Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Year class strength and catchability of mountain lake brook trout De Gisi, Joseph S. 1994

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-ubc_1995-0038.pdf [ 5.7MB ]
JSON: 831-1.0074808.json
JSON-LD: 831-1.0074808-ld.json
RDF/XML (Pretty): 831-1.0074808-rdf.xml
RDF/JSON: 831-1.0074808-rdf.json
Turtle: 831-1.0074808-turtle.txt
N-Triples: 831-1.0074808-rdf-ntriples.txt
Original Record: 831-1.0074808-source.json
Full Text

Full Text

YEAR CLASS STRENGTH AND CATCHABILITY OF MOUNTAIN LAKE BROOK TROUT by Joseph S. De Gisi  B.S., Cornell University, 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Zoology  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA December 1994 © Joseph S. De Gisi, 1994  In presenting degree  at the  this  thesis  in partial  University of  freely available for reference copying  of  department  fulfilment  British Columbia, and study.  of  by  his  or  her  Department of  o o 1 OCJ^J  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  12-  !>c-  i ^ f  that the  I further agree  representatives.  may be It  publication of this thesis for financial gain shall not permission.  requirements  I agree  this thesis for scholarly purposes or  the  for an advanced  Library shall make it  that permission for extensive granted by the  is  understood be  head  that  allowed without  of my  copying  or  my written  Abstract  Increased gillnet catch per effort (cpe) of juvenile salmonids occurred following intense exploitation of the adult population, for several studies conducted in mountain and arctic small lakes. Higher cpe may reflect increased catchability or greater numbers, so behavioral or numerical responses cannot be inferred from changes in cpe alone. I used age structured estimation methods, and gillnet depletion data from 1986 to 1992 for seven Sierra Nevada small lake brook trout populations, to reconstruct year class strength and prerecruit (age 1) gillnet catchability prior to and during the experimental removals. I made Walters-Collie (1988) estimates of year class strength for the seven study lakes across the years of the removals. The within-year depletions and available models consistently underpredicted the number offishremaining in the lake, so estimates did not use the within-year structure of the data. Ageing error correction provided little change in the estimated strength of cohorts produced during the mid- to late 1980's. Estimates showed an inverse relationship between year class strength and adult population size, for cohorts from 1984 to 1990. Prerecruit q also appeared inversely related to adult population density for most lake populations. This may have been either a direct effect of adult density, or indirectly mediated through the effect of adult density on prerecruit length at age. Year and cohort-specific adult q's showed little evidence for density dependence in adult q. The vulnerable proportion of the adult population appeared insensitive to population density. I developed a modification of the WCfittingto adjust for between-lake variation in encounter probability which estimated a relative activity parameter, k . Relative to q, variation in k was reduced and showed little apparent between-lake density dependence.  ii  Table of Contents Abstract  ii  Table of Contents  iii  List of Tables  vi  List of Figures  vii  Acknowledgements  ix  Chapter 1. General Introduction  1  Arrangement of the thesis  2  Literature Review: response of salmonid lake populations to experimental thinning  3  Summary  8  General study design and methods  10  Study site and field methods  10  Age determination  15  Size at age  15  Weather, year class strength and survival  17  Synopsis of the chapters  24  Chapter 2.  Chapter 2. Ageing error  24  Chapter 3. Depletion estimation at period level resolution  25  Chapter 4. Population and catchability estimates at depletion resolution  26  Ageing error estimation  28  Introduction  28  Methods  30  Background and general methods  30  Estimation of Q and P  33  Simulations  35  Performance of ageing error correction  35  Ageing error and population estimation  36  Results  37 Estimates of Q and P  37  Simulations  39  Performance of ageing error correction: age distributions  39  Ageing error and population estimation  42  Discussion  42  iii  Chapter 3. Depletion estimation at period-level resolution  45  Introduction  45  Methods  47  Field methods  47  Treatment of the data  48  Population and catchability estimation  49  Terminology and assumptions  49  Estimation  49  Schnute removal estimates  50  Models  50  Initial point catchability  52  Estimate bias  52  Walters-Collie depletion estimates  52  Survival  54  Leslie estimates  54  Age-aggregated removal estimates  55  Results  55 Schnute estimates  55  Day and night catchability  55  First period catchabilities  55  Schnute estimate bias  59  Walters-Collie estimates  59  Walters-Collie and Leslie estimate bias Catchability variation  59 59  Catchability related to size  59  Diel variation in catchability related to size  64  Age-aggregated estimates  64  Schnute estimates  64  Discussion  67  Chapter 4. Population and catchability estimates at depletion-level resolution  72  Introduction  72  Methods  74  General methodology  74  Field methods  74  Terminology and treatment of the data  74  Catch-age estimation  76 iv  WC estimator  76  Log transformation  78  Survival  79  Population estimation  80  Stock and Recruitment  80  Vulnerability  81  Catchability  81  Simple q  81  Encounter rate model  82  Results  85 Population size  85  Survival  85  Year class strength  85  Stock and recruitment  91  Vulnerability  91  Catchability  91  Simple q WC estimator  91  Encounter rate WC estimator  100  Prerecruit and new recruit catchability  100  Discussion  105  Chapter 5. Summary, conclusions and future research Major conclusions  Ill •  113  References  115  Appendix A.  121  v  List of Tables Table 1.1. Estimated catch per effort of Arctic char for Little Nauyuk Lake gillnet removals, based on Table 1 and Figure 5 in Johnson (1994)  6  Table 1.2. Selected characteristics of the eight study lakes, including elevation, total surface area, shoal area, mean and maximum depth and subjective estimates of angling use and stream access  13  Table 13. Summary information for depletions from 1986 through 1992 in seven study lakes, including starting date, effort, range of number of netsfished,and total catch  14  Table 2.1 Estimates for O, the vector of parameters describing the classification matrix, for normal and exponential models applied to 1129 multiply-aged brook trout  37  Table 2.2. Estimated ageing error classification matrix for 1129 multiply-aged brook trout  38  Table 23. Percentage of ages reassigned due to ageing error correction for depletions in the seven study lakes, 1986 to 1992  38  Table 2.4. Summary statistics for 2 sets of 500 runs of simulation of ageing error correction  40  Table 2.5. Summary statistics for 2 sets of 100 simulations of ageing error correction with population estimation  41  Table 3.1. Notation for models developed in Chapter 3  51  Table 32. Five Schnute removal models which werefitto study depletion data  51  Table 33. Schnute estimates of population size, with confidence intervals and catchability, for cohorts with catch of at least 20 fish for depletions in the seven study lakes, 1989 to 1992 Table 3.4. Schnute estimates of population size, with confidence intervals and catchability, for age aggregated removals from the seven study lakes, 1989 to 1992  56  66  Table 4.1. Notation for models developed in Chapter 4  76  Table 4.2. Estimates of relative activity, k , for three area parametrizations of the Walters-Collie encounter rate model for seven study lakes  100  vi  List of Figures Figure 1.1. Location of the study lakes  11  Figure 1.2. Bathymetric maps of the experimental study lakes  12  Figure 13. Mean length of age 1+ to 5+ brook trout gillnetted from the experimental lake populations, 1986 to 1992  16  Figure 1.4. East Piute Pass snowpack, in inches of water equivalent on May 1st, and Bishop California total degree-days for May through September, plotteed for 1971 to 1992. Values are deviations from the median for the period  19  Figure 1.5. Residuals from catch curve fit to pooled 1986 data from 51 sampled lakes  20  Figure 1.6. Gillnet catch by cohort for Gem Lake 2,1987 through 1991  22  Figure 3.1. Terminal q versus initial period q for 60 cohort-specific Schnute estimates from 1989 to 1992, using adult cohorts with catch > 20  58  Figure 3.2. Ratio of Schnute estimate to M K A estimate, plotted versus Schnute estimate, for adult cohort-specific estimates with catch > 20 from 1989 and 1991 depletions  60  Figure 33a. Leslie q for adult cohorts with catch > 20 plotted by year for six study lakes, 1986 to 1992. Also shown is the WC q using survival = .85  61  Figure 3.3b. Leslie q for adult cohorts with catch > 20 plotted by year for six study lakes, 1986 to 1992. Also shown is the WC q using survival = .85. Initial two catch-effort points ommitted for all estimates  62  Figure 3.4. Cohort-specific Schnute q plotted versus mean fork length for five study lakes 1989 to 1992  63  Figure 3.5. The effort-adjusted ratio of Schnute q ^ : q ^ plotted versus mean length, for precruit and adult cohorts with catch > 40 from five study lakes, 1989 to 1992  65  Figure 4.1. Estimates of age-specific survival for seven study lakes, as well as general age-specific and age-invariant survivals estimated from the seven lakes' data combined  86  Figure 4.2. Year class strength, with 95% confidence intervals for seven study lakes, 1976 to 1990 cohorts, estimated by the WC method and s = .82. Also shown is year class strength estimated using lake-specific age-varying mortality  87  Figure 43. Year class strength, with 95% confidence intervals for seven study lakes, 1976 to 1990 cohorts, estimated by the WC method and s = .82. Also shown is year class strength, for the same cohorts and lakes, estimated using catch data corrected for ageing error in Chapter 2  89  1  vii  Figure 4.4a. Year class strength at age 1+ plotted versus adult stock in the fall of the cohorts' 0+ year, for 1984 to 1990 cohorts in seven study lakes, estimated using the WC method and s = .82  92  Figure 4.4b. Year class strength at age 1+ plotted versus adult stock in the fall of the cohorts' 0+ year, for 1984 to 1990 cohorts in seven study lakes, estimated using the WC method and lake-specific age-varying survival  93  Figure 4 J . Year class strength at age 1+ plotted versus adult stock in the fall of the cohorts' 0+ year, for 1984 to 1990 cohorts in seven study lakes, estimated using log-transformed catch and a direct search method with s = .82  94  Figure 4.6. Year class strength at age 1+ plotted versus adult stock in the fall of the cohorts' 0+ year, for 1984 to 1990 cohorts in seven study lakes, estimated using the WC method with s = .82. Adult stock includes half of prerecruit numbers  95  Figure 4.7. Proportion vulnerable plotted versus total adult density, for cohorts with catch > 20,1988 to 1992. Estimates made using WC method with depletion level data and s = .82. The vulnerable population for each cohort was estimated by the Leslie method  96  Figure 4.8. Proportion of adults vulnerable, plotted versus adult density for ageaggregated adult data from five study lakes, 1988 to 1992. Population estimates made by the WC method with s = .82 and depletion-level data. Vulnerable population was estimated by the Leslie method using age-aggregated data  97  Figure 4.9. Estimates of q plotted versus mean length for adult cohorts with catch > 20, for five study lakes 1987 through 1992  98  Figure 4.10. Pooled yearly adult q plotted versus adult density for seven study lakes, 1987 to 1992, estimated using the WC method with s = .82  99  Figure 4.11. For seven study lakes, effort density plotted versus lake area, relative activity (k ) plotted versus adult density for two survival parameterizations, and relative activity plotted versus effort density for two survival parameterizations, all estimated using the WC encounter rate model  101  Figure 4.12a. Prerecruit q plotted versus adult density for seven study lakes, 1987 through 1991  102  Figure 4.12b. Prerecruit q plotted versus prerecruit mean length for seven study lakes, 1987 through 1991  103  Figure 4.13. New recruit q plotted versus pooled adult q in the same year, for seven study lakes 1987 to 1992, estimated using the WC method and s = .82  104  viii  Acknowledgements  Don Hall generously allowed me to build upon his research and was always willing to assist in any way possible. Committee members John Post and J.D. McPhail offered helpful comments on this thesis. No thanks would be too much for Carl Walters, who initiated this study and provided impetus for its direction.  In California, Department of Fish and Game biologists Curtis Milliron and Alan Pickard provided valuable space in their cramped office quarters in 1991. Steve Parmenter became involved in my work in 1992 and assisted in several aspects, including field and moral support. Tom Jenkins and Phil Pister shared their knowledge and experience with Sierra Nevada brook trout.  In the field, Peter Troffe was an able assistant and cheerfully endured unpleasant conditions. Kevin Honness worked efficiently despite persistent misgivings about whether killing thousands of fish was a good way to understand their biology. I also received much-appreciated help from Jordan Rosenfeld, Carl Walters, Karl Chang and Anthony Liscio.  Many have offered their ideas concerning field, laboratory, and computational methods. Among those I wish to thank are Gordon Haas, Joel Sawada, and Leonardo Huato Soberanis. Michael Folkes contributed to otolith preparation. Jon Schnute offered helpful explanation concerning his ageing error models.  I received personal financial support via a Graduate Fellowship from the National Science Foundation. Research support was provided from NSERC grants to J.R. Post and C.J. Walters.  ix  Chapter 1. General Introduction Prior to 1860, more than 95% of 16,000 western North American mountain lakes were Ashless (Bahls 1991). In the following century, extensive stocking programs driven primarily by the outdoor recreation industry led to the introduction of trout and char to most of the lakes. One widely introduced species was eastern brook trout, Salvelinus fontinalis (Mitchill), which often establishes self-sustaining stunted populations. Concern for the status of native aquatic organisms has led ecologists to reconsider the wisdom of widespread salmonid introductions, since many other species do not appear to coexist with introduced trout and char (Bahls 1991). As well, fishery managers generally consider stunted populations undesirable because of the small adult body size attained. It is clear that an ability to effectively manipulate the density of such populations would be desirable. Freshwater salmonids grow indeterminately, and their life history parameters are generally size- and thus density-dependent. As a result, the dynamics of self-sustaining populations are often characterized by strong interactions between size or age groups. Predicting the response of such populations to manipulation will likely hinge upon better understanding of recruitment dynamics and the interaction between age classes.  This study grew directly from Donald L. Hall's (1991) investigation of size-density relationships and the potential alleviation of stunting of Sierra Nevada brook trout. Hall began his work in 1985 with a survey of more than 50 small lake populations. He made experimental removals of hundreds offish from each of twelve lakes in 1987, repeating ten of the lakes in 1988 and eight in 1989. The removals were intended to accomplish three tasks simultaneously: reduce density, allow population estimation, and provide samples for evaluating growth and reproductive responses. Population estimation was fundamental, since without it the response to density reduction could only be evaluated qualitatively. Density reduction was apparently difficult to achieve (Hall 1991). Depletion of adult populations appeared to have been matched by new cohort recruitment to the catchable population. Minimal growth response of the remaining adults was observed (Hall 1991).  1  Nevertheless, the apparent recruitment response to removals was an intriguing hint of strong population regulation, and the primary motivation for this thesis. In 1991 and 1992,1 redepleted eight of Hall's study lakes. Additional removals have had two distinct benefits. First, the additional data have allowed me to follow the fate of cohorts produced during the original depletions, which were not yet fully vulnerable at the end of Hall's study in 1989. More fundamentally, the additional data have allowed me to use powerful estimation procedures to reconstruct population abundance and year class strength before and during the experiment. This in turn has allowed me to examine the numerical and catchability responses to removals in greater detail.  Arrangement of the thesis I have organized this thesis into three chapters. Each chapter is intended to stand independently, structured around the questions which I approached. Wherever possible I have used simulation in parallel with analysis of data fromfieldexperiments. This has been an important method of validating computational algorithms, as well as allowing me to examine the potential performance of the models and estimators I have used.  In this general introduction, I review the reported experimental thinning of small lake salmonid populations and reinterpret the results with regard to year class strength and catchability. I summarize the general methods and terminology used for the current experimental study. For the experimental populations, environmental conditions likely influenced year class strength and might have impacted the shape of the catch curves used for survival estimates. I examine weather time series for suggestions about mechanisms that may drive variation in year class strength. This information is also useful in the evaluation of the response of year class strength to removals, since the treatments for this study were not staggered with respect to time. I conclude with a preview of the material of Chapters 2 to 4.  2  Literature Review: response of salmonid lake populations to experimental thinning  Exploitation experiments on arctic and mountain lake salmonid populations have provided tantalizing suggestions of density dependence in reproduction and population regulation. Donald and Alger (1986) suggest that montane, subalpine, alpine and arctic lakes have dominant characteristics in common. These features include simple fish communities, low productivity, minimal human exploitation or other disturbance, and a long annual period of ice cover which may buffer the lakes from interannual environmental variability (Johnson 1980). Manipulation of the fish populations of these lakes has been characterized by two motives: a practical desire to determine the potential production and appropriate management of exploitation for such lakes, and the notion that such lakes might serve as simple, selfcontained homogeneous systems to test population regulation theory (Johnson 1983, citing Holling 1973). A common design has been several years' removals by gillnets. Removals provide samples to characterize the population before and during the experiment. Size and growth, relative abundance, maturity schedules and fecundity have all been monitored, usually with respect to age. Here I review the reported results of studies which have manipulated small lake salmonid populations through exploitation. I confine my review to studies with age specific results.  Lindstrom et al. (1970) and Fagerstrom (1972) report on a removal experiment in 10 ha Lake Langbjorsjon, Jamtland Mountains, Sweden. From 1958 through 1966 they removed, primarily by gillnetting, 147 - 556 brown trout (Salmo trutta) aged 1+ to 8+ and 83 - 479 arctic char (Salvelinus alpinus) per year from the lightly sportfished populations. They reported only the results for brown trout. They observed an increase in length at age of 4 to 18 % after the removals. Mark-recapture estimation failed due to small sample size and tag loss/mortality. This left relative abundance at age as the interpretable result, complicated by year to year changes in netting procedure. The 1959 year class recruited strongly to the nets at age 2, a year earlier than other cohorts, and was still strong at age 4 and 5. Subsequent cohorts did not appear strong, either at age 2 or later. From relative abundance data, they inferred that the pre-removal 1953 and 1954 cohorts were larger than the 1959 and later 3  cohorts, produced after removals. The study does not appear to document a consistent response, either in terms of year class strength or earlier recruitment to the nets, although the lack of population estimation makes interpretation difficult and the concurrent removal of char confounds the result.  From 1971 to 1978, Healey (1978,1980) gillnetted age 1+ to 12+ lake whitefish (Coregonus clupeaformis) from four previously unexploited lakes of 305 - 547 ha in the Canadian Northwest Territories. Small survey samples were taken in 197land 1972 to establish preremoval characteristics, and in 1975,1976 and 1978 to monitor the response. Exploitation was approximately 0,10, 20 and 30% annually in the four lakes during 1973 and 1974. Healey recorded that age 3+ and older fish were longer by 5 to 10% following the exploitation. Removal estimates for 1973 were possible for the two lakes subject to heavy exploitation, using ages 3+ and older. Otherwise, relative year class strength and recruitment were inferred from survey catch per effort (cpe). High cpe for the 1973 and 1974 cohorts in 1975 and later surveys in the most heavily exploited lake, compared to cpe's for the same ages prior to exploitation, led Healey to conclude that he had observed increased recruitment due to exploitation of adult whitefish. However, higher cpe's of young fish occurred principally in the most heavily exploited lake, where most of the adult population had been removed. Catchability of the younger fish presumably increased in response to the removal of larger adults (Healey 1980), so that comparisons of cpe between years provide weak inference concerning abundance. The gillnetting concurrently removed hundreds of predaceous lake trout from the exploited lakes (Healey 1978) which might be expected to have a large impact on both catchability and abundance of young whitefish. His cpe-based estimates of year class strength for the unexploited lake showed that the 1973 and 1974 cohorts were also the most abundant of the period 1961-75. In light of these details, Healey's conclusion that he observed a recruitment response to adult whitefish exploitation appears weakly justified.  Johnson (1976, 1983, 1994) documents studies on stunted arctic char populations in small lakes of the Canadian Northwest Territories. Two lake populations, Little Nauyuk (44.6 ha) and Gavia (17.4 ha) 4  were subject to heavy exploitation of age 1+ to 17+ fish by gillnetting, beginning in 1975. Johnson interpreted the results of the experiment through length and age frequency distributions and overall cpe. After initial removals of cannibalistic larger fish, small fish of variable age began to appear in the gillnet catch later in the first year's removals and appeared in both early and late removals of the following years.  I reworked Johnson's published results to examine cpe by age and cohort. In Little Nauyuk Lake following the 1975 exploitation, cpe for younger ages (1+ to about 8+) increased slightly from 1976 to 1977 and then declined through 1981. Abruptly in 1983, cpe for the same ages increased fourfold and was high again in 1985, declining in 1988 (Table 1.1). Data for Gavia shows a similar pattern except the abrupt increase occurred in 1981. Johnson's results are difficult to explain, moreso without population estimation. In both cases (Gavia in 1981, Little Nauyuk in 1983) the cpe increase was abrupt across many age classes, which is difficult to interpret in terms of recruitment. Perhaps cpe is too variable to infer abundance and recruitment from the available data; ageing error is also a strong possible accomplice (Johnson 1983).  Langeland (1986) gillnetted age 1+ to 11+ arctic char from 7m deep 163 ha Lake 0vre Stavatj0nn, central Norway, during 1979 to 1984. Population estimation was age/size aggregated using markrecapture in 1979 (ages 3+ and older) and 1981 (ages 2+ and older), and the removal method in 1983 (ages 2+ and older). Langeland did not estimate numbers at age but inferred from aggregated estimates and age frequency distributions that "recruitment of young fish was also reduced by the intense fishing. However, the high fraction of one-year-old fish in 1984 indicated increased recruitment and a strong 1983 year class." Without a population estimate, any conclusion regarding the numerical strength of the 1983 cohort is suspect.  Donald and Alger (1989) removed 321 to 423 brook trout aged 1+ to 7+ from 3.5 m deep 2 ha Olive Lake, Rocky Mountains, British Columbia each year during 1982-84. Population estimation was 5  Table 1.1. Estimated catch per effort for Little Nauyuk Lake gilllnet removals. Estimates are based upon Table 1 and Figure 5 in Johnson (1994). Catch from 1982 and 1984 was not sampled for age composition. Catch per effort increased abruptly from 1982 to 1983, apparently across many cohorts.  Catch Effort Total cpe 87 86 85 84 83 82 81 80 79 78 77 76 75 74 £ 73 O 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55  75 76 2724 855 26.0 11.3 104.8 75.7  c  0 3 3 5 3 4 4 6 8 8 7 12 10 6 6 4 5 4 2 2 75  2 77 88 2 4 7 6 7 5 6 5 5 4 2 1 2 1 1 1 2 0 76  77 506 6.2 82.1  78 754 9.4 80.5  Year 79 80 544 362 13.2 12.0 41.3 30.2  0 0 0 4 3 0 2 1 6 3 4 2 6 1 99 3 3 3 3 3 3 7 77 2 2 3 3 2 2 4 4 4 2 5 9 4 7 4 8 13 7 3 11 4 4 13 11 4 2 8 7 1 1 5 7 3 3 0 1 2 0 1 4 1 0 1 1 1 3 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 77 79 80 78 Year 6  81 501 11.8 42.5  0 1 3 3 1 2 7 4 4 5 4 3 1 2 0 0 0 0 0 0 0 0 0 0 0 0 81  82 83 84 85 88 602 713 1571 691 542 11.8 6.0 12.0 4.0 6.1 51.0 118.8 130.9 172.8 88.9 0 0 3 0 11 25 7 1 21 10 17 13 7 11 4 7 5 8 10 11 16 11 13 19 8 19 14 4 9 . 13 4 6 18 2 7 9 3 4 4 1 6 3 0 3 3 0 3 1 1 2 1 0 2 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 82 83 84 85 88  age/size aggregated by the mark-recapture method using gillnets for marking and electrofishing for recapture. In 1985, mean weight at age had increased by 30% (age 1+) to 250% (age 6+) compared to a 1981 pre-exploitation sample. Donald and Alger inferred increased recruitment at age 1+ from the increased proportion of age 1+ in the catch following 1981, and population estimates which did not decline during the study despite removals. However, they did not account for changing catchability of age 1+ fish as adults were removed, and its effect on population and recruitment estimates. Neither did they attempt to estimate year class strength for cohorts produced before removals, to rectify recruitment estimates with later years' abundance estimates for the same cohorts, or to examine year class strength for the same period for a comparison population not subject to exploitation.  Hall's work on density reduction of small lake brook trout populations was conducted in single-species lakes and used replication. The treatments were not effectively staggered; of the experimental units continued through 1989, one was begun in 1986 and seven in 1987 (Hall 1991). Cohorts produced during the experiments were only beginning to recruit to the sampling gear at the end of the study, so interpretation was incomplete. Again, increased size and catchability of young cohorts was apparent as the removals preceded (Hall 1991). Population estimation was incomplete for the large cohorts suspected to have resultedfromthe removals.  Borgstrom (1992) manipulated the stunted brown trout population of 49 ha 40m deep Lake L0yning, western Norway from 1985 to 1989. The population spawns in a river above and below the lake, as well as in inlet streams; juveniles begin to join the lake population at age 3+ with complete recruitment to the lake by 5+. Borgstrom removed about 2000 age 3+ to 11+ fish per year, corresponding to an approximate annual exploitation of 20 to 40%. Population estimation was accomplished by sizestructured mark recapture (seining and gillnetting, respectively) with the exception of the estimates for the 9-14 cm class, mostly 3+fish.This class was not recaptured in sufficient numbers to allow an estimate, so Borgstrom assumed equal seine catchability for this class and the next larger class, and estimated numbers of 9-14 cmfishbased on the population estimate for the larger class and the two 7  classes' proportional representation in the seine catch. He noted an inverse relationship between the estimated number of age 3+ fish in the lake, and the estimated number of 5+ and older fish in the lake. He inferred that recruitment of 3+ fish from the river and stream nursery grounds had responded to the removal of adults and deduced the same result from the work of Jensen (1977). If catchability for 3+ fish in the lake was lower relative to the next larger class in the early years of the study when adult densities were still relatively high, then bias across years in the recniitrnent-at-age-3+ estimates would have resulted. Still, such bias would probably only exaggerate the trend of earlier recruitment from nurseries as adult densities were lowered. Borgstrom notes other evidence that juvenile fish make twoway movements between streams and the lake as they approach recruitment to the lake population, possibly assessing lake conditions (Lien 1978). Presumably earlier recruitment would lead to higher relative year class strength because mortality rates in the stream and river nurseries are assumed higher than for recruited adults in the lake (Borgstrom 1992). However, Borgstrom did not report any attempt to reconstruct year class strength for cohorts produced before the experiment, or follow cohorts produced during the experiment to assess their eventual total contribution to the lake population.  Summary Increased cpe for young cohorts was observed following the initial removal of adults from small lake salmonid populations, in six of seven studies reviewed. Cpe increases have been interpreted as a recruitment response to exploitation. Authors have generally been unclear about whether they are referring to recruitment to the sampling gear or recruitment to the adult population. The term "recruitment" remains loosely defined in thefisheriesliterature and it is not my intent to criticize its use. Nevertheless the distinction is necessary, especially when attempting to deduce the mechanisms of population regulation (Healey 1980; Johnson 1983,1994; Borgstrom 1992)fromexploitation experiments. Interpretation of the results of these experiments has been hampered by one or more of the following: (1) lack of control / replication / staggerring of treatments; (2) other confounding manipulations - most notably, significant removals of other fish species; 8  (3) insufficient population estimation and short abundance time series; no estimate of preexploitation recruitment levels; no attempt to follow cohorts produced during experiments, to rectify abundance estimates across years and as adults.  These difficulties in design have not prevented speculation on the mechanisms of population regulation, inferred from the behavioral or numerical response of youngfishto adult removals (Power 1978; Healey 1980; Johnson 1983,1994; Borgstrom 1992). There is a burgeoning literature on the mortality risk - growth return optimization that presumably governs the behavior of juvenilefish(Walters and Juanes 1993). If the removal of adults changes the risk - return balance for youngfish,this might be expected to lead to some combination of faster growth and higher survival to maturity, and thus increased year class strength. Although implied, this has not been convincingly demonstrated in the lake salmonid population studies I reviewed. Increased cpe may reflect either higher catchability or higher numbers. When adults are removed, greater juvenile length at age often occurs and presumably has a positive influence on catchability, because longerfishare believed to have a proportionately higher probability of encountering the gear through increased swimming distance (Rudstam et al. 1984). Increases in cpe of youngfishwithin a single year may simply reflect growth in length during the same time period, possibly accelerated by the removal of adults. As well, however, adult density might have a direct effect on juvenile catchability. Adults may prey upon youngerfishor exhibit other aggressive behavior towards juveniles. Juvenile activity or use of some habitats, or both, could thus be increased in response to lower adult density, which might result in higher juvenile gillnet catchability.  In summary, increased juvenile cpe following adult removals suggests population changes which might result in increased year class strength. Increased cpe could be due to higher juvenile numbers in the sampled habitat or higher juvenile catchability. If catchability is higher, it may reflect simply increased length at age, or some additional behavioral response to lower adult density. Such a behavioral response could resultfroma change in either side of the risk-return balance for juvenile fish. Because  9  studies have notrigorouslyestimated both numbers and catchability of juveniles, their results have only been suggestive of suppression of year class strength and juvenile catchability by high adult density.  One or several additional mechanisms might lead to higher abundance for cohorts spawned after the start of adult removals. Among these are changes in population fecundity, egg mortality, and survival of juveniles (Hall 1991). These are all potentially important determinants of year class strength which might respond to adult removals, and represent fascinating topics for further investigation. However, the gillnet data I have collected cannot be used to examine the function of these mechanisms. Instead, my thesis focuses on population estimation methods which allow me to reconstruct the abundance and gillnet catchability of cohorts produced before and during experimental removals. Adult natural mortality is an important parameter of the models I use, so following a brief description of the study area and general methods, I consider how weather might interact with recruitment to impact its estimation.  General study design and methods Study site andfieldmethods This study was carried out in eight small lakes east of the crest of the central Sierra Nevada, Cahfornia (Figure 1.1). While the lakes differ in morphometry, (Table 1.2; Figure 1.2), before manipulation each brook trout population was characterized by maximum fork length of about 200 mm, which is typical of hundreds of Sierra Nevada populations (Hall 1991). Maximum age attained by individuals from these populations is double that attained in the native range. The populations are considered stunted because maximum length is lower than for most lake populations in the native range, and because growth slows or ceases long before maximum age. A 200 mm individual may be from 5 to 15 years of age (Hall 1991). Stunted brook trout resume growth when transplanted to lakes with greater food supply, which distinguishes stunting from dwarfism, a condition believed genetically determined (Hall 1991).  10  120"  38°  119°  118'  '  '  L  37'r  36°'  '  Figure 1.1. Location of the seven study lakes (labelled) along with other brook trout populations sampled in 1986. The contour shown is 3000 m elevation, and the inset shows the location of the study area within the state of California (figure reproduced from Hall 1991).  11  a) Flower  b) Wonder 3  c) Flshgut 1  d) Dingleberry  e) Hell Diver 3  f) Hell Diver 2  g) Par Value  h)  Gem 2 N  1 net  1 0 0 meters  Figure 1.2. Bathymetric maps of the eight study lakes. The contour interval is 1 m except for Par Value where it is 3 m. The length of a study gillnet is also shown, along with the map scale.  12  Table 1.2. Selected characteristics of the eight study lakes. Given are: elevation, total surface area, shoal area (area above the 3m depth contour), mean depth, maximum depth, and subjective estimates of the angling use and fish accesss to inlet or outlet streams. Lake elev (m) area (ha) shoal (ha) z (m) z^ (m) angling stream Gem 2 Hell Diver 2 Dingleberry Flower Fishgut 1 Par Value Wonder 3 Hell Diver 3  3335 3480 3195 3200 3315 3135 3375 3580  0.7 0.4 2.1 1.9 0.6 2.4 1.3 0.9  0.6 0.2 1.7 1.9 0.5 0.5 0.5 0.2  1.8 2.8 1.8 1.2 1.7 7.5 3.5 6.5  4.3 5.2 6.7 2.4 3.7 17.7 7.0 13.1  mod light heavy heavy light mod mod light  none low high high low low none low  Removals from the eight lakes were made each year from 1986 or 1987 through 1992, except 1990 (Table 1.3). Fish were captured by gill netting for 3 to 11 consecutive periods of 8 to 16 hours each. We fished Lundgrens (Sweden) light green, nylon, weighted gillnets of length 36 m, height 1.5 m, on bottom. The nets were composed of twelve randomly ordered panels of bar mesh size 4,6.25, 8,10, 12.5,16.5,18.5, 22,25, 30,33 and 38 mm, and were chosen from a pool of ten such nets. Shore anchored nets were usually set perpendicular to shore but we also made sets offshore oriented at random or downwind. Two to 6 nets werefishedsimultaneously at different locations in the lake. Each removal period ended with lifting and clearing of all nets and a new period began immediately with setting of the nets, usually in different locations than the previous period. At the end of each removal period the catch was weighed and measured and the saggitae removed, labelled and preserved in glycerin. I generally pool the catch at age from all netsfishedwithin a removal period. I also refer to removal periods as netting periods or simply as periods.. I use the terms depletion, depletion series, depletion experiment, and multiperiod removal to refer to catch at age and effort data collected for multiple consecutive removal periods and tabulated by period. Estimates which use this level of time resolution of the data are referred to as period-level estimates, since they extract information about population size from the change in cpe at age across periods within a depletion. Methods and estimates which instead aggregate the catch at age and effort for all periods within a depletion, are referred to as depletion-level estimates. Depletion-level estimates extract information solelyfromthe change in cpe at age across years.  13  Table 1.3. Summary information for depletions made from 1986 through 1992 in seven study lakes. Total effort is in units of net-hours, the number of nets multiplied by the time they werefished.For most depletions, the same number of nets wasfishedfor all periods but if not, the range of number of netsfishedis shown. Lake Depletion Starting Periods Nets Total Total date catch effort Hell Diver 2 1986 8-23 4 3 106 176 1987 7-26 2 54 5 105 1988 7-25 3 2-3 97 89 1989 8-12 6 4 233 284 1991 7-07 5 6 207 359 1992 7-22 4 5 242 245 Dingleberry 1987 7-20 9 659 \ 2-6 531 1988a 11 7-16 6 827 752 1988b 7-29 1 4 77 55 1989 8-6 9 6 641 913 1991a 4 7-13 5 647 243 1991b 7-28 9 5 773 535 1992 8-03 7 5 585 426 Flower 1987 6-17 2-4 8 557 326 1988 11 714 6-13 2-6 464 1989 7-11 921 5 6 382 1991 7-21 674 10 6 1027 1992 8-24 7 6 866 520 1987 Fishgut 1 7-16 2-4 3 266 115 1988 7-02 7 2-5 383 312 1989 8-19 5 6 463 352 1991 8-05 7 5 440 419 1992 7-29 6 5 373 343 Par Value 1987 8-17 9 644 592 3-6 1988a 9 8-01 6 685 638 1988b 1 79 8-20 5 65 1989 11 944 7-23 6 763 1991 8-11 9 6 905 655 1992 8-17 7 6 539 815 Wonder 3 2-4 1987a 6-27 242 5 180 1987b 4 8-28 3 287 127 1988 429 8-11 6 5-6 377 1989 9 8-23 6 616 636 1991 8-17 9 607 5 548 1992 6 342 8-11 5 350 Hell Diver 3 1987 2-4 7-28 5 81 213 254 1988 4 4 7-25 68 1989 4 8-13 68 148 3 342 1991 4 142 8-25 6 1992 4 54 7-25 4 180  14  While the Gem Lake 2 population gave no initial indication that it would behave differently, recruitment failed from 1987 through 1991, likely for reasons I discuss later. The population was apparently extirpated in 1991. I have excluded Gem Lake 2 from the analyses made for this thesis.  Age determination For each fish, the right side saggita was blotted dry and mounted half-embedded, sulcus-side up, in Crystalbond® thermoplastic resin on a standard microscope slide. The slide was inverted and the otolith half-sectioned to the saggital plane by polishing on 1200 grit abrasive paper followed by 9u lapping paper. Otoliths were examined under reflected and transmitted light at 15-30X magnification, and ages estimated according to criteria presented in Hall (1991b).  Size at age Demonstration of the effect of removals on size at age was not a primary objective of this study. Gillnets are highly size selective, and it was never established that the fish captured during removals were representative samples for size at age, especially for the younger ages. As well, comparisons are confounded by differences in the seasonaltimingof food availability and growth between years, and sampling dates which changed from year to year due to logistics. Nevertheless, gillnet catchability is influenced by size, and size at age may be useful as secondary evidence about population density. For ages 1+ to 3+ in most of the study lakes, mean length at age increased from 1987 to 1989, decreased to near pre-removal levels in 1991 but increased again in 1992 figure 1.3). Trends in mean length at age for older age classes were much more variable across years and lakes during the study QFigure 1.3). This is partly due to small sample size, but also may reflect early removal of individuals with the highest growth potential, reduced potential to resume growth at increased age (Reimers 1979), or changing asymmetric competition between age groups (Walters and Post 1993).  15  Dingleberry  87 210 i 190  88  215 195 175 155 135 115 95 75 89  90  91  92  5  I 3 2  Flower 5 4  170  3  150  2  4 3  I  3  90  86  87  88  89  90  91  Fishgut 1  92 4  130  1  110  1  90 88  89  90  91  92  87  Par Value «  $  150 1  87  5  1  170  2  130 110  190  Hell Diver 2  3  205 *  88  89  90  91  92  89  90  91  92  Wonder 3  185 165 145 125 105 85  87  88  89  90  91  245 i 225 205 185 165 145 125 105  92  87  Hell Diver 3 5 5 4  4 3 2  88  5  i 3  1  2  2  1 2  1  87  88  1 89  90  91  92  Figure 1.3. Mean size at age for age 1+ to 5+ brook trout captured in the seven study lakes during depletions from 1986 to 1992. Plot symbol indicates the age group. Across years for age 1+ to 3+ fish, size at age tended to increase from 1987 to 1989, decline in 1991 and increase again in 1992.  16  Weather, year class strength and survival The population estimation methods I use in this thesis rely on an independent estimate of natural mortality. Reliable estimates of age specific natural mortality are difficult to obtain. Authors have often assumed age andtimeinvariant natural mortality, lacking definite information to the contrary. Survival at age is often estimated by the catch curve method which involvesfittinga function to logtransformed catch at age data, typically combined across years to smooth discontinuities (Ricker 1975). However, catch at age is influenced by year class strength, age-specific vulnerability and ageing error, as well as survival. In this section I briefly consider the following questions concerning weather, year class strength and survival at age. First, are there interlake similarities in year class strength? Do they parallel any obvious patterns in the weather data I have assembled? A striking observation from Hall's study was the ubiquitous convexity of catch curves for 20 distinct lake populations (p. 66, Hall 1991). Here I consider whether similarities in the catch curves are more likely to have arisen from large scale patterns in year class strength due to environmental conditions, or from decreasing survival at age consistent among populations. What would be a highest estimate of adult survival? The depletion data across years might suggest plausible survival values, but the analyses in Chapter 3 require a starting point and for reasons explained there, a highest plausible estimate is needed. Finally, if there is evidence of recruitment-weather correlation, would year class strength during manipulation years likely have been enhanced or retarded by environmental conditions during those years? Given that treatments were not staggered, this information should be weighed when considering the numerical response to adult removals.  Mountain lake salmonid year class strength can be highly variable (Donald and Alger 1989; Hall 1991) and is likely influenced by weather (Lindstrom et al. 1970; Donald and Alger 1989). Droughts and cool wet periods of several years' duration are probably typical for the Sierra Nevada. Brook trout spawn in the fall so overwinter drying and freezing of stream and nearshore gravels can be catastrophic for eggs andfry(Cooper et. al. 1988) and might be implicated in the formation of some  17  weak year classes (Cooper et al. 1988). But conditions leading to freezing are complex and may occur on a time scale of days to weeks and thus be undetected in monthly or seasonal totals. Generally, year to year variability in winter conditions is presumed buffered by ice and snow cover (Johnson 1983). For this reason, and because studies have demonstrated a link between summer warmth and mountain lake salmonid growth (Jensen 1977) and recruitment (Lindstrom et al. 1970; Donald and Alger 1989), I examine spring and summer conditions as factors affecting year class strength in the study lakes.  Spring and summer lake temperatures are probably influenced both by seasonal atmospheric conditions and by meltwater from the previous winter's snowpack (T. Jenkins, pers. comm.). I created two time series from the data available. I used the East Piute Pass data for May 1 as an index of spring snowpack water content (data obtained from California Cooperative Snow Surveys, Sacramento, CA). This is a biased indicator since snowpack on May 1 is zero in some years, but as a rough index it should be sufficient. I subtracted the Bishop cooling-degree days from heating-degree days (65° F base) totalled for the months May to September as an index of summer atmospheric warming for the east slope of the central Sierra Nevada (data obtained from National Climate Center, Reno, NV). Brook trout spawn in October and November in the Sierra Nevada (Cooper et al. 1988). Hatching occurs from January to April and emergence about two months later, depending on temperature (Cooper etal. 1988). During the age 0+year, they experience winter conditions as eggs and sac fry, followed by spring and summer conditions as fry and fingerlings. I have labelled cohorts by the year in which fry emergence occurred. For instance, fry from eggs spawned in the fall of 1989 emerge in early-to-mid 1990 and are referred to as the 1990 year class. To look for patterns in year class strength across lakes, I pooled the catch at age data for all lakes sampled in the 1986 survey. The 1986 data is taken from more than 50 lakes and no single lake or group of lakes dominate the age distribution as for other years. Because it is not clear at what age full gillnet vulnerability occurs for unexploited populations, I plotted the residuals from the catch curve, using a linear fit to logtransformed pooled data and including all ages in the catch.  18  25  T  -300  ±  T - w n t m ( D N c o o ) O T - w n 3 i i ) ! D s a i o ) O T - w r— r-— — i— r— r ^ - r ^ o o o o o o o o o o o o c o o o o o c o o j o o  Year Figure 1.4. East Piute Pass snowpack measured in inches of water equivalent on May 1, and Bishop California total degree-days May through September (65 F base temperature) plotted for 1971 through 1992. Values are deviations from the median for the period 1971 to 92. High snowfall years (1978, 80, 82, 83, 86) tended to have colder than average following summers. Average to dry years with average to warm summers were 1977,79, 81, 84, 85 and the drought years 1987-90. The May 1 1992 snowpack was unmeasured; estimate based on April 1 1992 measurement and precipitation during April 1992.  19  20  The snowpack and temperature data confirm the tendency for runs of dry-warm and cool-wet years during the 1970's and 1980's (Figure 1.4). Cool-wet runs include 1973-75 and 1980-83, with 1981 an outlier year. Warm-dry runs were 1976-77 and 1984-90 with 1986 an outlier year. Residuals for the pooled 1986 catch curve do show strong and weak year classes across the group 0?igure 1.5). The overall pattern to the residuals is shaped by apparent lower vulnerability or lower year class strength at the left, which in turn causes the center residuals to be positive. Given the uncertainty about vulnerability and the shape of the survival-age relationship, the strength of a year class should be judged relative to its near neighbors. Clearly 1977,1979,1981 and 1984 represent stronger than average cohorts. These years either had low snowpack or high following summer temperatures, or both. Weaker cohorts appear to be 1978,1980 and 1983. All were high snowpack years, with cold following summers.  To some extent, weather does apparently synchronize year class strength across Sierra Nevada brook trout lakes, with summer lake warmth leading to strong cohorts. Considerable smoothing of the distribution by ageing error has probably diminished the apparent year to year variability of year class strength. As well, for most lakes summer temperatures may lead to stronger than average cohorts, but for some lakes other constraints are probably more important. For instance, the recruitment series for Gem Lake 2 is dissimilar to the general pattern Q?igure 1.6). The watershed of Gem 2 is very small and the lake does not have an inlet or outiet stream. Brook trout reproduction was apparently successful there in the winters of 1980,1983 and 1986. Total precipitation for those winters was far above average, although each was followed by a cool summer. Perhaps only wet years allow eggs and fry to survive the winter in tarn-type lakes.  21  120 T  0  >  0  )  0  )  C  »  0  >  0  )  0  >  0  )  0  >  0  )  Year class Figure 1.6. Gillnet catch by cohort for Gem Lake #2,1987 through 1991. Catches for 1985 and 1987 cohorts may represent ageing error. The years 1980, 1983 and 1986 all had high snowfall winters followed by cool summers.  22  Do the data suggest that the convexity of catch curves may be due to a weather-recruitment correlation? Probably not, since convexity would be created primarily by several adjacent strong years in the center of the distribution (1978 to 82) and several adjacent weak years at the farright(1973 to 75), which is not indicated by the weather data. It appears more likely that age specific survival generally does decrease with age, as reported for long-lived arctic lake Salvelinus populations (Power 1978), although to what extent is not clear. Regarding a first estimate of adult survival, the Bunny Lake study suggested an annual survival of about .85 for a single cohort of brook trout stocked into a previously Ashless alpine lake (Reimers 1979). The few abundance estimates in the years after stocking indicate a fairly constant rate of decline in numbers (Reimers 1979). Reproduction is believed to be a dominant agent of natural mortality for mature iteroparous salmonids. The change in sex ratios with age for the brook trout collected from the study lakes is evidence for the importance of reproduction as a mortality factor. More olderfishare females than males, and the disparity tends to increase with age. For iteroparous salmonids, it is believed that males spend longer at spawning locations and experience more aggression-related stress and injury (E. Parkinson, pers. comm.). The lack of reproductive opportunities for Bunny Lake brook trout (Reimers 1979) probably prolonged their lifespan but whether it impacted the shape of the age-survival relation is not clear.  The drought of 1987 - 1991 created weather conditions similar to those which led to stronger-thanaverage recruitments in some pre-study years. These years, during which the manipulations were made, were all low snowfall years followed by average to warm summers. These same conditions appear to have been associated with strong year classes in the majority of lakes in the late 1970's and early 1980's.  23  Synopsis of the chapters  Chapter 2. Ageing error The recent Uterature has emphasized the potential for ageing error to mask the patterns which might otherwise emerge from age-structured population estimation methods. Reader error is believed to result in smoothing of age distributions, as more members of dominant cohorts are misclassified into smaller neighboring cohorts than vice versa. The magnitude and rate of occurence of errors is likely to increase with fish age. In Chapter 2,1 use multiple independent ageings of 1124 brook trout otoliths to examine the error process. I follow the methods of Richards et al. (1992) in selecting a model which parameterizes the classification matrix of error probabilities. Repeatability estimates decrease from nearly 100 % at age 1, to 58% at age 15.  I use simulation to demonstrate the bias and variance in age distributions which are created by ageing error of the type estimated for my data. Ageing error correction reduces the sum of absolute mean deviations in the proportions to 17% and 11% of observed mean deviations for two different age distributions typical of study depletion data. I also examine the probable bias and variance of population estimates using the Walters-Collie estimator of Chapter 4, with uncorrected and corrected simulated data. Bias ranges from -2.7 to 6.7 % for estimates using corrected data, while its range is -10.2 to 85.3% for estimates using uncorrected data. However, standard errors for corrected estimates are up to 25% greater than comparable estimates using uncorrected data.  I use the model likelihood and numerical methods to make the most likely corrected estimate of age distributions observed for depletion data for this study. Percent of ages reassigned due to ageing error correction range from 0.9 to 9.9%. Depletions before 1989 tend to display greater percent reassignment due to higher abundance of older fish.  24  Chapter 3. Depletion estimation at period level resolution Removals from the eight study lakes were made as individual depletion experiments each year from 1987 through 1992, with no removals in 1990. In Chapter 3,1 examine the depletion data with regard to the within-series information it may contain about population size. My original goal was to apply a powerful age-structured depletion estimator which links and simultaneously analyzes removal series for all recruited cohorts across all years' data (Walters and Collie 1988). If the model describes the series well, the high number of observations (one for each cohort for each removal period) reduces the variance of the population estimates. As well, the analysis might suggest which mortality values are most plausible.  Hall (1991) made depletion estimates using age aggregated catch data and found evidence that catchability (q) for the first removal period was higher than for the subsequent periods. If uncorrected this would lead to biased low population estimates, so Ifirstexamine the cohort-specific series for evidence of higher initial period q. I use Schnute's (1983) variable q removal estimator which provides statistical criteria for choosing the appropriate number of q's. Most of the series show diel variation in catch per effort and most begin with a night removal period. I develop a model with distinct day and night q's to detect and account for this structure before evaluating for distinct initial q. I make depletion estimates for removal series where total catch was at least 20 individuals, using 1989 and later data obtained with consistent effort as required by Schnute's method. The analysis suggests that first removal period q's are not generally atypical.  I evaluate the bias of the Schnute estimates of population size (N ) for 1989 and 1991 cohort series by comparing them with minimum known alive (MKA) estimates. In most cases the Schnute N's are less than M K A estimates. Since the Walters-Collie (WC) estimator is essentially a linkage of each year's cohort-specific Leslie removal estimates, bias in the Leslie estimates will lead to bias and inflated variance for the WC estimates. I compare simple Leslie q's to WC q's, to demonstrate that the Leslie estimates are biased and this leads to bias in the WC estimates. Discounting the first two removal 25  periods does not alleviate the bias, corifirming that initial high q is not the main source of bias. For the data from this study the available models fail to describe the within-year structure of the removal series, which leads to biased population estimates. Essentially, the removal series and available models provide estimates which consistently underpredict the number of fish remaining in the lake. This leads to bias and inflated variance of the WC estimates. As well, this means that the estimates cannot provide reliable information about natual mortality.  Chapter 4. Population and catchability estimates at depletion level resolution Because the models tested in Chapter 3 failed to describe the observed catch series, in Chapter 41 use the catch data at a different level oftimeresolution to estimate population size. The WC method can also fit catch at age data with each cohort's catch for a single year's depletion series compressed into one observation. This application of the WC method is parallel to hkelihood-based methods of catch at age analysis but does not require any structure to recruitments, can fit series with catch of zero at some times, and uses simple linear regression. As long as the fraction of each cohort vulnerable is relatively consistent from year to year, recruitment of the invulnerable fraction to the vulnerable population is negligible during the depletion, and the vulnerable fraction is not fully depleted, catch per effort aggregated across removal periods can still be a reliable index of abundance even when withindepletion catch data provide biased estimates.  I make WC estimates of year class strength, and adult population abundance for the eight study lakes across the years of the depletions. Ageing error correction provides little change in the estimated strength of cohorts produced during the mid- to late 1980's. Because of uncertainty about natural mortality, estimates of year class strength for earlier cohorts are not reliable regardless of ageing error correction, and cannot provide additional information about whether strong cohorts in the late 1980's were an unusual event likely caused by removals. I use uncorrected data for the analyses presented in this chapter.  26  Estimates show an inverse relationship between year class strength and adult population size, for cohorts from 1984 to 1990. Age 1+ prerecruit q also appears negatively related to adult population density for most lake populations, but the results do not suggest whether this is a direct effect of adult density, or an indirect effect mediated through the effect of density on length at age. I present year and cohort-specific adult q's mainly to demonstrate variability and lack of evidence for density dependence in adult q. I use period level Leslie estimates of the vulnerable population to show that the vulnerable proportion of each cohort, and of the adult population in general, appears insensitive to population density.  The WC method estimates a time- and age-invariant "global" q for each lake population. A question of secondary interest in this chapter concerns the sources of between-lake variation in q. Current hypotheses hold that catchability variation may be explained by differences in the rate or probability of fish encountering the capture gear, which presumably is a function of swimming speed and the density of fishing effort (Rudstam et al. 1984; Borgstrom and Plahte 1992). The WC q's are not comparable because of between-lake differences in effort density and fish size, so I develop a modification of the WC fitting to adjust for these factors' presumed impact upon encounter probability. This model includes cohort mean length and lake area, and estimates a dimensionless "relative activity" parameter, k , rather than catchability. Key assumptions of such a model are that spatial pattern of movement and proportion of time active do not vary with length, and that effort density is not so high as to create gear competition. I compare between-lake variation in k using three different assumptions about depth zones ("effective area") used by brook trout. Variation in k is reduced relative to variation in q, when effective area is either total lake area or area above the 9 m depth contour. This analysis suggests that brook trout may use all benthic areas of the lake, or all but the deepest benthic areas, and that variation in encounter probability explains some of the variation in q. Hell Diver 2 does not fit this pattern, and one parsimonious explanation is that high effort density led to gear competition there. Without independent observations of brook trout movement and use of different areas of the lakes, such models will not be convincing. 27  Chapter 2.  Ageing error estimation INTRODUCTION  Ageing error is known to have potentially important impacts on the reconstruction of population abundance and estimation of recruitment time series using age structured models. Ageing error is expected to result in smoothing of age distributions, as more fish are misclassifiedfromabundant cohorts into less abundant cohorts than vice versa. Sensitivity analysis using simulated population data has demonstrated the biases created by smoothing of age data in sequential population analysis (Fournier and Archibald 1982; Rivard 1989; Bradford 1991). Recent sequential population analysis models for commercial fishery data (Fournier and Archibald 1982; Methot 1986; Kimura 1990) can explicity include ageing error as a component of the estimation if the error pattern can be independently estimated. The true age of fish sampled from wild populations is virtually never known. However, multiple independent ageings of samples can be used to examine the observation error pattern. Methods have been developed which use multiple ageings to estimate the classification matrix which describes the error process, and reverse the smoothing of age proportions (Hoenig and Heisey 1989; Richards et al. 1992).  For this study, brook trout removed from 1986 to 1989 were otolith-aged by D. L. Hall. I otolith-aged all fish removed in 1991 and 1992. Hall validated the ageing method by oxytetracycline marking (Hall 1991). Such validation experiments are important to verify the appearance and annular nature of patterns in the matrix of the age structure. However, validation is not a substitute for statistical analysis of patterns in ageing error. Validation studies are usually conducted under experimental conditions which do not mimic the typical methods for processing large numbers of otoliths efficiently. Generally, validation uses a small sample of structures which are handled very carefully. As well, the fish are usually recaptured one to two years after marking. The structures are examined with the expectation of one or two checks distal to the oxytetracycline mark, at the edge of the otolith where increments are most easy to discern. Other factors make ageing error more likely when large age  28  structure samples are being processed. Increments may be more difficult to identify as annuli towards the center of otoliths of older fish. Discrepancies in counting or in identifying increments as annuli are more likely when large numbers of structures are processed under time constraints. Whatever the process by which error occurs, it is a dominant component of most catch-at-age data. Agreement between two independent readings of the same structure has been reported as 41,44,64 and 79 % for Pacific ocean perch, sablefish, walleye pollock, and Pacific hake respectively (Kimura and Lyons 1991). Exact agreement between marked, known age fish and an independent otolith ageing was 45 % for 5- to 11-yr-old rainbow trout stocked into montane and alpine lakes (Donald and Alger 1986).  Methods to estimate and correct for error cannot eliminatefish-sourceerror: failure to generate annuli or generation of multiple increments within a single year, under certain internal or external environmental conditions. Such occasional conditions may not be detected in short-term, small sample validation experiments. Only long term validation (sensu Pikitch and Demory 1988) can establish the accuracy of the ageing method. However, Richards' et al. (1992) method should still be useful to parametrize the error process and to eliminate as much of the smoothing due to reader error, as is possible by statistical means. I examined the importance of ageing error as a component of this study, with the following questions and ideas in mind. (1) What is the best description of the error for the ageing which was done for this study? How much variation is displayed by independent readings of the same otolith? Which of the available models best describes the error displayed by the multiple-age data? Estimation of the matrix of age-specific error probabilities will allow me to address the questions below. (2) What are the best estimates of the true catch-at-age? Given the error probabilities, what is the best estimate of the true age structure of the removals carried out during the study? How much were the estimates of catch-at-age changed by the analysis?  29  (3) How accurate and precise are the estimates? What are the variances of the catch-at-age estimates? Applied to simulated data using the error probabilities estimated from my data, how effective is the "desmoothing" process?  (4) Given the likely error, what potential effects will it have on the population estimation methods I have chosen?  I examine questions (1) through (4) in this chapter, predorninately through the ageing error models of Richards et al. (1992). I use their models to analyze multiply aged otoliths, to select the model and parameters which best describe the error process for my data. I then use the model and parameters to correct the proportions-at-age and catch-at-age for removal data from 1986 to 1992. I also use Monte Carlo simulation to demonstrate the effectiveness of the methods and to suggest the residual error after correction. I use the estimated error matrix and Monte Carlo methods to examine how uncorrected and corrected error might impact population estimation.  METHODS  Background and general methods Although many authors have noted the potential effects of ageing error on age structured population estimates, few methods have been proposed for quantifying ageing error and reversing its smoothing effect on catch-at-age data. To date, the only thorough treatment has been that of Richards et al. (1992). They present a complete and consistent statistical framework for modelling ageing error. Their methods provide for estimating the classification matrix which describes the error generation process, as well as reversing the process to estimate either the true ages, or proportions at age for a sample of fish The estimation of the classification matrix and the age structure can be made simultaneously or independently. Their models are formulated using maximum likelihood and are easily modified for other specific analyses.  30  In discussing the theory and computational methods of ageing error analysis I follow the notation of Richards et al. (1992). I attempt only to present sufficient detail to clarify the general methods and assumptions. Further computational detail can be found in their work.  Let P represent a vector of proportions, or probabilities that a fish from the population has true age b. Then the vector P has an element p,, for each true age, and the elements of P must sum to one. P is acted upon by an error-generating process which results in a vector of observed proportions, represented as P*. The expected value of the error-generating process can be represented as a classification matrix. This classification matrix, designated Q , is a square matrix, each element q(a I b) of which gives the probability of observing the structure as age a given that its true age is b. Thus:  <?U|1)  Pi  •  Pi  q(n\n)_  Pn  (2.1)  can be expressed as P*= QP. If Q can be estimated, then the error process can be reversed to estimate P so thatP = Q P . Under certain restricted conditions, the estimation of P has an analytical _1  solution. When the inverse classification matrix Q- exists and is non-singular and when no elements 1  of P are near zero, the solution is direct. However, when the sample is small for some ages, these constraints may not be met and numerical methods must be used.  With true ages rescaled to range from 1 to A, the form of the classification matrix could be described by any set of up to A parameters. Richards et al. present two parsimonious representations, which 2  they designate as "normal" and "exponential" models. Each involves a vector of two to four parameters:  31  a i , a A , and possibly a , (3, or both. Together the parameters constitute  the parameter vector  which determines Q for the two models as follows: 1 _ Mb-D e  o(b) = c + {o -G ) _ _ _ ; l  A  l  i  e  a(A  a(b) = o + (a -o )-£—?; l  A  ce*0  l)  a  =  (2.2)  0  ( 2 3 )  l  Then for the normal model, a matrix Af(0) is determined by (2.4).  (2.4)  V27t;c(Z?) Finally, the column totals are rescaled to sum to one by (2.5).  (2.5)  For the exponential model, the matrix X(&) is calculated not by (2.4) but by (2.6)  X (*) ab  = c{bf-*'  ,2.6)  followed again by (2.5) to rescale the column elements, with <5\ and  constrained to values between  zero and one. Probably the most important assumption made by these models for Q is the modality assumption: for each true age b the distribution of observed ages has its mode at b. In other words, for any true age b, the most likely observed age must also be b, even if observing b is less likely than the total probability of observing "not b". The vector O parameterizes the shape of the general error probability distribution and the rate at which error increases with age. The models may also be  32  reduced by the constraints a = 0 and P = 1, which makes an additional three special cases of the two basic models. For a particular set of multiply aged samples, selection of the most appropriate model among these can be accomplished informally using the Akaike Information Criteria: (2.7). N equals the number of parameters so that the term 2N acts as a penalty for additional parameters (Akaike 1974). The inference function /(0) quantifies the fit of the model to the data. Generally the models are fit by minimizing the inference function 1(0) = -2 log L(0)  (2.8)  where L (0) is the likelihood for the specific estimation problem being addressed. Estimates of the variances of the parameters can be made if the asymptotic variance-covariance matrix can be determined. One approach would be analytical calculation of the variance-covariance matrix. However, in the maximum likelihood case, the asymptotic variance-covariance matrix is the inverse of the Hessian, which can be estimated directly through numerical derivatives using quadratic approximation (Richards et al. 1992; Mittertreiner and Schnute 1985). One disadvantage is that this method requires highly precise location of the function minimum. This can be difficult when proportions at age are estimated, since the inference function is relatively insensitive to small changes in the proportions (Richards et al. 1992).  Estimation of Q and P The methods of Richards et al. allow for simultaneous estimation of the parameters in O as well as either the vector B of estimated true ages for the fish in the sample, or proportions-at-age P. If A * is a matrix of observed ageings for a total of / fish each aged Jtimes,with observed ages rescaled to range from 1 to A, then the likelihood for estimating <E> and 6 is expressed as:  (2.8).  33  My approach was to estimate a general Q(<X>) using a large number of multiple ageings from different lakes and years. Since this did not constitute a distinct sample, I estimated Q(O) using likelihood (2.8), treating B as a vector of nuisance parameters. To create the matrix of multiple ageings A * for the estimation, I selected the first fifty otoliths each from the seven study lakes in 1991 and 1992, which had already been aged by my usual techniques. I covered the labels on these samples and shuffled them before reageing them. In order to increase sample size for ages 5+ and older, I independently aged two additionaltimesall of the otoliths which had been initially aged as 5+ or older in the 1991 and 1992 collections, with the exception of Fishgut 1 and Wonder 3 1991 samples. After removing unreadable samples, this gave a total of 1129 multiply aged brook trout, of which 680 were aged twice and 449 were aged three times. I excluded young-of-year from ageing error analysis.  After obtaining the model and parameters to best describe Q(O) for the multiply aged sample, I used the estimate of Q(<P) to correct the age frequencies P* obtained by tabulating the singly-aged observed catch-at-age A* for each depletion. I tabulated P* and made estimates of P by depletion rather than by removal period because period level data would give small samples, and was found uninformative about population size elsewhere in this thesis. For otoliths aged three times, I used the middle ageing when tabulating observed age frequencies P*; for those aged twice I used the first ageing.  The likelihood for estimation of P is expressed as:  (2.9) Conceptually, the likelihood of the data given the model is the product of the likelihoods for individual fish. In turn, the likelihood for each fish is the sum, over all possible true ages admitted, of the probability of observing the ageings which occurred. That probability is the product of the probability of observing a fish of true age b, multiplied by the probabilities of observing the ageings ai to a; given the true age b. Direct calculation of P = Q P was not expected to be reliable because some elements _1  34  of P*were zero or near zero. Instead, use of the likelihood (2.9) and numerical methods was always necessary. Once P had been obtained for a depletion, true catch at age was estimated as N = NP, where N is the total catch disregarding age O's.  I programmed the inference functions in BASIC and minimized the fitting criteria with a direct search routine. I used the AMOEBA implementation (Sprott 1991) of the simplex method (Nelder and Mead 1956) from multiple starting points and driven by a restarting algorithm, to find the minimum. The simplex method is computationally expensive and known to have problems with local minima. However, proper tuning and a suitable restarting algorithm to drive the search seem to produce reliable minima.  For each depletion I calculated the total percentage of ages reassigned after error correction as 50*X|P -P/  (2.10).  a  0=1  Simulations Performance of ageing error correction Richards et al. exercised their models with age data from a walleye pollock population for which true ages were unknown. The performance of their models could be expected to depend on sample size, age-dependence of the error process and smoothness of the age distribution. I wanted to know how much error might typically remain after their correction processes have been applied to my data. The most effective way to approach such questions is with Monte Carlo methods (Hilbora and Walters 1991). I used simulation to generate data to explore the performance of their model under different conditions. I generated two population age distributions similar to those observed for Sierra brook trout populations. Such distributions are often highly "uneven", with apparent strong and weak year classes persisting across several years' catch data (Hall 1991). Distribution A was typical of age  35  distributions early in the study, when fish of age 5 and older were a dominant component of the catch. Distribution B was more typical of age distributions after several years of depletions, when the catch was dominated by fish age 4 and younger. I made 500 runs for each population age distribution. For each run, I created a stochastic catch with each individual having the same capture probability, effectively a multinomial sample with mean total catch of 625. I subjected the catches to stochastic ageing error, using the error probabilities estimated from brook trout multiple ageings. I then corrected each observed data set by minimizing the inference function for the likelihood (2.9). I calculated the mean and variance for the observed and corrected proportions-at-age. To quantify bias, for each age I calculated the deviation of the mean observed proportion at age and the mean corrected proportion-atage, from the true proportion-at-age. I summed the absolute value of the deviations as an overall index of the mean bias of the observed and corrected proportions.  Ageing error and population estimation In order to examine the impact on population estimation of uncorrected stochastic ageing error, and ageing error with error correction using Richards' methods, I used a 22 yr time series of age 1 recruitments and the catch equation:  AU=(AT,-C,)*S to generate simulated population dynamics. I subjected the population to seven years' stochastic removals. Full recruitment was at age 2 with capture probability q = .462 and partial recruitment at age 1 with q = .042. Annual natural mortality was fixed at .3 . I subjected each year's catch to stochastic ageing error using the probabilities estimated for this study. I estimated the corrected age proportions for each year's catch by maximizing the likelihood (2.9), and analyzed the uncorrected and corrected catch data for each run using the WC method to estimate recruitment for cohorts 8 to 20 only. I made two identical sets of 100 runs, except the second set used q = 0 in the fifth year to parallel the removals for this study.  36  RESULTS  Estimates of Q and P Of the five models I evaluated, the exponential model with a = 0 and the full exponential model provided the bestfitand were equally likely given the data from 1129 multiply-aged brook trout (Table 2.1). In such cases, the Akaike criterion selects the model with fewer parameters, hence the selection of the exponential model with a = 0. Richards' et al. exponential distribution is more peaked than the normal density distribution (Richards et al. 1992). Selection of the exponential model implies lower sensitity to outlier observations and generally less blurring of age distributions due to error. Correspondingly, correction produces less adjustment of proportions.  Repeatability estimates range from nearly 100 % at age 1, to 58% at age 15 (Table 2.2). Repeatability increases at age 16 to 67% as an artifact of the estimation procedure which truncates the distributions at the highest observed age (Richards et al. 1992). This is a strongly diagonal matrix, relative to those which have been used in studies simulating the effect of ageing error on population estimation (e.g. Bradford 1991).  Table 2.1. Parameter estimates for O based on the normal and exponential models, applied to multiply-aged brook trout from 1991 and 1992 removals. Model Exponential Exponential Exponential Normal Normal  a 0.0000027 0.0000022 0.0000074 0.2687200 0.2964660  0.43664 0.31957 0.29259 1.16962 1.45443  -0.04983 -0.017009 0 0 -0.070961  37  P  /(e )  AIC  1 0.84076 0.82779 -  2932.8 2917.9 2917.9 3115.3 3109.3  5196.8 5183.9 5181.9 5377.3 5373.3  Ageing error classification matrix for 1129 multiply aged brook trout, estimated by procedures explained in the text Each entry is the probability for that true age (column), of obtaining the observed age (row). Column totals may not sum to one, due to rounding. Table 2.2.  1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  1  2 .02  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  .02 0 0 0 0 0 0 0 0 0 0 0 0 0  3 0 .04 32 .04 0 0 0 0 0 0 0 0 0 0 0 0  4 0 .01 .05 .88  .05 .01 0 0 0 0 0 0 0 0 0 0  5 0 0 .01 .07 .85  .07 .01 0 0 0 0 0 0 0 0 0  6 0 0 0 .01 .08 .81  .08 .01 0 0 0 0 0 0 0 0  true age 8 9 0 0 0 0 0 0 0 0 .01 0 .02 0 .77 .10 .03 .09 .74 .11 .02 .10 .71 0 .02 .11 0 .01 .03 0 .01 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 .02 .09  10 0 0 0 0 0 0 .01 .03 .12 .68  .12 .03 .01 0 0 0  11 0 0 0 0 0 0 0 .01 .04 .13 .64  .13 .04 .01 0 0  12 0 0 0 0 0 0 0 0 .01 .04 .13 .62  .13 .04 .01 0  13 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .01 0 .02 0.01 .04 .02 .14 .05 .59 .15 .14 .58 .04 .15 .02 .05  15 0 0 0 0 0 0 0 0 0 0 .01 .02 .06 .16 .58  .16  16 0 0 0 0 0 0 0 0 0 0 .01 .01 .03 .08 .20 .67  Table 2.3. Percent of ages reassigned due to ageing error correction for depletions from 1986 to 1992. Each year has two columns; column 'a' listsfirstdepletions in a year, column V second depletions. 1986a 1986b 1987a 1987b 1988a 1988b 1989a 1991a 1991b 1992 Hell Diver 2 9.0 1.7 7.4 0.9 4.6 4.9 2.9 Dingleberry - 1.4 3.0 2.7 4.0 3.1 2.7 1.5 Flower 2.5 2.5 2.8 3 1.7 Fishgut 1 4.1 3.4 2.9 2.2 2.5 Par Value 8.9 3.4 2.2 3.6 2.6 2.3 Wonder 3 4.4 2.2 2.4 2.1 5.3 3.5 Hell Diver 3 9.9 1.4 4.8 4.5 1.9  Estimates of corrected age proportions and standard errors for age 1+ to age 16+ catch aggregated by depletion are presented in Appendix A. Percent of ages reassigned due to ageing error correction range from 0.9 to 9.9% (Table 2.3). The percent of ages reassigned tends to decrease over the course of the  38  study (Table 2.3). Post-1988 age distributions tended to be dominated by fish of age 3+ and younger, and were generally more even distributions. Distributions which are already smooth are less prone to further smoothing by error, so estimated corrections for these distributions are correspondingly low. As well distributions dominated by young age groups will have experienced less smoothing since error is low for the youngest ages.  Simulations Performance of ageing error correction: age distributions Simulated catch-at-age data with stochastic ageing error of the form estimated for brook trout in this study, led to observed distributions which exhibit the smoothing typical of ageing error effects (Table 2.4). Age classes which are less abundant relative to their near neighbors tend to pick up more observations than they lose, while the opposite is true for the age classes which are more abundant than their near neighbors. The result was positive bias for relatively lower p*'s and negative bias for relatively higher p*'s (Table 2.4). Observed proportion bias was more severe for the more uneven distribution A than for the smooth distribution B. Correction relieved much of the smoothing for ages less than 10 and reduced the sum of absolute mean deviations in the proportions to 17% and 11% of observed mean deviations for A and B respectively (Table 2.4). Bias was still present in the corrected proportions for zero and near zero true proportions, but was generally quite reduced relative to uncorrected proportions 0"able 2.4).  Variance was less for the corrected than the observed proportions at the lowest ages, but became higher as ageing error increased and proportions decreased with age (Table 2.4). The increase in variance was primarily due to the lower proportions and higher error rates with increased age, which for some runs produce false modes. The correction method cannot distinguish false modes. Such modes were subsequently exaggerated by the correction method, which resulted in increased variance.  39  Table 2.4. Simulation of ageing error correction. Values shown are means of 500 runs. For each run, a sample of 625 was drawn from a population with true proportion-at-age b p , and subjected to stochastic ageing b  error, using error probabilities estimated from brook trout samples. Estimates were made from each sample according to methods described in the text. Symbols are: p estimated age b proportion; p* observed age b b  b  proportion. Variances are indicated V( ). Proportions are times 10 , variances are times 10 . Total = total of 2  3  absolute deviations. Distribution A is representative of age distributions obtained by pre-1989 removals. Distribution B is typical of 1989 and later removals. age  Pb  Pb ~ Pb  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total  12.8 14.4 5.6 0.8 2.4  0.14 -0.21 -0.05 0.34 0.87 -2.09 1.98 -1.14 1.32 -2.92 0.50 0.96 0.01 0.15 0.05 0.02 12.75  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total  11.04 22.40 42.24 13.44 4.80 0.80 2.72 1.12  19.2 1.6 12.8 7.2 17.6 4.8 0.0 0.8 0.0 0.0 0.0  0.32 0.00 0.16 0.48 0.32 0.16 0.00 0.00  0.41 0.39 -1.48 0.07 0.11 0.36 -0.29 0.00 0.06 0.08 0.02 -0.09 -0.03 -0.01 0.04 0.01 3.45  V(p„)  Pb ~ Pb  Distribution A -0.04 0.01 -0.01 -0.04 -0.04 -0.05 0.03 -0.08 0.29 -0.15 -0.14 0.23 -0.13 0.06 0.03 0.02 1.35 Distribution B 0.08 -0.03 0.08 -0.09 0.01 0.01 -0.04 -0.02 -0.02 0.06 -0.01 -0.04 -0.03 -0.02 0.03 0.01 .58  40  V(pl)  v(P.)  0.179 0.197 0.085 0.013 0.037 0.248 0.025 0.179 0.107 0.232 0.073 0.000 0.013 0.000 0.000 0.000  0.208 0.209 0.088 0.014 0.045 0.294 0.050 0.163 0.114 0.246 0.085 0.014 0.011 0.002 0.001 0.000  0.191 0.189 0.096 0.017 0.055 0.316 0.073 0.226 0.191 0.402 0.150 0.012 0.019 0.001 0.000 0.000  0.157 0.278 0.390 0.186 0.073 0.013 0.042 0.018 0.005 0.000 0.003 0.008 0.005 0.003 0.000 0.000  0.161 0.409 0.732 0.211 0.074 0.017 0.033 0.017 0.005 0.001 0.002 0.006 0.004 0.002 0.001 0.000  0.155 0.343 0.478 0.205 0.091 0.022 0.048 0.025 0.007 0.001 0.003 0.010 0.006 0.003 0.001 0.000  ^  ;  9  '  O  g  N  00  «  TJ- c<-> Tf (N  ON C)  O W)  N  W  :  m  H  3  "  ^  »3  2  *  © N  ^  O  N  '  7  t  ©  {  ^  >  OO  fi 9*  <  9  9  -  ©  0  r~  ©  !  ^  rH  9  t «  -  «  « ^ "i 2  5!  *  a  ^  M  m  q  1^1  t h i-< ON  N  9  ©  «  Tf  '  V  a  o  -r 8  £  N  00  H  ^  9  T'  00  b  H  <N  « o>  N  »  h>  '  V  •<(• N  4  "i«  9  ft  n  t~-  w  o \ ^ ^ q ^ i n 00 N r i 06 t> 0 1^ 0 oi vi N 1— <M N (<i -  ^' ^  i«  T  <f)  r,  TJ-  5  H  0  ^-  7  to  f  0  H  n »  co  ©  ©  H  «N Tt  o  ©  0  t~|  cs(S  m  N  -  C  »  ON CO H W  »  <  n  o  n  -<t  o  c  J  9  d  r  i  o  9  \  9  ci  «  d  9  </"> CO TT CS  O N VC * 00 ON TF O  N  Ifi ON C i  l«  h  H  »  f  V)  r-  © v> © © V) ^  1/1 I/)  co  TT  r-  rH Ifl  ©  VI  _  TT  t—  M  c  I  r<  N  to  Tt  vi «  > OO ON  41  2 ~ 2 2  Ageing error and population estimation Again, the uncorrected population estimates showed the expected pattern of smoothing of year class strength, while the corrected estimates had much lower bias (Table 2.5). Bias ranged from -2.7 to 6.7 % for corrected data, while its range was -10.2 to 85.3% for uncorrected observed estimates. Bias was highest for small cohorts. There was a variance increase due to correction, however. Estimated SE's are 120% higher for the estimates made from corrected data than from observed uncorrected data, with the greater increase in SE's occurring for older cohorts again due to occasional false modes.  DISCUSSION  Comparable estimates of ageing error matrices are virtually absent from the literature. Aside from Richards et al. excercising their methods on a small sample of multiply-aged pollock, not a single application of their models has been reported in the literature. Occasionally authors report on repeatability but rarely give results with enough detail to assess the age-dependence of error. For instance, Kristofferson and Klemmetson (1991) studied age determination methods for arctic charr (5. alpinus) but with regard to repeatability they reported only that "within-method agreement was reasonably good", showing "agreement within  year for 84.1 % of the otoliths" (my italics). Simulation studies (Fournier and Archibald 1982;  Rivard 1989; Bradford 1991) have generally used error matrices reflecting the authors' subjective notions about error rates and their dependence on age. The effect ("seriousness") of error and its correctibility can only be judged in the context of the analysis for which the ageing data is intended. In this chapter, I did not simulate fitting of stock - recruitment relationships or recruitment - environmental variable correlations. However, my analysis of multiply aged samples has given me an objective basis for making such simulations with both uncorrected and corrected catch at age data.  My simulations have assumed that the parameters comprising <P are estimated without error. I did not make formal simulations of the likely error in estimation of <J> and its dependence on sample size, nor the  42  likely error in P which results. I have implicitly assumed that the multiply aged sample was large enough to estimate O with negligible error. By doing so, I have underestimated the variance of proportion and population estimates by an unknown amount Trial simulations showed that estimates of the vector B were quite insensitive to the values of the parameters in O ; however, P is probably more sensitive.  Some lake populations tend to produce otoliths with very clear increments, while others are much less apparent as increments. One way to examine whether this apparent difference in the ease of ageing otoliths for different populations impacts the ageing error process, would be to examine the estimates and variances of the parameters in <P describing Q, the classification matrix, for each lake's reageing data treated separately. Independent analysis of each lake's data might seem an attractive approach. Large sample sizes for individual lakes would likely be necessary to give sufficient statistical power to detect differences in the ageing-error process between lakes. Again, simulation of the error in estimation of O could suggest sample size needed for such an analysis.  The ageing procedures used for this study were constrained fortimeand financial efficiency and were not optimal for ageing error analysis and correction. The proper design for ensuring a relatively consistent error rate would be randomly mixed otoliths from different lakes and years with blind labelling. As well, the multiple observations should be obtained by blind mixing of repeat samples with the singly-aged samples, so that extra care is not given to multiply-aged samples. Neither of these procedures was followed in this study. Multiply-aged samples were blind but were handled as a distinct batch. Batch processing of multiply-aged otoliths probably led to lower estimated error rates since the time spent per otolith was higher for these samples. As well, for singly-aged samples we aged otoliths from each lake for each year as a batch. This was done in order to speed processing, reduce tedium, and allow immediate preparation of the second otolith from a pair when the first was unreadable. Batch handling of singly-aged samples may tend to reduce error rates below those estimated by blind multiple ageings, and might even exaggerate differences in year class strength. For instance, an otolith reader who sees many samples of age 6 may begin to read samples that are age 5 or 7, as age 6 also. It would be possible to analyze the study 43  age distributions to determine whether they are consistently less smooth than would be predicted, based on estimated error rates from this study. I did not attempt such an analysis.  In addition, reader effects may occur where ageings are conducted by multiple readers (Richards et al. 1992). For this study, all ages for the 1986 -1989 depletions were read by one reader, while those from 1991 and 1992 were read by a second. Richards et. al. (1992) develop models for analysis of reader effects. I did not have multiple ageings from the first reader. Consequently I did not analyze the data for such effects.  44  Chapter 3. Depletion estimation at period-level resolution INTRODUCTION  Removals from the study lakes were made each year as depletion series of 3 to 11 consecutive half-day periods' duration. The removal method of population estimation rests on the assumption that an observable index of abundance declines in direct proportion to the decline in numbers, as members of the population are removed. To estimate population size, the study removal data could be used at either of two levels of time resolution. If the decline in catch per effort across capture periods during single depletions is informative with respect to population size using a simple Leslie (1939) removal estimator, then an extended model which links removal estimates across years and cohorts could estimate abundance with low variance by simultaneously using all the information present in all the series. However, if the removal series within each year do not provide reliable information about population size because of bias or high variance, use of the data at period level resolution will only degrade population and recruitment time series estimates. The alternative in this event is to use the data across years and cohorts at depletion level resolution, so that each removal series is compressed into a single relative abundance and catch data point. This chapter examines whether the removal data are informative at period level resolution.  In order to extract detailed information with regard to patterns in recruitment and catchability over time, I use age structured methods. Walters and Collie (1989) provide a multi-year multi-cohort depletion estimator for commercial catch at age and survey data. This model is statistically less efficient than catch-at-age methods introduced by Fournier, Deriso, Schnute and others in the 1980's (Walters and Collie 1989). However, it has a number of desirable properties, including: (1) ease of solution, by simple linear regression (2) does not require assumptions about a recruitment relationship with stock or time (3) occurrence of zero catch for some cohorts at some times is not problematic, as for loglikelihood based methods.  45  The estimator is easily adapted to simultaneously use all removal data for a closed population composed of cohorts which are subject to multi-period removals within each of several years. Essentially, the assumptions are negligible natural mortality during the removal period, population closed to migration, and constant and homogeneous catchability. Survival is assumed known as with virtual population analysis (Walters and Collie 1989). If the assumptions are met this model can link the cohort-specific removal data across years and cohorts to estimate recruitment and abundance with low variance for each recruited cohort present in the catch.  Many studies have found that removal data give estimates which are biased low (Bohlin and Sundstrom 1977; Cowx 1983; Peterson and Cederholm 1984; Kelso and Shuter 1989; Hall 1991; Hilborn and Walters 1992). Because the Walters-Collie (WC) model is essentially a statistical linkage of year and cohort specific Leslie estimates, bias in the Leslie estimates implies bias and inflated variance of the WC parameter estimates. Hall (1991) used Schnute's (1983) maximum likelihood removal estimator for 1989 data aggregated by age and concluded that for some lakes the initial capture period had higher catchability than the rest of the series. Distinctfirstperiod catchability has been used to model concavity of the cpe - cumulative removal relationship which would lead to biased low estimates if not corrected (Schnute 1983; Hilborn and Walters 1992).  In this chapter my primary objective is to establish whether the available estimators, and depletion data at period level resolution, can be used to obtain unbiased estimates of population size. I first use Schnute removal models to examine the series for evidence of diel variation in catchability and higher first period catchability. I show the potential bias of the Schnute estimates by comparison with minimum known alive population estimates. Similarly, I demonstrate the bias of the WC estimates by comparing the catchability to single-year single-cohort Leslie catchabilities. I examine the performance of age-aggregated estimates. Finally, I use patterns in catchability as evidence about brook trout behavior in the study lakes.  46  METHODS  Following a summary of field methods, data treatment, and terminology, in this section I present my approach to population and catchability estimation using the removal method. I use two estimators : Schnute's (1983) maximum likelihood estimator, and the Walters-Collie (1989) method, which is an extension of Leslie's (1934) regression technique. For each, I explain my use of the estimator to evaluate for distinct initial point catchability, and for estimate bias. Last, I detail my use of Schnute estimates to assess the size dependence of catchabiUty and the performance of age-aggregated estimates.  Field methods To ensure consistency of the data, I followed Hall's (1991) methods to the extent possible. I fished the same Lundgrens (Sweden) light green, nylon, weighted gillnets of length 36 m, height 1.5 m, on bottom. The nets were composed of twelve randomly ordered panels of bar mesh size 4,6.25, 8,10, 12.5,16.5,18.5,22,25,30,33 and 38 mm, and were randomly chosen from a pool of ten such nets. Nets were anchored at and set perpendicular to shore, but we also made sets offshore oriented at random or downwind. The removals began in 1987 with the exception of Hell Diver #2 which began in 1986. At least one depletion was made per lake each year through 1992, with no removals in 1990. Each depletion was structured as a continuous series of three to eleven removal periods over a 1.5 to 5.5 day period. The 1986 through 1988 data display greater variability in effort from period to period; effort often increased during a depletion. By 1989 and later we fished a fixed number of nets (4 to 6, depending on the size of the lake) throughout a particular depletion and maintained consistent set and haultimesfrom day to day through the depletion. In 1989 the day sets and night sets were each 12 hours, while in 1991 and 1992 night periods were longer than day periods.  47  Treatment of the data I used one net fished for one hour as the standard unit of effort, and pooled data from all nets fished during a removal period to provide a single estimate of catch-per-unit-effort (cpe). Some of the 1987 and 1988 removals had two short consecutive removal periods during the day, which I combined into one full day period. Occasionally, logistics made the final set of a depletion longer than 20 hours. I have treated these catches as removals but not as relative abundance data. In some years we made two depletions in some lakes. I have used the first depletion as relative abundance data and the second as removals only. An exception is the double removal for Dingleberry in 1991; the original removal was terminated with a series of 4 periods. I used the second series of 9 periods commencing 10 days later to make population estimates.  For a few removal periods during 1989, some or all fish were not sampled for age. For these periods, I have estimated catch-at-age based on the age proportions in the sampled catch for the period. If no fish were sampled for age during a period, I estimated the age proportions as the average proportions of the sampled catch of the previous and subsequent period  Fish were occasionally removed by other capture methods. The Leslie method allows the removal process and the estimation of relative abundance to occur independently (Hilbom and Walters 1992). I accurately accounted for all such removals in the estimation procedure. For these analyses I have considered age 2+ and older fish to be fully recruited to the gear (Hall 1991), except for Hell Diver #2 where full recruitment to the gear has been at age 3+. Prerecruit cohorts are age 1+ in all lakes except Hell Diver #2, where prerecruit cohorts are 2+, and 1+ in 1989.  48  Population and catchability estimation Terminology and assumptions When I use the terms "depletion series" and "removal series" I refer to data for a single cohort from a single multi-period depletion unless stated otherwise. I also evaluate estimates which group all recruited cohorts and refer to these as age aggregated. The WC method estimates a global catchability across cohorts and years. I refer to Leslie removal estimates made for single cohorts in single depletion experiments as local estimates. The methods assume independence of catches between recruited cohorts which is not strictly true due to ageing error. The low error rates demonstrated elsewhere in this thesis render this point minor. I evaluate models for removal estimates with multiple catchabilities. The motive is detection and elimination of initial points of high catchability. I refer to the estimated catchability, after initial distinct points have been separated, as the terminal catchability. In cases where diel variation in catchability is indicated, there are both day and night terminal catchabilities.  Estimation I required methods for two tasks for this chapter: to evaluate removal series for evidence of higher initial period catchability, and to evaluate potential bias of estimates of population abundance. The most developed single-series removal estimator is Schnute's (1983) maximum hkelihood method. It allows time variation in catchability but requires constant effort, a criteria not met by 1986-88 removals for this study. As well it would necessitate a new procedure for simultaneously analyzing multiple series across years and cohorts. However, Schnute's method offers a statistically rigorous way of evaluating and fitting series with multiple catchabilities, so I use his method for the first task The central problem in evaluating the bias of the removal estimates is that population size is unknown. Additional information about population size is present in depletions from subsequent years, for cohorts which appear in several years' catch. I use two distinct approaches to evaluation of potential bias of depletion estimates. First, I use the Schnute estimates of population size which were made to evaluate for distinct initial q. Minimal information about the likely population size during a depletion  49  can be obtained by summing the catch for the cohort for the years including and subsequent to the depletion series. For a closed population, this minimum known alive (MKA) estimate provides a low bound for population size during a depletion (Kelso and Shuter 1989). Such an estimate is itself biased since it neglects natural mortality subsequent to the depletion and fish still alive after the final year's catch. For this reason Schnute estimates which do not exceed M K A estimates can be considered to display severe bias. Second, I use Leslie estimates and the WC method. The WC fitting integrates information about population size across years within a cohort, and about q across cohorts. Essentially the method reconciles information about population size from the decline in cpe during the depletion series, with information about population size from subsequent years depletion series, weighted by natural mortality. In order for the WC estimates to be unbiased, the individual depletions must provide unbiased information about population size. The global q from the WC fitting should be similar, on average, to the individual Leslie q's. If the WC global q differs systematically from the local q's then the information about population size within the series is not in agreement with survival-weighted information about population size from earlier and later years' catch.  Schnute removal estimates Models Hall (1991) used three types of Schnute estimates: a single catchability model, and models with one and two initial distinct catchabilities. However, most of the study removal series display strong diel variation in cpe. Most depletion experiments for the study, and all depletions from 1989 to 1992, began with a night removal period. The analysis should account for diel catchability variation before evaluating for distinct initial period catchability. Schnute (1983) alluded to a model with distinct capture probabilities for alternating gear types. I developed a simple night-day model and a night-day model with distinct first period catchability, based on Schnute's (1983) methods for developing multiple catchability removal models. As well, I programmed the three models used by Hall (1991). I used 50  Schnute's (1983) approximate statistical criterion for model selection among the five choices which are listed in Table 3.2. The criterion requires that the negative log-likelihood be improved by at least 1.92 units, (.5 * x  2 w i t  h 1 df; a = .05 ) before rejecting a model for one with an additional parameter. At  each step, I evaluated the class of models with an additional q according to the criterion. Once the appropriate number of q's was determined I selected the best-fitting model for that class to provide the estimate of N and q's.  *  Table 3.1. Notation. Symbol  yu  Meaning Catch per unit effort for a cohort in the j Removals during all periods before the j  m  m  removal period of the i removal period of the i  m  m  year's depletion year's depletion  C,j  Catch during the j  N  Number of fish which were present before any experimental removals occurred  s.  Natural survival rate from year i to year i + 1, assumed independent of i  q  Catchability, or proportion of the population removed by one unit of effort  n.  Number of removal periods in year i  T,  Sum of all removals in year i  0  m  removal period of the i  m  year's depletion  Table 3.2. Five Schnute removal models which were fit to depletion series. Model Symbol Single q il Single terminal q with one distinct initial q i2 Single terminal q with two distinct initial q's 13 Independent day q and night q dn Independent day q and night q with one initial q dn3  51  Catchabilities 1 2 3 2 3  Initial point catchability I made Schnute population estimates for depletion series with catch > 20, from 1989, 1991 and 1992. If the best-fit model was not one with an distinct initial q, I estimated catchability for the first period as: (3.1) Some series had no catch for one or two periods. Since the estimates use log-hkelihood, values of zero catch are inadmissible. I used 0.001 instead of zero for these estimates. Simulations showed that the estimate was insensitive to the size of the surrogate value, near zero.  Estimate bias To evaluate potential bias of Schnute estimates, I included estimates for which there was at least one subsequent year's catch, so that comparable M K A estimates would include at least two years' data. Schnute's method offers no clear criterion for eliminating poorly determined estimates. For this analysis I arbitrarily chose to discard, as poorly determined, estimates for which the ratio of the value of the upper confidence limit to the value of the estimate was greater than five, based on the distribution of values of this ratio. This ratio was always less than 5 or greater than 100.  Walters-Collie depletion estimator The Walters-Collie age-structured depletion model requires an independent estimate of natural mortality along with data from at least two years' removals. The dependence of natural mortality on age can assume any form. The method assumes a single time- and age-invariant q and estimates the number of fish in each cohort at the time the cohort recruited to the fishery, along with the global q (Walters and Collie 1989). The estimator is derived as follows (symbols defined in Table 3.1):  (3.2)  52  yui=i( o N  - Ku)=qN  - qK  Q  ia  (3.3)  and generally for the first year:  yu=qN - K 0  q  (3.4).  1  Then for the second year:  Su =^(N -T )-K ) 0  1  = qN S -q\  zl  0  J2.2 = l{S {N -T )-K ) l  0  1  Z2  (3.5)  l  = qN S -q\{TA-K22) 0  l  (3.6)  and generally for all following years and periods:  (3.7).  The estimates of qN and q are made by least-squares linear regression as for the classic Leslie 0  (1939) method. The quantities within square brackets are the x j's in the multiple regression. I used the "corrected" cumulative removals (K), which includes the cumulative removals made before a removal period plus half the catch taken during the period (Braaten 1969; Ricker 1975). Confidence intervals for the recruitment parameters can be estimated as for standard least-squares multiple regression, Ifitthe estimator using the first depletion in each year, treating any subsequent depletions as removals but not catch. Negligible natural mortality was assumed in the elapsed time between multiple depletions in the same year. To demonstrate the influence of the initial removal periods I also fit the model with the first two relative abundance points omitted. This parallels Cross and Scott's (1975) ad hoc modification of the Leslie estimator to allow initial distinct q's. I omitted two initial points (both a night and a day point) to allow for diel differences in q.  53  Survival WC estimate bias can also be created by incorrect survival parameterization. For this analysis, I used age-invariant annual survival s=.85 . This is likely at the high end of the range of possible survival values for Sierra brook trout (Hall 1991; Reimers 1979). Use of the highest potential survival reflects my expectation that Leslie estimates and WC estimates are biased low (Hall 1991). If Leslie q's are systematically greater than WC global q's using the highest potential survival, then both estimates are definitively biased low.  Leslie estimates I made Leslie estimates of q for all series with catch > 20 from 1986 to 1992, to compare to the global q for each lake from the WC fittings. The Leslie method uses the regression of cpe on corrected cumulative removals. The estimate generally displays only slight bias due to its errors-in-covariates structure, although the variance may be considerably underestimated (Crittenden and Thomas 1989). I compared the global q from the WC model with 0 and 2 initial points omitted to the local Leslie q's made with 0 and 2 initial points omitted. When two points were omitted, I compared only series from Dingleberry, Flower, Fishgut 1, Par Value and Wonder 3 lakes since series for the Hell Diver lakes were usually less than 5 periods.  Catchability variation To examine how q varied among cohorts and between years, I included recruited and prerecruit cohorts and used q from the best-fit Schnute model for each cohort. I used the terminal q for series without significant diel variation, and the terminal night q for those with diel variation, as the most representative q for each series.  In order to examine how diel variation in q varied among cohorts, I included recruited and prerecruit removal series which used both day and night sets, for which catch in every period was greater than zero and total catch greater than forty. I used only series from Dingleberry, Flower, Fishgut 1, Par 54  Value and Wonder 3 lakes, since series for the Hell Diver Lakes were generally short (5 periods or less) and thus with poorly determined night-day q differences. I calculated the ratio # i ht <7day • :  T  o  n g  correct for differences in effort, I divided by the ratio of mean night period duration to mean day period duration.  Age-aggregated removal estimates I also evaluated the potential bias of age-aggregated removal estimates. I used Schnute's method for the fully recruited age-aggregated 1989 and 1991 data. I used the models and selection criteria already described and compared the estimates to age-aggregated MKA estimates.  RESULTS  Schnute estimates Day and night catchability Fifty-four of 60 depletions of fully recruited cohorts for 1989 to 1992 used both day and night removal periods. Use of distinct day and night q's provided a significant improvement in fit for 45 of the 54 series (83%) (Table 3.3). For those day-night series with catch in every removal period, 35 of 38 (92%) were best fit by a model with distinct day and night catchabilities.  First period catchabilities Twelve of the 60 series were best fit by the single catchability model and 39 by the simple day-night catchability model (Table 3.3). Nine of 60 (15%) were best fit by models with a distinct initial catchability. Of these nine, five showed higherfirstperiod catchability while four showed lower first period catchability. Estimatedfirstperiod catchability was higher than the corresponding night or terminal catchability for 32 of 60 series (53%) and lower for 28 of 30 (Figure 3.1). This is not significantly different from the expected occurrence of 30 of 60 higher first point catchabilities, if first point catchability is a random variable with mean equal to the comparable terminal q (p = .69,  55  CO in CO o  CM  1 co  CO o c  8 -2 " co S  CT  ® — cn .2  & 8 .E  to .E  O  CO a> o  s  a>  •55 E  o  o> CM i n in "i— o O o o o o  cn CD CM CO CM O  o  CD CM  ^~  o  o  s  in o e» o o  CO a> CO CO o  i n CO i n o in CM CM o d ci  00  O m i — T— o o o  CM i n CO o O o O  o %  " •ats o  co co i n  O)  2 £ 1" O  o  o  CT  —  >: 5 CM  CM  c  T  -  -r-  CM  CD  Q .  O) Q.  CO T3 » -C C .t:  1I II  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  2  o S CO N fo x co: g> o CT  -Q .> Q (0  o  s COCOOCMWi-OCOCMCMCOf^ _  co'^>-5  i i co cn ,-1 o o s w o CO CO ^~ CM CO 0 0 ^ S ™ ' -  'c  W  O TJ C J 3 "53 C To 03 o O) — "8 >, 03 •<- O E - . CO •a 2 co CD II c o °CO  0  s  <  c v  O CO CM CM in T— CO CO CM CM CM o O O O  l ' T ' ! ^ C M C M ' ^ i - c n£ci oi n , g_ , 1  T  r  i r °2 CmO T- m 0 ^ : l O C O O > C M ^ - ^ O C D ^ - r ^ Cm3 )CO CM  o>" 00  cn .  1  O  TJ  £Z  CM .E 00 CD  £1  C  ^  .2  >  \J i_T3 o Q . —  co* c c O CO  23 >  >% 03 T3 II  C T3  ~  CD  CO*  CO .-e  CT 55 « eg 03 co CD CD .> 03 "CO COc C o -C o c CO CO o J *  1^  0  3  w  03 CO CD  CO CO  CO co  II  CO  3 cr  II  E co. II  c  v  CO l h  iri  !i-ms ?u) ': R^n . u  ,  t  n  3  2  _CMCOCD .COCOCO . °. CD CO CO CO CM c d ^ ^ m oo c n * ^c^o c^n S k  TT  0  0  CM CO CO  C  M  <  0  1  0 0 ° ° - — :  O  , f t  mcojgJ  CM CO CO CO CD i n CM co' CO CM 0 0 in CM in  00  ~co^cMcooo^Ioo^^r^5-l^:cocMTririr-~  CO  co  c  CO 1- OJ , co i n 1^. CM SR co co 2 i CM i n m " CM co  C M C n i n g ^ C M C O ^ g S E ^ j C D ^ j g o C D C O ^ C M S  m  A  0  5  o  1 .1 CO  CD  •a  >.  c \ j c q T t s c q n c o N ( o c o c v i N i A < o c o c o ^ o ) n c o c o ^ N i - T - c M n ^ C N i T f c M C M O T r c d o d i ^ T f c d c M i n c d T ^ ^  c C c « T3 XJ "D  5 1 CD £i •§ -o  II  :s  iri O  "S3 Y  co  CD £ CO CO c "O CO 0 It:  FC  C  C  C  C  C  C  C  C  T3  CD  co  CO CO  00 00  LU . £  s oooocooooooooocnoooooooooooooooooooooooooocn  CO O ) CM CO 0 0 0 0  m c o s e o o j e o o i o c j n ^ i n c o s t D S c o c s s c o m o  2T-wc\iaaoifflmT-i-wc\iwoio)cio)0)0)T-i-7-T-c\iwc\iw oocncncnoooooooooscncncncncncooooooooooocncncncncncncncn CM CM CM * * *  TJ  <= 2 "co .<2 •2 53  "53 £ "° co a . CD II •i s 2CO "5 o .2 s CM w CD  o  |  00  05 . £  •u E c co  ir •S c o "55 21o 1 CO "8 2 5  T  N  'c  C 03  Q. II  8 O  w >. CD ( 0 Q. T J CD "D  Al  r - U) en en  * S fS  Q  Q Q Q  5355535353fca3555555a5 co co co CUCOCUCDCUCDCUCUCDCD  S S E E E E E E E E  1  bbbbbbbbbb  56  g 1  -  CD  5 5 5  5  LL LL Li-  o  0.0.0  LL  CD  CO  o  o  5 u_  5 LL  CD  5 o  LL  CO  O)  s  CM O )  o  CO CM  T —  m  CM 00 CM T — © d d d  T -  CO  ^ d  d  CO d  CM I - I CO CO CM  co m o o m CM  in  s  s  d  s  d  d  00 o 00 o d  CO  o  d  d  00  CO I CM O  h-  in  s CO d  OO  CD  t-  O  O  O  T -  00 00 00  CO CO I -  so a in o o  T  CM c o  go  in o  CM o>  O  O  O  T -  d  d  d  d  CM  o d o d oo d  CO i n I I - 00 CM CO CM O ) CO CO " CM en c i n CM d d o d d d d s  s  T-  s  —m en i n co -  8S  Tj-Lncoo-i-T-oocoi-  o O  -  d  o"  n c M c o o o n o o o ^ T r p T ^ O O T t i - O O C M  d  d  d d d d d d d d d  CM O ) I - CO CM i n O ) o 00 o c o CO I - CM o CM CO CO I - •^r I - O ) CO CO o o T — T— CM CM T - T — CO CO d o" d d d d d d d s  3 s  s  s  s  d  m  o co c o CM o> i n o CM CM  CO CO CM CM  I o> in CM  d  d  d  d  d  o CO 00 O O_ -yCO O ) r  s  o o  CO CM  g  CO  r-'  CM  T —  CM  m  TJ-  CT) i -  s  T -  CO CO  T- CO y-  I -  a>  I -  oo i r i  o r—  I s  CO  00  -r-_  1 O  "8 T3 3  C V c c •D - a T3  £= e  •o -o T J  2  .£ —  CO CO  Si  ca  .  ^  o  . o  CO  T -  co  CT)S in d  oo i n  . CM CO 00  r  o  -  £  s  c  c  c  C  c  c  :  c  • -2S"DT3"D-nT3-D-D C  S  f-  5  fs^  . « CM CM CO O) CM o> co m  3  _  o  CO I s  l<  ^ in  2  ^_  3t CM CT)  I m CT) t—  CM — CO CO CT) CO CM d s  c  U  CO  CO CM  co  CO S _ • C O  r o  _ _  CO CO CM S ^J: o> co  ^  CO  T  CM  d  ^ * ^ „ en m  § » 8 o> °  «?  s  c  o  CO  S 5 CO § <e s CO CM  s  T3  2  .  s  co I - i n , CO CT) O CO y— CO CO CM 00 •«* O I - CM O LO CO CM CT) CT) I - O i n CO CO CO i n CT) CT) 00 CO  T  <= c •a  o  CO c o in T—  -5 TJ -cc  c  TJ  c  S 3 S b S 5 3 3 9 ° " ' ' - o o ) N o o f f l O i - L n N N f f l o > o o o ) O N o i o oo co oo oo co oo o o c o c n r ' - c o o o o o o o o o c o o o o o o o c n o o o o c o o o o o c o o o o o c n c o o o c D |  V  r  (  D  s  ,  s  t  2 2 g > g i - ^ c \ i c \ i c \ i O ) O i c » c » T - T - T - N C M W c \ i r o o o n c o o o a c » c A a o ) o o a ) o o o o c » a ) c n a o ) c » a ) O D o o a  O c  8  a>  CO CM Lf)  3  s  3  CM  O CO CO CM I - CO CO CO o CM CM CO •<* CO CM CM s  00  CM • * CO i CO •<fr CT>CM O I • t CO  in  CM  a> cu  3  3  *^ "^3 3 3 3 3 3 3 3 « 0> O ) CD CD CD CD CD CD CD  3  . C J= CO CO CO CO c JZ £ £: .e i- i_ i_ cococococococaco J - L L L L L L L L - - 0  0  0  Val ue Val ue Val ue Val ue Val ue Val ue Val ue Val ue  P  _  O  t:  d  m  S  Par Par Par Par Par Par Par Par  O  d  o  •<- CO CM I -" l< O ^ W c M 0 6 ^ d ^ ! $ 3 C M O C D S c 5 ^ C M i f l d o 3 ^ S C M ' O CO CO s  o o  00  co CO  s  57  CO CO CO c o c o c o c o c o c o c o c o c o 3fc ^1: ^ 3fc ^ 4fc -tfc 4t -tt 4t ^t: k _ k _ l — C  O  C  O  C  O  I—  C  O  k—  C  O  k  C  O  _  C  V  O  _  C  O  l  I—  C  O  CO  >  Q  Q  Q  CD X  cu  o  0  0. , e  e e  *<  o  *-©e  o  .* £ ©  e  o  o  , ;  CN  CO  i/->  TJ-  v©  f-  OO  4 Figure 3.1. Terminal cf versus initial period <?i for 60 cohort-specific Schnute estimates from 1989 to 1992. Estimates are for fully-recruited cohorts with total catch >19. Estimation methods are described in the text. Initial period q's do not differ systematically from q's for the remainder of the series.  58  binomial test). The estimates do not support the hypothesis thatfirstperiod catchability is generally higher than comparable catchabilities later in the series, for data from 1989 through 1992.  Schnute estimate bias Five of 40 estimates for recruited cohorts from 1989 and 1991 were eliminated as poorly determined. Of the remaining 35 estimates, only seven were equal to or greater than the corresponding M K A estimate, and only one exceeded the M K A estimate by more than 10% (Figure 3.2). Schnute estimates were on average 84% of corresponding M K A estimates. Of 14 prerecruit series from 1989 and 1991, eight estimates were poorly determined. Of the remaining 6, the M K A estimate exceeded the Schnute estimate in all cases; on average the Schnute estimates were 70% of the corresponding M K A estimate (Fig 3.2).  Walters-Collie estimates Walters-Collie and Leslie estimate bias If the Leslie and WC estimates are unbiased, then the Leslie q's should be distributed approximately evenly about the WC global q. Of 120 Leslie estimates, 108 (90%) showed q greater than the comparable WC global q (Tigure 3.3a). Similarly, 87 of 99 (88%) of Leslie q's made with the first two points omitted, were greater than the comparable WC global q with two points omitted (Figure 3.3b).  Catchability variation Catchability related to size For most lakes in most years, q is higher for recruited fish than for pre-recruits (Figure 3.4). There appears to be a general pattern of positive corelation between q and size, although this may be blurred by inter-year variation in q (Figure 3.4).  59  •4  o 0  o 0  2 •4  O O  o  8  o  o o c>  o  o o o o °° o  _o % o  <D CO  8  c 0  •s  !  o  o  o  o  o  C N  £ •a  o  o o  <  « 3  1  oo  o  °  ON  OO  O  d  d  d  d  ajBuinsa uonBmdod v ^ P M °J aironps jo opB>i  60  d  S3 5  0.025  0.015  Hell Diver 2  0.02  0.012  0.015  - 0.009  0.01  0.006  0.005 85  Dingleberry o o 0 0  0.003 1 86 87  88 89  90 91 92  86  87  88  Year  Flower o  0.004  o o  92  0.015  0 q  0.01 0.005 0  88  89  91  90  92  -0.005 86  87  88  Year  0.01 0.005 o 88  89  90  91  92  90  91  92  Year  Wonder 3  0.04 0.03  o  q 0.02  o  0.01  -s87  89 Year  Par Value  0.015  0 86  91  Fishgut 1  0.02  0.002  87  90  Year  0.008 0.006  89  0 86  o  -887  88  89  90  4  §  91  92  Year  Figure 33a. Leslie estimates of q for recruited cohorts with catch > 19, plotted by year for six study lakes. The solid line shows the WC estimate of q, using survival = .85. No initial points were eliminated from the fittings.  61  o Dingleberry  0.01  0.009  0.008  Flower  0.006 +  9 0.006  8 6  0.004 0.002 0— 86 87  88 89 Year  o  87  88  89  90 Year  91  92  Par Value  0.008  0.007 0.002  o  90 91 92  Fishgut 1  0.012  0.003 f  0.006 o o  0.004 0.002  -0.003  8 _o_  -0.008 87  88  89  90 Year  91  86  92  87  88  89  90  91  92  Year  Wonder 3  0.0085 T  o o  0.0065 0.0045 0.0025 0.0005 -0.0015 87  88  89  90  91  92  Year  Figure 33b. Leslie estimates of q for depletions forfivelakes from 1986 to 1992. Includes all fully recruited cohorts with total catch > 19. Solid line shows WC estimate of global q. Initial two points omitted for all estimates.  62  Dingleberry  0.7 T  0.4 0.3 +  •  A  0.4 0.3  A •  0.2  •  100  150  •  0.1  200  120  Fishgut #1  140  160  q 0.4  0.3  •  •  0.2 +  A)  0.3  180  200  0.1  0.2  Par Value  A  O  •  A  o  •  0.1 0 120  140  160  180  200  100  mean length (mm)  150 mean length  200  Wonder 3  0.5 0.4 0.3 0.2  (3  0.1 100  220  mean length  •  0.6 0.5  •  O  O  •  0.2  •  mean length (mm)  0.7 T  A  •  0.5  0.1  Flower  •  0.6  120  140 160 mean length  180  200  Figure 3.4. Mean fork length versus Schnute estimates of q for five study lakes from 1989 to 1992. Estimation methods are explained in the text. For most lakes in most years, q increases with length. Plot symbols: squares are 1989 estimates, circles are 1991 estimates, triangles are 1992 estimates. 63  a  Diel variation in catchability related to size The effort-adjusted ratio of ^ night 4 day t0  w  a  s  tower for prerecruits than for recruited cohorts  (Figure 3.5). The general pattern is that of greater t 7  night  relative to q^  y  with increasing age/size.  Age-aggregated estimates Schnute estimates For the seven study lakes, twenty of 21 removal experiments from 1989 to 1992 used both day and night capture periods. Of the 20,17 were best fit by a model with day-night structure (Table 3.4). Six of the 21 (29%) showed significantly different q ]. For five of the six, q j was higher than the corresponding terminal q.  Of fourteen age-aggregated estimates from 1989 and 1991, one was eliminated as poorly determined. Only 3 of the remaining 13 (23%) were equal to or greater than the corresponding M K A estimate and only one exceeded the M K A estimate by more than 10% (Table 3.4). Schnute estimates averaged 92% of corresponding M K A estimates.  64  1.8  T  Dingleberry  91  1.4  89  8»  1.5  89  Flower  92  1.3  92  1.1  92 92. "92  J,  0.6 +  89 91  .91. 0.9  91 92  0.7  92  0.2  0.5 90  140 190 mean length (mm)  100  120  140 160 180 mean length (mm)  200  no ex  "S  2.5 2 1.5  89  91 .91  1 0.5 O-i  100  2.5  92  2  92  91  1.5  92  92  .92.  1  120  1  1  •  200  90  1.5  1.25  89  91  0  1  140 160 180 mean length (mm)  91  92  91  0.5 •  92  Par Value  3  92  89  91  3.5  89  Fishgut#l  140 190 mean length (mm)  j, j  Wonder 3  91  91 92 92 92 1—  100  120  1  1  1  1  140  160  180  200  mean length (mm)  knight  Figure 3.5. The effort-adjusted ratio of to-day. plotted versus fork length for prerecruit and recruited cohorts with catch >40. Plot symbol indicates the year of the estimate. In most years, the ratio tends to increase with length.  65  NO ON  8 8  00  OO  ©  00  t »  ON  ©  ^  J.  H  O  d  '  d oo  d  d oo  —  v>  CN  CN  • *  TT  O  t  N  d  d  d  H  d oo vj  ON  "3  3  ©  N  d  NO  r- o V)  N  co O  r-  CO  ON  if)  M  r-  o  *o  -  H  (S  CN  CO  CM  r-  OO  o d  CN  o NO  ON  o  OO  NO  o d  o  N  NO  r-  wo  d  o  d © d o  Tfr r» co  d  CN  © d  d  ON  oo oo  ro d  CO  o d  NO  r- V ) p CN rd d  NO  oo CN  o CN o CN d d  <N •H  ~ CO  d  C N  *—i >—i  VI ©  © d o  3 3 ON  VN  ©  ©  J £ © 0 0 C N N O C O C O O N 0 0 © ^ H S V N C N C N f O O N V N V l O C — O ^ , V N C O V ) C N N O 0 0 T f C O V O C O  ^ NO  CN CN  ON  CN  ©  « 2  ©  00  §  ©  <n rr oo oo O N N O  8 oo  CN  -2  CN  oo  « e, y «—  . S U M  r  a -a  q vi  —  CO  co  oo £  N  Tt  o  H H  c i  IO  ^  o  co  in  NO CN vO  ~  oo c  oo  a  v i  q vi  vi  f»  H  N  ON  H  N  0\  ON  ON  oo  ON  ON  00  $ S $ JlT «_. > £ & & % I Q Q  Q *ob "ob "oo  3 ^  y->  VN  r-  <N  ©  <o  P CN •<+  CO  r-  CN  ON h ON  co  PCN NO  VO  ON 00  2i g  co  r»  © yo oo ^ .  «0 CN  <3  Tf-  N  V)  (f)  CO  T«of  f ^ O N C O V O c O C N O O O N * - * CN co ON CN oo p- c o «o c o p- p»  00 V)  ON  JIJ oo co  ^  .  ©  ON  TJ-'  ON  CO  r~  CO  vi  CN CN  ON V)  V)  ON  ON  v!  CN  r~  r-  ON  2  *  ^  ^  © V)  CO *-H ON VI  CO  P-;  P-;  V)  CO  *-!  O N O N O O O N O N O O O N O N O O O N O N O O O N O N  CO i i  0  0  c c c E5 E E  3B s s s X co  CN  22  9 |2  NO ON  ON  66  % 3  00  •4-t  3  00  ish  —i  d r~  r-  CM  o *o o  CN  vo CO  r»  NO  ish  ON  <N  (S  C-CN  ON  d  _  ON  CN v>  CM  CN  d  ^  O co  Pu b  5 3  op CA  Pu  (0  CO  4t  cu  CO  3fc  (0 CO •a a •a *CO * * > Q Q >a >a >a OH cu £o £ P£ s=3 9S  3  3  CO ifr  3  •a •a  Q  DISCUSSION  In a study of the use of the removal method for estimation of small lake fish populations, Kelso and Shuter (1989) used gillnets to capture brook trout, rainbow trout (0. mykiss) and lake trout (5. namaycush) released accidentally into an 11.7 ha lake. Over three years, they made 50 day-long sets of 210m of gillnet They could not account for natural mortality but the populations were otherwise closed during the study. Although during the depletion, a constant q model and then a declining q model fit the data well, both were underestimating the true number of fish present Their study highlights two observations for removal experiments on salmonids in small lakes: catches frequently follow a pattern for which available models fit poorly, and even when models do fit the data well, population numbers are underestimated.  One mechanism which has been implicated in the underestimation of population size by removal estimates is atypical initial period q. Concavity of the cpe-K relationship is often hypothesized as due to early catch of some individuals with high capture probability (Schnute 1983; Hilborn and Walters 1992). Analysis of depletion series collected during this study suggest that initial period q was not atypical, for the 1989-92 series which I modelled using Schnute's (1983) methods. Nevertheless, the pattern of decline in cpe within removal series was not informative about population size, at least in the manner suggested by available models. Comparison of M K A with Schnute estimates, and of Leslie q's with WC global q's, showed that the removal estimators consistently underestimated population size. Omitting the first two points of the Leslie and WC fitting confirmed that this bias was not mainly due to atypical q for initial points. The removal estimates in each year generally give the appearance that almost all of the cohort has been caught. The next year's catch there nearly always shows that this was not the case. This bias translates into bias of the WC estimate. The information present in the pattern of decline of cpe only serves to degrade the WC estimates as well as inflating the variances. Bias of the WC estimates would be more serious with lower (and probably more realistic) estimates of survival. This finding is not surprising in light of results with the early part of this data set (Hall 1991),  67  and experience with subsequent depletions in the same year. Generally cpe for a cohort rebounds considerably from the end of the first depletion after an unfished period of ten days or more (Hall 1991). It appears there is a substantial portion of the population that is essentially invulnerable during any single multi-period depletion like those used in this study.  Age aggregated Schnute N's also showed negative bias relative to M K A estimates. Bias of ageaggregated estimates was not apparently as severe as for cohort-specific Schnute estimates. As well, there was greater suggestion of distinct initial point catchability. These two observations may be related. Aggregating data for cohorts with different q's will tend to produce a concave, curvilinear relation between cpe and K. This could increase the likelihood of assigning distinct (higher) initial q's, leaving a lower terminal q and thus a higher population estimate.  The removal method has been criticized in several recent studies using both passive and active gear (Kelso and Shuter 1989; Riley and Fausch 1992; Miller and Mohn 1993). The assumptions of the removal method (constant and homogeneous capture probability, or in the case of Schnute's method, simply homogeneous capture probability) have never been shown to hold for any animal population. Minor violations of the assumptions may not cause serious bias, but the method itself does not allow the assessment of how seriously its assumptions are being violated. Nonlinearity of the cpe-K relation implies violation of the assumptions. Statistical detection and correction of nonlinearity may improve the fit, but goodness-of-fit does not indicate an accurate or unbiased estimate (Kelso and Shuter 1989; Miller and Mohn 1993), despite assertions by some primary investigators (DeLury 1947; Seber 1982). Variance in catch per effort is often high, which means that it is difficult to detect nonlinearity in the later depletion points. Cone et al. (1988) found violation of nearly all of the assumptions of markrecapture estimation, including capture probability heterogeneity, for brook trout in an Adirondack pond which they drained to allow complete enumeration.  68  Explanations for the downward bias of the estimates should account for the apparent variation of q with time. For abundant cohorts, cpe generally increases from the last period of a depletion to the first period of the following year's depletion. For a closed population, this implies that q has increased in the interim. One possible explanation concerns the spatial pattern of netting: study gillnets did not fish pelagic areas of the lakes. Although we have seldom observed fish in the pelagia, it is conceivable that a portion of the population is essentially pelagic and uncatchable, but may later occupy benthic-littoral areas when fish there are removed. A second explanation is that a portion of the population has low capture probability which increases after part of the population is removed. Low q might be due to low basic activity, different spatial pattern of activity, different feeding style, or a behavioral hierarchy, any of which might change in response to the removal of other fish. Hall (1991) suggested that net shyness may change withtime,increasing during a depletion but then forgotten in the interim between depletions. The first two explanations imply that capture probability varies not only with time but among individuals, a situation which invalidates the use of any of the available estimators. Gillnet removal data alone cannot be used to distinguish among these hypotheses, although trials with pelagic nets could suggest whether the first hypothesis has merit.  Estimate bias may not interfere with interpretation of patterns in q. If bias is relatively constant or even a linear function of another variable, q's can still be compared among cohorts and between years. My analyses do not distinguish between age and size as variables influencing catchability. Size increases with age, across the cohorts which are sufficiently abundant to allow confident estimation of q with these models. The variance of length-at-age is low enough that grouping and analyzing by length rather than age would still effectively be an age-based analysis, although the largest size class would also include data for older less abundant cohorts.  A positive relationship between size and q has been reported previously (Borgstrom 1992; Crecco and Savoy 1985). For most lakes in most years of this study, the data are suggestive of such a relationship. Diel variation in cpe is another common feature of lake gillnetfisheries.For this study, most series with 69  both day and night removal periods were best fit by models with distinct night and day q's. The results suggest effort-corrected night q is usually greater than day q and that diel differences in q increase with size or age. Several hypotheses might account for this difference. One possible explanation is that nets may be easier to see and avoid during the day. Visual acuity improves with size, which might exaggerate this difference. A second possibility is that diel differences in basic activity level may vary with size. Third, the spatial pattern of activity may be diel and may vary with size. Larger fish may tend to occupy day-time habitats where they are less vulnerable to our gillnets, while smaller fish may not use such habitats. Or foraging style may change dependent on size, with a resulting effect on the spatial pattern of activity. Cursory examination of adult stomachs often reveals freshwater clams (Pisidium .$/?.) as a dominant component of the gut contents. Daytime benthic foraging may result in lower encounter rate than other foraging modes. My design does not allow me to distinguish between the hypotheses I have suggested.  Current models of gillnet catchability decompose q into encounter rate and retention probability. Retention probability is partially a function of the size, shape and swimming velocity of the fish and the configuration of the capture gear (Hamley 1975). Assuming identical behavior, the relation between body size and swimming speed would govern variation in encounter rate (Rudstam et al. 1984; Borgstrom and Plahte 1992). Such simple physical explanations for catchability variation are favoured because fish size and shape are easy to measure, and the length - routine swimming speed relation has been quantified in laboratory studies. Other size-based variation in behavior and its impact upon q is much more difficult to quantify (Borgstrom and Plahte 1992). More complex models have been used to try to isolate encounter probability variation. Borgstrom and Plahte (1992) developed a model of gillnet retention probability based on fish girth and mesh size, implying wedging as the dominant retention mechanism. They applied the model to catch data for a stunted brown trout (Salmo truttd) population, and used seining and gillnetting to make mark - recapture estimates of population size. They found that encounter probability appeared to decrease with length. Borgstrom and Plahte (1992) suggested that large brown trout might adopt a piscivorous ambush foraging mode which would lower 70  their probability of encountering nets. Again, gillnet data can suggest such patterns, but without direct observation offishbehavior in thefield,residual variation in q cannot be attributed to swimming speed, spatial pattern of movement, visual acuity, wariness or any other single factor. Further development with regard to population estimation will likely rest upon improved understanding of fish behavior, through observation techniques such as metabolic radio tagging and video monitoring.  71  Chapter 4. Population and catchability estimates at depletion-level resolution  INTRODUCTION  Previously reviewed studies suggested numerical or catchability responses of juvenile lake salmonids to removals of adult conspecifics (Lindstrom et al. 1970; Fagerstrom 1972; Healey 1978,1980; Johnson 1976, 1983,1994; Langeland 1986; Donald and Alger 1989; Hall 1991; Borgstrom 1992). The primary goal of this chapter is to examine the relationships between year class strength, prerecruit gillnet catchability and adult population density during experimental manipulation of adult brook trout density in the study lakes. Estimates of population size before and during the removals are necessary to interpret the response to experimental exploitation. Depletion data at period level resolution gave downward biased estimates of population size in Chapter 3. In this chapter I make population estimates which do not use the period level structure of the data, but instead compress each cohort's catch in a depletion into a single catch-effort observation. Bias in the period level estimates does not necessarily lead to bias in estimates made with depletion level resolution. If the fraction of each cohort vulnerable is relatively consistent from year to year, the invulnerable fraction does not recruit substantially to the vulnerable population during the depletion, and if the vulnerable fraction is not fully depleted, catch-age analysis at depletion level resolution can provide reliable estimates of year class strength, population size and catchability.  Of secondary interest in this chapter are patterns in adult brook trout gillnet catchability (q). Gillnets are often used forfishsurveys, as well as experimental and commercial exploitation. Because of the difficulty in obtaining direct observations offishbehavior in lakes, recent work has attempted to use gillnet data to deduce how behavior may change with body size and population density (Borgstrom et al. 1992). This chapter's population estimates and the catch data can be used to estimate year and cohort-specific q's. Analysis of within-lake adult q's for size and density dependence might seem a tempting focus. However, such q's are likely to be quite variable due to ageing error, errors in survival parameterization, changes in survival due to the removals, variation in q due to sampling date 72  and small sample size, as well as possible size and density-dependence. Essentially, the pattern of removals and year class strength during the study combined with errors of the type mentioned, are virtually certain to blur any within-lake across-year patterns in adult q. I report within-lake adult q's in this chapter to demonstrate the variability and lack of pattern across years.  Among lake patterns in q may also carry information about fish behavior (Hall 1991; Borgstrom 1992). The Walters-Collie (WC) method estimates a single global q for each lake adult population. This parameter is less sensitive to the previously mentioned error sources because it is estimated across years and cohorts; the parameter may be biased by such errors but the bias should be relatively consistent between lakes if the populations were treated and responded similarly. Current models decompose q into encounter and retention probability (Rudstam et al. 1984; Borgstrom and Plahte 1992). The WC q's are not directly comparable because of between-population differences in lake area and fish size which presumably effect thefish-gearencounter rate. Size at age varied between lakes, and the magnitude of the size response to removals also varied. In this chapter, I develop an encounter rate model based on fish size, lake area and effort density, to attempt to explain variation in q between lakes.  Finally, period level estimates of adult population size, such as those made in Chapter 3, can be interpreted as estimates of the adult population which was vulnerable to gillnetting during the depletion. Of interest is how that population, as a fraction of the true population, might vary with density. I use estimates made with depletion level resolution as estimates of the true population, to examine how the apparent vulnerable fraction changed from year to year during the removals.  73  METHODS  The objectives of this chapter require methods for population and catchability estimation, using the catch data at depletion level resolution. I first review the field methodology used for gillnet depletions, and establish the terminology which I use during the remainder of the chapter. Next I introduce methods to estimate year class strength and population density for the years prior to and during the experimental removals. I use two estimators: the Walters-Collie (WC) multiple regression technique, and an alternative non-linear estimation method which uses logarithmically transformed catch data. I describe the method used for survival parameterization, required by the estimation procedures used in this chapter. I detail estimation of the fraction of the population vulnerable to gillnetting, using period level estimates of the adult population. Finally, I develop the methods for catchability estimation, including a model based on fish-gear encounter probability which allows between-lake comparisons of relative activity.  General methodology Field methods I described the depletion methodology in Chapters 1 and 3 so I reiterate only briefly here. We fished Lundgrens (Sweden) light green, nylon, weighted gillnets of length 36 m and height 1.5 m, on bottom. The nets were composed of twelve randomly ordered panels of bar mesh size 4 to 38 mm, and were chosen from a pool of ten such nets. Nets were anchored at and set perpendicular to shore, but we also made sets offshore oriented at random or downwind; we usuallyfished4 to 6 nets throughout a depletion. The removals began in 1986-87 with at least one depletion per lake each year through 1992, but no depletions in 1990. Nets were hauled, cleared of fish and reset in different locations twice every 24 hrs, for a total fishing time of 36 to 132 hrs per depletion.  Terminology and treatment of the data I used one net fished for one hour as the standard unit of effort, and pool data from all sets to provide a single estimate of catch-per-unit-effort (cpe) for each cohort for the entire depletion. In some years for some lakes, two depletions were made, separated by 7 to 30 days. Except for Dingleberry Lake in  74  1991,1 used thefirstdepletion as relative abundance data for estimation and the second as removals only. The data were collected, and analyzed in Chapter 3, at period-level resolution. Accordingly, I refer to estimates which do not use the period-level structure of the data, as "depletion-level" estimates.  The term "recruitment" remains loosely defined in thefisheriesliterature and I avoid its use to the extent possible. I use "recruit" as a verb, meaning to join as a full member. For this study, "recruitment" might be used in reference to two important stages: the time or age when year class strength is considered determined, and that when catchability can be considered full adult catchability for the purposes of an estimation scheme. Instead, I use the term "year class strength" to refer to the number offishpresent in a cohort when the cohort's numerical strength is roughly established. In contrast, I refer to the catchability of cohorts when discussing their vulnerability to sampling. I use the term "prerecruit" to refer to cohorts in the year before they are recruited to the gear, and "new recruit" to refer to cohorts in their first year of recruitment to the gear. Neither time of year class strength determination nor catchability is believed primarily determined by age, but rather by size for most fishes. However, I generally rely on age-structured rather than size-structured or mixed estimation methods in this thesis, and I provide explanation for my choice of ages for these definitions in the appropriate context below.  75  Catch-age estimation  Table 4.1. Notation. Symbol  Meaning Catch per unit effort for a cohort in the i * year's depletion Removals for a cohort during the i * year, before the start of the i  Q  Catch for a cohort during the i  t h  year's depletion  year's depletion  m  Number of fish in a cohort, present before any experimental removals occurred s  Natural survival rate from year i to year i + 1, assumed independent of i  1  Catchability, or proportion of the population removed by one unit of effort  T,  Sum of all removals for a cohort in year i  t  WC estimator I presented the development of the WC estimator for period-level data in Chapter 3, so I reiterate only briefly here (symbols defined in Table 4.1). The general assumption is that cpe is related to abundance and catch as:  y =q(N -K ) l  0  l  v =q[S {N -T )-K ] 2  l  0  1  2  = qN -qK 0  (4.1)  l  = qN S -q{S T + K ) 0  l  l  1  2  (4.2)  And generally: (4.3)  =qN \nS 0  yi  a  L«=i  The estimates of q and qN are made using least-squares linear regression. I programmed the 0  multiple regression in BASIC, performing the matrix inversion by the partitioned matrix method 76  (Searle 1967). I validated my algorithm by comparing its parameter output for a reduced problem to the manually calculated regression parameters. The quantities in square brackets are the x j's in the multiple regression. Confidence intervals for the parameters are generated as for standard least squares linear regression.  Two important points should be made concerning my use of the WC estimator for depletion-level data. First, although analyses in Chapter 3 revealed that the data at period level resolution gave downward biased estimates, under certain conditions cpe aggregated across removal periods is still a reliable index of abundance. The analyses in Chapter 3 suggested that only part of the population was vulnerable during any particular depletion. As long as the fraction vulnerable at the beginning of the depletion is relatively consistent across years and recruitment from the invulnerable fraction is negligible during a depletion, aggregated cpe can still be a reliable abundance index for population estimation. Second, if q is size- or density-dependent across years and a simple WC estimator is fit to the data, minor estimate bias may result When co-ocurring with other error, size or density dependence in q will be blurred and possibly undetectable. Bias will generally not be so severe as to mask, or falsely create, relationships between adult stock size and year class strength or between adult stock size and juvenile catchability.  I fit the WC estimates across all depletions and used the corrected definition of cumulative catch (Ricker 1975). Period-level data suggest that in most years gillnet catchability approaches full adult catchability by age 2+ (Hall 1991; Chapter 3 of this thesis), while age 1+ catchability is highly variable. Accordingly, the estimation used cohorts aged 2+ and older for all populations except Hell Diver 2, which are fit to age 3+ and older cohorts since length-at-age is lower there. I also made estimates using catch data which was corrected for ageing error using methods described in Chapter 2.  77  Log transformation Other likelihood-based catch at age methods transform catch data using logarithms (Fournier and Archibald 1982; Deriso 1985). Simple linear least squares fitting (as used by the WC method) results in parameter estimates which may be dominated by a few of the largest cohort catches. Log transformation gives greater weight to the catches from cohorts which are less abundant due to low year class strength, age, or previous experimental removals.  To examine the sensitivity of year class strength, population, and catchability estimates to the fitting criterion, I made estimates using a non-linear search method. My algorithm uses a direct search to simultaneously estimate N , the number of fish present in each cohort at the beginning of experimental 0  depletions or at recruitment, and a global q. The algorithm looks forward in time from the first year of removals, so that each cohort's abundance is calculated using the following relation recursively:  N MN -T )*S, t+  t  t  (4.5)  Thefittingcriterion is the sum of squared deviations between logarithm of predicted and observed catch. I used the AMOEBA implementation (Sprott 1991) of the simplex search method (Nelder and Mead 1959) to find the minimum. Because the catches are log transformed, values of zero are inadmissible. Collie and Sissenwine (1982) and others suggest pooling catches of fish greater than age x into a single "plus group", with x chosen so that the plus group always has catch greater than zero. When age estimates are at least moderately uncertain for older fish, this method is additionally reasonable but requires assuming age-invariant natural mortality for fish of age x and older. I pooled catches older than 6+ into the plus group, except for Hell Diver 3 where the plus group included fish older than 5+ due to the absence of 6+ fish in the 1989 catch. Unlike the catch-age methods of Fournier et al. (1982), Deriso (1985) and others, my approach is not statistically rigorous. Their estimators generally require longer catch-age series and implement a variety of assumptions about stock-recruitment relationships and variance contributions to extract more information from the fitting. My informal method should be sufficient to indicate whether the patterns in year class strength,  78  population size and catchability which emerge from the WC fitting, are generally robust to the fitting criterion. Survival The estimators require an independent estimate of age specific survival. Ideally, estimates would be available for each population. The catch data offer the only means of making such estimates, but the data are not necessarily informative about mortality rates since they are also influenced by age specific vulnerability, year class strength variation, and ageing error. Smoothing of discontinuities by combining multiple years' catch is possible (Ricker 1975) but must include the same ages for all years data used, and the population must be roughly at equilibrium. For this study, the equilibrium assumption requires that thefitbe made across cohorts which existed before the experiments began. Assuming full vulnerability to the gear at age 2+ (Hall 1991), combining data beyond 1989 would necessitate dropping one age for each additional year's catch used. Post-1989 catches contain few older fish, so they would contribute little to defining or smoothing the survival estimates. Given the numerical dominance of the first two years' data, year class strength variation and ageing error could have a major impact on the age-specific survival estimates.  Faced with high uncertainty about population-specific survival estimates, I estimated two general survival parameterizations to use for population estimates. I pooled the 1986 to 1988 catch-at-age data andfittwo functions to the logged frequencies for ages 2+ and older. First, I used a linearfitto estimate a single age invariant survival. Second, I used the four parameter equation (Hall 1991) log  l0  C =Y-b\ a  k +a m  m  y  j  (4.6)  to smooth the same data, and estimated survival at age as  §  _ jQf°gioAi i- gio4 1 0  +  79  (4 7)  as described by Hall (1991). Finally, I also used (4.6) and (4.7) to make lake-specific survival estimates using age 2+ and older 1986 to 1989 catches. No information is available about survival for ages before full vulnerability to the sampling gear. To estimate N for cohorts in the year before recruitment to the gear, I assumed that survival during the year before recruitment was the same as estimated for the first year following recruitment Population estimation I used the catch equation:  N =(N,-C,)*S  (4.8)  M  to make population estimates from the year class strength estimates.  Stock and Recruitment Both the WC method, and my direct search method, estimate time series of the numerical strength of cohorts produced before and during the experimental removals. While suchtimeseries offer a general picture of how year class strength varied with time, it is often more useful to examine year class strength with respect to the adult stock from which it resulted. Year class strength is probably established by the 1+ year for most cohorts; many individuals are sexually maturing at that age (Hall 1991), and their length by thattimeis usually >50% of population L„ so it is unlikely that they experience variable natural mortality much higher than older fish. Thus I chose to use estimated numbers before experimental removals in the summer of the 1+ year, as an index of year class strength.  Because the experimental design manipulated adult numbers every year except 1990, adult population varied widely and in different ways for cohorts, during the 18 months between spawning of a cohort and its age 1+ summer. Which estimate should be used to examine the relationship between year class strength and adult population size ("stock")? I chose to use the estimate of adult population size following removals during the summer of the age 0+ year. This is about midway during the 18 months between spawning and the 1+ summer for a cohort, and represents the adult population size 80  experienced by the cohort during the late summer, fall and winter of the 0+ year. Evidence presented in Chapter 1 suggested that low snowpack and high summer warmth during the 0+ year often led to high year class strength, so this is probably an important time period for year class strength determination. I considered the adult population to include fish aged 2+ and older (3+ in Hell Diver 2). The number of age 1+ fish may influence growth and survival of age 0+ cohorts. I also calculated stock including age 1+ prerecruits but discounting their numbers by .5 to reflect my subjective feeling that they have less impact on 0+ growth and survival. Vulnerability Period-level analyses of catch data gave downward biased population estimates, suggesting a fraction of the population is invulnerable to gillnets. To examine how the vulnerable fraction varied with total adult population density, I used the Leslie removal method for adult cohorts with catch > 20 and for age-aggregated adult catch, to estimate the size of the vulnerable population in each lake for each depletion. I used the WC method to estimate the true population, and divide the estimate of the vulnerable population by the estimate of the true population, to estimate the vulnerable fraction. I excluded the Hell Diver lakes from this analysis because depletions there were of short duration so estimates were poorly defined. I also excluded the 1987 Leslie estimates because "effort was adjusted from period to period to attempt to maintain a constant total catch" (Hall 1991) which I felt resulted in unusually severe bias.  Catchability Simple q The WC method and my direct search method estimate a single global catchability, q. I estimated year-specific cohort-specific catchability q „ using N 's obtained from the year class strength t  t  estimates and the catch equation, as: (4.9).  81  I made both cohort-specific estimates as well as estimates pooled across cohorts within a year. Like the Leslie estimator, the WC method uses linear regression, so negative population estimates occasionally result from the use of year class strength estimates and forward calculation of population size using (4.8) across several years' catch. When I have pooled population and catch estimates, I have excluded cohorts whose catch estimate exceeds the population estimate for that year. Encounter rate model Recent models decompose q into encounter and retention probability (Rudstam et al. 1984; Henderson and Wong 1991; Helser et al. 1991; Borgstrom and Plahte 1992). Encounter probability is thought to reflect the intersection of the volume swept by an animal per unit time and the volume sampled by the gear as a proportion of the total volume used. A general model for q should thus take into account changes in these volumes within a single lake across cohorts and years, and between lakes. Such a model would factor out the differences in encounter probability caused by size-based variation in area swept between lakes and years, and variation in effort and population density. In theory, this would alleviate bias caused by changes in size at age, put all q's on a common scale, and potentially reveal relationships between q and density across lakes.  Here I develop a two dimensional representation of the study depletion situation, based on the assumption that variation in gear encounter probability drives most of the variation in catchability between lakes. Consider a fish swimming constantly and randomly with respect to other fish and the gillnets, at an hourly velocity v directly proportional to its body length. Imagine gillnets set along various straight-line paths across the lake bottom, so that each period there are a total of t| meter-hours of net available to capture the fish. If the lake has area A , the animal's probability p of encountering a net is then approximated by: P = t r 3  A  (  The dimensionless "relative activity" parameter k combines the proportion of time that the fish is active and the constant of proportionality between body length and swimming speed. The key assumptions  82  are that the proportion of time active and retention probability are constant for all sizes of fish considered and that spatial pattern of activity is the same across sizes. The observation model is then just  G>/>N,  (4.11).  The models (4.10) and (4.11) can be converted into the basic WC estimator observation model y, = qN, where y is expressed in units of fish per unit effort, in this case nethrs. In the WC t  formulation, q represents the proportion of the population captured by a unit of effort, so q is expressed in units of (effort)" . To make the encounter probability model compatible with the WC estimator, 1  substitute (4.10) into (4.11) and move effort, rj, to the left side of the formulation so that q r f =kvA~ N 1  (4.12)  1  t  with the units cancelling in expression (4.11) so that k is dimensionless: fish • m" -hr1  1  = k • m • hr" - n r • fish 1  2  (4.13).  Expression (4.12) is directly compatible with the WC fitting, so that where q appears in expression (4.3), kvA  _ 1  is substituted. Computationally, the regression x j's are multiplied by the value of v A  1  for that cohort in that lake and year, converting all terms to units of m and hr. I assume mean swimming velocity v for each cohort proportional to mean body length of fish captured in gillnets for each cohort in each year. When fit using the encounter probability model, the WC method estimates k and kN . 0  The model requires an estimate of the "effective area" of the lake used by brook trout. We set bottomfishing nets in all areas of the lake but shore anchored nets always caught more fish than offshore deep water sets. However, I have no independent data on the use of different depth zones by brook trout, so I cannot assert that brook trout do not use benthic areas in deep water. Low occurrence in sets there might also be due to low catchability. Because I wanted to examine how k varied among lakes, and 83  area used was uncertain, I estimated k using area above the 3 m and 9m depth contours, symbolized Aa 3 and A b  a b 9  with corresponding fc and fc , as well as total surface area ( A ab3  ab9  tot  and k ). The three tot  definitions of effective area reflect three general hypotheses about the use of habitats within the lakes: (1) ab3 : brook trout mainly use relatively shallow benthic areas; (2) ab9: brook trout use all but the deepest benthic areas of the lakes; (3) tot: brook trout use all benthic areas of the lakes. Areas above the various depth contours were estimated by weighing polygons cut from photocopies of bathymetric maps prepared by Hall (1991). Using the encounter rate model for the WC fitting, the year class strength estimates are independent of area. The estimate of k is sensitive to effective area, but since  (4.14),  the k ^ 's can be estimated directly as k^ = k^* A^J A^, . One important additional assumption is that competition between nets is negligible. I calculated the mean number of netsfishedduring depletions for each lake, and the mean density of adults during the period 1987 to 1992, to look for potential relationships between lake-specific k and these variables.  I fit the WC estimates across all depletions using the encounter rate model and the corrected definition of cumulative catch (Ricker 1975). The estimates were made across cohorts aged 2+ and older for all lakes except Hell Diver 2 (age 3+). Inclusion of age 2+ cohorts in the encounter rate fitting assumes that residual variation in catchability of age 2+ fish is explained primarily by size, whereas this is probably not the case for age 1+ fish so they are excluded. I estimated year-specific cohort-specific activity, k for the encounter rate model as: t  i*v A - 1  (4.15).  Again, because this is a regression method, negative estimates can result, and I exclude these from any estimates pooled across cohorts within a year. 84  RESULTS  Population size Survival Use of a linear fit to catch at age data gave an age-invariant survival estimate of s = .82, while the four parameter model fit to the same catch data resulted in the general and lake-specific age-survival relationships shown in Figure 4.1. Of the lake specific age-varying survival estimates, those for Dingleberry, Flower, Fishgut 1, and Wonder 3 are relatively similar to the general age-varying survival estimate. Those for the Hell Diver lakes and Par Value are quite disunilar, and those for the Hell Diver lakes appear unlikely since they imply no natural mortality up to age 8+. Lacking a method of resolving uncertainty about survival parameterization, I often present analyses using both the ageinvariant value s = .82 and the lake-specific age-varying parameterizations, in order to demonstrate whether patterns and conclusions are robust to the survival parameterization. I do not present results using the general age-varying parameterization since it is usually intermediate to the others. Year class strength For both survival parameterizations using the WC method, the study populations show increased year class strength from 1988 through 1990, relative to year class strength in the early and mid- 1980's (Figure 4.2). The apparent strength of 1980 and earlier cohorts is more dependent on the survival parameterization; use of age-invariant s = .82 produces time series for which the 1988 to 1990 cohorts are still generally the largest observed, while for some lakes the age-varying parameterization implies that equally large cohorts may have been formed in the 1970's O^igure 4.2). Only for Par Value was year class strength in the first year of removals definitely higher than earlier in the 1980's Q^igure 4.2).  Estimates made with data corrected for ageing error produced only minor changes in the pattern of year class strength Q?igure 4.3). As expected after correction, estimates for locally strong year classes were increased while those for locally weak year classes were decreased. Estimated ageing error was relatively low for young fish, so year class strength estimates for the cohorts produced during the  85  Figure 4.1. Estimated age -specific survival for seven study lakes. Estimation method explained in the text. Also shown is a general age-specific and age-invariant survival estimated from the seven lakes' data combined.  86  350 300 250 200 150 100 50 0  Hell Diver 2  -*  76  77  78  79  80  81  82  1800  83  84  85  86  87  Dingleberry  88  89  90  ON 00  o  X  1500 1200 900  I  600 300 0  LX r-  1600-  rr-  oo r-  o\ t-  fri  O 00  00  •  1200  00  00  3  wi  vo  r-  00  00  00  oo oo  X  Flower  I I .  800 400 0  .  T  z t-  r-  00  600  o  —  OO  00  00  00  3  00  00  00  oo 00  OO  Fishgut 1  500  x  400 300  T  200  .*  100 0  ©  i -x 76  77  78  79  80  81  82  83  84  85  86  87  88  89  90  Figure 42. Year class strength estimates for seven study lakes, 1976 to 1990 cohorts. The WC estimation method is explained in the text. Estimates made using s = .82 lie on the dashed line. Error bars show 95% confidence intervals. Filled circles are estimates using lake-specific age-varying mortality. Recruitment is at age 2, except Hell Diver 2 at age 3. The symbol X shows catch for the cohort in the year before recruitment, added to the s = .82 estimate. The arrow indicates thefirstyear of removals. 87  1200  X  Par Value  1000  x  800 -  600  X  X \  2  400 200  •  0 t  ~  ~  rr  -  r  oo ~  -  X  ©\ r -  -  © o  V o  o  — < c N p n T t o o c o c o c  800  so  r-  oo  o\  o  OO  00  OO  00  ON  X  Wonder 3  I  600  vt 00  ,1  400 - -X  200  x  -  83  84  1  X  1  X  0 76 140 120  77  78  79  80  81  82  85  86  87  88  89  90  T  Hell Diver 3  X  100 80  I-  --*  60 40 20  •r  I - -Z  0 76  77  78  79  80  81  82  Figure 4.2 concluded.  88  83  84  85  •I  86  87  89  90  350  Hell Diver 2  300 250 200 150 100 50 0  oo  — r-  X 00  CN 00  00  C«1 00  1800  X  00  oo  roo  vo oo  roo  oo oo  o\ oo  o o\  vo oo  roo  oo oo  o\ oo  o o\  00  o  VO  oo oo  oo  o  Dingleberry  1500 1200 900 600 300 0  -Ivo  r— c-»  oo r-  e\ t--  o oo  »-> oo  CM  oo  m oo  s  in oo  1600  Flower 1200 800  i  400 0  i i i  v o r - o o o o - H C S c n r-t— r - r - o c o c o c o c  600  »/•> oo  Fishgut 1  500  i  400  -I.  300 200 100 0  3  s  vo  t-» t—  00  ii  -i  o  — <  cs  co  00  00  00  00  3  00  00  oo 00  Figure 43. Year class strength estimates for seven study lakes, 1976 to 1990 cohorts. The WC estimation method is explained in the text. All estimates were made using age-invariant s = .82. Error bars show 95% confidence intervals. Filled diamonds are estimates using ageing-error corrected catch data. Recruitment is at age 2, except Hell Diver 2 at age 3. 89  1400  Par Value  1200 1000 800 600 400  •  I •  s  I--t.  200 0  2 • \o r-  rr-  oo r-  o\ r~  00  00  00  00  3  800  vi oo  vo oo  r» oo  oo oo  o\ oo  o\o  ON OO  ON  Wonder 3  600 400  H  200 0 r»  p-  00  p-  ON  p-  I--I.  I O  oo  —  oo  CN  oo  CO  oo  3  >/-> oo  vo  r-  oo  OO  00  00  o  140  Hell Diver 3  120 100  I  80 60  I.  40 20 0 NO P»  pp-  00  ON  O  —i  CN  CO  r-  r-  oo  oo  oo  oo  Figure 43. concluded.  90  3  V)  NO  t •  oo  oo  oo  oo 00  ON  oo  O ON  removals were relatively unaffected (Figure 4.3). Estimates for very strong year classes in the late 1970's and early 1980's, for example Par Value in 1977 and Wonder 3 in 1981, were most sensitive to ageing error correction because of their greater age during the experimental removals. Stock and recruitment Adult stock and year class strength appear to be inversely related, over the range of stock sizes created by the experimental removals and the year classes formed during the removals Q?igure 4.4a). The pattern is robust to survival parameterization, although lake-specific parameters lead to greater apparent variability for some lakes (Figure 4.4b). Nor did logarithmic transformation of catch data affect the general negative relationship between the number of recruits and adult stock size, when estimates were made using my informal method Q?igure 4.5). Inclusion of prerecruit numbers, weighted by .5, apparently reduces the variation in the relation between stock and year class strength for some lakes Q?igure 4.6).  Vulnerability Estimated adult cohort vulnerability did not appear to vary systematically with adult population density (Figure 4.7). Pooled adult vulnerability also was not related to adult density, for the limited estimates available Q?igure 4.8).  Catchability Simple q WC estimator Estimated adult cohort q was highly variable 0?igure 4.9). Length of fish captured in gillnets did not appear to explain much of the variation in cohort q figure 4.9). Pooled adult q was less variable. For some lakes (Dingleberry, Par Value) pooled q appeared relatively constant over a wide range of adult densities Q?igure 4.10). Others were more variable and show a suggestion of an inverse relationship between density and q, but no dominant relationship between q and adult density is apparent.  91  400  Hell Diver 2  89 88  2000 1500  300 200  1000  86  500 87  84  200 •S oa c  a «5 C/3  2000  400  500  73 1000  87  1500  500  88  800  87 90  89  600  90  400  89  300  8<* 85  0 500  1000  Wonder 3  1000  88  900  87 86  2000  Par Value  1200  90  0  0 1000  85  100  90  500  89  200  86  Fishgut 1  88  300 85  90  1500  84  500  84  1000  600 400  89  86  0  Flower  88  C3  600  84 87  600  1500  1500  85  85  100 0  Dingleberry  88  89  1000  1500  140 120 100 80 60 40 20 0  200 84  ft 87 86  0 500  2000  1000  1500  Hell Diver 3  90 89 87  86  88 8584  100  200  300  Adult stock Figure 4.4a. Estimates of age 1+ year class strength plotted versus estimates of adult stock in the fall of the cohort's 0+ year. Adult stock includes age 2+ and older fish. For Hell Diver 2 adult stock was considered age 3+ and older, and year class strength determined at age 2+. Estimates were made with the WC estimator and age-invariant s = .82; methods explained in the text. 92  300 250 200 150 100 50 0  Hell Diver 2 89 88  2 "to CO CO  m o  89 88  1000  86  85  85 90 86  500  87  87 1000  400  300  Flower  87  400 *4 86  84 88  89  85  8  500 1000  cc  2000  90  200  90  0  3000  Fishgut 1  600 89  2000  800  1500 1000  84  0 200  88  2000  Dingleberry  1500  100  cz  2000  87 86  0 500  3000  1000  1500  CD  Par Value  1200 900  88  87  600 300  Wonder 3  800  88  600 90  400  89  89  90 87  200  ¥4 86  0  0 500  1000  500  1500  120  1000  1500  Hell Diver 3  90  90 89  60 30  86  87  88  84 85  0 0  50  100  1 50  Adult stock Figure 4.4b. Estimates of year class strength during the summer of the 0+ year, plotted versus adult stock for seven study lakes. Estimates made using the WC method with lake-specific survival parameters. For Hell Diver 2, adult stock includes age 3+ and older cohorts and year class strength is at age 2+. Plot symbol indicates the cohort's calendar year of emergence. Year class strength appears negatively correlated with adult stock over the observed range. 93  Dingleberry  2000 88  89  1500 1000  85  500  s  84 87  0 500  C CU  tt <Z5  1600  800  89  84  500  1000  900  86  0 500  1500  1000 Wonder 3  1000  88  800 90  89  600  90  400  89  300  86 85  0 500  87  100  Par Value 87  90  200  86  88  1200  85  300  87  90  600  88  400  89  Fishgut 1  84  500  400  1500  1500  600  1200  C*  CU  Flower  88  1000  1000  1500  200 84  50  84 86  0 500  2000  1000  1500  Hell Diver 3  90  150 100  87  89 88  87  86  85 84  0 100  200  300  Adult stock Figure 4.5. Estimates of age 1+ recruitment plotted versus estimates of adult stock after removals in the cohorts 0+ year. Adult stock includes age 2+ and older cohorts. Plot symbol indicates the cohort's year of emergence. No estimates were made for Hell Diver 2. Estimates made using log-transformed catch data and a direct search method explained in the text.  94  400  89  Hell Diver 2  2000  88  300 86  85  84  200  87  0  400  1000  600  Flower  2000  88  2000  3000  Fishgut 1  600  84 88  1500  400  89  85  1000  2000  0 500  3000  Par Value  1500  87  900 600  90  89 90  400  0 1000  88  600  8*85  500  1500  800  89  300  1000  Wonder 3  1000  88  1200  87 86  90  1000  90  200  84 85 86  500  CU  90  86  84  500 87  0  OO </5  89  1000  85  100  s  Dingleberry  1500  200  a  88  1500  200  84  500  2000  1000  1500  2000  Hell Diver 3 90 89 87  50  86  0  150 100  885  87  86  88 85 84  100  200  300  Adult population Figure 4.6. Estimates of year class strength during the summer of the 0+ year, plotted versus adult stock for seven study lakes. Adult stock includes half of precruit numbers. Estimates made using the WC method and age-invariant s = .82. Plot symbol indicates cohort year of emergence. Hell Diver 2 year class strength was considered established at age 2+ and adult stock was age 3+ and older.  95  1.00  1.00  Dingleberry  0.75  0.75 §  0.50 o O  0  1.50  1  1.00  <u 0.50  I  CD  0.00 0.05  ( 2.00  &<  0.25  0.00  o  8  0.50  0.25  o  o  Flower  0.1  0.05 1.50  Fishgut 1  0.1  Par Value  1.00 o  0.00 0.05  I  0.50  o o  8  0.00  0.1  0.15  0.02  0.04  JS S3 >  0.1!  2.50 2.00 1.50 1.00 0.50 0.00  Wonder 3  0  0.05  0.1  Adult density (fish / sq. m.)  Figure 4.7. Estimated proportion of cohort vulnerable, plotted versus estimated adult density for five study lakes, 1988 to 1992. Population estimates were made using the WC estimator with s = .82 and depletion-level data. For each cohort, the vulnerable population was estimated by the Leslie method using period level depletion data, for adult cohorts withcatch >19. There is litde evidence of density-dependence in vulnerability.  96  0.0(  Dingleberry  1  1 0.75  0.75 0.5  8»  88  92 18  0.5  91b  91a  92  0.25  91  0.25  0  0 0.05  s  Flower  0.1  0.15  0.05  0.1  0.15  es  u  e dul  0.75  o  0.5  rtio  1  0.25  e a g M  CU  Fishgut 1  92  89  91  Par Value  1 0.75  88  88  0.5  89  92 91  0.25  0  H  0.05  0.1  ,  0.15 1  0  0.02  0.2  0.04  0.06  Wonder 3  0.75 0.5  91  89  0.25 0 0.05  0.1  Adult density (fish / sq. m.) Figure 4.8. Estimated proportion of adults vulnerable, plotted versus estimated adult density for five study lakes, 1988 to 1992. Population estimates were made using the WC estimator with s = .82 and depletion-level data. Vulnerable population was estimated by the Leslie method using period level depletion data. With the possible exception of Fishgut 1, there is little evidence of density-dependence in vulnerability.  97  0.0012  0.0016  Dingleberry 89  88 91  0.0008  9 1  88  »  160  T  0.0008  88  180  8  9  200  220  88  88 88  91  91  140  0.0014  Fishgut 1  160  180  200  220  89  T  Par Value  92  89  0.0012  92  % 0.0035 + U  88 87 88 87  91  8  89  7  887 92 91  0.001 •• 88  88 8  8989  8  87  92 92 91 88  91  92 8 7  0.0008 ••  88  0.0015 0.0005 130  89  0.0004  I  0.0025  91  87 8 91  88 »  0.0045  88  87 8  92  87  0.0004 140  89  0.0012  8787 87 87 87 87 88  89  Flower  89  88  150  170  0.0006 150  190  0.002  92 92 91 ~  $7 88  0.0008  180  195  210  225  8 8  0.0016 92 91 87  165  1  88  Wonder 3  0.0012  H  88 87 88  8988  89  89  0.0004 +  120  140  160  180  200  220  Mean length (mm) Figure 4.9. Estimates of catchability, plotted versus mean length, for cohorts age 2+ and older with catch > 19, forfivestudy lakes 1987 through 1992. Estimates made using the WC method with s = .82. Plot symbol gives the year of the estimate. Estimated catchability is highly variable, and length does not appear to explain much of the variation.  98  0.003 0.0025 0.002 0.0015 0.001 0.0005 0  0.0016  88 87  0.0012  86 89  92  0.0004  Hell Diver 2 0.1  89  0.05  0.1  87 89  0.002  91  0.001  Flower 0.05  92  0.003  87  *»%8  0.0008  0.1  9  1  88  Fishgut 1  0  0.15  0.05  0.0016  0.0016  0.0012  0.0012  88 89 92 s i  0.0008 0.0004  87 91  0.004  0.0012  o crj O  92  Dingleberry  0.15  0.0016  CO  88  0 0.05  0.0004  89  0.0008  91  0.0004  0  0.15  9S  0.2  87 91  0.0008  Par Value  0.1  89  Wonder 3  0 0.02  0.04  0.06  0.05  0.004  89 92  0.003  88  0.1  0.15  87 91  0.002 0.001  Hell Diver 3  0 0  0.005  0.01  0.015  0.02  Density (no. / sq. m.) Figure 4.10. Pooled yearly estimates of adult catchability plotted versus estimated adult density for seven study lakes, 1987 to 1992. Estimates made using the WC estimator and age-invariant s = .82, with the plot symbol indicating the year of the estimate. For most of the lakes, there is no apparent strong relationship between adult catchability and adult density.  99  Table 42. Estimates of activity, k, for three area parameterizations of the WC encounter rate model for seven study lakes. All values are multiplied by 100. Ab3 = area above the 3 m depth contour, Ab9 = area above the 9 m depth contour; Total = total lake area. Also shown is j from the simple WC estimator. Lake Hell Diver 2 Dingleberry Flower Fishgut 1 Par Value Wonder 3 Hell Diver 3  Ab3 0.0172 0.0727 0.0988 0.0621 0.0219 0.0298 0.0244  Ab9 0.0350 0.0889 0.0988 0.0795 0.0666 0.0776 0.0720  Total 0.0350 0.0889 0.0988 0.0795 0.1055 0.0776 0.1098  simple q 0.1900 0.1135 0.1002 0.2328 0.0954 0.1146 0.2912  Encounter rate WC estimator With the exception of Hell Diver 2, k is much less variable among lakes than q, when effective area is assumed to be either total lake area or area above the 9m contour. (Table 4.2). The k's for Par Value and Hell Diver 3 were lower than the other lake k's when area assumed was Ab9, but higher at total area. Maximum depths for Par Value and Hell Diver 3 are 18 and 13m respectively. Probably an intermediate area parameterization, such as area above the 1 lm depth contour, would bring their k's within the range displayed by the other four similar lakes. Regardless, the estimates do not support the hypothesis that adult brook trout use only littoral benthic areas, but instead suggest that they use all, or almost all, of the lake benthic areas. The estimate of it for the low density population of Hell Diver 3 is not dissimilar to those of the other lakes. Q7igure 4.11). The estimated k for Hell Diver 2 is quite different from the other lakes (Table 4.2). Although mean population density for Hell Diver 2 was apparently similar to the other lakes, effort density was much higher there (Figure 4.11). Prerecruit and new recruit catchability With the exception of Par Value, prerecruit q tended to vary inversely with adult population density 0?igure 4.12a). Prerecruit q was positively related to mean prerecruit length Q?igure 4.12b). New recruit catchability did not vary in any systematic way from pooled adult q OFigure 4.13).  100  10  c  H2  8  FG  6  c •a  4  ts  2  H3  W F D  w 1  2  Lake area (ha.) 0.001 T '£  0.0008  Z >  0.00061  .3 a;  0.0004  t  0.001 D W P  H3  FG  o  FG  0.0006 H2  0.0004  H2  0.0002  H3  0.0008  0.0002  s = .82  lake-specific  0 500  1000  500  1000  Density ab9 (fish / ha.)  0.001  0.001  ^H3  D  > •a % >  0.0008  *H3  0.0008  FG  FG  0.0006  0.0006 +  0.0004  0.0004  0.0002  H2  H2  0.0002  s = .82  lake-specific  0  0 10  .  0  10  Effort density (nets / ha.) Figure 4.11. The top panel shows mean effort density, nets fished per area (ha), plotted versus lake area. Smaller lakes received much higher effort density. The center panels show relative activity, k, estimated from the WC encounter rate fitting, plotted versus mean adult density 1987 to 1992, using area above the 9m depth contour. The left panel shows the fitting made with age-invariant s = .82, while therightshows fittings made with lake specific age-varying survival. The single low density lake does not show k different than the other lakes. The bottom two panels show k versus effort density for the same area and survival paramters. High effort density may be associated with lower k, implying gear competiton at high effort density. Plot symbols: H2 - Hell Diver 2; H3 - Hell Diver 3; D - Dingleberry; F - Flower; FG - Fishgut 1; P - Par Value; W - Wonder 3. 101  0.003  0.00045  0.002  0.0003  0.001  0.00015  0 0.05  0.1  0.0006  Dingleberry  0.0006  Hell Diver 2  0.004  0  0.15  0.05  Flower  0.1  0.15  Fishgut 1  0.002 0.0015  0.0004  0.001 •s  0.0002  0.0005  0 0.05  0.0008  0.1  0  0.15  0.05  0.0015  Par Value  0.0006  0.1  0.15  0.2  Wonder 3  0.001  0.0004 0.0005  0.0002 0 0.02  0.04  0.05  0.06  0.004  0.1  0.15  Hell Diver 3  0.003 0.002 0.001 0 0  0.005  0.01  0.015  0.02  Adult density (fish / sq. m.) Figure 4.12 a. Pre-recruit q plotted versus adult density for seven study lakes, 1987 through 1991. Estimates made with the constant q WC method using s = .82; details provided in the text. With the exception of Par Value, most populations show an inverse relationship between prerecruit q and adult density. Two depletions were made for Dingleberry in 1991; thefirstis labelled '91a' and the second '91b'.  102  0.0036  88  0.0027  0.0003 8*1  •g JC o  0.0004  Q  0.0002  91b  0.00015  87  110  0.0006  89  88  0.00045  0.0018 0.0009  Dingleberry  0.0006  Hell Diver 2  9ll  89 130  150  Flower  170  80  89  120  100  0.002 j Fishgutl  88  0.0015  140  89  91  0.001 87  80  0.0008 0.0006  91  120  100  87 88  0.0005 80  0.0015  Par Value  Wonder 3  87 88  h  9  88 89  0 J 87 1 80 100  100 105 110 115 120  Hell Diver 3  140  91  0.0005  0.0002  0.004  120  0.001  0.0004  0 95  100  .  1  120  140  89  0.003 0.002  91  0.001  87  88 110  120  130  140  1 50  Length (mm) Figure 4.12b. Estimates of prerecruit catchability plotted versus mean length of prerecruits for six study lakes. For most of the lakes, prerecruit q is positively related to prerecruit length.  103  0.003  88  Hell Diver 2  0.0025  86  89  0.002  89  87  0.001  Dingleberry  92>1' - 87  0.0008  92  91  0.0015  0.0012  88  0.0004  0.0005  0*  0 0.001  0.0015  0.002  0.003  0.004  Flower  89 0.001  9i ;  0.0012  89 - „„ 88, ' 92 91' 87  0.002 0.001 0  0 0.0005  0.001  0  0.0015  87  0.001  0.0015  Par Value  0.0011 0.001  0.0008  Fishgut 1  0.003  S?' '87  0.0005  0.0012  0.0004  0.002  0.003  Wonder 3  0.001  0.004  87 89  91, '  88'92  88  9)92"89  0.0005  0.0009  0^ 0  0.0008 0.0008 0.0009 0.001 0.0011 0.0012 0.004  Hell Diver 3  0.003  0.0005  0.001  0.0015  89 91  8 8  SI  0.002 87  0.001 0^ 0  0.001  0.002  0.003  0.004  Pooled adult q Figure 4.9. Estimated catchability of cohorts newly recruited to the sampling gear, plotted versus estimated pooled adult catchability in the same year, for seven study lakes 1986 to 1992. Estimates made by the WC method, s = .82. New recruit catchability does not differ in any systematic way from pooled adult catchability.  104  DISCUSSION  The results of this chapter confirm Hall's (1991) observation that as adult density declined due to the removals, large cohorts were produced by the study populations. Additionally, as those large cdhorts matured, year class strength again declined. Because the treatments were not staggered, strong year classes in 1988 and 1989 might also have been interpreted as due to drought conditions. However, 1987 year classes which were not unusually strong and weak year classes in 1989 or 1990 also occurred during drought conditions. While year class strength in some years may have been exaggerated by weather conditions, the full results suggest that the observed variation is not explained primarily by weather but that adult population density plays a strong role in regulating year class strength.  The uncertainty about age-specific survival for the study populations translates into greater uncertainty about year class strength for older cohorts. Depending on the survival parameterization, time series of year class strength may show old cohorts which appear stronger than those produced during experimental removals. The uncertainty in survival means that the strength of those cohorts, relative to those produced during the experiments, cannot be established. One approach to survival parameterization which I did not utilize, would be to estimate survival parameters which produce a "flat" time series of year class strength estimates prior to the removals, when analyzed with catch-age methods. Given the drought cycle of the Sierra, the influence of weather on year class strength, and the lifespan of alpine lake brook trout, I did not expect that year class strength would necessarily be flat across the relevant timespan.  One reason for attempting ageing error correction was to reverse the downward bias of recruitment estimates for large cohorts occurring in the decade prior to the start of the experiment. Better estimates of the size of the largest cohorts produced in the past might have provided additional evidence about whether strong recruitments during the experimental removals were an unusual occurrence, likely due to the experimental removals. Second, I wanted to ensure that true pattern of strong and weak year classes during the removal years was reproduced in the data. However, given the uncertainty about 105  natural mortality, the size of cohorts produced before the mid-1980's is highly uncertain regardless of ageing error correction. The low error rates for the youngest ages made the second point of minor importance. The tendency of correction to increase the variance of the estimates, and the differences between methods used for error estimation and procedures used for general ageing, led me to rely on uncorrected data for the analyses in this chapter.  Gillnet catchability of prerecruits appeared inversely related to adult brook trout density, and positively related to prerecruit size. But the results do not resolve how much direct effect adult density has on prerecruit catchability, independent of the presumed effect of adult density on prerecruit size and thus prerecruit encounter rate. Prerecruit size and adult density are confounded for this study, and statistical distinction of their (possibly nonlinear) effects on prerecruit q is not possible, given the limited observations for each lake. Multiple depletions made in the same year, as for Dingleberry in 1991, do little to resolve the two effects. The second depletion invariably has lower adult density cooccurring with greater prerecruit length since the prerecruits grow rapidly in the period between depletions.  The results leave open the intriguing question of which mechanism(s) are most important in the suppression of year class strength by adult brook trout. Young brook trout are occasionally found among the stomach contents of adult brook trout in Sierra Nevada lakes. It seems likely that cannibalism is an important mortality source for young brook trout, and it is quite possible that the observed relationship between adult stock and year class strength is driven mainly by cannibalism upon young brook trout. As noted previously, young fish are presumed to carry out a delicate balancing act, playing off the risk of being eaten against the need to feed, outgrow predation risk, and reach reproductive size (Walters and luanes 1993). If the tradeoff is manifested in the habitats used by young brook trout, the amount of time spent in those habitats, or their activity or other behavior within those habitats, changes in gillnet q might reflect this. Such changes could be due to altered predation risk, foraging return or both. Regardless, the sensitivity of prerecruit q to adult density confirms that  106  earlier studies which did not account for the catchability response of juvenile fish in their population estimation, were unjustified in inferring a numerical recruitment response to adult removals.  The estimates of cohort-specific adult q might seem disconcertingly variable. Estimation of q using population estimates made by forward calculation from the WC N (year class strength) parameters, 0  could be variable within and between years for a number of reasons. Among these are ageing error, errors in survival parameterization or changes in survival, small sample size, and density- and sizedependence of q. Other variation in q might be due to year-to-year variation in sampling date, and unintended changes in nets or netting procedures. Any combination of these sources of variation could occur, and some sources, such as size and density, are likely confounded. Nor is there any particular reason to assume that such effects are linear. This combination of factors makes estimation of sizeand density dependence in adult catchability implausible for the study. I have presented adult catchability estimates mainly to demonstrate that given the apparent variation in q, there is little positive evidence for density dependence using my data and methods. I cannot conclude that such mechanisms did not occur during the manipulations.  This discussion points to the inability of the field design to reveal such relationships in q. The removal method requires a distinct numerical decline in numbers in order to gain information about population size. As well, exploitation must produce contrast in density sufficient to overcome other error and allow detection of density-dependence in whichever parameter is under study. For small populations such as those used for this study, cohorts cannot persist for more than 2 to 3 years under such exploitation. To detect trends in catchability without reliable information about population size from within-year catch, cohorts must be abundant across several years' data and must be "interwoven" in abundance. Producing sufficient contrast in density is difficult given the demostrated numerical response and may destroy the interwoven structure needed to detect or reject density-dependence in q.  Nevertheless, the observed relationships between stock and year class strength, and between stock and prerecruit catchability, are fairly robust to errors in survival parameterization and to variation in 107  catchability. This is due to the short duration (generally three years or less) over which most cohorts contribute significantly to the catch, and the short period (1984 to 1990) used in the adult density - year class strength comparison. Only major changes in catchability and survival could produce the pattern of catch at age observed, without implying the relationships between adult stock, year class strength and prerecruit q which I have estimated. Detection of such changes generally requires longer catch time series and auxiliary data which were not available.  My encounter rate model for q neglects other size-based variation in behavior. As well, as a two dimensional model it does not account for differences in morphometry of the study lakes, which were intentionally selected for such heterogeneity. However, the similarity in k across lake morphometries and population densities suggests that a simple encounter rate model, which assumes that brook trout use benthic areas to roughly 10m depth, can explain much inter-population variation in q. Some studies have modeled swimming speed, and thus encounter probability, as a power function of length (Rudstam et al. 1984; Henderson and Wong 1991) rather than the simple linear function I chose. The parameters used by those studies resulted in length-encounter probability relationships which were nearly linear over the observed range of fish lengths, so the distinction does not appear important  Other gillnet selectivity studies have also attempted to account for size-based variation in retention probability (Helser et al. 1991; Henderson and Wong 1991; Borgstrom and Plahte 1992). Such studies have modeled wedging as the dominant retention mechanism. "Wedging", the retention offishencircled by the mesh posterior to their gillcovers, is an important retention mechanism which may be easily explained by the geometry of the mesh and fish girth (Borgstrom and Plahte 1992). However, other forms of entanglement are common. "Tangling" of fish by their mouthparts or other protrusions leads to retention in mesh sizes which do not necessarily have any simple correspondance to fish girth. Generally, to limit tangling the cited studies have used a narrower range of mesh sizes relative to the range of fish sizes captured, as well as simply excluding tangled fish from their analyses. Compared to the cited studies, the number and range of mesh sizes used in this study was greater relative to the range of fish sizes. I did not record mesh size of capture or mode of retention but tangling was 108  certainly an important retention mechanism (Figure 2.3 in Hall 1991) and may imply that retention probability was positively related to size. However, any resulting bias in it should have been similar across lakes.  Density dependence in q has been reported for other gillnetted fish populations (Henderson et al. 1983; Borgstrom 1992) including montane small lake stunted brown trout populations similar to Sierra brook trout (Borgstrom 1992). Although most of the lake populations for this study were apparently similar in density, the single population whose density was much lower, Hell Diver 3, did not show q variation unexplained by the simple encounter rate model. One lake, Hell Diver 2, did show q variation unexplained by the encounter rate model and a parsimonious explanation is that high effort density for Hell Diver 2 depletions led to gear competition.  The results of this chapter do not provide an explanation for the full pattern of variation in gillnet catchability shown by most cohorts across multiple years' catch. The downward bias of within-year population estimates suggests that a fraction of each cohort is virtually invulnerable to gillnets in any year. However, the fraction vulnerable appears generally consistent across years. This result rules out only innate, maintained differences in capture probability of individuals across years. Fish which are apparently invulnerable to gillnetting during a depletion become vulnerable by the next year's depletion, and the total fraction vulnerable appears relatively independent of population density. I am unable to distinguish between density-independent turnover of the population between active and inactive states as hypothesized by Hall (1991), the spatial hypothesis which holds that the invulnerable population occupies unfished pelagic areas of the lake (Chapter 3 of this thesis), or simply poor resolution in the estimation. Other studies, which have used both benthic and pelagic gillnets to capture salmonids in small lakes, have also found an apparent significant invulnerable fraction (Kelso and Shuter 1989; T. Johnston, pers. comm.), evidence which weakens the spatial hypothesis.  Despite the importance of gillnets asfishinggear and as tools for gathering information about fish abundance and behavior, the literature is surprisingly devoid of direct observations of fish behavior 109  with regard to gillnets. Increasingly parameterized models of catchability have been proposed (Helser et al. 1991; Henderson and Wong 1991; Borgstrom and Plahte 1992). Such models have been tested on wild populations for which there are essentially too many unknowns to allow convincing distinction of the specific importance of size- and density-dependent encounter and retention rates. Both encounter and retention are complex emergent properties of fish behavior and gear configuration/deployment. While models of these procesess are suggestive, they will remain unconvincing without concurrent direct observations of lake fish individual behavior.  110  Chapter 5. Summary, conclusions and future research  The resilience of Sierra Nevada small lake brook trout populations to gillnet exploitation appears due to at least three distinct phenomena operating on different time scales. First, at any time a significant densityindependent proportion of the adult population is apparently invulnerable to bottom-set gillnets. Second, removal of adults leads to increased year class strength of ensuing cohorts. Third, faster growth of young fish following removals probably leads to earlier maturity (Hall 1991). Acting together, these phenomena frustrate attempts to reduce adult population density. Following three years of removals, in 1991 length at age of gillnetted brook trout was similar to or lower than length prior to the experiment, and total adult densities were similar or even higher. This result reinforces the conclusions of several authors that increased exploitation of stunted salmonid populations is unlikely to alleviate stunting unless recruitment is inhibited (Langeland 1986; Donald and Alger 1989; Hall 1991; Borgstrom 1994). The results of the current study are more convincing due to replication, duration of the experiment and more rigorous estimation methods.  "Stunting alleviation" studies (Langeland 1986; Donald and Alger 1989; Hall 1991) have not clearly stated prior expectations with regard to the growth response to density reduction. A theoretical or even empirical approach to predicting how fish size might relate to population density has been lacking until recently (Walters and Post 1993). Stunted populations have been explicitly or implicitly considered abnormal, because larger adult body size occurs for lake populations elsewhere in the species' range (Hall 1991). Brook trout stunting cannot be considered abnormal unless it is demonstrated that theory would predict a different life history, given adult and juvenile growth and mortality rates and size-specific fecundity (Hutchings 1993).  Due to the paucity of information about exploitation rates for Sierra lakes, it is unclear whether low productivity lake populations could produce much larger fish, without high vulnerability to overexploitation at lower density. Of eight lakes I netted in both 1991 and 1992, all were visited at least once by anglers while I was working. Some of these lakes are relatively distant from developed trails. It is clear that 111  anglers often return to such lakes year after year and have the expectation of retaining fish to eat As noted by Hall (1991), "few lakes on the eastern side of the Sierra Nevada crest contain large brook trout." He observed that "these populations are usually in the most remote lakes suggesting that periodic catastrophic events such as avalanches or partial winter-kill regulate population abundance." Instead, I propose that lakes with large brook trout tend to be those with infrequent recruitment, and that such lakes are those with spawning habitat only occasionally capable of supporting eggs and sac fry through the winter to emergence. Some may be remote, high elevation lakes near the "top" of watersheds and thus without permanent inflow and outflow streams to produce spawning habitat. Others, however, are accessible lower elevation tarns which lack year-round inlet and outlet streams. The evident persistence of some low-density populations suggests that the idea of producing larger brook trout in small alpine lakes was not completely unfounded. The recruitment response makes the point irrelevant for wild brook trout in most Sierra lakes.  While biologists may consider 200 mm brook trout undesirable, I met few anglers who expressed outright dissatisfaction with the size of mountain small lake brook trout Most appeared to appreciate the ability of wild brook trout to thrive in an unproductive environment Nevertheless, there is continued interest in manipulating brook trout populations. Fish managers wish to replace brook trout with species which do not reproduce in alpine lakes, so that density and fish size can be controlled. As well, introduced fish have been implicated in the decline of native aquatic species, and agencies are interested in eliminating fish from some watersheds to attempt to restore aquatic communities. At least six methods for extirpation of selfsustaining brook trout populations have been suggested. Among these are piscicides, gillnetting, stocking with other salmonids, introduction of sterile brook trout to reduce population fecundity, blocking access to spawning areas (Hall 1991), and introduction of a species-specific disease. At this time the least disruptive and most reversible manipulation techniques are considered most desirable. Agencies are currently reluctant to use piscicides, and some lakes are simply too deep for poisoning. In the past, other salmonids have been airplane stocked "over" brook trout populations in the hope that large non-brook trout adults would be produced and consume young brook trout, reducing brook trout density and improving their growth. This approach appears to have failed in most cases (Hall 1991). Gillnetting now appears likely to succeed only in lakes where recruitment is irregular. 112  Future research This study and its predecessor have yielded minor returns toward improved management of stunted brook trout populations, for the effort expended. I hesitate to claim that advances in the ability to manage, manipulate, and enhance the size and yield of lake salmonids will be best achieved by further intensive study of recruitment dynamics. Nevertheless, experimental manipulation of Sierra lake brook trout populations has verified a seldom demonstrated inverse relation between adult density and year class strength, at least partly because recruitment appears less "noisy" than for most freshwater fish populations. Other characteristics of the lakes also make them ideal for further research on recruitment dynamics: ease of replication, freedom of manipulation, and lack of other disturbances (Hall 1991). Future research will likely be directed to determining which mechanisms that suppress year class strength for natural populations, respond to adult density reductioa In particular, testing of ideas about how individual behavioral mechanisms of young fish lead to whole population dynamics (Walters and Juanes 1993) may be tractable. While gillnet sampling has also suggested the sensitivity of young fish to either adult-associated risk or adult effects on foraging return, further understanding of recruitment dynamics will be contingent on the use of methods other than gillnetting to observe their numbers and behavior.  Major conclusions 1. Repeatability of brook trout age estimates decreases with estimated age  2.  Ageing error correction, using the methods of Richards et al. (1992), relieves much of the bias for age composition and year class strength estimates, but results in increased variance of the estimates  3.  For age-specific period level removal estimates, initial period catchability does not differ systematically from catchability for the remainder of the depletion  4. Period-level removal data give downward-biased estimates of population size  113  5. Effort-adjusted catchability is often higher for night than day removal periods, and the disparity may increase with fish size or age  6. Year class strength appears inversely related to adult density  7. Gillnet catchability of young fish is positively related to size or inversely related to adult density, or both  114  References Adelman, H.M., J.L. Bingham and J.L. Maatch. 1955. The effect of starvation on brook trout of three sizes. Prog. Fish. Cult. 17:110-112. Bahls, P. 1991. The status of fish populations and management of high mountain lakes in the western United States. Northwest Sci. 66: 183-188. Bohlin, T., and B. Sundstrom. 1977. Influence of unequal catchability on population estimates using the Lincoln index and the removal method applied to electrofishing. Oikos 28: 123-129. Borgstrom, R. 1992. Relationship between annual recruitment and density in a lacustrine population of allopatric brown trout (Salmo trutta). Can. J. Fish. Aq. Sci. 49: 1107-1113. Borgstrom, R. 1992b. Effect of population density on gillnet catchability in four allopatric populations of brown trout (Salmo trutta). Can. J. Fish. Aq. Sci. 49: 1539-1545. Borgstrom, R., and E. Plahte. 1992. Gillnet selectivity and a model for capture probabilities for a stunted brown trout (Salmo trutta) population. Can. J. Fish. Aq. Sci. 49:1546-1554. Borgstrom, R. 1994. Production in a lacustrine brown trout population with large recruitment potential and low naturaal mortality: implications for mangement. N. Am. J. Fish. Manage. 14:488-499. Braaten, D.O. 1969. Robustness of the DeLury population estimator. J. Fish. Res. Board Can. 26: 339-355. Bradford, M . 1991. Effects of ageing errors on recruitment time series estimated from sequential population analysis. Can. J. Fish. Aq. Sci. 48: 555-558. Collie, J.S., and M P . Sissenwine. 1983. Estimating population size from relative abundance data measured with error. Can. J. Fish. Aq. Sci 40: 1871-1879. Cowx, I.G. 1983. Review of the methods for estimating fish population size from survey removal data. Fish. Manage. 14: 67-82. Cone, R.S., D.S. Robson and C.C. Krueger. 1988. Failure of statistical tests to detect assumption violations in the mark-recapture population estimation of brook trout in Adirondack ponds. N. Am. J. Fish. Manage. 8: 489-496.  115  Cooper, S.D., T.M. Jenkins, Jr. and C. Soiseth. 1988. Integrated watershed study: an investigation of fish and amphibian populations in the vicinity of the Emerald Lake basin, Sequoia National Park. Final Report, California Air Reesourcees Board Contract A4-122-132. Crittenden, R.N. and G.L. Thomas. 1989. A conditional generalized least squares method for estimating the size of a closed population. Can. J. Fish. Aq. Sci. 46: 818-823. Crecco, V.A., and T.F. Savoy. 1985. Density-dependent catchability and its potential causes and consequences on Connecticut River American shad, Alosa sapidissima. Can. J. Fish. Aq. Sci. 42: 1649-1657. Cross, D.G., and B. Stott. 1975. The effect of electric fishing on the subsequent capture of fish. J. Fish Biology 7: 349-357. DeLury, D.B. 1947. On the estimation of biological populations. Biometrics 3: 145-167. Deriso, R. B., T.J. Quinn II, and P.R. Neal. 1985. Catch-age analysis with auxiliary information. Can. J. Fish. Aq. Sci. 42:815-824. Donald, D.B., and D.J. Alger. 1986. Dynamics of unexploited and lightly exploited populations of rainbow trout (Salmo gairdneri) from coastal, montane and subalpine lakes in western Canada. Can. J. Fish. Aq. Sci. 43: 1733-1741. Donald, D.B., and D.J. Alger. 1989. Evaluation of exploitation as a means of improving growth in a stunted population of brook trout. N . Am. J. Fish. Manage. 9: 177-183. Fagerstrom, A. 1972. Netting for better angling in a small mountain lake. Rep. Inst. Freshw. Res. Drottn. 52: 38-49. Fournier, D. and C P . Archibald. 1982. A general theory for analyzing atch at age data. Can. J. Fish. Aq. Sci. 39: 1195-1207. Gatz, A.J. and J.M. Loar. 1988. Peterson and removal population size estimates: combining methods to adjust and interpret results when assumptions are violated. Env. Biol. Fish. 21: 293-307. Hall, D.L. 1991. Growth, fecundity and recruitment responses of stunted brook trout populations to density reduction. Doctoral dissertation. University of British Columbia, Vancouver. Hall, D.L. 1991b. Age validation and aging methods for stunted brook trout. Trans. Am. Fish. Soc. 120: 644-649.  116  Hamley, J.M. 1975. Review of gillnet selectivity. J. Fish. Res. Board. Can. 32: 1943-1969. Healy, M.C. 1975. Dynamics of exploited whitefish populations and their management with special reference to the Northwest Territories. J. Fish. Res. Board Can. 32:427-448. Healey, M.C. 1978. Fecundity changes in exploited populations of lake whitefish (Coregonus clupeaformis) and lake trout (Salvelinus namaycush). J. Fish. Res. Board. Can. 35: 945-950. Healy, M.C. 1980. Growth and recruitment in experimentally exploited lake whitefish (Coregonus clupeaformis) populations. Can. J. Fish. Aq. Sci. 37: 255-267. Helser, T.E., R.E. Condrey, and JP. Geaghan. 1991. A new method of estimating gillnet selectivity, with an example for spotted seatrout, Cynocion nebulosus. Can. J. Fish. Aq. Sci. 48: 487-492. Henderson, B.A. and J.L. Wong. 1991. A method for estimating gillnet selectiity of walleye (Stizostedion vitreum vitreum) in multimesh monofilament gillnets in Lake Erie, and its application. Can. J. Fish. Aq. Sci. 48: 2420-2428. Hilborn, R. and C.J. Walters. 1992. Quantatativefisheriesstock assessment: choice, dynamics and uncertainty. Chapman and Hall, New York. Hoenig, J.M., and D.M. Heisey. 1987. Use of a log-linear model with the E M algorithm to correct estimates of stock composition and to convert length to age. Trans. Am. Fish. Soc. 116: 232-243. Holling, S.C. 1973. Stability and resilience in ecosystems. Annu. Rev. Ecol. Syst. 4: 1-23. Hutchings, J.A. 1993. Adaptive life histories effected by age-specific survival and growth rate. Ecology 74: 673-684. Jensen, K.W. 1977. On the dynamics and exploitation of the population of brown trout, Salmo trutta L., in Lake 0vre Heimdalsvatn, southern Norway. Drottn. Rep. Inst. Freshw. Res. 56: 18-69. Johnson, L. 1976. Ecology of arctic populations of lake trout, Salvelinus namaycush, lake whitefish, Coregonus clupeaformis, Arctic char, 5. alpinus and associated species in unexploited lakes of the Canadian Northwest Territories. J. Fish. Res. Board Can. 33: 2459-2488. Johnson, L. 1983. Homeostatic characteristics of single species fish stocks in Arctic lakes. Can. J. Fish. Aq. Sci. 40: 987-1014. Johnson, L. 1994. Long-term experiments on the stability of two fish populations in previously unexploited arctic lakes. Can. J. Fiish. Aq. Sci. 51: 209-225. 117  Kelso, J. R. M . and B. J. Shuter. 1989. Validity of the removal method for fish population estimation in a small lake. N. Am. J. Fish. Manage. 9:471-476. Kimura, D. K., and J.J. Lyons. 1991. Between-reader bias and variability in the age-determination process. U.S. Fish. Bull. 89: 53-60. Kristoffersen, K and A. Klemetsen. 1991. Age determination of arctic charr (Salvelinus alpinus) from surface and cross section of otoliths related to otolith growth. Nordic. J. Freshw. Res. 66: 98-107. Langeland, A. 1986. Heay exploitation of a dense resident population of Arctic char in a mountain lake in central Norway. N. Am. J. Fish. Manage. 6: 519-525. Leslie, P.H., and D.H.S. Davis. 1939. An attempt to determine the absolute number of rats on a given area. J. Animal Ecol. 8: 93-113. Lien, L. 1978. The energy budget of the brown trout population of 0vre Heimdalsvatn. Holarct. Ecol. 1:279-300. Lindstrom, T., A. Fagerstrom and K.J. Gustafson. 1972. Fishing pressure, growth and recruitment in a small high mountain lake. Rep. Inst. Freshw. Fish. Drottn. 52: 100-132. Methot, R.D. 1989. Synthetic estimates of historical abundance and mortality for northern anchovy. Am. Fish. Soc. Symp. 6: 66-82. Miller, R.J. and R.K. Mbhn. 1993. Critique of the Leslie method for estimating sizes of crab and lobster populations. N. Am. J. Fish. Manage. 13: 676-685. Mittertreiner, A., and J. Schnute. 1985. Simplex: a manual and software package for easy nonlinear estimation and interpretation in fisheries research. Can. Tech. Rep. Fish. Aq. Sci. 1384. Nelder, J.A. and R. Mead. 1965. A simplex method for function minimization. Comput. J. 7: 308-313. Peterson, N.P., and C.J. Cederholm. 1984. A comparison of the removal and mark-recapture methods of population estimation for juvenile coho salmon in a small stream. N. Am. J. Fish. Manage. 4: 99-102. Pikitch, E. K. and R. L. Demory. 1988. Assessment of scales as a means of aging Dover sole. Tran. Am. Fish. Soc. 117:345-349.  118  Power, G. 1978. Fish population structure in Arctic lakes. J. Fish. Res. Board. Can. 35: 53-59. Reimers, N., J.A. Maciolek and E.P. Pister. 1955. Limnological study of the lakes in Convict Creek Basin, Mono County, California. Fishery Bulletin 103. Reimers, N. 1979. A history of a stunted brook trout population in an alpine lake: a lifespan of 24 years. Calif. Fish Game 65: 196-215. Richards, L.J., J.T. Schnute, A.R. Kronlund and R.J. Beamish. 1992. Statistical models for the analysis of ageing error. Can. J. Fish. Aq. Sci. 49:1801-1815. Ricker, W.E. 1975. Computation and interpretation of biological statistics of fish populations. Bull. Fish. Res. Bd. Can. 119. 382 p. Riley, S.C. and K.D. Fausch. 1992. Underestimation of trout population size by maximum likelihood removal estimates in small streams. North Am. J. Fish. Manage. 12: 768-776. Rivard, D. 1989. Overview of the systematic, structural and sampling errors in cohort analysis. Am. Fish. Soc. Symp. 6:49-65. Rudstam, L.G., J.J. Magnuson and W.M. Tona 1984. Size selectivity of passive fishing gear: a correction for encounter probability applied to gillnets. Can. J. Fish. Aq. Sci. 41:1252-1255. Schnute, J. 1982. A manual for easy nonlinear parameter eestimation in fishery research with interactive microcomputer programs. Can. Tech. Rep. Fish. Aq. Sci. 1140. Schnute, J. 1983. A new approach to estimating populations by the removal method. Can. J. Fish. Aq. Sci. 40: 2153-2169. Searle, S.R. 1967. Matrix algebra for the biological sciences. Wiley and Sons, New York. Seber, G.A.F. 1982. Estimation of animal abundance and related parameters (2nd. ed.). Griffin, London. Sprott, J.C. 1991. Numerical recipes: routines and examples in BASIC. Cambridge Press, New York. Walters, C.J. and J.S. Collie. 1988. An experimental strategy for groundfish management in the face of large uncertainty about stock size and production. Can. Spec. Publ. Fish. Aq. Sci. 108: 13-25.  Walters, C.J and J. R. Post 1993. Density-dependent growth and competitive assymetries in sizestructured fish populations: a theoretical model and recommendations for field experiments. Trans. Am. Fish. Soc. 122: 34-45. Walters, C.J., and F. Juanes. 1993. Recruitment limitation as a consequence of natural selection for use of restricted feeding habitats and predation risk taking by juvenile fishes. Can. J. Fish. Aq. Sci. 50: 2058-2070.  120  Appendix A Table Catch -at-age, corrected catch-at-age and standard errors for corrected catch-at-age for Hell Diver 2 removals, 1987 to 1992. For years with more than one depletion, the depletion number follows the year. Correction methods are given in the text. Standard errors cannot be estimated when corrected catch-at-age is 0.  2  3  4  5  6  7  age 8  9  10  11  12  13  14  15  16  1986 1 1 1 1 4 4  1 1 4  3 1 8  23 26 16  11 10 11  11 12 10  6 2 10  18 22 13  14 15 12  10 11 9  4 3 10  3 2 8  0 0 -  0 0 -  0 0 -  Hell Diver 2 1986-2 catch 3 0 corrected 3 0 S.E. 5  0 0 -  0 0 -  5 5 5  2 2 4  2 2 5  3 3 5  5 6 3  3 3 5  3 3 5  4 4 5  0 0 -  0 0 -  0 0 -  0 0 -  Hell Diver 2 catch corrected S.E.  1987 0 12 0 12 4  1 1 8  0 0 -  5 5 8  4 4 8  4 3 7  8 9 7  8 10 7  2 0 6  3 3 7  4 5 7  1 0 -  2 2 5  0 0 -  0 0  Hell Diver 2 catch corrected S.E.  1988 1 40 0 41 4 16  27 28 14  2 1 6  0 0 -  3 3 7  6 7 9  4 4 9  1 0  5 7 9  2 1 8  2 2 7  0 0 _  0 0 -  0 0  -  4 4 8  Hell Diver 2 catch corrected S.E.  1989 152 1 152 0 19 -  52 54 15  17 16 4  0 0 -  1 1 4  1 1 5  1 1 5  0 0 -  0 0 -  4 4 9  3 3 8  0 0 -  0 0 -  0 0 -  0 0  Hell Diver 2 1991 catch 0 56 corrected 0 52 S.E. 27  133 143. 11  6 0 4  10 10 13  0 0 -  0 0 -  0 0 -  0 0 -  1 1 4  0 0 -  0 0 -  0 0 -  0 0 -  0 0  0 0  -  -  Hell Diver 2 catch corrected S.E.  102 106 5  61 64 16  7 4 10  1 0 5  1 1 5  1 1 5  0 0  0 0  0 0  0 0  0 0  0 0  0 0  0 0  1 Hell Diver 2 catch corrected S.E.  1992 8 60 7 58 10 15  121  -  -  Table . Catch -at-age, corrected catch-at-age and standard errors for corrected catch at age for Dingleberry Lake depletions, 1987 to 1992. For years with more than one depletion, the depletion number follows the year. Correction methods are given in the text. Standard errors cannot be estimated when corrected catch-at-age is zero.  3  4  5  6  7  age 8  9  10  11  12  13  14  15  16  120 123 12  37 29 26  83 90 28  53 54 28  25 20 21  32 35 20  23 23 22  20 21 19  1 0 -  2 1 8  1 1 5  0 0 -  0 0 -  0 0  Dingleberry 1988 -1 catch 92 231 246 corrected 87 230 257 S.E. 28 36 16  88 87 27  18 9 17  49 56 25  25 23 19  18 17 18  16 16 17  15 15 18  15 19 17  3 0 -  0 0 -  1 1 6  1 1 6  0 0 -  Dingleberry 1988-2 catch 5 20 corrected 5 20 S.E. 7 5  20 20 10  14 15 10  2 1 6  5 6 7  1 0 -  4 5 7  1 0 5  1 1 5  2 2 6  0 0 -  0 0 -  0 0 -  0 0 -  0 0 -  Dingleberry 1989 catch 409 56 corrected 408 55 S.E. 35 24  81 83 13  55 58 25  17 16 17  6 4 12  15 18 17  7 6 13  7 8 14  4 4 12  2 1 10  5 7 12  1 0 -  0 0  0 0  0 0  -  -  -  Dingleberry 1991-1 catch 6 303 302 corrected 0 303 321 S.E. - 46 16  14 2 12  7 6 12  6 7 12  2 2 7  1 1 6  1 1 6  2 3 9  1 1 5  0 0 -  0 0 -  0 0 -  0 0 -  0 0 -  7 0  4 4 10  2 2 7  1 0 6  3 4 10  1 1 5  0 0  0 0 -  0 0 -  0 0  -  1 1 4  0 0  -  5 5 10  -  -  78 79 24  4 0 -  6 6 11  3 3 9  3 3 8  0 0  0 0  0 0 -  0 0 -  0 0  -  0 0 -  0 0  -  1 1 4  1  2  Dingleberry 1987 catch 23 225 corrected 18 229 S.E. 19 41  Dingleberry 1991-2 catch 85 421 241 corrected 76 429 250 S.E. 29 37 15 Dingleberry 1992 catch 150 163 corrected 146 162 S.E. 28 30  177 184 11  122  -  -  -  Table . Catch -at-age, corrected catch-at-age and standard errors for corrected catch at age for Flower Lake depletions, 1987 to 1992. For years with more than one depletion, the depletion number follows the year. Correction methods are given in the text. Standard errors cannot be estimated when corrected catch-atage is 0.  1 Rower 1987 catch 28 corrected 25 S.E. 18  2  3  126 103 126 103 25 26  6  7  age 8  9  10  11  12  13  14  15  16  92 97 26  56 59 21  18 13 16  19 22 16  6 3 12  6 6 12  8 11 13  3 1 8  0 0 -  0 0 -  0 0 -  0 0 -  4  5  89 88 25  Flower 1988 catch 156 111 154 111 corrected S.E. 28 29  113 117 30  55 54 23  37 36 18  34 32 23  .47 55 21  14 9 15  12 14 15  3 1 9  1 0 5  0 0 -  2 3 8  1 1 5  0 0 -  0 0 -  Flower 1989 catch 237 corrected 233 S.E. 27  177 182 24  53 51 22  38 38 19  31 32 19  19 17 17  23 26 18  11 11 16  4 2 11  5 6 12  1 0 -  3 3 8  0 0 -  0 0 -  0 0 -  0 0 -  Flower 1991 catch 25 corrected 16 S.E. 18  394 470 391 499 42 41  66 52 28  27 25 20  16 16 17  11  5 , 4 12 16 12  5 5 12  4 5 11  1 0 -  0 0 -  1 1 4  0 0 -  0 0 -  0 0 -  Flower 1992 catch 242 corrected 240 S.E. 32  65 58 25  218 198 223 213 30 26  35 26 21  14 13 15  5 3 10  1 0 -  4 5 10  2 2 9  1 0 7  2 2 7  0 0 -  0 0 -  0 0 -  8 9 12  123  Table A.ld. Catch -at-age, corrected catch-at-age and standard errors for corrected catch-at-age for Fishgut 1 depletions, 1987 to 1992. For years with more than one depletion, the depletion number follows the year. Correction methods are given in the text Standard errors cannot be estimated when corrected catch-at-age is zero.  1  2  3  4  5  6  7  age 8  9  10  11  12  13  14  15  16  Fishgut 1 1987 catch 6 corrected 5 S.E. 9  48 46 20  98 104 21  24 20 15  38 42 18  16 15 15  9 9 11  1 0 -  3 4 9  1 1 5  0 0 -  1 1 4  0 0 -  0 0 -  0 0 -  0 0 -  Fishgut 1 1988 catch 37 corrected 36 S.E. 18  32 28 18  115 118 23  100 106 21  27 22 16  29 30 17  22 24 15  7 5 11  6 6 12  7 8 11  1 0 -  0 0 -  0 0 -  0 0 -  0 0 -  0 0  Fishgut 1 1989 catch 215 corrected 213 S.E. 23  81 84 20  12 9 13  33 33 17  46 51 19  15 11 14  20 23 14  9 9 12  3 0 9  8 10 13  5 5 11  1 0 -  0 0 -  0 0 -  0 0 -  0 0 -  Fishgut 1 1991 catch 93 corrected 90 S.E. 23  169 172 24  105 110 23  12 8 13  8 7 11  10 10 13  11 11 13  12 12 14  15 19 17  5 4 11  1 0 -  1 1 5  0 0 -  0 0 -  0 0 -  0 0 -  Fishgut 1 1992 catch 136 corrected 135 S.E. 24  61 60 22  88 92 23  42 43 20  12 11 14  3 1 8  10 11 12  10 12 14  3 2 9  2 1 8  3 4 10  2 2 7  0 0 -  0 0 -  0 0 -  0 0 -  124  -  Table A.le. Catch-at-age, corrected catch-at-age and standard errors for corrected catch-at-age for Par Value removals, 1987 to 1992. For years with more than one depletion, the depletion number follows the year. Correction methods are given in the text Standard errors cannot be estimated when corrected catch-at-age is zero. Corrected catch and standard errors are rounded to the nearest integer.  2  3  4  5  6  7  age 8  9  10  11  12  13  14  15  16  Par Value 1987 catch 82 corrected 80 S.E. 23  88 90 22  36 36 19  9 6 12  23 15 17  101 120 21  26 8 16  70 80 21  54 44 17  86 111 17  37 31 17  6 0 -  2 0 -  0 0 -  0 0 -  1 1 4  Par Value 1988-1 catch 319 corrected 317 S.E. 35  73 74 30  38 38 24  23 23 19  16 16 17  7 0 -  52 62 23  5 0 -  21 18 20  32 32 22  45 58 23  22 19 22  15 13 20  1 0 -  1 0 -  0 0  Par Value 1988-2 catch 49 corrected 49 S.E. 15  6 6 9  0 0 -  2 2 6  0 0 -  0 0 -  5 5 2  2 2 7  2 2 7  2 2 7  4 6 9  1 0 -  2 3 7  1 1 5  0 0 -  0 0 -  28 23 20  12 12 14  9 10 13  2 1 7  4 0 -  28 35 23  14 11 19  15 15 19  16 13 19  27 39 22  9 2 15  0 0 -  0 0 -  1 1 4  190 296 185 312 34 33  86 84 27  8 2 12  7 7 12  5 5 11  3 3 9  2 1 8  6 8 13  4 4 11  1 0 -  0 0 -  5 6 12  3 2 9  0 0 -  104 112 27  36 35 22  7 4 13  5 5 10  0 0  0 0  3 3 8  3 4 10  1 0 7  1 1 7  1 0 -  3 5 11  1 0 6  1  Par Value 1989 catch 415 302 corrected 409 313 S.E. 33 29 Par Value 1991 catch 286 corrected 282 S.E. 34  Par Value 1992 catch 288 223 corrected 283 229 S.E. 31 31  72 67 28  125  -  Table A.lf. Catch -at-age, corrected catch-at-age and standard errors for corrected catch-at-age for Wonder 3 depletions, 1987 to 1992. For years with more than one depletion, the depletion number follows the year. Correction methods are given in the text Standard errors cannot be estimated when corrected catch-at-age is zero.  2  3  4  5  6  7  age 8  9  10  11  12  13  14  15  16  Wonder 3 1987-1 catch 0 corrected 0 S.E. -  63 63 19  37 38 15  19 18 14  12 7 13  51 60 16  17 14 12  11 11 11  8 8 11  6 6 10  6 7 10  4 4 9  2 2 8  1 0 7  2 2 7  0 0 -  Wonder 3 1987-2 catch 23 corrected 21 S.E. 13  75 77 18  29 29 16  12 10 12  16 12 12  56 66 15  17 11 13  22 24 13  15 15 13  11 12 13  6 6 11  2 1 7  0 0 -  1 1 4  0 0 -  0 0 -  Wonder 3 1988 catch 106 corrected 105 S.E. 19  39 39 18  28 24 17  85 91 18  46 47 15  8 0 -  39 45 13  25 24 14  19 19 13  14 14 13  10 11 12  4 3 9  1 0 -  0 0 -  0 0 -  0 0 -  Wonder 3 1989 catch 392 corrected 391 S.E. 29  58 60 22  16 14 15  28 30 19  15 14 15  14 14 15  3 0 -  26 32 18  8 5 14  6 5 14  7 7 13  8 11 15  3 2 11  2 1 8  0 0 -  0 0 -  Wonder 3 1991 catch 146 237 146 141 241 152 corrected S.E. 24 27 27  28 25 19  9 6 12  19 22 17  6 5 12  3 2 8  0 0 -  9 11 13  3 2 9  0 0 -  1 1 4  0 0 -  0 0 -  0 0 -  Wonder 3 1992 catch 38 corrected 36 S.E. 18  72 76 22  16 13 15  8 8 12  3 3 9  1 0 6  2 2 8  2 2 7  0 0 -  1 1 4  0 0  0 0  0 0  0 0  -  -  -  -  1  92 91 25  104 107 27  126  Table Alg. Catch -at-age, corrected catch-at-age and standard errors for corrected catch-at-age for Hell Diver 3 depletions, 1987 to 1992. For years with more than one depletion, the depletion number follows the year. Correction methods are given in the text. Standard errors cannot be estimated when corrected catch-atage is zero.  2  3  4  5  6  7  age 8  9  10  11  12  13  14  15  16  Hell Diver 3 1987 catch 8 corrected 8 S.E. 7  2 2 5  2 2 6  9 10 10  3 2 7.  5 4 7  15 18 7  7 5 7  12 14 8  10 12 9  2 0 7  1 0 4  0 0 -  0 0 -  0 0 -  0 0 -  Hell Diver 3 1988 catch 6 corrected 6 S.E. 7  25 26 5  4 4 6  3 3 10  1 1 7  3 3 7  1 0 7  3 2 7  8 10 8  5 5 9  1 0 7  2 2 4  0 0 -  0 0 -  0 0 -  0 0 -  Hell Diver 3 catch corrected S.E.  1989 22 22 10  22 23 10  6 6 7  2 2 5  2 2 5  0 0 -  2 2 5  3 4 7  1 0 5  2 2 6  4 6 6  1 0 -  0 0 -  0 0 -  0 0 -  0 0 -  Hell Diver 3 catch corrected S.E.  1991 67 66 16  50 52 12  9 8 10  5 5 9  3 3 7  1 1 4  0 0 -  0 0 -  2 2 5  0 0 -  1 1 4  0 0 -  1 1 5  1 1 5  0 0 -  1 1 4  Hell Diver 3 1992 catch 6 corrected 6 S.E. 7  22 23 9  9 9 6  7 7 6  6 7 7  1 1 4  0 0 -  1 1 4  0 0  0 0 -  0 0  2 2 4  0 0 -  0 0 -  0 0 -  0 0 -  1  127  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items