COMPUTER ANALYSIS; OF HOMACH CONTENT. LENGTH-WEIGHT RELATlONSHiP AND GROWTH Q? FEEH PDPULATSONS Thai: For fhc Degree of Ph. D. MICHIGAN STATE UNNERSIW Ross 3. J. Mama‘b 1963 THESIS WIW/I/,Iwwlfllfi/kii/iiI/i/x‘z/‘fi/mflm This is to certify that the thesis entitled COMPUTER ANALYSIS OF STQ‘IACH CONTENT, LENGTH-WEIGHT RELATIONSHIP AND GROWTH OF FISH POPULATIONS presented by Ross B. J. Macnab has been accepted towards fulfillment of the requirements for Ph.D. Fisheries and Wildlife degree in gfikj/M// fM/EW/‘Um Major professor Date July 29, 1963 0-169 LIBRARY Michigan State University ABSTRACT COMPUTER ANALYSIS OF STOMACH CONTENT, LENGTH-WEIGHT RELATIONSHIP AND GROWTH OF FISH POPULATIONS by Ross B. J. Macnab Most scientific studies of fish population dynamics have taken place in recent years. This new approach to classical biology in addition to requiring a certain compe- tence in mathematics, has also burdened the research worker with great masses of manual calculations. Many of the standard computations used in fish popu- lation studies are directly adaptable to electronic computers. It is the purpose of this study to present certain areas in which computers may greatly assist the student of fish popu- lations, and to develop the necessary computer programs to carry out these computations. The programs are develOped in such a way that the fisheries biologist may have the calcué lations performed, without any knowledge of computer science. Complete instructions, from tabulation of raw data to computer console operating instructions are presented. ROSS B. J. Macnab The calculations involved in the analysis of life history studies are particularly well suited to treatment with electronic computers. Specifically, in the present study, stomach content, age and growth and length—weight rela- tionship are the areas developed. The list of tables of analysis computed by the com- puter programs is as follows: 1. Percentage of the Total Number of Stomachs Containing Each of Four Food Items and the Percentage of Stomachs Which Were Empty. 2. Dominant Food Item in Stomachs, Expressed As a Percentage of the Number of Stomachs Which Contained Food. 3. Dominant Food Item in Stomachs, Expressed As a Percentage of the Number of Stomachs Which Contained Food, When Sorted into Ten Length Intervals. 4. Specimen Number, Sex, Age, Total Length, Stand- ard Length, Fork Length, weight, Logarithms of Length and weight, Condition Factors and Ummagnified Scale Radius of Each Fish in the Sample. 5. Leg weight vs. Log Length, Regression and Corre- lation-Analysis. 6. Length vs. Scale Radius, Regression and Corre- lation Analysis. Ross B. J. Macnab 7. Length vs. Length, Regression and Correlation ~Analysis. 8. _Mean Condition Factors Separated Into Ten Length Intervals As Well As the Length Frequency Distribution of the Sample. 9. Mean Condition Factors By Age As well As the Age Frequency Distribution of the Sample. 10. Specimen Number, Sex, Age, Length, Scale Magni- fication and Calculated Lengths at Previous Ages, of Each Fish in the Sample. 11. Mean Calculated Lengths at Successive Annuli For All Fish in the Sample. 12. Mean Calculated Lengths at Successive Annuli For Males. 13. Mean Calculated Lengths at Successive Annuli For Females. 14. Mean Calculated Lengths at Successive Annuli For Uhsexed Fish. In tables of analysis which involve body length, a choice of total, standard or fork length is available. If all three length measures are included in the input data, three variations of most of the fourteen basic tables of analysis are available. Most of the tables present the anal- ysis of the entire sample as well as for each of the three Ross B. J. Macnab sex classifications (male, female and unsexed) separately. Three options of length interval size are available. The computer used in the analyses is the IBM 1401 with a minimum of 8000 locations of storage and two magnetic tape units. Certain other special features are required. The analyses may also be performed using IBM 1410 or 1460 computers. COpies of the programs developed are available from the author, c/o The Department of Fisheries and Wildlife, Michigan State University. Copyright by ROSS BERNARD JAMES MACNAB 1964 ,, COMPUTER ANALYSIS OF STOMACH CONTENT, LENGTH-WEIGHT RELATIONSHIP AND GROWTH OF FISH POPULATIONS BY Ross B. J1 Macnab 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 1963 3 ’._'F‘ Ux \Q 3 2L) %/4 J; ACKNOWLEDGMENTS Many individuals have assisted extensively in the development of this study. Unfortunately space dictates that indebtedness can be expressed to only a few. The author wishes to express his sincere appreciation to Mr. Ross L. Parsons, Branch Operations Manager, and Mr. Ivan P. Phelan, Controller, of Avon Products of Canada, Ltd. who arranged that all computer testing be done at the Pointe Claire, Quebec, laboratory. Without this assistance this study would not have been possible. It is particularly no- table that this aid was given by a corporation without any personal interest in the outcome of the study. Mr. C. Brodeur of R. L. Crain of Canada, Ltd. arranged for the supply of all computer paper which was used for the final computer runs and which appears in this volume. For this both he and his firm are sincerely thanked. Dr. E. W. Roelofs, committee chairman and Dr. P. Tack, Chairman of the Department of Fisheries and Wildlife at Michigan State University are both to be thanked for their patience and assistance during the preparation of this study as well as generally during the author's doctoral program. ii Mr. Maxwell DeKoven of International Business Machines (Canada) made valuable suggestions on technical matters in certain areas of the computer programs developed. Sincere gratitude must be extended to Dr. H. J. Montoye of the School of Public Health, University of Michigan, who originally stimulated the author's interest in research. For continued encouragement during the formative years the author wishes to express deep thanks to his parents. Their unselfish dedication indirectly enabled the study to be- come a reality. Last, but by no means least, sincere gratitude is extended to a most helpful and encouraging wife, Sherry, and to daughters Carol and Sandra who received far less than their share of attention during the preparation of this work. The assistance of the author's wife, from typing to proof-reading, is too extensive to state in detail. iii Chapter II. III. IV. TABLE OF CONTENTS GENERAL INTRODUCTION TO THE STUDY The Problem The Computer General Procedure Definitions of Terms Used Related Studies GENERAL DISCUSSION OF INPUT AND OUTPUT Input Output TABULATION AND KEY PUNCHING OF INPUT DATA Tabulation of Input Data Key Punching of Input Data COMPUTER ANALYSIS OF INPUT DATA . Basic Computer Requirements Console Operating Instructions MISCELLANEOUS INFORMATION AND SUMMARY Miscellaneous Information Summary LITERATURE CITED iv Page 11 12 l3 17 17 24 39 39 43 44 44 45 54 54 56 59 Table II. III. IV. LIST OF TABLES Sense switches for Program 1 . . Sense switches for Program 2 . . Programs halts . . . . . . . . . Running time for Programs 1 and 2 V Page 46 47 51 57 LI ST OF FIGURES Figure Page 1. IBM 1401 Installation . . . 2. Tabulation Sheet . . . . 3. Computer Flow Charts . . . . LI ST OF APPENDICES Appendix Page A. Output Tables . . . . . . . . . . . . . . . . 62 B. Block Diagrams of Programs 1 and 2 . . . . . . 119 C. Programs 1 and 2 . . . . . . . . . . . . . . . 128 vii CHAPTER I GENERAL INTRODUCTION TO THE STUDY Most scientific studies of fish population dynamics have taken place in recent years. This new approach to classical biology, in addition to requiring a certain compe- tence in mathematics, has also burdened the research worker with great masses of manual calculations. The investigator, interested in the biological sta- tistics of fish populations, must spend many hours of tedious manual, or at the best semi-automatic calculations, for each hour of creative investigation. The result has been that many data fail to reach publication for many years, because the research worker has been unable to complete the necessary calculations. werkers, in all fields of research, realize the relatively small percentage of their busy schedules they are able to devote to productive research. So much time must be devoted to administrative tasks, to lengthy library searches, to writing and re—writing research papers as well as to com- plicated statistical computations. While one must not subject scientific investigation to the rigid efficiency standards of a factory production line, one must nevertheless strive to free the research worker, as much as possible, from his non- creative burdens. The development of high—speed electronic computers has revolutionized data processing in many areas. Commercial applications have become so widely developed and publicized that they hardly need mention. Sales analyses, insurance tables, scheduling of reservations by airlines, capital in— vestment, inventory control, invoicing, to mention a few, are all areas in which computers have drastically reduced the time required for former procedures, and made possible the introduction of new techniques. The field of operations research, developed during the Second WOrld War, has rapidly progressed with the aid of electronic computers. Linear programming has led to many techniques of "least costing", which involve such lengthy calculations that they were im- practical, to suddenly become widely used. Simulation of plant operations by computers is resulting in more efficient operatidn of plant facilities. In the field of forestry, inventories of woodlands are being made to plan present and future operations. Engineering has employed computers to assist in the development of new dams and in the study of electrical circuits. -An entirely new branch of science has evolved during recent years, dealing with control and communication in living organisms and machines. This new area, cybernetics, has been investigated quite extensively, particularly by Wiener (1961) and his associates. Many of the standard computations used in fish popu- latiOn studies lend themselves directly to adaptation to electronic computers. It is the purpose of this study to present certain areas in which computers may greatly assist the student of fish populations, and to develop the necessary computer programs to carry out these computations. The pro- grams will be developed in such a way that the fisheries biologist may have the calculations performed, without any knowledge of computer science. The calculations involved in the analysis of life history studies, are particularly well suited to treatment with electronic computers. Specifically, for the present study, stomach content, age and growth, and length-weight relationship, were the areas chosen for development. These analyses are, for the most part, fairly standard in nature, being employed by fisheries workers throught the world. The calculations involved are generally tedious, requiring many hours, even with the aid of desk calculating machines. The Problem Objectives of the Study The objectives of this study are (l) to develop a coding system to enable the stomach content, age and growth and length-weight relationship, raw data, to be transferred into punched-card form; (2) to develop a series of electronic computer programs to accomplish the analysis of the raw data, as well as to print the results in tabular form; (3) to pre- sent a series of logical steps which the fisheries worker must follow, in the preparation of the raw data in punched- card form; and (4) to present the necessary computer console operating instructions, for the programs, such that a computer operator could perform the actual computer analysis for the fisheries worker. While it was not the purpose of this study to contrib- ute directly to the literature of fish populations, it is hoped that the system of analysis presented will greatly in- crease the efficiency of other workers. Similarly, it was not the purpose of this study to present a system of analysis which would be an end in itself. Rather, it is hoped that the present study will stimulate further refinements of data processing in the area chosen, as well as new developments in other areas. Limitations of the Study A basic aim of the study was the development of a system of analysis which would be sufficiently sophistocated to meet the precise needs of research workers, yet simple enough to encourage its use. The resulting compromise may lack certain details required by some investigators. However, it is hoped that this limitation will serve to stimulate the development of more specialized programs to meet these specific needs. Perhaps an example might be in order. For the sake of simplicity, certain advantages appeared for having all raw data condensed onto one punched card per fish. This presented restrictions to the quantity of raw data possible. For stomach content analysis, space dictated that only four different food items or groups could be included, while many studies require a dozen or more items. Future programs could be developed in which one punched card per fish could be de- voted solely to stomach content raw data. This would allow for inclusion of as many as twenty-five different food items. The attempt was made to create a sufficiently general- ized system of analysis to insure its adaptability to varied needs. This generalization was obtained at the expense of certain features possible in computer programs designed for one specific research project. Certain of the tables of analysis involve length-frequency distributions. The compromise was ten intervals, with three choices of interval size. A program developed for one particular group of data could be planned in such a way as to include more than ten intervals with a specific pre-chosen interval size. Still another limitation is the possible inclusion of undetected errors. In the development of computer programs of this type there exist certain advantages to constructing a hypothetical sample for testing purposes. This allows for the inclusion of as many sets of conditions as can be en— visioned. 'Nevertheless, the possibility still exists that a' set of conditions, in some particular sample of fish, has not been encountered in the development of the present programs. In such an event, it is hoped that the author will be notified immediately, so that the necessary adjustments can be made. Test Sample The sample used in the testing and demonstrating of the computer programs was hypothetical. No significance should be attached to the actual results presented. The sample was constructed to include as many sets of conditions as possible. Extreme values were included in the test sample to allow for the eventuality that they might exist in certain fish populations. Scale radii, for example, were made greater than would be expected in normal samples, but this was intentional. Similarly, condition factors in many cases are well below what might be expected in nature. However, the advantages of a hypothetical sample appeared to far outweigh the disadvantages. The Computer The computer selected for the analyses was the IBM 1401 Data Processing System. However, either the IBM 1410 or the IBM 1460 may also be used. Designed and manufactured by the International Business Machines Corporation, the 1401- is a solid state (transistorized) digital computer readily available in IBM Data Centers or Service Bureaus across North America as well as in most foreign countries. Because of the complexity of this and other computers, they are well beyond the financial limits of fishery departments of universities or state or provincial fisheries and wildlife departments. However, the introduction of the “Data Center" or "Service Bureau" concept has meant that machine time of any short duration may be rented, and trained operators provided. Thus, a fisheries research worker, after tabulating the data in a prescribed manner could have the data key-punched and processed in an extremely short time at a reasonable expense. This was a key factor in the selection of the IBM 1401. The 1401 system provides high-speed input output and arithmetic and logical ability, with the advantages of stored- program techniques. Both actual and symbolic language program- ming are possible. The computer is sequential and has the variable word length feature. It is available with magnetic tape units for additional storage capacity. A typical 1401 installation is shown in Figure 1. From left to right may be seen two magnetic tape units, the 1402 Card Read-Punch, the 1401 Processing Uhit with a 1406 Storage Unit, and the 1403 Printer. The 1401 Data Processing System is comprised of all of the above units. The 1401 Processing Unit contains the core storage and circuitry that perform the machine logic. Storage capa- city is available in 1400, 2000, 4000, 8000, 12,000 or 16,000 alphamerical characters of 8-bit core storage. The eight bits consist of six bits for binary coded decimals, a check bit and an eighth bit for field definition. The programs developed in this study require a minimum storage capacity of 8000. Simultaneous punched-card input and output is provided by the 1402 Card Read-Punch. This unit has two card feeds. The read section has a maximum reading speed of 800 cards per minute. Actual speed is governed by the amount of processing between read commands. The punch section has a maximum aoSmflspmcH Si 28 a 85mg 10 punching speed of 250 cards per minute. Actual punch speed is again governed by the amount of processing between punch commands. Another output medium for the 1401 Data Processing System is the 1403 Printer. Printing speeds of up to 600 lines per minute are possible. The standard printing capacity, per line, is 100 positions with an additional 32 positions available as a special feature. Each position can print 48 different characters. These include 26 alphabetic, 10 numer- ical and 12 special characters. Magnetic core storage is used in the 1401 Data Pro- cessing System. All data in core storage are instantly available and each position of storage is individually ad- dressable. The physical make-up of each core storage location makes it possible for arithmetic operations to be performed directly in the storage area. Magnetic tape is made of a plastic material, coated with a metallic oxide. It can be magnetized in tiny spots in such a way that patterns of these spots are codes for digits, and alphabetic and special characters. Thus, magnetic tape may be used as data storage, and this data may be part of input or output. 11 General Procedure The investigator wishing to make use of the computer programs developed in this study, must follow a prescribed set of instructions. These instructions will be dealt with in detail in the chapters that follow. Briefly, however, the procedure is as follows. Tabulation of Data A special tabulation form was develoPed such that the raw data, when measured, could be recorded in a prescribed manner. This tabulation sheet may then be taken directly to an experienced key—puncher, who can directly transcribe the raw data into punched-card form. Analysis of Data The computer programs develOped in this study, were reproduced in condensed form into decks of cards. Copies of these, may be obtained through the author. These program decks must then be taken to the IBM Data Center or Service Bureau where the analysis is to take place. Instructions are provided, for the computer operator, to complete the analysis. 12 Definitions of Terms Used Computer The term computer has many different meanings. In its most liberal definition it may be referred to as any instrument used for computations. However, of late, the term has taken on a more restricted meaning. For this study, com- puter is taken to refer to an electronic devise used for com- putations, and governed by a set of instructions called a program." This program is stored within the computer. Elec- tronic calculators, using wired panels, would not be included. Computer Program -A particular set of instructions, designed to solve a specific problem, is known as a program. When these in- structions are stored internally, within the computer, it is called a stored—program. The instructions, developed in this study, were key-punched into cards and enter the computer through this medium. Computer Input The raw data fed to the computer, prior to analysis, are referred to as the computer input. For this study input is in the form of punched-cards. In one of the programs, images of the punched-cards are placed on magnetic tape. 13 Later, in the same program, this magnetic tape becomes a source of input. Computer Output The tables of analysis, produced by the computer are called the output. These are produced by the high speed printer of the 1401 Data Processing System. Logarithm Logarithms are calculated and analyzed in several of the tables of analysis developed in this study. In all instances these logarithms are to the base 10. Related Studies Electronic computer processing of data in fisheries or wildlife investigations has not been widespread. Certain developments in this area may have occurred without having reached publication. Others which have been published make use of "unit record" electronic calculating, sorting and tabulating machines rather than high speed electronic com- puters. However, a brief discussion of techniques developed in both fisheries and wildlife is of‘interest. Leeper gt_§1. (1957) published a paper in which certain uses for punched-card methods, in the tabulation and 14 analysis of fishery research data, are indicated. Both ad— vantages and disadvantages of this technique of data proc- essing are cited. In a somewhat similar review, Lambou (1959) described the use of machine methods in processing fishery data. The general area of punched card techniques is discussed. Basic principles, advantages and disadvantages, and arrangements for securing machine time are considered. Mansueti (1959) also commented on the need for critical fishery research planning and electronic data processing. In this analysis the author stresses the impor- tance of good design in research planning as well as automatic proCessing of data. An extensive listing of applications developed in fisheries and wildlife data processing is in- cluded. The advantages and disadvantages of cooperative electronic data processing programs are also emphasized. Some long term effects of machine methods on fishery science are cited. Lambou (1959) has contributed toward a bibliography on use of machine methods in processing fishery data. Most of the references cited do not deal with fishery problems directly but describe methods which might be applied to fishery problems or deal with automatic data processing in a general manner. 15 A simplified creel census program for punch-card tabulation has also been detailed by Lambou (1959). The machines employed are "unit record" in nature. However, in personal correspondence Lambou has indicated the development of as yet unpublished computer programs to process length- weight data. The California Bureau of Marine Fisheries was one of the first natural resource organizations to apply machine methods to fishery data. IBM equipment was installed in 1931 to aid in processing the commercial fish catch of the state. Since 1931, the system has been elaborated and expanded. Tomlinson and Abramson (1961) of the California Department of Fish and Game, have employed an IBM 7090 computer in fitting a von Bertalanffy Growth Curve by "least squares." El-Zarka (1959), according to Mansueti (1959), pro- grammed studies of Yellow Perch populations in Lake Huron so that multiple correlation and regression analyses of many years of biological environmental data were possible. The U.S. Fish and Wildlife Service has also been active in processing commercial catch records using punched cards. A Maryland general canvas has been conducted by this agency cooperatively with the Maryland State Department of Tidewater Fisheries. This work has been reported in mimeo- graphed form by Dumont (1959). Other Maryland commercial 16 fisheries statistical techniques have been described by Hammer §£_al. (1958). Eberhardt and Hayne (1958) describe a method of estimating duplication in licensing. Benson (1957) calls attention to a method of mechanically analyzing hunters' re- ports in Nova Scotia. In addition, Schultz (1954) outlines the use of punched card techniques in wildlife surveys of Tennessee. The National Oceanographic Data Center with head- quarters in Washington D.C., has been using and is increasing its use of electronic computers in processing oceanographic data. This institution has developed computer programs to prepare cruise data, compute and list cruise data and to pre- pare geographical card and magnetic tape files. This work is analyzed using a Burroughs 205 computer with Cardatron (including one punch card input; one punch card output; and one 407 line printer output) and magnetic tape facilities (3 tape units). In addition, this center has been involved in the develOpment of biological information (data) holding-re- call systems. CHAPTER II GENERAL DISCUSSION OF INPUT AND OUTPUT It is of utmost importance that the investigator, wishing to make use of the system of analysis developed in this study, have a thorough understanding of the raw data required as well as the tables of analysis develoPed by the computer. These are referred to, in computer terminology, as the input and output. The present chapter discusses in de- tail the items of raw data included and the various tables of analysis available to the investigator. The input, after being tabulated by the fisheries worker is key-punched into punched-card form. Each fish in the sample is represented by one punched-card. Input Experiment Number This indication allows the investigator to identify the particular sample of fish being processed. The number is key-punched into the deck of punched—cards which are the raw data. The researcher may thus have a permanent record of the 17 18 sample of fish which the deck of cards represent. The range of experiment numbers available is 001-999. The experiment number is not printed in any of the tables of output. Specimen Number An identification for each fish in the sample is provided by the specimen number. The range of specimen numbers is 0001—9999. This limits the maximum number of fish in any given sample to 9999. In tables of output, where calculations are printed in detail for each individual fish, the specimen number is included. Age The age of each individual fish is included in the raw data input. The range of ages possible in this study is 01-12. Age is included, in tables of output, where calcu— lations are printed in detail for each individual fish. In certain output tables, summarizing the data of the sample, the fish are sorted by age prior to analysis. Sex The raw data input includes the sex of each individual fish. Fish within the sample may be classified as male, fe— male or unsexed. This latter classification is included to 19 allow for immature fish, or other instances where sexing is impossible. Sex is included in tables of output which are printed in detail. In tables which summarize the data of the sample, analysis is generally performed for the entire sample, for males only, females only and unsexed only. The coding system used for sex is 0 for males, 1 for females and blank for unsexed fish. Units The usual unit of measure for body length is milli-V meter and for body weight is the gram. However, after con- sulting "Total length" below, a decision may be made to change the units, for the entire sample, to the centimeter and the dekagram. The coding system for units is blank for the millimeter-gram and l for the centimeter-dekagram. Total Length The total length of each fish may be recorded. Pro- vision is also made for the use of standard length and fork length. All three length measurements may be recorded in any given sample of fish. However, one of the three must be designated as the "basic" length measurement. Information on designating the "basic" length measurement is given in Chapter IV. This "basic" length measurement is used in certain tables 20 of analysis where calculations are based on only one of the three length measurements. At least one of the three length measurements must be included in the raw data. The normal range of lengths is 001—999 expressed in millimeters. If fish within the sample exceed 999 millimeters in length, the range, for the entire sample, may be altered to 001—999 ex- pressed in centimeters. However, if the decision is made to use centimeters as the unit for one of the three length measurements, it must also be used for the other two if they are recorded. Similarly if centimeters are used for length- measure, the unit of body weight must be the dekagram. Standard Length Opportunity for recording standard length is provided. The discussion above, under "Total length," is applicable to this item of raw data. Fork Length Fork length may also be included as part of the in- put data. The discussion, under "Total length," is again valid. Weight The weight of the fish expressed in grams, must be included in the input data. The range of weights possible is 21 0001-9999 grams. If individual fish in the sample exceed 9999 grams, the unit of weight measure for the entire sample, may be changed to dekagrams (10 grams). However, if this decision is made the unit of length measure must be the centi- meter. Scale Radius at Capture The scale radius at capture must form a part of the input data. The unit of measure is the millimeter. If magnification is used to accomplish the measurement, reduction to an unmagnified value is performed automatically by the computer. For example, if the scale is magnified 47 times and a reading of 141 millimeters is recorded, the computer will calculate the unmagnified value to be 3.00 millimeters. This variable magnification feature is discussed at length below. The range of the scale radius, in its unreduced or magnified form, is 001—999 millimeters. Scale Radius at Previous Ages Provision is made for the inclusion of scale radii at previous annuli, up to a maximum of 12 years. These data must comprise part of the computer input. The discussion above, under scale radius, is also applicable for these data. It should be emphasized that the maximum possible age is 22 twelve. The range for each of the radii is as above, 001-999 millimeters. Scale Magnification Scale magnification is intimately connected with both the scale radius at capture and the scale radii at previous ages. Its inclusion allows for a variable amount of magnifi— cation, from fish to fish, for scale measuring. However, in any given fish the amount of magnification must remain con- stant for all scale measurements. The range of magnification possible is 01-99. No magnification would be indicated by 01, while 99 would indicate a magnification of 99 times. This allows all scale radii data to be reduced automatically, to unmagnified form, by the computer. All scale radii data are then computed and printed in output tables of analysis, in unmagnified form. Percent of Each of Four Food Items in Stomach The remaining raw data are those concerned with stomach content analysis. The contents of the stomach may be subdivided into four food items or groups. The estimated percent of the total stomach content, comprised by each of the four food items is included in the input data. The four food items are designated A, B, C, and D. Item A may be 23 pre-selected by the fisheries worker to represent any one food item or group, such as crustacea, insects or forage fish. The range of values possible for “percent of food item A in stomach" is 000-100. Thus 000 would indicate that food item A did not occur in the stomach. Similarly 070 would indicate that food item A made up 70% of the total stomach content. Should the entire stomach content be made up of food item A, the value 100 would be given in the raw data input. If 000 is given as the value for each of the four food items, it indicates an empty stomach. Items B, C and D represent the- other food items or groups. Two of the tables of stomach content analysis, indicate the dominant food item in the stomachs of groups of fish in the sample. These groups are sorted by sex and by body length intervals. The computer in its analysis selects the dominant food item in each stomach, that is, the largest percentage value from the four food groups. Should two or more of the four food items share this distinction the computer will consider the dominant item to be the one further in the alphabet. Thus, if the entire stomach content is indicated to be made up of 50% food item A and 50%.food item C the computer will consider item C to be the dominant food item in the stomach. Therefore, the in- »vestigator should attempt to make a decision as to which comprises the greatest percentage of the entire stomach 24 content. In the example just cited the values 49%,food item A and 51% food item C, or 51% food item A and 49% food item C, should be given as input. Otherwise, the possibility ex— ists of bias in the output data. Summary of Input Data The preceding description of input data is meant to familiarize the fisheries worker with the type of raw data analyzed by the computer programs developed in this study. More concise details of methods of tabulation, and instructions to be followed in having the data transferred into punched— card form, are given in Chapter III. Output Introduction The analysis of the input data was divided into two phases. The first phase involves the calculations necessary for the analysis of stomach content data while the second performs the remaining analyses. One computer program was written for each of the phases. Program 1 reads in the punched card raw data input deck (1 per fish), performs the necessary calculations and prints output Tables 1, 2 and 3. Program 2, in a separate operation, rereads the input deck, performs the necessary calculations and prints output Tables 25 4—14. Details of operating instructions are given in Chapter IV. Samples of output Tables 1-14, and variations of these tables are given in Appendix A. Table 1.--Percentage of the Total Number of Stomachs Containing Each of Four Food Items and the Percentage of Stomachs Which Were Empty The first of a series of three tables of stomach con- tent analysis is given in Table l, which indicates: (l) the percentage of the total number of stomachs which contained each of the four food items; (2) the percentage of stomachs which were empty; (3) the number of fish which contained each of the four food items; (4) the number of fish with empty stomachs; and (5) the total number of fish in the sample. These figures are given for the total sample as well as separately for the three sex classifications. Table 1 in Appendix A presents the analysis of the hypothetical test sample employed in the present study. It may be seen, for example, that in this sample of fish, 55.9% of the total num- ber of fish contained food item C, 9.1% of the males had empty stomachs and 42 out of a total of 93 fish were females. 26 Table 2.--Dominant Food Item in Stomachs, Expressed as a Percentage of the Number of Stomachs Which Contained Food Table 2 in Appendix A continues the analysis of stomach content. The table analyzes only those stomachs which contained food at the time of capture. This table is concerned with the dominant food item, that is the one which made up the largest percentage of the total content of each stomach. The percentage of stomachs in which each of the four food items was dominant is calculated. Separate percent- age figures are given for male, female and unsexed fish. A14 so included are the number of fish in which each of the four food items was dominant, the number of fish in the sample containing food, as well as a breakdown of this into the num— ber of males, females and unsexed. Tables 3, 3A and 3B.—-Dominant Food Item in Stomachs, Expressed as a Percentage of the Number of Stomachs Which Contained Food, When Sorted into Ten Length Intervals A further refinement of the previous table is presen- ted in Table 3 in Appendix A. This series of calculations indicates the dominant food item, expressed as a percentage, for males, females and unsexed fish. However, the additional feature of a breakdown of the data by body length is included. The particular body length measure used, that is total, 27 standard or fork, is the "basic" length measure discussed under "Total length" in this chapter. If the "basic" measure chosen is total length, the table of analysis appears as Table 3. If standard length is selected it appears as Table 3A, while Table 3B is based on fork length. Table 3 and its variations (A and B) excludes all fish with empty stomachs. When no fish occur in a particular length interval, for a particular sex classification, a blank appears in the output table. For example, Table 3 in Appendix A shows that there were no male fish in the total length intervals of 501—600 and 801-900. It may also be seen that Table 3 and its variations perform the analysis by sex classi- fication but not for the sample as a whole. In the hypothetical test sample results, which appear in Table 3 of Appendix A, certain of the findings are as fol- lows. In the total length interval 401—500 food item A was dominant in 28.6% of the males, while item B was dominant in the remaining 71.4%. No female or unsexed fish appear in this length interval. There were a total of 15 fish con- taining food, in the total length interval 001—100. Simi- larly there were 19 males in which food item B was dominant. Three choices of size interval are available in Tables 3, 3A and 3B. The example in Appendix A employs a 28 length interval of 100 with a maximum length of 999. Addi- tional options are an interval of 50 with a maximum length of 500 or an interval of 25 with a maximum length of 250. In all cases the number of intervals is fixed at 10. These options are further discussed in Chapter IV. Tables 4, 4A and 4B.——Specimen Number, Sex, Age Total Length, Standard Length, Fork Length Weight, Logarithms of Length and Weight}. Condition Factors and Unmagnified Scale Radius of Each Fish in the Sample Table 4 gives a detail printing of certain items of. raw data and certain calculations, for each individual fish. The specimen number, sex, age, total length, standard length, fork length, weight, logarithm of total length, logarithm of weight, total length condition factor (metric), standard length condition factor (metric), fork length condition fac- tor (metric), and scale radius (unmagnified) are included. In calculating condition factors, those based on millimeters and grams use the formula, 100,000 W L3 K: while those based on centimeters and dekagrams use the formula, 29 Table 4A is identical to Table 4 except that the for- mer gives the logarithm of standard length in place of the logarithm of the total length. Similarly, Table 4B gives the logarithm of fork length in place of the logarithm of total length. This is another example of the use of the "basic" length measure. Tables 5, 5A and 5B.--Log Weight vs. Log Length, Regression and Correlation Analysis Table 5 and its variations (A and B) present the log weight vs. log body length, regression and correlation analysis. The regression phase of the analysis is based on the equation, log weight = 109' c +11 log length where log c is the y-intercept and n is the slope of the re— gression. The x variable is the logarithm of length and the y variable is the logarithm of weight. Log c is calculated using the equation, 1 Elog w- 2(log L)2 - Slog L-( 5109 L-log W) °9 c = 2 2 N- 2(1og L) - ( Slog L) while n is developed from the equation, n- Elogw-Nlogc Slog L 30 The correlation coefficient "r" is calculated using the equation, = NSXy- (SX)(§y) V[N2X2 — <2x)21[N2y2 - (5y?) r Table 5 gives the regression and correlation analysis of log weight vs. log total length for the entire sample as well as separately for male, female and unsexed fish. Also included are the total number of fish, the number of fish in each sex classification and the partial calculations used in the analyses. That is, the sum of x, sum of y, sum of x2, sum of y2 and the sum of xy. Table 5 in Appendix A is the analysis of the test sample. Table 5A differs from Table 5 in that it presents the analysis log weight vs. log standard length while Table 5B involves itself with the analysis of log weight vs. log fork length. This is still another example of the computer performing its analysis on the "basic" length measure. In Table 5 and throughout the study, minus quantities are signi- fied by a minus sign at the right end of the series of digits, 'rather than to the left as is normally the case in non-com- puter work. 31 Tables 6, 6A and 6B.--Length vs. Scale Radius, Regression and Correlation Analysis The regression and correlation analyses for body length vs. scale radius is given in Tables 6, 6A and 6B. The regression equation used is, y = alpha+beta x where alpha is the y—intercept and beta is the lepe of the line. The x variable is scale radius while the y variable is body length. The equation employed to develop alpha is, Ey- 2x2 - ZX( ny) NZXZ — (2.02 alpha = and for beta is: zy~- N alpha 12x beta = These are essentially the same equations used in the calculations for the previous table. It is easily demon— strated that these equations can be reduced to the more com— monly seen versions. nExy - (ZXHZY) beta = n 2x2 — (2x)2 alpha ='y - beta R 32 The correlation coefficient "r" uses the same equation as given under "Table 5, 5A and 5B." Table 6 gives the regression and correlation analyses for total length vs. scale radius. The analyses are given for the entire sample as well as separately for male, female and unsexed fish. Also included are the numbers of fish involved as well as the partial calculations used in the study. Table 6A differs from Table 6 in that the analyses are based on the standard length vs. scale radius relationship. The fork length vs. scale radius relationship is analyzed in‘ Table 6B. Here again is an example of the computer performing the analyses on the "basic" length measure. The analysis of test sample is given in Appendix A. Tables 7, 7A and 7B.--Length vs. Length, Regression and Correlation Analysis Tables 7, 7A and 7B give the regression and corre- lation analyses between the three length measures. Table 7 gives the standard length vs. total length analyses with the former being the y variable. Table 7A calculates the fork length vs. total length relationship with fork length as the y variable. Table 78 presents the fork length vs. standard length relationship with fork length again being the y vari— able. The equations used in this analyses are identical to those given for the previous series of tables. 33 The analyses are again performed for the entire sample as well as for each sex classification. The partial calcu— lations and the number of fish involved are also included. The analyses of the hypothetical test sample appear in Appendix A. Tables 8, 8A and 8B.--Mean Condition Factors Separated Into Ten Length Intervals As Well As the Length Frequency Distribution of the Sample The condition factors for each individual fish in Tables 4, 4A and 4B are summarized in Tables 8, 8A, 8B, 9, 9A and 9B. Tables 8, 8A and 8B give the mean condition fac- tors of the fish in the sample, when broken down into ten body length intervals. Again, as was discussed under the heading "Tables 3, 3A and 3B" in the present chapter, three choices of interval size are available. Table 8 analyzes the condition factors with total length as the "basic" length measure. The condition factors are analyzed, and the body length intervals are those based on total length. The total length frequency distribution is also calculated in this table. The analyses are performed on the entire sample as well as separately for each sex classification. The test sample results are presented in Table 8 of Appendix A. 34 Table 8A employs standard length as the "basic" length measure. Table 8A in Appendix A shows that the con— dition factors used are those based on standard length (KSL) and that length interval breakdown is also standard length. Similarly, Table BB performs the analysis with fork length as the "basic" length measure. Tables 9, 9A and 9B.--Mean Condition Factors By Age As well As the Age Frequency Distribution of the Sample Tables 9, 9A and 9B summarize the condition factor data by age. The individual fish in the sample are sorted by age in the computer and the mean condition factors are calculated. This is performed not only for the entire sample but separately for each of the three sex classifications. The maximum age possible is again 12. In Table 9 the analysis involves the total length condition factors while Tables 9A and 9B analyze standard length and fork length condition factors respectively. The number of fish in each classifi- cation is also given. Thus the age frequency distribution are given in these tables. 35 Tables 10, 10A and 10B.-—Detail Listing of Specimen NUmber, Sex, Age, Length, Scale Magnification, and Calculated Lengths at Previous Ages, of Each Fish in the Sample Tables 10, 10A and 103 give a detailed report of the growth history of each individual fish in the sample. The equation employed in this analysis is, L' = C +-§ (L—C) where L' is the body length when annulus x was formed, 5' is the scale radius to annulus x, L is the body length at cap- ture, S is the total scale radius and C is a correction fac- tor. This factor is the y-intercept (alpha) from the total length vs. scale radius regression given in Tables 6, 6A and 6B. This calculation is performed from age 1 to a maximum age of 12. In Table 10 the growth history is based on total length. Tables 10A and 10B differ in that the calculations are performed for standard length and fork length, respec— tively. Also included in these tables are the specimen number, sex, age, body length at capture, and the scale—magnification factor employed. The analysis of the test sample is found in Appendix A. 36 Tables 11, 11A and llB.--Mean Calculated Lengths at Successive Annuli For All Fish in the Sample A summary of the detail calculations of the previous set of three tables is given in Tables 11, 11A and 11B. The analysis is given for the entire sample without regard to sex. Analysis for each of the sex classifications are given in later tables. The analysis performed is commonly found in the literature. In the present study, allowance is made to process ages from 1 to a maximum of 12. The mean length at capture for each age is calculated, as well as the mean calculated lengths at previous ages. The mean of each of these calculated lengths at previous ages, for each age, is also given. Table 11 employs as the basis of calculation total length. Tables 11A and 11B use standard length and fork length. Tables 11, 11A and 11B, located in Appendix A indi- cate the analysis of the test sample data. Tables 12, 12A and l2B.—-Mean Calculated Lengths at Successive Annuli For Males Tables 12, 12A and 12B perform the same analysis as the previous set of tables, except that it is calculated for only the male fish in the sample. Again Table 12 com— putes on the basis of total length, 12A on standard length 37 and 12B on fork length. The analysis of the test sample is found in Appendix A. Tables 13, 13A and 13B.—-Mean Calculated Lengths at Successive Annuli for Females The mean calculated lengths at previous ages for fe- males are given in Tables 13, 13A and 13B. Once again the A and B versions are based on standard length and fork length. Appendix A contains the test sample analysis. Tables 14, 14A and l4B.--Mean Calculated Lengths at Successive Annuli for unsexed Fish. Tables 14, 14A and 14B present the mean calculated lengths at previous ages for unsexed fish. The A and B versions base calculations on standard length and fork length. The test sample analysis is again located in Appen- dix A. Summary of Output In Tables where A and B versions occur, only one of the three variations can be obtained from a single computer run. The normal situation is for the computer to produce Tables 1-3 with Program 1 and Tables 4-14 with Program 2. However, if certain sense switches on the computer console are turned on, other combinations are possible. A choice of 38 Tables 7, 7A or 7B is available on any given computer run. If another switch is turned, Table 3 from Program 1 and Tables 4—6 and 8-14 from Program 2 appear in their A vari- ations while still another switch causes the B versions to be computed. All possible versions may be obtained with three passes of the input cards for each of the two programs. The choice of length—interval size, discussed earlier in this chapter, is also accomplished through this method. Details of these options appear under "Console Operating Instructions" in Chapter IV. CHAPTER III TABULATION AND KEY-PUNCHING OF INPUT DATA The preparation of input data for presentation to the computer may be divided into two distinct phases. These are the collecting, measuring and tabulating of the raw data on a prescribed tabulation sheet by the fisheries worker, and the transcribing of data from the tabulation sheet into punched card form by the key—puncher. The importance of ac- curacy in the preparation of the input data hardly needs to be emphasized. However, a rigid, literal following of in- structions presented in this chapter is a prerequisite to a smooth processing of the data. 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