THE DYNAMICS GE FIVE ROCK BASS PGPLELAFEQN$ M A WARM-WATER SWEAM The“: 509* {rim Daqzma of DH. D. MICHEGAN STATE UNIVERSETY Kenneth Jack Linton 1967 M: TH S 77/77/7777 7777 77777 77777 7777777777 1129310775 This is to certify that the thesis entitled THE DYNAMICS OF FIVE ROCK BASS POPULATIONS IN A WARM-WATER STREAM presented by Kenneth Jack Linton has been accepted towards fulfillment of the requirements for 7 Ph.D. l degree in Fisheries and Wildlife OMQM Major professor Date February 23, 1967 0-169 ABSTRACT THE DYNAMICS OF FIVE ROCK BASS POPULATIONS IN A WARM-WATER STREAM by Kenneth J. Linton The dynamics of five rock bass populations in the Red Cedar River were compared in order to determine their ability to maintain themselves by natural reproduction under the various environmental conditions. Fish were collected by an electrofishing technique and the age-classes and total popu- lations were estimated by the Bailey modification of the Petersen method. The age distributions differed in the five zones. Rapid declines occurred during the course of the study in two of the populations and a lesser decline occurred in another. One population remained relatively steady and the remaining one increased. The smallest variation in age distribution and the smallest proportion of older fish were observed in the increasing population. The age—specific fecundity of the rock bass in the Red Cedar River was higher than in comparable studies. The number of eggs produced per female increased through age VI, then declined, although the low observation for age VII may have been due to chance. An estimate of sex ratio indicated that Kenneth J. Linton the population consisted of 48.2% females, but the 95% con— fidence limits included 50%. Overall survival of the immature stages was poorest in the zones in which a decline occurred and highest in the in- creasing population. No relationship was demonstrated between the numerical size of the parent stock and the immature sur- vival. The smaller, declining populations had a larger propor- tion of older fish and showed a tendency to produce more eggs per female on the average due to the age—specific nature of the fecundity. The data suggested a trend toward a larger number of fish surviving to age III from larger cohorts of eggs. The calculation of r, the intrinsic rate of natural in- crease, was adapted to the rock bass populations, expressed on an annual basis, and called ra, the annual potential in- stantaneous rate of natural increase. It was calculated for three cohorts and two vertical age distributions for each of the five zones. The difference between the zones was statis— tically significant. The value of ra was consistently negative in the two most polluted zones and was positive in every case in the least polluted zone. The associated mean generation times, T9, were consistent and had a mean of about five years. The net reproduction rate, R0, was less than unity for all of the estimates in the two polluted zones and greater than unity for all those in the least polluted zone. Kenneth J. Linton Values of r, R0, and Tg were compared with similar values for other organisms and were consistent with expectations. Variations in these values are discussed with respect to the environmental conditions and it is concluded that the success of the rock bass populations is impaired by the presence of pollutants. The use of ra is recommended in the management of impor- tant fisheries and in the evaluation of chronic low-level pollution. THE DYNAMICS OF FIVE ROCK BASS POPULATIONS IN A WARM-WATER STREAM BY Kenneth Jack Linton A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Fisheries and Wildlife 1967 ACKNOWLEDGEMENTS I want to sincerely thank Dr. Robert C. Ball for his invaluable guidance through this program. I am grateful to Drs. Eugene W. Roelofs, T. Wayne Porter, and William E. Cooper for their excellent sugges- tions and criticisms. I also wish to express my gratitude to my fellow graduate students for aid in the field work. Special thanks go to Dr. Gerald R. Bouck and Mr. Willard L. Gross for their suggestions and encouragement. The research was conducted during the tenure of a Predoctoral Research Fellowship (WP-15,866) sponsored by the Division of Water Supply and Pollution Control of the United States Public Health Service. ii TABLE OF CONTENTS INTRODUCTION . . . . . . . . . . . . . DESCRIPTION OF THE RIVER . . . . . . . METHODS. . . . . . . . . . . . . . . . Description of Physical Features. Macrophytes . . . . . . . . . . . Rock Bass Populations . . . . . . Population Estimates . . . . Fecundity. . . . . . . . . . Sex Ratio. . . . . . . . . . Survivorship . . . . . . . . Potential Instantaneous Rate Increase. . . . . . . . Age Determinations . . . . . Net Reproduction Rate. . . . Mean Generation Length . . . RESULTS. . . . . . . . . . . . . . . . Fish Population Estimates . . . . Fecundity . . . . . . . . . . . . Sex Ratio . . . . . . . . . . . . Survival of Immature Rock Bass. . of Natural Potential Instantaneous Rates of Natural Increase . . . . . . . . . . Net Reproduction Rate and the Mean Generation Time . . . . . . . . . . . . R0, Ta, and ra. ... . . . . . . . Rock ass and Their Cedar River. . . . . . . . . Zone V . . . . . . . . . . . Zone IV. . . . . . . . . . . Zone III . . . . . . . . . . Zone II. . . . . . . . . . . Zone I . . . . . . . . . . . On the Use Of ra In Fisheries Pollution Study Involving ra. . . SUMMARY. . . . . . . . . . . . . . . . LITERATURE CITED . . . . . . . . . . . APPENDICES . . . . . . . . . . . . . . iii Environments In the Red Management. . Page 56 42. 45 51 58 61 63 63 68 7O 71 75 75 81 86 89 92 LIST OF TABLES TABLE 1. 2. Physical features of the five intensive study stations in the Red Cedar River. . . . . . . . Sample calculation of the potential instan- taneous rate of natural increase, ra, for rock bass in the Red Cedar River. . . . . . . . . Estimated numbers of rock bass per mile of stream by age, zone, and year of collection. . Estimated proportion of fish aged II or older which are at least age V. Data are for the rock bass in the Red Cedar River according to the zone and the year of collection. . . . . . Age-specific fecundity of the rock bass in the Red Cedar River. . . . . . . . . . . . . . . . Percent survival of rock bass from ovarian eggs to age III for each of the five intensive study zones in the Red Cedar River for the ” 1959 and 1961 cohorts. . . . . . . . . . . . . Annual potential instantaneous rates of natural increase, ra, for the rock bass in the five intensive study zones of the Red Cedar River for the cohorts of 1956, 1957, and 1958 and the vertical estimates for 1962 and 1964 . Daily potential instantaneous rates of natural increase, rd, for the rock bass in the five intensive study zones of the Red Cedar River for the cohorts of 1956, 1957, and 1958 and the vertical estimates for 1962 and 1964 . . . Net reproductive rate in numbers, R0, for rock bass in the five intensive study zones of the Red Cedar River based on the cohorts of 1956, 1957, and 1958, and the vertical estimates of 1962 and 1964. . . . . . . . . . . . . . . . . iv Page 18 54 57 59 41 44 55 59 6O LIST OF TABLES - Continued TABLE 10. 11. 12. Page Mean generation length, T , of the rock bass in the Red Cedar River, calculated on the basis of the cohorts of 1956, 1957, and 1958 and the vertical estimates of 1962 and 1964. . 62 Standing crop of macrophytes in g dry wt./m2 and percentage of area stocked by.macrophytes in the five intensive study areas of the Red Cedar River on July 4, 1964. . . . . . . . . . 64 Standing crop of biomass (in lbs/acre) of rock bass in the Red Cedar River for zones I—V in the years 1959 through 1964. . . . . . . . . . 69 FIGURE 1. LIST OF FIGURES Map of the Red Cedar River showing location of zones (delineated by arrows) and intensive sampling stations (triangles). . . . . . . . . Temperature of the Red Cedar River in 0F. as measured with a Taylor thermograph at the Michigan State University river farm at Okemos, Michigan, for the years 1957 through 1960. The upper curve represents the mean weekly temperature at 6:00 P.M. and the lower curve represents the mean weekly temperature at 6:00 AIM. . . . . . . . . . . . . . . . . . Temperature of the Red Cedar River in 0F. as measured with a Taylor thermograph at the Michigan State University river farm at Okemos, Michigan, for the years 1961 through 1964. The upper curve represents the mean weekly temperature at 6:00 P.M. and the lower curve represents the mean weekly temperature at 6:00 A.M. . . . . . . . . . . . . . . . . . Mean monthly discharge of the Red Cedar River at Farm Lane bridge for the years 1957 through 1960 (data furnished by the United States Geological Survey Field Office, Lansing, Michigan . . . . . . . . . . . . . . . . . . . Mean monthly discharge of the Red Cedar River at Farm Lane bridge for the years 1961 through 1964 (data furnished by the United States Geological Survey Field Office, Lansing, Michigan . . . . . . . . . . . . . . . . . . . Estimates of the numbers of rock bass of vari- ous age—classes in the intensive study zones of the Red Cedar River based on gross Petersen estimates versus the corresponding actual age-class estimates. . . . . . . . . . . . . . The logarithmic relationship of the number of eggs produced by the rock bass populations in the Red Cedar River to the number of three- year—old fish resulting. . . . . . . . . . . . vi Page 10 12 14 26 49 LIST OF FIGURES - Continued FIGURE Page 8. The relationship between the total number of mature females per mile and the total number; of eggs produced per mile for the rock bass in the Red Cedar River. . . . . . . . . . . . 52 vii LIST OF APPENDICES APPENDIX Page A. Mean weekly temperature in 0F of the Red Cedar River at 6:00 PM and 6:00 AM at the Michigan State University river farm, Okemos, Michigan, for the years 1957 through 1964. . . . . . . . . . . . . . . . . 93 Mean monthly discharge of the Red Cedar River at the Farm Lane bridge gauging station for the years 1957 through 1964 (data furnished by the United States Geological Survey Field Office, Lansing, Michigan). . . . . . . . . . 98 Results of selected interviews with some earlier Red Cedar River fishermen concerning composition of sport catch. Interviews con- ducted by author in February and March of 1966. . . . . . . . . . . . . . . . . . . . . 101 viii INTRODUCTION We are destroying our natural waters as a suitable en- vironment for those organisms that we desire to maintain. The problem has been recognized for centuries, but ignored in the name of economy unless human lives were endangered. One of the reasons why this situation has persisted until very recent times is the lack of agreement as to what consti- tutes damage to the environment. Certain forms of gross damage are easily isolated and defined, such as accidental spillage of highly toxic industrial wastes. In these cases, provided that the toxic material does not persist in the en- vironment, the damage is reparable by replacement of the organisms. But it is extremely difficult to assess the effects of a low level of a complex mixture of pollutants such as we may often find in our natural waters. The bioassay, in which death is the criterion for harm and in which only a limited age span of the test organism is represented, is useless as a tool for the evaluation of such effects. It has been recognized for some time that the biota of an environment reflects the totality of pollutional influences. This is the basis for "indicator" organisms. Other approaches involve the measurement of specific physiological effects on the organisms, estimates of the standing crops of various species, or estimates of the production of the populations. The approach taken here is to evaluate the status of the populations of an organism (the rock bass, Ambloplites rupgstris (Rafinesque)) by means of an index as to the ability of the populations to maintain themselves through natural re- production. If the environment created by the addition of low level pollutants is unsuitable for the continued mainte- nance of a natural population of the organism, then this index should reflect the effects of the pollutants. Rock bass have been present in the Red Cedar River in sufficient numbers to provide potentially extensive sport fishing since at least the early part of this century. A ser- ies of personal interviews (Appendix C) with about twenty of the older residents of the drainage area indicated that these fish have been present in large numbers throughout nearly all of the river for most of that time. Yet a recent study (Linton and Ball, 1965) showed that in the early 1960's, the rock bass in certain parts of the stream declined sharply in numbers. But this decline did not occur over the entire watershed, so it is unlikely that climatological conditions during one or more Spawning periods were strongly unfavorable and no evidence is available to show that some cataclysmic change had occurred in the environment. Therefore, it is be- lieved that the cause of this population decline is one that has persisted over a period of several years and that, given the proper information and an appropriate index, it would have been possible to predict this decline prior to its occur- rence. If this impending decline or collapse of the population were reflected in the adjustment of the age structure of the populations, then the potential instantaneous rate of natural increase should have been consistently negative prior to the collapse and it should have been positive or near zero and fluctuating slightly in those populations which did not collapse and are not in immediate danger of collapsing. It should re- main strongly positive in the expanding populations. This procedure cannot result in a statement of the cause of the damage in itself, but it is a definite indication that damage has been or is being done to the collapsing popu- lations. It is the intent and purpose of this study to demonstrate that the potential instantaneous rate of natural increase does or does not reflect impending or occurring changes in the size of a population of fish in the natural environment. DESCRIPTION OF THE RIVER The Red Cedar River is a warm—water stream in south- central Michigan. It arises in Cedar Lake, Livingston County, and flows northwesterly through Ingham County, entering the Grand River within the city of Lansing. The river is about 50 miles long and drains a total area of about 472 square miles (Figure 1). In the upper drainage area, consisting largely of farm land, the channel has been extensively dredged and straightened. The lower portion of the river flows through some farm land and considerable urban areas, which contribute agricultural, domestic and industrial pollution. The stream ranges from 25 to 80 feet wide and the average gradient is about 2.4 ft/mile. The mean weekly 6:00 P.M. and 6:00 A.M. temperatures for the years of 1957 through 1964 are shown in Figures 2 and 5. The data indicate that the maximum summer temperatures may have increased over the period of this study. The monthly mean discharge for the years 1957 through 1964 is graphically represented in Figures 4 and 5. The discharge data were furnished by the United States Geo- logical Survey, which maintains a recording station at the Farm Lane bridge. The study section of the river extends from the Farm Lane bridge on the Michigan State University campus in East Lansing to the VanBuren Road bridge about one mile upstream from Fowlerville, comprising about 50 miles of the main stream (Figure 1). The arrows in Figure 1 indicate the physi- cal features which delineate the five zones represented in this study. Since the Sycamore Creek drainage is not in- cluded here, the land area drained through the study section is about 555 square miles. The study section was divided into five zones for this investigation. Zone I is that three and one-half mile por- tion of the stream from the Farm Lane bridge to Okemos Road. The water here is slow-moving and drops silt and detritus on the mud bottom. The river is influenced by the dam lo- cated about i-mile below the zone on the Michigan State Uni- versity campus. The bottom at the upstream end of this zone is largely sand and rubble. Zone II (eight and one-half miles long) consists of that part from the Okemos Road bridge to the Zimmer Road bridge below Williamston. It is the cleanest of the five zones, having a sand bottom in a large portion and gravel and boulders in most of the remaining portion. There are no urban areas in this part of the river except for the influence of Okemos at the extreme lower end. The number of riffle—pool combinations is higher in the part from the bridge at M-45 to Zimmer Road than in any other part of the river. Below M-45, the water is slower and deeper with fewer riffles. Zone III extends from Zimmer Road bridge to the dam at Williamston, two and one-half miles upstream. The bottom .mCOHDMum mcHHQEmm o>HmcoucH can Amzouum >9 coumocflaocv mmcom mo coflumooH mafizonm uo>flm umUoO com on» mo mmz .H musmflm {W U F0 LERVILLE l>' " Ha . 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(3.) ummodmu |963 O O) S I I I I O O 8 3 [s 0 ( 3.) emimodwu, 8 12 .m xHUCQO< CH mmCHm> UmumHCQme .x. .ACmmHCUHE .mCHmCmq .moflemo eamam >m>usm HmUHmoHome mmumum nouns: may ma enema: Imam mumcv ome Cmsounu nmmH mnmom mCu MOM mmUHHQ mCmq Eumm um Co>Hm Hmpmo pom mCu mo *mmHMCUmHU MHCuCoE Cmmz awlwmmmww 15 ('4; -'083) afiJDuossa 14 .m xHUCmQQ¢ CH mmSHm> UmumHDQme * .ACmmHCUHS .mCHmCmq .monmuo anode >m>usm HmoflmoHome mmumum amuse: we» we emnmfle Imam mumcv emmH Cmsounu HmmH mummm mCu How mmUHHQ mCmq Eumm um uo>Hm umpou com 0CD wo *ooumzome hHCuCoE Cmoz amlwmmMflM 15 1 com I 00m 000. ('4; 409$) afiJDuosm 16 varies from silt to sand and cobbles, with some detritus. It is strongly influenced by the Williamston sewage disposal plant. There are extensive beds of rooted higher aquatic plants immediately below the dam. Zone IV includes the largest impoundment in the system and extends from the dam at Williamston to the bridge at Dietz Road. The reservoir proper comprises approximately half of the four-mile length, but its influence extends throughout the zone. The reservoir is confined to a narrow basin, but the flow is very slow. For the present study, the reservoir has been disregarded due to sampling problems and other considerations. Therefore, the results discussed refer only to the upstream portion of this zone. The mean width included in the calculations is also based only on this upstream portion. Further description of the impound- ment may be found in Brehmer (1956). Zone V represents the remaining 12 miles of the study section from the Dietz Road bridge to the bridge at VanBuren Road. It is influenced by the Webberville and Fowlerville urban areas. Probably the greatest influence is the industrial waste of the metal plating plant in Fowlerville. A large por- tion of this zone has been dredged and straightened and flows through farm land. The bottom is largely silt and mud. The depth and width of the dredged portions are quite uniform and the flow is slow. 17 The randomly selected half-mile zones used for the con- centrated study of the rock bass populations in 1962 and 1964 are indicated by triangles in Figure 1. Selected physical features of the five intensive study areas are sum- marized in Table 1. The major macrophyte populations en- countered throughout the five zones are Valisneria sp. and Sagittaria sp., although others may be locally abundant. For example, Elodea sp. is particularly abundant in parts of Zone III, fairly abundant in Zones I and V, and unimportant in Zones II and IV. More extensive treatments of the macro- phytes of the Red Cedar River are found in a later section of this paper and in King (1964) and Vannote (1965). 18 Table 1. Physical features of the five intensive study stations in the Red Cedar River. Zone I II III IV V Mean width (feet) 60.6 68.6 51.5 65.2 28.5 Mean depth (inches) 19.1 15.1 17.0 25.6 14.9 Total area (acres) 5.67 4.16 5.11 5.85 1.72 Bottom types* (percent) Silt 11.1 4.5 10.0 10.7 5.5 Boulders 1.5 6.2 5.9 0.5 1.0 Cobbles 4.0 25.2 15.4 0.7 2.5 Gravel 20.2 16.6 17.1 0.0 1.9 Sand and gravel 0.0 0.0 2.9 0.0 15.2 Sand 48.8 45.8 40.9 79.8 65.5 Detritus 14.4 5.7 9.8 8.6 12.7 *- Approximately according to the Wentworth scale (Leet and Judson, 1958). METHODS Description of Physical Features Selected physical features of the five intensive study areas were observed during the summer of 1962 while the river was at base flow. A 100 foot steel tape was used to measure the half-mile reaches. At the end of each 100 foot interval, paint was sprayed on a convenient tree or structure on the bank and the width of the river was measured at that point. Depths were recorded for five points along a line perpendicular to the thread of the river, starting at the left bank: at 1/6 and at 1/5 of the distance to the right bank, in the middle of the river, and at 2/5 and at 5/6 of the distance to the right bank. Subsequently, the crew started at the downstream end of the same reach and proceeded upstream, estimating the per- centage of each bottom type in the categories listed for each 100 foot interval. The averages of the three estimates were recorded and summarized. Macrophytes In June and early July of 1964, approximately midway through their growing season, the aquatic macrOphytes in 19 20 each of the study zones were sampled by the harvest method. Sample plot sites were located in the following manner. A table of random numbers was used to select ten 100 foot strata in each of the study reaches. For each stratum, 10 numbers were selected from the table of random numbers to represent distances from the lower end of the stratum. On arrival at the prearranged site, the width of the stream was measured. Again, from the table of random numbers, a number was selected to serve as a measurement from the right bank (facing upstream). This point then served as the upstream right-hand corner of the sample plot. The following possi- bilities were omitted from the plot selections: the extra 40 foot stratum at the upper end of the zone; the measurement "0" as a distance from the lower end of the stratum; and the last one foot of the width. This method results in a bias toward selection of a sample plot lying in a narrow portion of the stream. The in- tensity of the bias is dependent on the uniformity of the width. Since the widths were quite uniform within a zone, this bias is not great in the present study. The sample consisted of all macrophyte parts which were attached to roots or rhizoids in the sample plot and also included the roots and rhizoids. Two pieces of equipment were used to obtain the samples. When the water was shallow enough to permit its use (91% of the samples), a rectangle composed of 1 inch boards enclosing 21 a 1 square foot area was pressed into position on the river bottom. The plants were removed by hand and washed gently in the river water to remove silt and larger insects. This washing did not remove periphyton and associated small ani- mals. The samples were drained for a constant period (50 seconds) and weighed immediately on a Hanson dietetic balance. When the water was too deep to employ the square foot sampler (the remaining 9% of the samples), a Petersen dredge was used. The dredge sampled 0.85 square feet of the bottom. Appropriate corrections were made in the values. Three representative samples of approximately 500 grams each were returned to the laboratory for determination of dry weight. These were subsequently dried to constant weight at approximately 550C. The wet weights were converted to dry weight, the mean was calculated for each zone, and these stocks were converted to g/me. All the means were corrected to the estimated stock on July 4, 1964, the median collection date. The correction factor was obtained from the data of 16-17 July, 1962 re- ported by Vannote (1965) and consisted of the mean production per day expressed as a percentage of the standing crop on that date. The value used was 1.409% per day, which resulted in a maximum correction of 15.4% in the estimates reported above. 22 Rock Bass Populations Population Estimates The rock bass were collected prior to 1962 as part of a large limnological study of the Red Cedar River. Produc- tion of biomass was estimated for several components of the five stream communities (King, 1964; Linton and Ball, 1965). The rock bass collections in 1962 and 1964 were ex- panded expressly for the purpose of evaluating, from the standpoint of age structure and other factors, the changes in population density that were observed in the earlier study. The alteration of the methods in 1962 was largely a matter of increasing the size of the operations in order to secure an adequate sample for this type of analysis. The rock bass population numbers were estimated by the Bailey modification of the Petersen method (Formula 5.7 in Ricker, 1958) using an electrofishing technique. The fish were collected with a 220-volt Homelite direct- current generator which was mounted in an eight-foot wooden boat. The hand-held positive electrodes consisted of coiled copper tubing or straight copper pipe mounted on six-foot wooden handles and were opposed by a metal negative electrode plate on the bottom of the boat. The stunned fish were re- trieved at the positive electrodes with dip nets having a one-fourth-inch mesh woven nylon bag or a graded mesh (one inch to one-eighth inch) cotton bag. t 25 The stations were randomly selected within the limits of accessability. In 1959 through 1961, block nets were used to delineate the station during the estimation proce- dures. The stations ranged in length from 528 feet to 910 feet in 1959 and 1960. In 1961, all stations were 500 feet long. But in 1962 and 1964, the stations were 2640 feet long and no block nets were used. In 1959 and 1960, the crew started at the downstream net and shocked upstream, fin—clipping all fish and releasing them at the approximate place of capture, recording only the number handled. On the second and subsequent runs, the fish were placed in a metal tub in the boat. About half-way through the station and again at the end, the fish were weighed and measured, scale samples were taken, and all the fish were released. In 1961, six live-boxes outfitted with nylon mesh bags were distributed through the station after the block nets were in place. The crew shocked upstream, putting all fiSh;h1the live-boxes. At the completion of a run, the fish were weighed and measured and scale samples were taken prior to releasing the fish. On subsequent runs, recaptures were recorded and released and the usual data were collected on the remainder of the fish. In 1962 and 1964, the only changes employed were the following: use of a half-mile station instead of the smaller ones sampled previously; elimination of the block nets (un- necessary for this length of station); and estimation by age class as well as total population. 24 In view of the fact that both size-class and total estimates of the population numbers were obtained in 1962 and 1964, it was possible to investigate the relationship between the two types of estimates. It was believed that a consistent relationship probably existed between them. If true, it would be possible to obtain useful age-class esti— mates from the gross estimates made during previous years. The procedures employed in the earlier sampling involved the determination of the ages of the rock bass comprising the census catch (fish collected on the second run). This yielded an observed distribution of the percentage of fish of each age which were handled in the census catch as well as the gross estimate of the total population numbers. The product of the proportion of the total number of fish handled which were of a given age and the total number of fish estimated to be in that area is an estimate of the number of fish of that age in that area. But it is known (Cooper and Lagler, 1956; Sullivan, 1956; Linton and Ball, 1965; et alia) that the electrofishing technique is biased toward capture of the larger fish. Therefore, the use of these percentages in a direct manner would yield erroneous and biased estimates of the potential instantaneous rate of natural increase. But if this bias was consistent and observable, it would be possible to construct a correction to the previous observations and make them useful. 25 From the 1962 and 1964 gross population estimates, the observed percentages of each age in the census catch were used to estimate the total number of fish of each age (Tg) present in the population. These estimates were then com- pared (Figure 6) to the actual age-class estimates (Tk) made from the unmodified data. Two types of bias may be seen in this relationship: the vertical displacement of the observed line over the expected line; and the bias toward capture of the fish which occur in smaller numbers (the larger fish). The first of these is explained at least in part by the nature of the Bailey modifi- cation of the Petersen estimate. In both of the present types of estimates, the Bailey formula was used. It is: m(c+1) R+1 T: It is preferred since it is a slightly lower estimate, whereas the Petersen formula, T = MC/R, tends to overestimate the population (Bailey, 1951; Chapman, 1951; Ricker, 1958). This is brought about by the fact that the inflation of the number of recaptures, R, is proportionately greater than the increase in the product of the number marked, M, and the number taken in the census catch, C. But in the gross population estimates in the present study, this correction appears only once. In the size-class estimates, TX, it appears once for each size— class. Thus, the sum of the size-class estimates will be smaller than the overall estimate, or the observations in Figure 6 will tend to be displaced above the expected values. 26 Figure 6. Estimates of the numbers of rock bass of various age-classes in the intensive study zones of the Red Cedar River based on gross Petersen esti— mates versus the corresponding actual age-class estimates. l000 27 IOO- -l» AEstimotod by “’9:on suresz loo'o {0.54904 V U W U ‘ ff' l0 28 The bias toward capture of older fish is demonstrated in Figure 6 by comparing the vertical distance between the two lines (calculated and expected) expressed as a percentage of the value on the abscissa. For example, for x=2, the ob— served Y value is 150% greater than the expected Y value. For X = 200, the observed Y is only 55% greater. Since the older fish occur in smaller numbers, it may be seen that they constitute a disproportionately large segment of the number of fish handled in the estimation procedure. From Figure 6, it was learned that the bias was indeed reasonably consistent and predictable. The equation for the least squares approximation to the relationship is: loglo 9X = 1.17952 loglo f; - 0.54904 » where TX and TX are as indicated above. This equation was ap— plied to correct the estimates of age—classes based on the gross estimates from 1959-61 and the observed ages of the rock bass in the corresponding census catches. Fecundity Two collections were made with hook and line in zone II (June 15 and 15, 1966). Of the total of 189 fish collected, 70 gravid females were used for the fecundity study. Some of the females from the first day of collection were rendered unsuitable for the study by decomposition of the ovaries (these had been left overnight in 10% formalin). These were not included in the 70 fish used in this study. Immediately 29 after collection, the fish taken on the second day were given an intraperitoneal injection of from 0.5 to 2.0 ml of 10% Formalin, which was a successful solution of the earlier problem. In every case, the ovaries were removed and placed in tap water for at least ten minutes. They were then blotted on paper towels and weighed on a Mettler balance to the nearest 0.1 mg. Twenty samples were severed from the ovar— ies of fish of various ages, weighed to within the nearest 0.1 mg, and the eggs contained therein were counted. The samples counted contained from 95 to 926 eggs. The weights of the oVaries were then multiplied by the mean number of eggs/gm to obtain the numbers of eggs/female. These were then separated according to age, and the mean number of eggs/female at each age was calculated. These values constituted the age-specific fecundity for the calcu— lation of the potential instantaneous rate of natural in- crease . Sex Ratio The sample of 95 rock bass collected on June 15, 1966 was used to estimate the sex ratio in the populations. The sex of the individuals was determined by gross inspection of the gonads. Survivorship It is not necessary to know the shape of the survivor— ship curve for the juveniles of the population in order to 50 calculate the potential instantaneous rate of natural in- crease (Birch, 1948), but it is necessary to know the overall survival from the egg stage to the reproductive age for the females. To obtain this information, it was necessary to estimate the number of eggs produced at a given time and the number of three-year-old females resulting from that cohort. Observations were available on the numbers of rock bass in various age—classes in the five study zones for the years 1959 and 1961 (each three years prior to one of the years of intensive sampling for this study). Applying the results of the fecundity study, it was possible to estimate the numbers of eggs produced by the populations in 1959 and 1961. Since the sex ratio in the population was nearly unity, it was only necessary to divide the numbers of three-year-old females found in the intensive sampling years by half the numbers of eggs produced by the respective populations three years prior to the intensive sampling. This yielded two independent esti- mates of juvenile survival (or mortality) for each of the five zones, which could then be employed to calculate the total survivorship for the mature females. Immigration and emigra- tion are considered as part of the mortality curve. The only remaining data necessary for this calculation are the numbers of females of each age observed in the populations. These data were obtained as described above. 51 Potential Instantaneous Rate of Natural Increase The estimates of the potential instantaneous rates of natural increase for the various populations were computed as recommended by Birch (1948). The term used to describe this value was selected in preference to "intrinsic rate of natural increase" since the latter connotes a maximum value for the species considered. In every other respect, the two terms are synonymous and the calculations are identical. The calculation of ra entails the solution of the following equation for ra by trial and error: E e-qx l m = 1 x x where e is the base of the natural logarithms, ra is the po- tential instantaneous rate of natural increase expressed as an annual rate, lx is the survival of female offspring ex- pressed as the ratio of the numbers of females alive at age x to the number of Iemale"eggs originally present in the cohort, mx is the number of eggs produced by a female of age x, and x is the age expressed as the midpoint of the year. The values of the variables were obtained as described above under the appropriate headings. The use of estimates of abundance for the various age- Classes of female rock bass resulted in two possible abnor- malities in the calculation of the survivorship column. First, it was possible to estimate that one year-class was absent, while an older year-class was present. Thus, it can 52 result in the statement that the probability of being alive at age X+1 is greater than the probability of being alive at age X. Therefore, in the event that a zero occurred, it was replaced by the mean of the immediately preceding number and the immediately succeeding number. But since this only occurred in the older age groups, the effect on the value of "r " is negligible. Secondly, it is possible to estimate a that an older year-class was present in larger numbers than a preceding year-class, even if the latter is present. This results in the same untenable position with respect to sur— vivorship as stated above, but is handled in a slightly dif— ferent manner. In this case, where X+1 exceeds X, but both are present, ((x+1) + X)/2 was used to replace both of the values for the calculation of survivorship. It is to be ex- pected that such "aberrant" relationships will arise in random sampling and it is believed that neither of these ad- justments will lead to a less accurate value of ra. The initial computations were carried out on a desk calculator to provide a close, but minimum, value of ra for each of the cases considered. The input data for the com- puter consisted of the ages, X, the leX products, and the hand-calculated upper and lower approximations to ra, which covered a span of 0.1 in length. The initial ra with which the computer worked was a value to the nearest tenth such that the actual value of rawould be reached if 0.001 were added to this value (and the Ze-rxlxmx were recalculated) exactly 55 100 times. In fact, before the 100th computation was reach- ed, the value of the sum would exceed unity. Thus, if a one is subtracted from the sum each time, a point is reached where this quantity, say Y, becomes negative. At this point, the computer was instructed to print out the last value of ra (and Y) for which Y was positive as well as the first value of ra (and Y) for which Y was negative. The value of ra correct to the nearest 0.001 is then that value of ra for which the associated value of Y is closest to zero. The program for these computations has been made available to the computer librarian on the Michigan State University campus. A sample of the final step of the calculations ap— pears in Table 2. Age Determinations For all age determinations, scale samples were removed from the region of the tip of the compressed left pectoral fin. The samples were dried and impressions were made on small squares of acetate without heat, as recommended by S. H. Smith (1954).. These impressions were projected at a magnification of about 22 diameters and the ages were de— termined by the number of annuli present. No growth rate information was obtained during this study. The growth rates of the rock bass in the five zones for the years 1958 through 1961 were reported by Linton (1964). 54 Table 2. Sample* calculation of the potential instantaneous rate of natural increase, ra, for rock bass in the Red Cedar River. For r = 0.159 —rX Age (X) rX e l 2 e l x mx X xmx 5 5 0.5565 0.575 8.9720 x 10-4 542 4.5 0.7155 0.489 1.7557 x 10'4 4878 5.5 0.8745 0.417 0.8045 x 10-4 8881 8.5 1.0555 0.558 0.8045 x 10-4 9174 1.00058500 0.180 -rX -rX rX e lX mX i e leX 5 5 0.5800 0.571 8.9720 x 10“ 542 4.5 0.7200 0.487 1.7557 x 10-4 4878 5.5 0.8800 0.415 0.8045 x 10'4 8881 8.5 1.0400 0.555 0.8045 x 10‘4 9174 0.99542888 * Example is for rock bass in Zone II, 1962 vertical estimate (based on simultaneous sampling over all age classes). 55 Net Reproduction Rate The net reproduction rate was calculated for each cohort and each vertical estimate by the technique recommended by Birch (1948), which is: where RO is the net reproduction rate and 1X and mX are as defined above (see page 51). Mean Generation Length The mean length of a generation, or, more properly, the mean age of a reproductive female, was estimated by the formula (Birch, 1948): logeRO T: r where T is the mean length of a generation, RO is the net reproduction rate, and r is the intrinsic rate of natural increase. In this case, ra was used in place of r. In the natural populations of rock bass in the Red Cedar River, it is probably not necessary to distinguish between mean generation length and mean age of a reproductive female, since it is unlikely that any of the fish present in the popu- lation are of post-reproductive age. RESULTS Fish Population Estimates The total numbers of rock bass per mile of stream were estimated by the Petersen method. These estimates are pre- sented in Table 5 according to the age of the fish and the year and zone where the estimates were made. The method used precluded reliable estimates of fish less than two years old. These tabled numbers represent "vertical" estimates of abun- dance, i.e., fish present in the station which were of the given age at the time of sampling. In the following discus- sions, these are to be distinguished from "horizontal" age distributions which result from estimating the number of survivors of a given cohort at successive intervals of time. In this study, the time intervals are one year. Due to certain sources of bias inherent in the electro- fishing technique, confidence intervals may not be assigned to the estimates. This same bias makes the estimates of numbers of age II fish questionable. Although this is of some importance in the population estimates, it does not in— fluence the estimates of the potential instantaneous rates of natural increase. But certain features of the changing popu- lations are evident in Table 5. 56 57 Table 5. Estimated numbers of rock bass per mile of stream by age, zone, and year of collection. Zone Age Year 1959 1960 1961 1962 1964 I II 2515 267 1220 8 556 III 255 609 57 16 70 IV 148 704 127 12 10 V 14 129 4 ' 2 VI 14 4 2 Total 2944 1709 1404 44 640 II II 2142 865 1596 2550 2728 III 450 285 178 1096 958 IV 214 105 221 276 1422 V 51 29 59 92 182 VI 7 98 10 VII 4 Total 2817 1287 2054 4092 5284 III II 558 244 468 550 458 III 184 145 101 616 524 IV 558 218 117 142 540 V 114 85 28 58 180 VI 6 9 8 56 VII 4 4 4 Total 974 696 727 1558 1522 IV II 556 62 151 70 80 III 81 62 29 186 28 IV 184 62 0 6 14 V 27 4 4 8 VI 4 2 2 VII 12 4 VIII 2 Total 621 215 188 282 156 V II 149 94 2 6 III 66 155 64 4 IV 47 15 24 8 V 86 5 2 4 VI 15 0 2 2 VII 5 2 2 VIII 5 2 Total 561 257 0 98 26 58 Note especially that drastic reductions occurred in the numbers of rock bass in zones I and V during the course of this study. By random happenstance, the estimate for zone V in 1961 was made near the upstream end of that zone shortly after a severe fish kill (Parker, 1961). But the population in the lower end of the zone was declining prior to the kill above and continued to decline throughout the course of this study. The numbers in zone IV were comparatively stable, but an overall decline occurred during these years. Zone III was apparently unaffected during this period or showed a slight increase in numbers. In zone II, the numbers increased considerably. Of at least equal importance in this study is the numeri- cal relationship of the young fish to the older members of the population (Table 4). The populations of zone II re- mained most consistent throughout the study with respect to age distribution as well as consistently showing the largest standing crop of rock bass, at least in numbers. This was also true of the biomass (Linton and Ball, 1965). A compari- son of the remainder of the zones to zone II indicates that the age structures of the fish in the remaining zones showed a larger proportion of older fish. This would not be obvious in total population estimates or in biomass estimates, yet it is of extreme importance to the continued maintenance of the population. 59 Table 4. Estimated proportion of fish aged II or older which are at least age V. Data are for the rock bass in the Red Cedar River according to the zone and the year of collection. Year zone* 1959 1960 1981 1982 1984 mean I 1% 8% 0% 18% 1% 5.8% II 1 5 2 5 4 5.0. III 12 15 8 4 17 10.4 IV 0 15 5 7 10 7.0 v 27 8 ** 8 51 18.0 * I Polluted II Cleanest III Receives sewage IV Reservoir zone V Polluted ** No observation 40 Fecundity The fecundity of the rock bass was estimated by the gravi- metric method. As stated above, it is necessary to obtain this information on an age-specific basis, but, as will become obvious in the calculation of the potential instantaneous rate of natural increase below, the first two or three years of maturity are of prime importance. When the intrinsic rate of natural increase is quite high, as in the case of invertebrates (Birch, 1948; Leslie and Park, 1949; Cooper, 1965; etc.), the first period or two of egg production will contribute an ex- tremely large portion of the value of r. In the case of lower rates, such as are found in the vertebrates (Leslie and Ranson, 1940; Lotka, 1956; Leslie, 1945), the contribution of the first reproductive periods is relatively smaller, but still much greater than for the older segment of the popu- lation. The estimates of the age-specific fecundity and the 95% confidence limits on the estimates are presented in Table 5. The total fecundity reported here is somewhat higher than that reported by Eddy and Surber (1947) of 5000 eggs/female, but in a random sample of mature females, with considerable weight placed on the younger fish, the figures are comparable. The figures for the present study are appreciably higher than those given by Vessel and Eddy (1941), who reported on the number of eggs by size-classes of the females. Their esti- mates ranged up to 11,000 eggs/female as compared with about 41 Table 5. Age—specific fecundity of the rock bass in the Red Cedar River. Mean estimated number of 95% confidence limits Age eggs/female lower upper III 11084 458 1,750 IV 9,755 7,775 11,755 V 15,521 9,575 17,069 VI 18,548 14,585 22,515 VII 15,017 7,027 25,007 VIII 10,150* * Estimated graphically from the curve for ages III through VII; no age VIII fish appeared in the sample for fecundity. 42 18,000 eggs/female for the six-year-old fish in the present study. The confidence limits on these estimates are wide, so there is insufficient evidence to indicate a real dif- ference. It has been reported (Allen, 1951; McFadden, 1961; Vessel and Eddy, 1941) that, in most fish, there is a strong positive relationship between the size of the female and the number of eggs produced per year. Table 5 does not offer strong evidence against those observations. Considering the confidence limits, such a relationship could easily be the case for the rock bass being studied. But, for the present purposes, it is desirable to use the best empirical evidence for the population being studied, so these means will be used in the calculations below. However, as will be shown, the differences are of little consequence in the calculation of the potential instantaneous rate of natural increase. Sex Ratio The sex ratio of the sample studied indicated that the population consisted of 48.2% females with 95% confidence limits based on the Clopper and Pearson "Confidence belts for proportions" (Dixon and Massey, 1957) of 0.57 and 0.60. Consequently, a sex ratio of unity was assumed. There was no indication that the sex ratio changes with age in the rock bass. 45 Survival of Immature Rock Bass As indicated above, it is necessary to estimate the over- all survival of the immature stages of the organism in order to compute ra. It is not necessary to know the shape of the survival curve through this period for these computations, although this information is required for the calculation of the stable age distribution (Birch, 1948). Two estimates of survival of the immature fish were com- puted for each of the zones, as well as the combined estimate of the rate. The latter is not a simple mean of the two esti- mates, but rather the estimate obtained when the sum of the number of survivors in each case is divided by the sum of the original complement of eggs. The estimates appear in Table 6. The original complements of eggs were obtained by multi- plying the numbers of females of each age by the appropriate fecundity figures. Since the most reliable estimates of the numbers of three-year-old female rock bass were obtained in 1962 and 1964 (these were not based on the correction factors), the egg complements were estimated for 1959 and 1961. But the estimate of no rock bass in zone V in 1961 precluded the possibility of making this survival estimate. In the compu— tations below, the combined estimate for the appropriate zone was used in every case. The survival of the immature rock bass in the Red Cedar River is obviously low. Of course, the mortality which leads 44 Table 6. Percent survival of rock bass from ovarian eggs to age III for each of the five intensive study zones in the Red Cedar River for the 1959 and 1961 co- horts. Zone* year I II III IV v 1959 0.0015% 0.0759% 0.0246% 0.0198% 0.0087% 1981 0.0108 0.0854 0.0551 0.0455 -~— Com- bined 0.00497 0.06975 0.02759 0.02154 0.0067 * I Polluted II Cleanest III Receives sewage IV Reservoir zone V Polluted 45 to these figures has been operating over a period of three years. Although no comparable figures are available on rock bass, the survival of eggs of salmonids up to sac fry is usually over 90% (McFadden, 1961). In his Lawrence Creek brook trout, McFadden states that the initial high survival of the eggs is followed by a period of nine months during which about 98% of the cohort is lost to some form of mortal— ity. However, it should be noted that salmonid eggs enjoy much more protection in the gravel of the redds than do the centrarchid eggs in their exposed nests. Particularly in warm-water streams, the instabilities of flow, temperature, turbidity, etc., would expose the eggs and sac fry to con- siderable mortality risks. Slobodkin (1962) points out that most fish probably dis- play a survivorship curve characterized by a large initial loss followed by a decreased, fairly constant percentage mortality. However, at least one exception to this type of curve has been reported for centrarchids. Jenkins (1955) reported that 15 pairs of adult black crappies yielding a potential of 590,000 eggs resulted in 156,000 yearlings. This implies a survival of 59% of the potential number of eggs. If the curve described by Slobodkin were applied here, it would be necessary to have some of the surviving crappies, if the subsequent survival was, say, 60%, living at the end of 25 years. This is unlikely. However, Jenkins' results are un— usual and it is also true that this survival occurred while 46 the population was recovering from a severe reduction in numbers. The instantaneous mortality rate for adult rock bass in the Red Cedar River was calculated from an estimate of the survival rate based on the Robson-Chapman (1961) technique. It was used for the estimates of net production by Linton and Ball (1965). If the mortality of the immature rock bass in the Red Cedar River occurs over a period of three years and if the rate of mortality during the last two years of this period is assumed to be constant and equal to the adult instantaneous mortality rate, ia, then a reasonable approxi- mation to the curve suggested by Slobodkin should result. This should also be similar to that found for the Lawrence Creek brook trout (McFadden, 1961), for which the total sur- vival for the first nine months from the egg stage was about two percent. In the present study, the overall immature survival for three years in zone II was estimated to be about 0.07% or, the annual instantaneous mortality rate, if con~ stant, was 2.42291. Thus, if a three-year period is being considered, where a = 10 + i1 + i2 and i0 is the instantaneous mortality in the first year of life, i1 that in the second year of life, etc. Now, if as stated above, the adult mortality is assumed to be constant 47 and equal to the mortality rate for the last two years of the immature stage, then i1 = i2 = i Then a. a - Zia i0 The value of "a" associated with the total observed immature survival is 7.26872. Therefore, the instantaneous mortality rate for the first year of life of the rock bass would be 5.885, or the survival rate would be about 2%, which agrees closely with McFadden's results and with what is to be ex- pected on the basis of Slobodkin's suggestion. Allen (1951) found the survival over the first six months of the 1940 cohort of brown trout in the Horokiwi Stream to average about 1.4% over his six stations reported and range from 0.4% to 2.5%. In general, attempts (McFadden, 1961; Jenkins, 1955; Watt, 1959; Allen, 1951; Fry and Watt, 1957; Latta, 1965) to relate size of the egg complement to the number of offspring resulting at some later time have not been successful. McFadden (1961) was able to show a positive relationship be- tween the number of eggs produced and the mortality from the egg stage to the fingerling stage. Which is another way of saying that, regardless of the number of offspring produced, only a certain, but ill-defined, number can survive. This was borne out in his comparison of the progeny per acre to egg production per acre. In this case, the numbers of progeny referred to the number of resulting nine-month-old fingerlings. 48 From about 20,000 eggs per acre to the largest number re- ported, the regression line was horizontal. Below this point, i.e., 20,000 per acre, there is reason to believe that some point exists less than which there is a positive relationship between the number of progeny and number of eggs, since the line must pass through the origin. For the rock bass in the Red Cedar, an attempt to relate the original size of the parent stock (numbers per mile of stream) to the survival rate of the offspring to sexual ma- turity failed to demonstrate a recognizable relationship. The correlation coefficient, r = +0.25, was not significantly different from zero for nine independent pairs of observations. The relationship between the initial number of eggs pro— duced in the population and the resulting number of 5-year-old fish is expressed in Figure 7. There is a slight but variable positive relationship apparent in this figure. This indicates that if more eggs are produced, there is a trend toward the production of more fish of a mature age. But of even more importance is the relatively small dif— ference in the number of eggs produced regardless of the initial population size. That is, the numbers of eggs pro- duced which are recorded in Figure 7 reflect the entire range of population sizes of the rock bass in the five zones in 1959 and 1961. This suggests that some regulatory device is in operation. If so, it is probably the following. As discussed above under "Fish population estimates," a characteristic of 49 Figure 7. The logarithmic relationship of the number of eggs produced by the rock bass populations in the Red Cedar River to the number of three-year—old fish resulting. The line was drawn by inspection. No. of eggs 50 7,000,000 1 I d 1 500,000 1 4 200,000 . l00,000 - - 1 70,000 a 50,000 '7 1 50,000 ‘ 20,000 -' 0 Zone I Polluted G) Zone I! Cleanest 0 Zone! Receivee Sewage X Zone I! Reservoir Zone a Zone I Polluted l0,000 I fi 1 1 Vi", V ‘— r""" I U ' ""' IO |00 IOOO No. of 3yr. old fish resulting 51 those rock bass populations which have undergone a decline during this study is the relative preponderance of older fish. It is true that in the present study and in other studies, the older (or larger) fish produce many more eggs per individual. Thus, for the same population size, more eggs would be produced by the population which consisted of a higher proportion of old fish. Or, if the smaller of two populations had a larger proportion of older fish, it would be possible for the two populations to exhibit a similar total egg production. If this regulatory mechanism is operative in the present study, then the number of eggs produced per mile of stream by the five populations of rock bass should show a tendency to be similar in spite of variation in the number of mature females per mile. Figure 8 depicts this relationship for the rock bass populations in the Red Cedar River. The linear approximation (solid line) was calculated by the method of least squares, and the broken line was drawn by inspection. The data suggest that the higher proportion of older fish in the smaller populations resulted in a tendency toward the production of the same number of eggs in Spite of differences in the population sizes. But more extensive study is needed to adequately test and describe the phenomenon. Potential Instantaneous Rates of Natural Increase The potential instantaneous rate of natural increase was computed on an annual basis for the five populations of rock 52 Figure 8. The relationship between the total number of mature females per mile and the total number of eggs produced per mile for the rock bass in the Red Cedar River. 55 2.6 2.4- .- .N (n o I 1 LG! in In 1 l 7.0+ Number of eggs/mi (x106) .0 .0 O) m s L e Zone I Polluted Q Zone 1!. Cleanest X Zonem: Receives Sewage Q ZoneI! Reservoir Zone 0 Zone I Polluted OOdJ"lj"'ITUIII'U'Uj'U'IlrUfU'U'I 0 5O '00 750 200 250 Number of mature QWmi 300 350 54 bass in the Red Cedar River. For each of these five zones, three estimates were computed on the basis of the cohorts (1956, 1957, 1958) and two estimates were made from the vertical sampling in intensive study zones (1962 and 1964). In all cases, the age-specific fecundity, total immature mortality, and survivorship schedule for the adult females, as used in these calculations, consist of empirical observ- ations of the rock bass populations in the Red Cedar River. The calculated values of ra are found in Table 7. We may now examine the effects of certain of the assump- tions and observations made for the computation of ra. For example, the schedule of fecundity could not be estimated each time the populations were estimated, since it requires killing the fish. Killing enough fish for these purposes would have a significant effect on the population. But it was noted above that the number of eggs per female is, in most studies, positively correlated with the size (or in this case, age) of the fish and continues to increase throughout the size range of the fish as the size of the fish increases. We may then look at the effect this would have on the calcu- lations of ra for the rock bass of the Red Cedar River. To investigate the effect of increased fecundity in the older age groups, which is strongest at a low value of ra, we can recalculate ra for the 1962 vertical estimate in zone V. This is among the lower values of ra and is based on one of the more reliable population estimates (the correction factor 55 Table 7. Annual potential instantaneous rates of natural in- crease, ra, for the rock bass in the five intensive study zones of the Red Cedar River for the cohorts of 1956, 1957, and 1958 and the vertical estimates for 1962 and 1964. (Units are numbers/head/year.) *- Year Type Zone I II III IV V 1956 Cohort -0.058 0.210 0.114 0.006 —0.468 1957 Cohort -0.595 0.549 0.155 -0.120 -O.545 1958 Cohort -0.400 0.547 0.207 ~0.081 -0.197 1962 Vertical -0.171 0.159 -0.104 —0.204 -0.288 1964 Vertical —0.506 0.584 0.200 0.066 —0.045 * I Polluted II Cleanest III Receives sewage IV Reservoir zone V Polluted 56 was not used here). An alternate schedule of fecundity which results from extending that of the younger age groups linear- ly through the older age groups is 542; 4876; 6661; 9174; 11,000; 15,000 for ages III through VIII, respectively. These numbers represent the number of eggs per female, which are expected to give rise to females, or may be compared to 0.5 times the observations in Table 5. The value of ra for the 1962 vertical estimate in zone V, which is reported below as -0.288, remains, with the alternate fecundity schedule, about -0.5. Thus, the effect of using the alternate fecundity schedule rather than the preferred empirical one is quite small. Another possible source of error with regard to the fe— cundity schedule concerns the use of one schedule observed in zone II for the computation of ra for all five zones. If a density-dependent mechanism for compensating for the reduced population in zone V were operating through the fecundity of the individual females, we might expect a larger number of eggs per female at a given age in zone V than in zone II. No empirical evidence is available to check this, but we may observe the effect it would have on ra and compare this to the observed differences in ra between the zones. For example, we might recalculate r for one of the estimates using twice a the number of eggs per female. The differences in the values of ra between zones II and I are of the order of about 0.5. 57 But such recalculation of ra for the 1962 vertical estimate in zone II (using twice as many eggs) changes the value from 0.159 to 0.512, or a difference of about 0.15. Thus, even if twice as many eggs were produced by each female in the smaller populations, which seems to be extremely unlikely, there would be insufficient compensation to make up the ob- served differences in ra. Yet it is still possible that some compensation could occur, which would tend to raise the values of zones I, IV, and V slightly. We have already observed above that no such mechanism is operative through the juvenile mortality, since it is much higher (see Table 6) in those populations which are smaller. Thus, if there is any such effect, it is "depensatory." The underlying distribution of ra is obscure. But it is not likely to be normally distributed and perhaps not of the strength of an interval scale. The degree of dependence among the values for the five zones in each year (see "Methods” above), together with the immediately preceding considerations, suggests the Friedman analysis (Siegel, 1956) as an appro- priate test. But it should be noted that there is a degree of dependence within the zones over the several years of the study in that a single estimate of the juvenile mortality was used for each zone. Although the juvenile mortality would be expected to vary from year to year, in the rock bass popu- lations, only two estimates of this parameter were possible for each zone. The mean of these two estimates was used for 58 the juvenile mortality in that zone for the calculation of the potential instantaneous rate of natural increase. Nevertheless, the observed differences may be cautiously interpreted as real differences in the populations in view of the low probability (P‘< 0.01) of chance deviations as great as these. No individual comparisons can be made with this test. For comparative purposes, the value of ra can be con- verted to the daily rate, say rd, which is the commonly re- ported rate, by the simple expedient of dividing it by 565. This has been done for the rock base in the Red Cedar River and the values are assembled in Table 8. The observed values of r may be more readily compared with other values in the literature once the values of the net reproductive rate, R0, and the mean generation time Tg’ have been considered. Net Reproduction Rate and the Mean Generation Time The net reproduction rates, R of the five populations 0' of rock bass in the Red Cedar River are arranged in Table 9 according to the zone, year, and type of estimate of ra with which they are associated. The concept of net reproduction rate may be described as the ratio of the number of females in generation X + 1 to the number of females in generation X. Thus, the rate may be considered with respect to absolute time units only where the mean length of a generation, Tg, is known. The relationship of r, R0, and T9 was outlined in 59 UmusHHom > oCON HHO>Hmmmm >H mmmBom mm>Hmumm HHH ummemoao HH Umusaaom H * mlOmemH.Ol oIOHmea.O olOmewm.o mIOmemO.H mlOmemm.Hl HMUHuHm> emmfi mIOmeme.OI mIOHXmmm.OI oIOHXmmN.OI MIOmemw.o oIOme©¢.OI HMUHuHm> mmmH otOonwm.OI mIOmeNN.OI MICmemm.o mlOHmem.o mIOmemo.Hl HMOCOU mmmH gloaxmm¢.Hl mIOHXmNm.OI mIOmeH¢.O mIOwamm.O olOmeN©.Hl DHOLOO emmH MIOHmeN.HI mIOHXmHO.O olOHxNHm.O mIOmeem.o mIOHX¢OH.OI DMOCOU mmmH > >H HHH HH H ®Q%B new? *mCON A.>mp\pmoC\mquECC mum muHCDV .emmH UCm NmmH Mom moumEHumm HMUHDH0> 0:» pCm mmmH pCm .emmH .mmmH mo muuosoo ozu Mom uo>Hm Hmpmo pom mnu mo moCON Mpsum m>HmCmuCH m>Hm mnu CH mmmn xoou mSH How .UH .mwmeUCH HMHSDMC mo mmumu msooCmquumCH HmHquuom hHHmQ .m mHQME 60 Table 9. Net reproductive rate in numbers, R0, for rock bass in the five intensive study zones of the Red Cedar River based on the cohorts of 1956, 1957, and 1958, and the vertical estimates of 1962 and 1964. (Units are numbers/head/generation.) Zone* year Type I II III IV v 1956 Cohort 0.852 2.975 1.695 1.029 0.117 1957 Cohort 0.080 5.700 2.155 0.505 0.059 1958 Cohort 0.155 5.552 2.918 0.665 0.565 1962 Vertical 0.405 2.191 0.615 0.521 0.218 1964 Vertical 0.084 5.741 2.704 11424 0.775 *. I Polluted II Cleanest III Receives sewage IV Reservoir zone Polluted 61 "Methods" above. T9 is defined by this relationship. The values of T9 associated with the net reproduction rates are presented in Table 10. If a comparison of the net reproduction rates is to be meaningful, it is necessary that the associated values of T9 be similar. Therefore, a Friedman analysis was done on the values in Table 11. The effect of zones was not significant (P < 0.50). Consequently, it was assumed that an overall mean was the best description of the mean generation time for rock bass in the Red Cedar River. This was found to be 5.029 years. Of course, if they are computed on the basis of the daily potential instantaneous rates of natural increase and the associated values of RO (which, incidentally, are not affected by the scale of ra), the values of T9 and the mean of T9 are expressed in days. Thus, the mean becomes 1856 days, which simplifies the com— parison of these statistics to those reported for other organ— isms. R T , and r a 0’9 The maximum possible value of the potential instantaneous rate of natural increase, ra, for a species is the "intrinsic rate of natural increase, r," for that species. This value was not determined in the present study and has not been de- termined in the past for the rock bass. But the closest ap- proximation to that value would be the maximum observed value in the present study. Cooper (1965) and Hall (1964) indicated that natural populations of Hyalella and Daphnig, respectively, 62 Table 10. Mean generation length, T , of the rock bass in the Red Cedar River, calculated on the basis of the cohorts of 1956, 1957, and 1958 and the vertical estimates of 1962 and 1964. (Units are years.) Zone* year Type I II III IV v 1956 Cohort 4.84 5.18 4.60 4.95 4.58 1957 Cohort 4.28 4.99 5.00 5.69 5.19 1958 Cohort 5.01 4.82 5.18 5.07 5.14 1962 Vertical 5.29 4.95 4.67 5.57 5.29 1964 Vertical 4.90 4.55 4.97 5.51 5.72 96 I Polluted II Cleanest III Receives sewage IV Reservoir zone V Polluted 65 were both turning over at about 60 to 70% of their maximum rate based on laboratory determinations of the intrinsic rate of natural increase. No comparable data are available on fish, but it is not unreasonable to assume that the rock bass in zone II are exhibiting a similar relationship. F. E. Smith (1954) compiled the available data on the intrinsic ratecfifnatural increase of various organisms up to the time of his publication and prepared a figure showing the relationship between r, R0, of the species. This permits the comparison of the present and T (T9 in this paper) for each data on rock bass to the relative magnitude of these para- meters for other species of organisms. Such a comparison places the rock bass among the other fairly long—lived verte- brates, which is to be expected if ra is of the same order of magnitude as r. Thus, some slight credence is added to the observed values for rock bass. Rock Bass and Their Environments In the Red Cedar River Zone V Generally speaking, this zone should be capable of sus- taining a fairly large population of rock bass. Reference to Table 1 indicates that although the bottom is largely sand, there is a considerable amount of detritus, consisting mostly of fallen trees and branches, which provides adequate cover. Further cover for the developing fry is found in the extensive beds of macrophytes (Table 11) during the summer months. 64 Table 11. Standing crop of macrophytes in g dry wt./m2 and percentage of area stocked by macrophytes in the five intensive study areas of the Red Cedar River on July 4, 1964. Zone I II III IV V Dry weight standing crop 58.61 109.04 58.42 2.77 82.88 (g/ma) Percent of area stocked 66 55 12 14 75 65 King (1964) ranks this as the highest of the five zones in total primary production (including the autotrophic aufwuchs) and second highest in the production of heterotrophic auf- wuchs. So the food base is adequate for the maintenance of extensive fish populations if it is qualitatively adequate. Yet Linton and Ball (1965) have shown that the total fish production in zone V is the lowest of the zones. The rock bass production is ranked as the second lowest. And in the present study, it ranks (along with zone I) as the lowest with respect to the potential instantaneous rate of natural increase of the rock bass populations. In fact, these values were consistently negative, which indicates that the rock bass population is incapable of sustaining itself with natural reproduction as long as the present environmental conditions are maintained. Thus, the present population is probably being supported in part by movement of fish into this area, perhaps from the tributaries or the upstream areas. However, reference to Tables 5 and 7 shows that this immigration is inadequate in zone V for maintaining the present population size. The population is rapidly decreasing to a critical level. Apparently, if the environmental conditions are not altered, the rock bass will either continue to decline until the "population" consists entirely of the fish moving into the area, or they will disappear entirely. Of particular interest is the pattern of their decline. An inspection of Table 7 shows that the minimum value of ra 66 is -0.545 for zone V. Since these are expressed on an annual basis, a table of natural logarithms shows us that the popu- lation could be declining (if the conditions were constant and the population parameters "tuned" to them) at a rate of about 42% per year. Of course, the conditions are not con- stant and the picture is further complicated by movement of some fish into and out of the area. But it is also obvious that, although no cataclysmic "fish kill" has occurred, the population is being lost. And this condition was reflected in the value of ra at least as early as the 1956 cohort even though as late as 1959 and perhaps 1960, the population, as judged by its total biomass, did not appear to be in trouble. Thus, the "sublethal" conditions of stress in zone V are operating to reduce the population of rock bass in a fashion that would not be noticed in a casual pollution survey. There are three likely causes of this decline in zone V. One of these is the runoff from the agricultural areas sur— rounding the stream, which is probably contributing variable concentrations of potentially lethal agricultural chemicals. Another possible cause is the sewage effluent from the small urban areas of Fowlerville and Webberville. But the most likely source of low levels of fish toxicants is the metal plating plant effluent from Fowlerville. Probably all three are affecting the fish populations to some extent. Because the physical aspects of the environment in zone V are less suitable for rock bass than those in zone II, we can 67 say with some certainty that the rock bass populations in zone V were not likely to have exceeded those found in zone II at the present time. If this is true, then the rate of decline of the rock bass in zone V indicates that either the source of the problem has existed for less than perhaps 15 years or that it has increased in severity within that time. It should be recalled that the personal interviews and other (admittedly scanty) records show that a substantial popula- tion of rock bass has existed here for at least several de- cades. Thus, it is unlikely that the domestic pollution alone is responsible for the decline, unless the community growth has been large in the last few years. And it has not in these two small communities. Therefore, it appears that an increased use of pesticides or the advent of the plating plant, or both, has been responsible for the decline. The hypothesis that movement of fishes into an area of pollution is supporting the population there should be ex- amined in more detail. At first glance, it may appear that this is an unlikely phenomenon, i.e., that the fish would tend to avoid this area. However, it should be recalled that one characteristic of the stream environment is its intrinsic instability. Strong seasonal changes occur with respect to temperature (Figures 2 and 5) and discharge (Figures 4 and 5). These even fluctuate considerably from day to day. For this reason, there are extensive times during the year when the area may not elicit an avoidance reaction in a wandering 68 fish. On the contrary, with temporary alleviation of the deleterious concentrations of chemical constituents, a fish entering the area would find ample lebensraum. Even though the subsequent stress might prevent him from participating successfully in reproduction. Again, the usual form of bio- assay would fail to show any lethal environmental conditions. Zone IV This portion of the river is probably the least suitable for rock bass of all the five zones. Reference to Tables 1 and 11 shows that the bottom consists largely (about 80%) of sand and that the macrophytes and detritus fail to offer much cover for the fish. The river here is deeper than in the other zones and the flow rate is slower. King (1964) shows that the primary production is quite high, but the production of heterotrophic aufwuchs is low. He also shows that the in— organic sedimentation rate is exceptionally high, being a function of the flow rate, which is also reflected in the accumulation of silt reported in the present study (Table 1). All of which results from the fact that the zone is, for the most part, a reservoir backed up by the dam in Williamston (Figure 1). The population reduction in this zone is less severe, started from a lower initial population, and is occurring at a slower rate than in zones I or V (Table 12). The latter, of course, would be expected if the cause is a polluting 69 Table 12. Standing crop of biomass (in lbs/acre) of rock bass in the Red Cedar River for zones I—V in the years 1959 through.1964. Zone* year I II III IV v 1959** 28 42 28 10 26 1960** 44 26 28 15 15 1961** 10 22 16 5 0 1962*** 4 56 26 9 8 1965 No Observations 1964**+ 19 65 40 4 2 * I Polluted II Cleanest III Receives sewage IV Reservoir zone V Polluted , ** Linton and Ball (1965) *-** Present study 70 effluent near the upstream and of zone V. The total fish production was at an intermediate level up until 1961, at least, and was due largely to the presence of substantial numbers of white suckers and spotted suckers (Linton and Ball, 1965). Zone III This zone, according to Tables 1 and 11, appears to be rather good habitat for rock bass. There is extensive rocky bottom, considerable cover in the form of detritus, and, although this is not indicated in Table 11, there are large Elodea beds along part of the banks, which form excellent cover for the developing fry during the summer. Also, a short distance upstream are found heavy beds of Valisneria and Saggitaria. However, King (1964) reported that the total primary production is low on the average over the entire zone. The production of heterotrophic aufwuchs is excellent, being higher in this zone than in any of the other four. A very high production of the latter along with a low primary pro- duction seems incompatible, but is reasonable when one con— siders the effluent of the Williamston primary sewage treat— ment plant. In addition to the usual instability of a stream, the discharge rate in zone III until a few years ago was also Sub- ject to the needs of the dam owner in the production of power for a private frozen food storage plant. The periodic flush- ing resulted in excessive siltation and inorganic sedimentation 71 from the reservoir above. This was responsible in part for the low primary production rate, although the heterotrophic regime is mainly due to the allochthonous material from the sewage treatment plant. In response to the abundant food supply, the total fish production in this zone exceeds that of any of the other zones (Linton and Ball, 1965). However, the rock bass pro- duction was of an intermediate magnitude, while the bulk of the production occurred in the northern hog suckers, white suckers, and redhorse. The total production of game fish was low. The value of ra (Table 7) also reflected the status of the rock bass pOpulations, being second only to the value for zone II, but appreciably lower. Another factor should be considered in the study of any of the fish in zone III. Even a random movement of fishes around the lower end of the river would result in an accumu- lation of fish below the dam at Williamston, which provides an effective barrier to movement (the head is about 15 feet). Therefore, it should not be assumed that the high levels of the populations are maintained by natural reproduction alone. However, it is true that the food base is high and can sustain a large number of fish, even though the species composition is not a desirable one. Zone II This is the cleanest of the five zones with respect to pollution sources and is the most desirable habitat for rock 72 bass in a physical sense. Nearly half the bottom is rocky (Table 1) and there is a profuse array of riffles and pools in the upper half of this zone. The macrophyte crop (Table 11) provides excellent cover during the summer, compensating for the rather sparse detritus cover. The gradient is quite high. This results, along with the higher discharge, in a low rate of inorganic sedimentation and relatively little silt deposition. Primary production is intermediate (King, 1964), as is heterotrophic aufwuchs production, and a large standing crop of crayfish (Vannote, 1965) provides a staple part of the diet for the rock bass. This is the only zone which supports a large population of smallmouth bass. These together with the rock bass, contribute the largest centrarchid production to be found in the study section of the river. It is more than twice as great here as in the next lower zone. But the total fish production is lower here than in zone III. The northern hog sucker is present in fairly large numbers, although the total catostomid production is not high. From the standpoint of sport fishing, the Species composition is most desirable in this zone. The value of ra for the rock bass in this zone is higher than for any other zone. It is consistently positive (Table 7) and shows that the population here is capable of maintaining itself and of expanding rapidly or providing a large, sustained surplus for harvesting. Table 12 shows that the standing crop 75 of biomass was increasing up through 1964 and subsequent qualitative observations have Shown that this increase has probably been maintained through 1966. The reason for this increase is not clear, although it may be tied to the rapid expansion of macrophyte stocks in this zone (King, 1964, and Vannote, 1965). 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