather changes are significant (X25, X26, X27, X29, and X35, Table 11). As mentioned earlier, these complex interactions probably affect female yellow perch activity patterns, possibly by causing perch to seek an area that is less affected, (a more preferred environment). Stations Five and Six The only significant variables at these stations are ones that influence gonadal development and spawning (Table 11). Both water temperatureenuiphotoperiod act as trigger 44 mechanisms to produce sperm and eggs and initiate the onset of spawning (Kaya and Hasler, 1972, Matthews, 1939, Burger, 1939, Hoover, 1937, and Jones gt_§1., 1971). The inverse relationship of gonad:body weight (X41) at station 5 indicates that as spawning occurs, yield of female yellow perch increases. Since these variables are the only significant terms, one may conclude that stations 5 and 6 are preferred spawning sites. Since it has been shown that males are in a ripe spawning condition longer than females and are over the spawning beds for a greater period of time (Scott and Crossman, 1973) this may also indicate that female yellow perch select an apprOpriate spawning site. Pearse and Achten- berg (1917-1918) also point out that many males follow one female indicating that she may be responsible for site selec- tion. There are obvious differences between male and female yellow perch as the regressions indicate. “At the control station, 1, the catch of the males is directly related to water temperature. The females exhibit an inverse relation- ship. This same phenomenon is also true for barometric pressure at station 3. The yield of male perch has an inverse relationship with barometric pressure and the female yield is directly related to pressure. There are also the obvious differences at stations 5 and 6. The males reflect 45 climatic effects and seasonal migration whereas the females are influenced by variables (gonad:body weight and its inter- action with photOperiod and/or water temperature) that influ- ence development of eggs and spawning. Also there are basic similarities. Photoperiod and water temperature, as they affect seasonal migration, appear to affect yield similarly for both sexes, although it becomes more difficult to establish in the females. In general, weather does seem to influence activity and in turn gill net yield. Also, the prevalence of interaction terms and curvilinear relationships, at like stations indicates the complexity of interrelationships that govern yellow perch movements. SUMMARY This investigation was undertaken to determine which of several factors affected the yield of yellow perch near the Ludington Pumped-Storage Power Plant. Yellow perch were chosen due to their local abundance and popularity for sport fishing. The yield, or dependent variable, was analyzed by a step-wise deletion multiple regression routine. The inde- pendent parameters were climatic variables such as wind direction and velocity, barometric pressure and air tempera- ture. Water condition factors included bottom water tempera- ture, light penetration and turbidity. The gonad:body weight ratio and photOperiod were also incorporated into the regres- sions as these variables would reflect changes in gonadal deve10pment and influence spawning. Quadratic polynomial terms were used to express curvilinear relations between yield and the independent factors. Also, two-factor inter- actions were considered. The results indicate that the independent variables examined could explain 77 to 99 percent of the variation in yield of male yellow perch. Standardized regression coeffi- cients at station 1 show that yield of male perch was affected 46 47 by changes in the weather pattern and water temperature. Barometric pressure was the main parameter that affected yields at station 2, 3 and 5. The catch at station 4, like station 1, was primarily influenced by complex climatic interaction terms. Wind direction and its various inter- action terms were the main influencing factors at station 6. Barometric pressure may be highly significant for several reasons. Pumping and generating may slightly alter pressures by causing a head to be formed to move large amounts of water. Pumping, which generally coincides with the two major activity periods of yellow perch (pre-sundown and sunrise), may cause a general water pressure decrease. This may complement and magnify the effects of a decrease in barometric pressure. Also, barometric pressure may be reflecting changes in weather conditions. Photoperiod and water temperature influence seasonal inshore and offshore migration of male yellow perch. Similarities were noted between station pairs 2-6 and 3-5 in that the sampled areas may be biologically alike in that thermal stratification, yield, distance from the power plant (current affects) and depth was similar, but their regression coefficients were statistically different. Stations 1 and 4 were similar in that cross-product terms involving weather patterns were the primary influenc- ing factors. The significant regression coefficients at 48 station 4 also included a number of non-linear terms. The importance of these curvilinear terms may be due to depth. The variation in yield of female yellow perch as explained by the independent variables had a range of 45 to 95 percent. The yields of stations 1 and 2 are primarily determined by complex climatic terms. Barometric pressure exerts the greatest influence at station 3 and photoperiod is the dominant factor at station 4. The catch at stations 5 and 6 is due to variables that directly relate to spawning and gonadal develOpment. The significant variables that affect spawning at stations 5 and 6 indicate that these areas may be the only spawning stations in this sampling design and that female yellow perch may actually choose the spawning site. The multiple correlation coefficient was more vari- able from station to station for female perch. Different variables were significant from station to station for the female yellow perch, making those results more difficult to interpret than results for male perch. LITERATURE CITED 49 LITERATURE CITED Alley, W. P. 1968. Ecology of the burrowing Amphipod Pontoporeia affinis in Lake Michigan. Spec. Rep. #36 Great Lakes Res. Div. Inst. Sci. and Tech. 77-86. Blaxter, J. 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