May 21, 2002 - Copyright by Theodore R. Castro-Santos 2002 ...... Relating swimming performance of lake sturgeon, Acipenser fulvescens, to fishway design.
SWIMMING PERFORMANCE OF UPSTREAM MIGRANT FISHES: NEW METHODS, NEW PERSPECTIVES
A Dissertation Presented by THEODORE R. CASTRO-SANTOS
Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY May 2002
Organismic and Evolutionary Biology
© Copyright by Theodore R. Castro-Santos 2002 All Rights Reserved
SWIMMING PERFORMANCE OF UPSTREAM MIGRANT FISHES: NEW METHODS, NEW PERSPECTIVES
A Dissertation Presented by THEODORE R. CASTRO-SANTOS
Approved as to style and content by:
Alexander J. Haro, Chair
William E. Bemis
Elizabeth L. Brainerd
George V. Lauder
Elizabeth L. Brainerd, Program Chair Organismic and Evolutionary Biology
DEDICATION
To Jocelyn
ACKNOWLEDGEMENTS This dissertation could never have been written without the vision, generosity, and support of Alex Haro, my adviser and mentor. The idea to construct a flume with which to measure swimming performance in terms of Dmax was his own, conceived of before I arrived at the Conte Anadromous Fish Research Center. The flume itself was designed and constructed by the Fish Passage Engineering Section at the Conte Laboratory: with engineering directed by Dr. Mufeed Odeh and John Noreika, construction by Phil Rocasah, and electronics and instrumentation by Steve Walk—each of these individuals deserves full credit for their contributions to this work, which could not have been carried out without them. Likewise, I must thank two directors of the Conte lab, Henry Booke and Steve Rideout, as well as the U.S. Geological Survey for supporting this work and paying my salary while I pursued this degree.
In addition, we had extensive help with collection of fish and the running of experiments. For the former, I am particularly grateful to Phil Herzig (U.S. Fish and Wildlife Service), Ken Sprankle (New Hampshire Fish and Game), and Phil Brady (Massachusetts Division of Marine Fisheries); for the latter, to Joseph Capeche, Greg Bacos, Christopher Koch, Gail Huntley, Jody Peloquin, and Russ Lindgren.
Finally, I wish to thank my wife, Jocelyn, for her encouragement and support throughout; and my daughter, Chlöe, for patiently putting up with my absences, even when it was clearly “Daddy’s turn”.
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ABSTRACT SWIMMING PERFORMANCE OF UPSTREAM MIGRANT FISHES: NEW METHODS, NEW PERSPECTIVES MAY 2002 THEODORE R. CASTRO-SANTOS B.A. COLGATE UNIVERSITY M.S. WASHINGTON STATE UNIVERSITY Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Alexander J. Haro
The ability to traverse barriers of high water velocity limits the distributions of many diadromous and other migratory fish species, and is central to effective fishway design. This dissertation provides a detailed analysis of volitional sprinting behavior of six migratory fish species (American shad Alosa sapidissima, alewife A. pseudoharengus, blueback herring A. aestivalis, striped bass Morone saxatilis, walleye Stizostedion vitreum, and white sucker Catostomus commersoni), against controlled water velocities of 1.5 – 4.5 m · s-1 in a large, open-channel flume.
In Chapter 1, I develop models of maximum distance traversed (Dmax) by fish ascending these flows, accounting for water velocity and other covariate effects. I then demonstrate the application of these models, using them to predict proportions of active migrants capable of traversing a range of distances and flow velocities.
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Chapter 2 focuses on behavior and swimming performance of American shad, analyzing covariate effects on attempt rate as well as Dmax, and formalizing how rate and distance jointly affect overall rates of passage. Models describe a complex pattern of varying responses of attempt rate and Dmax to hydraulics, temperature, effort expended on and recovery time since the previous attempt.
In Chapter 3, I use the effect of swim speed on fatigue time to calculate an optimal swim speed that maximizes the over-ground distance fish can traverse, and hence defines their maximum ability to traverse velocity barriers. This speed reduces to a constant groundspeed within a given gait, regardless of the speed of flow. Data from all six species support this view, although only American shad exhibit a clear shift from the optimum prolonged speed to the optimum sprint speed at the predicted critical flow velocity.
Throughout this dissertation I make extensive and novel use of statistical techniques developed for survival analysis to analyze and model behavioral data, both with respect to attempt rate and to Dmax. Chapter 4 provides an overview of these methods and demonstrates their application to a fish passage study of downstream-migrating Atlantic salmon (Salmo salar) smolts. An understanding of the principles described here will help the reader to better understand the findings of the previous three chapters.
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CONTENTS Page ACKNOWLEDGEMENTS .......................................................................................... v ABSTRACT ................................................................................................................. vi LIST OF TABLES ....................................................................................................... xi LIST OF FIGURES.....................................................................................................xii CHAPTER 1.
SWIMMING PERFORMANCE OF UPSTREAM MIGRANT FISHES IN RELATION TO WATER VELOCITY BARRIERS .................... 1 Abstract ................................................................................................. 1 Introduction ........................................................................................... 2 Methods................................................................................................. 5 Flume Apparatus ....................................................................... 5 Data Collection.......................................................................... 8 Data Analysis .......................................................................... 10 Results ................................................................................................. 12 Discussion ........................................................................................... 13 References ........................................................................................... 22 Tables .................................................................................................. 25 Figures................................................................................................. 27
2.
FACTORS AFFECTING ATTEMPT RATE AND SWIMMING CAPACITY OF AMERICAN SHAD (ALOSA SAPIDISSIMA), AND THEIR IMPLICATIONS WITH REGARD TO PASSAGE SUCCESS ....... 35 Abstract ............................................................................................... 35 Introduction ......................................................................................... 36 Methods............................................................................................... 41 Facilities, Apparatus, and Study Animals ............................... 41 Attempt Rate ........................................................................... 42 Distance of Ascent .................................................................. 47 Combined Effects of Attempt Rate and Distance of Ascent.......................................................................... 48 Results ................................................................................................. 49
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Attempt Rate ........................................................................... 49 Distance of Ascent .................................................................. 55 Discussion ........................................................................................... 57 Attempt Rate ........................................................................... 57 Distance of Ascent .................................................................. 62 Effect of Multiple Attempts .................................................... 64 References ........................................................................................... 67 Tables ................................................................................................. 71 Figures................................................................................................. 75 3.
BEHAVIORAL OPTIMIZATION DURING HIGH-SPEED VOLITIONAL SWIMMING IN FISHES ...................................................... 89 Abstract ............................................................................................... 89 Introduction ......................................................................................... 90 Methods............................................................................................... 95 The Flume ............................................................................... 95 Data Collection........................................................................ 96 Analysis................................................................................... 97 Results ............................................................................................... 101 Flume Tolerances and Behavior............................................ 101 Swim Speed-Fatigue Time Curves........................................ 102 Discussion ......................................................................................... 105 Assumptions and Parameters ................................................ 105 Swim Speed Optimization..................................................... 107 References ......................................................................................... 115 Tables ............................................................................................... 117 Figures............................................................................................... 120
4.
QUANTIFYING MIGRATORY DELAY: A NEW APPLICATION OF EVENT-TIME ANALYSIS.................................................................... 130 Abstract ............................................................................................. 130 Introduction ....................................................................................... 131 Methods............................................................................................. 133
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Rational and Techniques of Event-Time Analysis................ 133 Life Tables and Nonparametric Analysis.............................. 135 Parametric Models for Event-Time Data with Censoring .................................................................. 136 Cox’s Proportional Hazards Regression ............................... 139 Competing Risks ................................................................... 142 Logistic Regression ............................................................... 143 Dataset ................................................................................... 143 Results ............................................................................................... 145 Discussion ......................................................................................... 148 References ......................................................................................... 154 Tables ............................................................................................... 158 Figures............................................................................................... 162 BIBLIOGRAPHY ..................................................................................................... 166
x
LIST OF TABLES Table
Page
1.1
Species and Hydraulic Characteristics of Sprinting Tests .............................. 25
1.2
Regression Models for Distance of Ascent ..................................................... 26
2.1
Glossary of Terms ........................................................................................... 71
2.2
Hydraulic and Other Experimental Conditions............................................... 72
2.3
Proportional Hazards Models of Attempt Rate ............................................... 73
2.4
Parametric Regression Models of Distance of Ascent .................................... 74
3.1
Species Characteristics and Flume Velocities............................................... 117
3.2
Maximum Prolonged Swim Speeds, Coefficient Estimates, and Predicted Optima............................................................................... 118
3.3
Effect of Deviating from Predicted Optima .................................................. 119
4.1
Life Table of Passage Time Data .................................................................. 158
4.2
NonParametric, Parametric, and Semi-Parametric Analyses ........................ 159
4.3
Predicted Delay Times .................................................................................. 160
4.4
Logistic Regression Models of Passage Route Selection.............................. 161
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LIST OF FIGURES Figure
Page
1.1
Fish Passage Complex and Flume Apparatus ................................................. 27
1.2
Cross-Sectional Velocity Profiles of Flume Apparatus .................................. 29
1.3
Maximum Distance of Ascent by Species and Nominal Water Velocity ....... 31
1.4
Model Predictions ........................................................................................... 33
2.1
Effect of Multiple Attempts on Passage Success ............................................ 75
2.2
Hydraulic Effects on Attempt Rate ................................................................. 77
2.3
Thermal and Seasonal Effects on Attempt Rate.............................................. 79
2.4
Interaction of Date and Temperature on Attempt Rate ................................... 81
2.5
Effort Expended and Swim Speeds Over Time at Each Nominal Velocity.... 83
2.6
Rate and Cumulative Proportion Staging Attempts ....................................... 85
2.7
Conditional and Unconditional Predictions of Passage Success..................... 87
3.1
Predicted Distance Maxima from Swim Speed-Fatigue Time Relationship in Still and Flowing Water ........................................... 120
3.2
Cross-Sectional Profiles of Relative Flume Velocities ................................. 122
3.3
Swim Speed-Fatigue Time Relationship by Species..................................... 124
3.4
Observed Groundspeeds and Predicted Optima............................................ 126
3.5
Critical Flow and Swim Speeds for Prolonged-Sprint Gait Shift ................. 128
4.1
Kaplan-Meier Curves of Passage Times with Censored Data ...................... 162
4.2
Goodness-of-fit of Parametric Regression Model......................................... 164
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CHAPTER 1
SWIMMING PERFORMANCE OF UPSTREAM MIGRANT FISHES IN RELATION TO WATER VELOCITY BARRIERS
Abstract The ability to traverse barriers of high water velocity limits the distributions of many diadromous and other migratory fish species. Very few data exist that quantify this ability, however. We provide a detailed analysis of sprint swimming ability of six migratory fish species (American shad Alosa sapidissima, alewife A. pseudoharengus, blueback herring A. aestivalis, striped bass Morone saxatilis, walleye Stizostedion vitreum, and white sucker Catostomus commersoni), against controlled water velocities of 1.5 – 4.5 m · s-1 in a large, open-channel flume. Performance was strictly voluntary: no coercive incentives were used to motivate fish to sprint. We used these data to generate models of maximum distance traversed (Dmax), taking into account water velocity, body length, temperature, sex, and year of testing. Although Dmax decreased with increasing velocity, the extent of this effect varied between species. Other covariate effects were likewise variable, with divergent effects of temperature, and nonuniform length, sex, and year effects. The shape of the distributions that best described swimming capacity differed between species. Failure rates increased at a decreasing rate among alewife, blueback herring and white suckers, and increased at an increasing rate among American shad, striped bass, and walleye. Although morphology does influence swimming performance, performance may also reflect life history traits of each species.
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We describe how these data can be used to develop criteria for fish passage structures, culverts, and breached dams.
Introduction Zones of high velocity flow characterize many natural rivers and are often unavoidable, or even intentional features of fishways, dams, and culverts (Haro et al. 1998; Clay 1995). These zones may constitute velocity barriers that exceed the physiological or behavioral capabilities of fish populations, thus defining the upstream boundaries of their distributions. The swimming performance of diadromous and other riverine fishes characterizes their ability to traverse these velocity barriers, and is therefore central to their life history.
Many studies describe swimming endurance at sustained and prolonged speeds (see (Beamish 1978) and (Videler 1993) for reviews); but few provide empirical measures of sprinting performance, which defines these behavioral and ecological limits. Of those studies that do measure sprinting performance (Table 1 in Beamish (1978)), most are largely anecdotal, based on small sample sizes and collected under poorly controlled conditions. Even less common are studies that have allowed fish to volitionally ascend large-scale experimental open-channel flumes that more closely approximate natural conditions, allowing fish to express normal upstream migratory behaviors (for examples, see (Breder, Jr. 1976); (Videler and Weihs 1982); (Webb 1994); (Colavecchia et al. 1998)).
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(Bainbridge 1958) and Beamish (1978) recognized the relevance of this information to improved fish passage and fishway design, but only (Dow 1962) and (Weaver 1963; Weaver 1965) quantified performance in units of distance fish were able to negotiate against a velocity challenge, the appropriate units for most applications. Weaver’s work is exceptional, describing various aspects of swimming performance of thousands of individual salmon (Oncorhynchus spp.) and American shad (Alosa sapidissima) that entered his structure volitionally, with no handling and minimal human interference. Weaver’s analyses were limited, however, to describing species-specific performance during fixed-velocity tests, and gave only cursory treatment to covariates like sex, length, or temperature.
Although the techniques used by Dow (1962) and Weaver (1963; 1965) provide close approximations to conditions fish encounter in nature, most studies on swimming performance have followed the approach of Brett (1964) where fish swim against carefully controlled flow within enclosed chambers. None of these studies has matched the scale of Weaver’s work, however, and the ability of fish to traverse velocity barriers has remained poorly quantified.
The lack of information on sprinting performance is problematic for the design of structures for passing fish around dams and other obstacles. Water velocities that form impassible barriers for some fish species characterize many fishway designs (Clay 1995). In contrast, if maximum sprinting ability is underestimated (and this may often be the
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case (Videler and Wardle 1991)), then some fishway designs could be simplified, facilitating mitigation efforts and making available much-needed habitat.
The value of low-cost mitigation efforts is not trivial. A recent inventory identifies more than 77,000 dams greater than 8 m throughout the United States, and smaller structures that also impede passage of anadromous and riverine fishes are even more numerous (Robert Banks, Program Director, National Inventory of Dams, Headquarters, U.S. Army Corps of Engineers, pers. comm). It is reasonable to expect that similar densities of riverine obstructions can be found throughout the developed world (e.g., several references in (Jungwirth et al. 1998)). Of the lower-head structures, many are nonfunctional or in disrepair, and could be easily breached to form routes of passage, provided fish are capable of traversing the resulting velocity barriers (Odeh 1999).
Because of the lack of detailed information on sprinting performance, however, engineers and managers are often unable to assess whether species of concern will be able to pass such simple structures as breaches, culverts, etc.: manuals for fish passage engineers provide scant estimates of instantaneous maximum sprint speeds, and no estimates of sprint distances through high-velocity flow (e.g., (Bell 1991); (Clay 1995)). The need for reliable data on volitional fish swimming performance is increasing as fish passage issues and concerns expand to include riverine species that are not anadromous, but may regularly migrate considerable distances throughout a watershed. Very little is known about swimming performance of these species.
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In this study, we provide the most detailed description to date of high-speed swimming performance (i.e., prolonged and sprint modes) by six species of anadromous, amphidromous, and potomodromous fishes that are common in rivers of eastern North America. We present models of maximum distances of ascent under linear flow conditions throughout a range of water velocities, providing biologists, engineers, and fisheries managers with estimates of sprinting abilities that are of unprecedented accuracy and resolution. These data will help identify distributional limits, and can also be used to design and evaluate new and existing passage structures or, conversely, to create velocity barriers for nuisance species.
Methods Flume apparatus A large open-channel flume (1 m width x 1 m depth x 24 m length, zero slope) was constructed in the S. O. Conte Anadromous Fish Research Center (CAFRC) fish passage complex (Figure 1.1), located at Turners Falls, Massachusetts, USA, next to the Connecticut River. The flume was constructed of a wood and steel frame, with the floor and one wall made of plywood. The opposite wall was made of 2.5 cm thick clear acrylic sheet. Mirrors installed at a 45° angle to the transparent wall permitted simultaneous side- and top-views to video cameras arrayed above the flume. The plywood wall and floor were covered with white retroreflective material (Scotchlite 6780, 3M Corp), on which reference marks (black crosses 10 x 10 cm) were painted at 0.5 m (horizontal and vertical) intervals.
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Ambient river water was supplied to the flume from an adjacent hydroelectric power canal fed by the Connecticut River. Water entered the fish passage complex and was directed through a 0.9 m diameter pipe to an upstream chamber (headpond). Water flowed from the headpond under an electronically actuated sliding gate (headgate) into the flume, and finally into a downstream staging area (8 m long by 3 m wide by 0.6 – 1.35 m deep). Mean velocities were slower in the staging area because of its greater width and depth, the latter being controlled by a variable height weir (tailwater weir) at the downstream end. This weir was fitted with a screen to retain fish in the staging area while allowing flow to pass through. After passing over the tailwater weir, water was conveyed to the river downstream of the fish passage complex through a 1.4 m diameter pipe.
We used a 1:6 physical model of the flume to establish experimental hydraulic test conditions. The flume was later constructed to be geometrically, kinematically, and dynamically similar to this model, ensuring identical hydraulic characteristics (Chow 1959). The model was used to identify the gate settings and water surface elevations in the headpond, flume, and staging area that characterized each test velocity (1.5 – 4.5 m · s-1), and to quantify the response of flume velocity to variations in these conditions.
Detailed velocity measurements were also made in the model to describe the flow field through which fish would swim. A two-directional electromagnetic velocity meter (Marsh-McBirney Model 523) with a 13 mm probe was used to measure model velocities; actual velocities were then measured throughout representative cross-sections
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of the full-scale flume on a 5 cm grid using a propeller meter (Ott Model 1-113040). Figure 1.2a-c shows flow velocity profiles at depths characteristic of 1.5, 2.5, and 3.5 m · s-1 trial conditions, respectively. We were unable to collect similar data for the 4.5 m · s-1 condition due to excessive forces on the velocity probe; however, hydraulic principles dictate that the profile should be similar to that of the 3.5 m · s-1 condition. Although velocities were lowest near the walls and floor of the flume, the extremes were generally within 10% of the mean cross-sectional velocity. Only the 1.5 m · s-1 condition was characterized by subcritical flow (Froude number < 1); all other flows were supercritical (Chow 1959).
Velocities within the flume were controlled by a valve on the 0.9 m inflow pipe, the headpond level, the headgate opening, and the tailwater weir level. At supercritical flows (Froude number > 1), tailwater weir level controlled the depth of the staging area, as well as the location of a hydraulic jump, which was maintained inside the flume at a distance of 0.5 m – 1.0 m upstream of the staging area. The tailwater weir controlled the water level in both the staging area and in the flume at subcritical flows (Froude number < 1). Water velocities in the flume were maintained at nominal settings of 1.5, 2.5, 3.5, and 4.5 m · s-1 that were relatively uniform for the length of the flume; actual velocities varied within each of these categories (Table 1.1). Water depth in the flume differed between velocities; this was a result of limited total flow available from the headpond, flume hydraulics, and the need to minimize velocities and turbulence in the staging area. Table 1.1 describes flow and hydraulic characteristics of the flume, as well as species, lengths, and temperatures at various water velocities.
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To ensure uniform lighting and to block sunlight from the skylights of the fish passage complex, a black tarp was laid out on a grating 4.5 m above the flume, covering its full length, and the flume was illuminated with eight 400W halogen flood lamps. Light intensity measured at the water surface was regulated to 0.03 - 2.5 µW · m-2, depending on the perceived preference of each species.
Data collection We used an automated passive integrated transponder (PIT) system to position fish swimming up the length of the flume (see (Castro-Santos et al. 1996) for a description of the PIT system, tagging method, and its application). Ten PIT antennas were mounted along the length of the flume at 2.5 m intervals; of these, eight were in place for the first half of the study, two more were added in May 1998. Tags were detected within 0.5 m of the plane of each antenna loop. A control computer logged tag detection data (tag code, date, time to the nearest 0.1 s, and antenna location) from PIT readers. The readers interrogated for tags at rates of 10-14 Hz. Video verification of the PIT data showed that by using the average time of all the reads at a given antenna, location for that time was measured with an accuracy of ± 18 cm from the plane of the antennas.
Fish collection and testing were performed during the period from April through July, 1997-1999. Six species of test fish were captured from traps at nearby fishways (American shad (Alosa sapidissima), striped bass (Morone saxatilis), and white sucker (Catostomus commersoni)), coastal streams (alewife (A. pseudoharengus) from the
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Herring River, Bourne Massachusetts, and blueback herring (A. aestivalis) from the Charles River, Watertown, Massachusetts), or electrofished (blueback herring, striped bass, walleye (Stizostedion vitreum), white sucker) from the Connecticut River on dates corresponding periods of upstream migration for each species. Fish were transported to the flume facility in one of two truck-mounted tanks (1000 and 4000 L capacity). After transport, fish were measured (fork length), sexed, and fitted with an externally attached PIT tag (Castro-Santos et al. 1996). Tagged fish were transferred into open, flow-through holding ponds (Burrows and Chenoweth 1970) that were hydraulically continuous with the fish passage complex, and held 24 h before testing. At the start of a test, groups of 20-30 fish were seined from the holding ponds into the staging area, and the tailwater weir and screen were raised to confine the fish to the staging area. Fish were initially prevented from entering the flume by an exclusion screen. Once the water velocity in the flume was brought to the desired level, the exclusion screen was opened, and fish were allowed to ascend the flume of their own volition. Only those fish that entered the flume during a given trial were included in our analyses. Although duration of runs ranged from 1 to 6 h, we use only the first hour’s data from each trial to maintain consistency in our analyses.
Mean hourly water temperatures were logged using a datalogger (Licor LI-1000) and thermocouple probe (Omega T-type). Average temperatures for times corresponding to each trial were included as a covariate in analyses.
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Data analysis Because the PIT antennas effectively graduated the flume into 2.5 m intervals, we were able to estimate maximum distance of ascent (Dmax) by selecting the location furthest upstream that was logged for each fish. This is an incremental measure, and provides a conservative estimate of Dmax: the reader might detect a fish as far as 0.5 m below an antenna, but the same fish could also be as much as 2 m above that antenna without being logged at the next location. The configuration of the PIT antennas, along with the length of the flume, imposed restrictions on the methods used to develop predictive models. Since PIT antennas were installed only for the first 18 m of the flume during the first half of the study, and the first 23 m thereafter, Dmax values corresponding to maximum antenna locations do not reflect the true maximum ability of the fish, but rather the maximum that our apparatus was able to measure -- the actual performance capacities may have been higher. This condition, where the magnitude of a measured variable exceeds the ability of an instrument to measure it, constitutes censoring (Lee 1992). Ordinary least-squares (OLS) regression techniques are unable to accommodate censoring, so we applied the maximum likelihood (ML) regression techniques commonly used in survival analysis ((Allison 1995); (SAS 1999); Chapter 4) to develop our predictive models. For the reasons just described, as well as to negate any effect of fish avoiding the upstream end of the flume, fish attaining Dmax values of 18 m or greater were included in the analyses as censored observations.
Maximum likelihood regression generates models similar to those generated by OLS, i.e.:
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(1.1)
(ln Dmax)p = β0 + β1x1 + … + βkxk + wp
Where (ln Dmax)p is the pth quantile of the natural log of Dmax, β’s are coefficients, xi’s are the k-covariates, and wp is the pth quantile of the baseline distribution. One advantage of ML regression is that does not require the error term to be normally distributed. For this reason, it takes on a more complex structure than that of OLS regression, with scale (σ), and shape (δ) parameters that influence the value of wp.
We determined which distribution best described our data by first including a complete suite of covariates: velocity, temperature, body length, sex, and year of testing, as well as the interaction of sex G length. We then generated separate models, based on exponential, lognormal, Weibull, log-logistic, and generalized gamma distributions (Lawless 1982), as well as their non-logged counterparts. Next, we ranked these models by their log-likelihoods, and selected the one with the best fit (Allison 1995). Where the fit of two or more distributions did not differ significantly, we selected the one requiring the fewest parameters (i.e., scale or shape). Finally, we refined the models by removing covariates in a stepwise fashion, retaining only those with P-values less than 0.30.
Results Hydraulic conditions, sample sizes, body lengths, and temperatures at which trials were run are summarized in Table 1.1. Mean velocities, as estimated from headpond and flume depth, differed consistently from the projected nominal velocities. The one exception is the single 1.5 m · s-1 striped bass trial, where velocity was intentionally 11
modified as part of a companion study. Otherwise, test velocities varied little, with most standard deviations less than 0.1 m · s-1. This variability arose primarily as a result of fluctuating headpond levels in the power canal. Because impingement of smaller species (alewife, blueback herring, and walleye) on the tailwater weir screen was high at 4.5 m · s-1 and a low proportion of individuals entered the flume under 3.5 m · s-1 condition (Figure 1.3), these smaller species were not run at 4.5 m · s-1. Maximum distance of ascent (Dmax) for each species and velocity is presented in Figure 1.3.
Increasing water velocity consistently reduced Dmax for each species (negative β, Table 1.2). The effect of temperature, however, was ambiguous. Performance increased with temperature among blueback herring, striped bass, and white sucker, but decreased among American shad and alewife, although these effects were significant only for blueback herring and American shad. Except for blueback herring and white sucker, Dmax also varied between years, with strongest performance by striped bass in 1997, by walleye and alewife in 1998, and by American shad in 1999.
Performance improved with length for blueback herring, striped bass, and walleye. The results for American shad were more complex: although there was no uniform length effect, greater length was associated with superior performance among males (positive sex G length interaction). This effect was not present among females, however, which tended to traverse shorter distances despite their greater size: of the four species for which we were able to differentiate sex, shad were the most dimorphic in length, with
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males averaging 88% the length of females, compared with 95%, 96%, and 97% for white sucker, alewife, and blueback herring, respectively.
The distributions that best describe the performance data differ among species. The gamma distribution provides the best fit to the data for American shad, alewife, striped bass, and walleye; the Weibull distribution best describes the blueback herring and white sucker data (σ > 1). Complete models describing covariate effects on Dmax are presented in Table 1.2; predictive models based on these tables for velocities of 1 - 5 m · s-1 are presented in Figure 1.4.
Discussion Few studies of unsustained (i.e., prolonged and burst) swimming performance have been conducted on this scale, and this is the first to do so with such resolution and large sample sizes. Weaver (1963, 1965) provided empirical quantile curves similar to those generated in Figure 1.4, for American shad, steelhead (Oncorynchus mykiss), Chinook salmon (O. tsawytscha), and silver salmon (O. kisutch), but these were descriptions of raw data, and made no allowances for size, sex, or temperature. Other efforts have focused on timing the movements or recording the success of individuals ascending fishways (Dow 1962), or on angled fish running out a line attached to a tachometer (Gero 1952). All these approaches have been done under poorly controlled conditions, or failed to gather detailed individual information. As a result of the large sample sizes and individual information we were able to collect, we were able to construct models that accurately describe the shapes of probability functions, thus permitting realistic estimates of
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percentiles of populations capable of passing barriers of specific velocities (Figures 1.3, 1.4). The ability to estimate the full range of quantiles passing a barrier should be of use to fisheries managers who wish to protect more than the 50% or so of a population that estimates of means and medians provide ((Venditti et al. 2000); Chapter 4).
Two cautionary points need to be considered when applying these data. First, we do not include all fish in our analyses, only those that initiated attempts. This was done to eliminate the effect of motivation or attraction (quantified in this study by proportion of fish entering the flume from the staging area), which differed nonlinearly between velocities (Chapter 2). Thus, our percentiles may be inflated by omitting fish that made no attempts to ascend the flume. Indeed, attraction varied by species as well as velocity, and it may be that in some cases only the most motivated fish entered the flume. The second concern is that there may be hydraulic effects resulting from different depths and flow types (super- vs. subcritical) that influence swimming performance. Nonetheless, we feel that these data provide realistic estimates of swimming performance of fish in the field, and the above concerns should not preclude their application to management situations.
Because we collected actively migrating fish that attempted to traverse our flume of their own volition, we are confident that data in Table 1.1 represent values typical for these species in the northeastern United States. Test velocities covered a range they commonly encounter; temperatures are characteristic of the periods during which they migrate; and lengths are typical of adult migrant Alosa spp. and white suckers. Our walleye sample
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includes smaller individuals than are present in the adult migratory spawning population, however (we did not collect large walleye in order to accommodate concerns of local fisheries managers). Striped bass, in contrast, showed the greatest size variability of all. This is because upstream migration of striped bass includes both feeding and spawning individuals, tested fish of this species are not necessarily mature adults.
Due to the limitations of large-scale, open-channel hydraulics, uniform cross-sectional flow velocity was not attained within the flume (Figure 1.2). However, assertions that fish will consistently seek out zones of lowest velocity (e.g., (Beamish 1978)), were not borne out by our experiments. Although some species (most notably white suckers) actively selected these low velocity zones at the 1.5 and 2.5 m · s-1 condition, all species swam near the middle of the flume at the higher velocities (Chapter 3). Moreover, these experimental conditions approximate those found in nature, where flow is moderately turbulent and uniform cross-sectional velocities are uncommon.
Our data still cannot be viewed as perfectly representative of a true riverine situation, however. We constructed the flume to be of such a length as to provide realistic estimates of passage ability past breached low-head dams. Thus, at the lowest test velocity, most individuals were able to successfully negotiate the full length of the flume (Figures 1.3 and 1.4). Other places where high velocities exist, such as culverts, natural obstructions, etc., may extend well beyond the length of our structure, and our data may have limited relevance to such situations. Nevertheless, using the maximum likelihood
15
approach (Table 1.2), our data allow for modest extrapolation beyond the actual length of the flume, as well as beyond the experimental test velocities (Figure 1.4).
The results of the maximum likelihood models (Table 1.2) highlight some important differences between these species. Coefficients indicate the relative effect of each covariate on log-distance of ascent, i.e., each unit increase in covariate results in an increase in distance of 100 G (1- eβ) percent. Thus, although all species showed the expected negative effect of water velocity on Dmax, the degree of this effect varied widely between species (e.g., 100 G (1-eβ) = 49.6 % decrease in distance per m · s-1 for walleye vs. a 68.8% decrease for blueback herring). Although this effect was similar among the three alosine species, alewife showed the smallest response to increasing velocity. The contrast between blueback herring and alewife (Figure 1.4) is interesting because of the morphological and ecological similarity of these two species (Table 1.1). They do differ in preferred spawning habitat, however, with blueback herring and alewife spawning in lotic and lentic environments, respectively (Loesch 1987). This might cause one to expect the inhibitory effect of velocity to be greater for alewife. Instead, the models reflect the fact that alewife performed poorly at low velocities, resulting in a smaller overall velocity effect compared to the blueback herring, which performed better at low velocities, but similarly at higher velocities (Figures 1.3, 1.4). In the context of their life histories, this suggests that blueback herring are the more motivated swimmers, perhaps more willing to risk fatigue when traversing velocity barriers.
16
Numerous studies have shown that temperature is positively correlated with endurance in both sustained and prolonged swimming (Brett 1965; (Videler and Wardle 1991)). Few studies quantify this effect on sprinting performance, however, and there is disagreement over its importance (Beamish 1978). We observed a positive correlation between temperature and Dmax for blueback herring, but the opposite was true of American shad, and the correlations of the other species were not significant. Lack of significance should not be confused in this case with absence of effect: the range of temperatures at which species were run was relatively small (Table 1.1), and because it corresponds with periods of fitness-crucial activity, may reflect a performance optimum for these species. Thus, the signs of these coefficients may reflect nonlinear effects of migratory motivation rather than physiological capacity.
Variations in seasonal and thermal optima may also account for differences in performance of American shad, alewife, striped bass, and walleye between years. American shad and alewife performed best during 1999, and worst during 1998. No such pattern was observed for blueback herring, however. Striped bass performed best in 1997, and walleye performed best in 1998. We have observed similar annual differences in performance previously (Haro et al. 1999). These divergent results suggest the cause of interannual variability in performance is biological or environmental, rather than annual changes in flume hydraulics (e.g., changes in flume instrumentation and calibration). Because all tests were conducted in spring, when water temperatures are increasing, it is possible that imperfect randomization with respect to velocity and temperature, coupled with potential seasonal effects, could have lead to the observed differences.
17
As with temperature, numerous studies have shown length to be correlated with swimming performance, so much so that performance data are usually normalized for length, particularly when there is substantial variation in the lengths of the study animals (Bainbridge 1959); (Brett 1962; Brett 1965; Brett and Glass 1973). We too found significant correlations between length and Dmax, but the effect was not universal. Performance improved with length among blueback herring, striped bass, and walleye. The same effect was present among American shad, but only for males.
Differences between the sexes in both length and performance can obscure the effect of the former on the latter. In the case of the shad, females are larger than males, but their observed Dmax values were generally less and did not increase with length, as they did for the males. A similar relationship exists for white sucker, but the effects are weak and nonsignificant. The absence of a significant length effect among the alewife and white sucker may be due to its relatively small variance in these species; although in both species it equaled or exceeded that of blueback herring in both relative (CV) and absolute (SD) terms.
The scale (σ) and shape (δ) parameters of the regression models describe the shape of the underlying distribution, and can be used to draw inference on processes that might be limiting Dmax. For example, σ = 1 is the case of the exponential distribution, and occurs when failure rate (called the “hazard” in the survival analysis literature) is constant across the entire distance traversed. Under the Weibull distribution, failure rate is allowed to
18
vary with distance. In the case of the blueback herring and white sucker, 0.5 < σ < 1, meaning that failure rate increased with distance, but at a decreasing rate. Interpretation of these parameters under the gamma distribution is more complicated, however. The values for alewife suggest a hazard function similar to that of blueback herring and white sucker. The values for American shad, striped bass, and walleye, however, indicate failure rates that increase with distance at an increasing rate. The latter condition is most congruent with what one would expect if fish were actually swimming to exhaustion: failure rate is initially low, but increases as the fish fatigue. A constant, decreasing, or slowly increasing hazard, suggests that failure rate may be more indicative of motivation or other behavioral factors than of physiological capacity.
The purpose of the regression models is not only to identify significant factors influencing swimming performance, but also to quantify these effects in a way that enables managers and engineers to apply our data to populations that might differ in one or more of these variables. Figure 1.4 demonstrates how they can be used to predict proportions of populations able to pass barriers under various velocity conditions. For these models, we set all variables except velocity to their mean values. Field application will require that local information be substituted for the values collected in this study. Proportions can then be estimated for each model as follows:
Weibull:
19
(1.2)
é æ ω − µ öù S ( D) = exp ê − exp ç ÷ú è σ øû ë
Gamma:
(1.3)
æ æ æ ω − µ ööö Γ ç δ −2 , δ−2 exp ç δ ç ÷÷÷ è è σ øøø è S ( D) = , Γ ( δ −2 )
Where the survivorship function S(D) is the proportion of fish successfully passing a velocity barrier of distance D (Chapter 4), ω = ln(D), σ = the scale parameter, δ = the shape parameter, Γ(a), and Γ(a,b) are the complete
(1.4)
∞
Γ(a) = ò D a −1 × e− D dD 0
and incomplete
(1.5)
∞
Γ(a, b) = ò D a −1 × e − D dD b
gamma functions, respectively (Lawless 1982) , and µ = Xβ , the vector product of covariate values and their coefficients. Thus, the data in Table 1.2 can be used to generate estimates of passage success for these species throughout their range. These equations can be applied equally effectively to situations where managers wish to exclude certain species using velocity barriers.
20
Consider the following example: a fisheries manager wants to estimate the proportion of 50 cm walleye passing a 10 m long barrier of 3.2 m · s-1 flow. Because these fish are larger than the ones we tested, Figure 1.4 does not provide a realistic estimate of passage. Instead, values from Table 1.2 are entered into Equation 1.3 to generate an estimate of 82.6% passage through this barrier. A similar process could be used to describe a population with a range of sizes by breaking it down into meaningful ranges (e.g., by age class).
Recently, dam removal has been gaining favor as a method of providing fish passage, as well as restoration of river ecosystems. This approach raises a number of controversial issues, including aesthetic and recreational value of natural versus modified riverine habitat, commercial value of impounded waterways, potential future use of dam structures, and fate of hazardous substances that may have built up in sediment behind the dam. In many cases, particularly at low-head dams, it may be more feasible to create a breach to provide passage while retaining intact the bulk of the structure. This approach is often much less expensive than complete removal, and bypasses some of the other concerns. Using the data presented in this study and elsewhere (i.e. Weaver 1963, 1965), this may provide an alternative to technical fishway construction, and may serve as an interim measure while structures await complete demolition.
Our data suggest that while some aspects of high-speed swimming performance can be generalized between similar species, important differences may exist among fishes with similar body forms or sizes. Performance may also vary substantially by life history
21
stage, migratory motivation, or environmental conditions (i.e., temperature, illumination, turbulence). The findings should therefore be used with caution when being applied to species not tested in this study, or at passage sites where environmental features are substantially different from our test conditions.
The information gained in this study defines characteristics of high-speed swimming of upstream migrant fishes in response to velocity barrier challenges in a novel way and at a realistic scale. The distance that fish are able to ascend high velocity flow is a useful parameter for defining swimming performance and potential distributional limits. Thus the technical and numerical approaches that we have described have broad applicability both to site-specific fish passage problems and to understanding implications of velocity barriers for population ecology of migratory riverine species.
References
Allison, P.D. 1995. Survival analysis using the SAS system: a practical guide. SAS Institute, Cary, NC. Bainbridge, R. 1958. The speed of swimming of fish as related to size and to the frequency and amplitude of the tail beat. J. Exp. Biol. 35: 109-133. Bainbridge, R. 1959. Speed and stamina in three fish. J. Exp. Biol. 37: 129-153. Beamish, F.W.H. 1978. Swimming capacity. In Fish Physiology, Vol. VII, Locomotion. Edited by W.S. Hoar and D.J. Randall. Academic Press, London pp. 101-187. Bell, M.C. 1991. Fisheries handbook of engineering requirements and biological criteria. U.S. Army Corps of Engineers, Portland, OR. Breder, C.M., Jr. 1976. Fish schools as operational structures. Fish. Bull. 74: 471-502. Brett, J.R. 1962. Some considerations in the study of respiratory metabolism in fish, particularly salmon. J. Fish. Res. Board Can. 19: 1025-1038.
22
Brett, J.R. 1964. The respiratory metabolism and swimming performance of young sockeye salmon. J. Fish. Res. Board Can. 21: 1183-1226. Brett, J.R. 1965. The relations of size to the rate of oxygen consumption and sustained swimming speeds of sockeye salmon (Oncorhynchus nerka). J. Fish. Res. Board Can. 22: 1491-1501. Brett, J.R., and Glass, N.R. 1973. Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature. J. Fish. Res. Board Can. 30: 379-387. Burrows, T.E., and Chenoweth, H.H. 1970. The rectangular circulating rearing pond. Prog. Fish-Cult. 32: 67-80. Castro-Santos, T., and Haro, A. 2002. Quantifying delay in andadromous fish migrations: a new application of event-time analysis. Can. J. Fish. Aquat. Sci. Castro-Santos, T., Haro, A., and Walk, S. 1996. A passive integrated transponder (PIT) tagging system for monitoring fishways. Fish. Res. 28: 253-261. Chow, V.T. 1959. Open channel hydraulics. McGraw-Hill, New York, NY. Clay, C.H. 1995. Design of fishways and other fish facilities. Lewis Publishers, Boca Raton, FL. Colavecchia, M., Katapodis, C., Goosney, R., Scruton, D.A., and McKinley, R. S. 1998. Measurement of burst swimming performance in wild Atlantic salmon (Salmo salar L.) using digital telemetry. Regul. Rivers: Res. Manage. 14: 41-51. Dow, R.L. 1962. Swimming speed of river herring Pomolobus pseudoharengus (Wilson). J. Cons. Perm. Int. Explor. Mer 27: 77-80. Gero, D.R. 1952. The hydrodynamic aspects of fish propulsion. Am. Mus. Novit. 1601: 1-32. Haro, A., Odeh, M., Castro-Santos, T., and Noreika, J. 1999. Effect of slope and headpond on passage of American shad and blueback herring through simple Denil and deepened Alaska steeppass fishways. N. Am. J. Fish. Manage. 19: 51-58. Haro, A., Odeh, M., Noreika, J., and Castro-Santos, T. 1998. Effect of water acceleration on downstream migratory behavior and passage of Atlantic salmon smolts and juvenile American shad at surface bypasses. Trans. Am. Fish. Soc. 127: 118-127. Jungwirth, M., Schmutz, S., and Weiss, S. 1998. Fish migration and fish bypasses. Fishing News Books, Cambridge. Lawless, J.E. 1982. Statistical models and methods for lifetime data. John Wiley and Sons, New York.
23
Lee, E. T. 1992. Statistical methods for survival data analysis. Wiley, New York. Loesch, J.G. 1987. Overview of life history aspects of anadromous alewife and blueback herring in freshwater habitats. Am. Fish. Soc. Symp. 1: 89-103. Odeh, M. 1999. Fish passage innovation for ecosystem and fishery restoration. In Innovations in Fish passage technology. Edited by M. Odeh. American Fisheries Society, Bethesda, MD pp. 1-24. SAS, Institute. SAS Version 8.0. (6.12). 1999. Carey, NC, SAS Institute. 1989. Venditti, D.A., Rondorf, D.W., and Kraut, J.M. 2000. Migratory behavior and forebay delay of radio-tagged juvenile fall chinook salmon in a lower Snake River impoundment. N. Am. J. Fish. Manage. 20: 41-52. Videler, J.J. 1993. Fish swimming. Chapman & Hall, London. Videler, J.J., and Wardle, C.S. 1991. Fish swimming stride by stride: speed limits and endurance. Rev. Fish Biol. Fish. 1: 23-40. Videler, J.J., and Weihs, D. 1982. Energetic advantages of burst-and-coast swimming of fish at high speeds. J. Exp. Biol. 97: 169-178. Weaver, C.R. 1963. Influence of water velocity upon orientation and performance of adult migrating salmonids. Fish. Bull. 63: 97-121. Weaver, C.R. 1965. Observations on the swimming ability of adult American shad (Alosa sapidissima). Trans. Am. Fish. Soc. 94: 382-385. Webb, P.W. 1994. Exercise performance of fish. In Comparative vertebrate exercise physiology: phyletic adaptations. Edited by J. H. Jones. Academic Press, San Diego pp. 1-49.
24
Table 1.1. Species characteristics, sample sizes, and hydraulic conditions of tests performed in the swimming flume, all years pooled. Lengths, temperatures, and measured velocities are given as means ± SD; length ranges in parentheses.
Hydraulics Species
American Shad
Alewife
Blueback Herring
Striped Bass
Walleye
White Sucker
N
Length (mm)
Temperature (°C)
Nominal Velocity
Measured Velocity (m
(m s )
s )
Water Depth (m)
Q (m s )
-1
-1
3
-1
92
421 ± 34 (355 - 495)
16.8 ± 1.5
1.5
1.74 ± 0.07
0.96
1.6704
233
417 ± 33 (355 - 495)
18.9 ± 2.1
2.5
2.69 ± 0.09
0.26
0.6994
285
415 ± 36 (325 - 520)
18.4 ± 2.0
3.5
3.43 ± 0.09
0.45
1.5435
92
416 ± 35 (350 - 510)
18.2 ± 2.4
4.5
4.53 ± 0.04
0.46
2.0838
122
235 ± 12 (210 - 265)
10.2 ± 1.4
1.5
1.60 ± 0.15
0.96
1.536
75
239 ± 11 (215 - 265)
10.0 ± 1.4
2.5
2.59 ± 0.06
0.26
0.6734
53
237 ± 11 (215 - 260)
10.4 ± 1.9
3.5
3.39 ± 0.03
0.45
1.5255
19
228 ± 11 (210 - 245)
16.7 ± 2.3
1.5
1.61 ± 0.09
0.96
1.5456
24
219 ± 11 (205 - 245)
16.7 ± 3.4
2.5
2.69 ± 0.07
0.26
0.6994
38
215 ± 11 (200 - 240)
17.1 ± 2.4
3.5
3.40 ± 0.13
0.45
1.53
12
523 ± 257 (290 - 970)
18.6 ± 0.0
1.5
1.40 ± 0.44
0.96
1.344
57
430 ± 118 (235 - 780)
19.9 ± 2.7
2.5
2.64 ± 0.07
0.26
0.6864
65
482 ± 119 (280 - 760)
19.3 ± 2.8
3.5
3.40 ± 0.05
0.45
1.53
48
553 ± 162 (285 - 835)
17.2 ± 1.3
4.5
4.55 ± 0.09
0.46
2.093
13
313 ± 45 (240 - 395)
12.6 ± 2.5
1.5
1.74 ± 0.11
0.96
1.6704
24
314 ± 41 (270 - 410)
15.7 ± 3.4
2.5
2.73 ± 0.11
0.26
0.7098
12
316 ± 53 (225 - 415)
10.3 ± 0.7
3.5
3.34 ± 0.01
0.45
1.503
35
385 ± 41 (285 - 505)
11.8 ± 0.9
1.5
1.75 ± 0.05
0.96
1.68
35
383 ± 29 (305 - 430)
14.9 ± 3.6
2.5
2.62 ± 0.05
0.26
0.6812
35
391 ± 33 (310 - 450)
17.9 ± 5.4
3.5
3.37 ± 0.03
0.45
1.5165
31
398 ± 26 (340 - 450)
15.0 ± 3.6
4.5
4.51 ± 0.04
0.46
2.0746
25
Table 1.2. Maximum likelihood regression models of covariate effects on log maximum distance of ascent (ln (exclusion screen)). Length is in mm, temperature is in °C, Sex is binary, with male=0 and female=1.
Species Am. Shad Variable
DF
Alewife
Blueback Herring
Striped bass
Walleye
White Sucker
β
P>χ
β
P>χ
β
P>χ
β
P>χ
β
P>χ
β
P > χ2
2
2
2
2
2
Intercept*
1
6.281
= ti; and Yij = 0 if tj < ti; βx refers to the vector product of the covariates and their coefficients, either for individual i, or for members of the risk set j. As with ML estimation, the PL is then maximized with respect to β using the Newton-Raphson algorithm. Note that by constructing the denominator in this way, combined with the censoring indicator δi, censored data are included in the analysis, and contribute to the denominator until the last extant observation.
Because the PL is based on the rank of time, rather than its actual value, combined, relative covariate effects on the hazard function can be tested without requiring the baseline hazard to follow a particular distribution. In addition to significance, software packages may generate estimates of coefficients in equation (4.7); their interpretation is simplified by using an alternate coefficient, the risk ratio, which equals eβj. This is
140
directly analogous to the transformations on parametric models described above, except that these are now being used to estimate effects on passage rates rather than delay time, hence the signs of the coefficients will be reversed between the two models.
Another attractive feature of proportional hazards regression is that, because it makes no assumptions about the underlying hazard function, inclusion of covariates that change over time is a simple process that is included as a standard feature in many software packages. Hazard ratios are calculated at each event time based on the current risk set, regardless of whether individuals had previously been exposed to a different set of covariate values.
Although Cox’s proportional hazards regression is not fully parametric, it still requires certain assumptions about the data, primarily that the effects of covariates on hazard are constant over time; deviation from this assumption can cause misleading results. The proportional hazards assumption can be tested by plotting Shoenfeld residuals (Shoenfeld 1982; Grampsch and Therneau 1994) against the log of time—any significant slope indicates that proportionality is time-dependent. Another residual, called the score residual, is useful for identifying influential and poorly fit observations (see Hosmer and Lemeshow (1999) for a thorough discussion of fit evaluation for proportional hazards models).
141
Competing Risks The binary approach to censoring applied in the previous paragraphs is complicated by the availability of multiple passage routes, a common feature of downstream passage studies. Prior to passage, fish are available to pass through all routes, i.e. they are part of the risk set. Once a route is selected, however, they no longer contribute to the passage rate of any route. In other words, an individual passing via a given route is effectively censored with respect to the other routes. This constitutes a competing risks situation, the implications of which are discussed by Allison 1995).
When confronted with a competing risks situation, a multi-step approach is appropriate. First, all covariates except passage route are included in the model. This allows inclusion of individuals that were not observed passing through either route (i.e. censored) and provides the best estimate of overall passage rate. Next, separate models are developed for individuals passing through each route by modifying the censoring variable. For each model, non-passers as well as those that pass through alternate routes are included, censored at time of passage; only those that pass through the route in question are noncensored. The advantage of this step is that it evaluates separately variables that affect the rates at which fish pass through each route. Different results for competing passage routes imply some underlying difference in covariate effects on passage rate that may be of substantial biological interest. This approach permits researchers to use the entire risk set when analyzing passage rates of fish that pass through each route, and can be applied to any of the three analyses detailed above. The only assumption required is that fish that
142
have not yet passed the dam are equally likely to pass via any route, and should be included when evaluating the effects of covariates on the groups.
Logistic Regression Although the competing risks approach allows separate analysis of rates of passage through various routes, it does not directly quantify which variables most influence the likelihood of selecting one route over another. Logistic regression is a standard method for quantifying covariate effects on the likelihood of selecting one of two or more categorical variables (Hosmer and Lemeshow 1989). By including time as a covariate, the effect of delay on passage route selection can be tested directly. Censored individuals, since they are not observed to actually pass, are generally not included in such analyses (Allison 1995).
Dataset A sample dataset was selected (RMC Environmental Services, Inc., currently Normandeau Associates, Drumore, PA, unpublished data) that was designed to test the effect of different depth settings of a bypass sluice gate on passage route selection. We have adapted this dataset to demonstrate the utility of each of the event-time analysis methods for describing the effect of this and other variables on delay.
Atlantic salmon smolts were obtained from two sources: a bypass sampler on the Connecticut River mainstem ("wild" fish; n=65, FL=137-235 mm, X =179 mm), and the White River National Fish Hatchery in Bethel, VT ("hatchery" fish; n=93, FL=152-218 mm, X =190 mm). Source of fish is referred to as “origin”, and coded 0 and 1, 143
respectively, for wild and hatchery smolts in analyses. Smolts were anaesthetized using MS-222 and radio-tagged using esophageal implants. Following a 24-h recovery period, fish were released one km upstream of Wilder Station, a hydroelectric facility on the Connecticut River mainstem. This was considered sufficient distance to prevent any predisposition on the part of the smolts to pass through one route over the other. Smolts were released in six groups of 21-33 individuals on 13, 17, 19, 21, and 25 May, and 02 June, 1994 (Figure 1), and time to passage was calculated from release time. Wild fish composed 48% (33% – 58%) of the first five releases; the last release comprised only hatchery fish. Telemetry receivers were placed in such a way that smolts were detected when they entered the forebay of the project, and were monitored continuously during their forebay residence. A four-element YAGI antenna situated halfway down the sluice identified sluice passers, and antennas submerged at the entrance of each intake identified turbine passers.
Turbine flow ranged from 19.8 – 308 m3s-1, X = 255 m3s-1, and was logged at time of passage. Sluice gate depth was set to 1.07 m for the first two releases, 1.52 m for the third release, and 0.76 m for the last three releases. For each of the last three releases, the sluice gate depth was increased to 1.52 m after 46 h (Figure 1). In order to prevent the artificial association of greater gate depth with long passage times, we censored these data at 46 hours for the life table and parametric regression analysis, but included the data with gate depth as a time-dependent covariate in the proportional hazards analysis.
144
Because there were two possible passage routes, this constituted a competing risks variable in this study. Separate models were generated for each route as well as for the combined data using nonparametric, parametric, and proportional hazards techniques. Adequacy of the parametric models was evaluated both numerically and graphically, using each of the methods detailed above. Where nested models were not significantly different from each other, we selected the most parsimonious model, i.e. the one with the fewest parameters. We evaluated adequacy of Cox’s proportional hazards models using Schoenfeld and score residuals.
In addition to the above tests, we used logistic regression to test for covariate effects on likelihood of passing through the bypass sluice, including log of delay time as a covariate. All analyses were conducted using SAS software (SAS 1999).
Results
Of the 158 Atlantic salmon smolts used in this study, fourteen (8 hatchery and 6 wild) had undetermined passage routes or failed to pass; these were included in the analyses, censored at their last extant observation. In all, 144 smolts passed the station by known routes: 106 over the bypass sluice and 38 through the turbines.
A life table with passage times and associated probability functions is presented in Table 4.1. To improve resolution, interval duration increases with time from 1 to 12 h. Also, we include a new variable, Ŝ*(ti) in the life table to provide a comparison with standard techniques. This is analogous to Ŝ(ti), but calculated only on uncensored individuals.
145
Kaplan-Meier survivorship curves (Ŝ’(t); Kaplan and Meier 1958) for each release group are presented in Figure 4.1. Median passage time (Ŝ(t) = 0.5) occurred within the first 12 h, but 22% of the fish took longer than 36 h to pass. The proportion of available fish passing, (hazard, or passage rate (ĥ(t)), was moderate on the first hour (5.2% · h-1), jumped to 27.5% · h-1 in the second hour, and ultimately declined to 1.7% · h-1 on the last (12 h) interval.
Nonparametric tests show delay varied with gate depth, release date, and turbine flow, with the latter effect differing between tests and passage routes; origin had no apparent effect (Table 4.2). Note that these tests are for individual covariates only and do not account for variance due to other covariates; all other statistics are for complete models, accounting for variance due to all covariates in the model (Type III hypotheses (SAS 1999)).
Parametric regression described reduced delay with increased gate depth for combined passage data and for smolts that passed over the sluice, as indicated by a significant negative coefficient (Table 4.2). The interpretation of this for the combined data is T = 100 · (e-3.5018 – 1), or mean delay decreases by 97% for every meter of increased gate depth. The same transformation for sluice passers shows a 99% decrease in delay time per meter of gate depth. For the current dataset, this implies that by increasing gate depth from the shallowest to deepest settings, median delay declines from 20.8 h to 1.4 h when both passage routes are available, and delay of the 90th percentile declines from 93.9 h to 6.5 h (Table 4.3). The parametric approach also suggests that fish released later in the
146
study passed more slowly than earlier releases (positive β), regardless of passage route, and fish that passed over the sluice experienced greater delays associated with higher turbine flows.
The gamma distribution provided a better fit to the combined data than did the Weibull, or exponential distributions ( χ 2 ; 1 and 2 df, respectively; P < 0.001). However, the lognormal and gamma distributions provided nearly identical fit ( χ 2 ; 1 df; P = 0.88). Based on these results, combined with the Hollander and Proschan test (P = 0.332) and analysis of Cox-Snell residuals (Figure 4.2), we concluded that the lognormal was the most appropriate and parsimonious of the distributions tested, and that it adequately described the data.
Results of proportional hazards regression indicate that gate depth was the only variable to significantly affect passage rate across all of the models. Faster passage rate at greater depths is indicated by a significant positive coefficient (greater hazard; note the contrast with the parametric approach). By transforming the data to risk ratios, we find a 43-fold increase in passage rate associated with each meter of gate depth for combined data, and a 69-fold increase for sluice passers. In addition to gate depth, turbine flow reduced passage rate of sluice passers by 0.4% · m-3 of flow, i.e., fish exposed to the lowest flow conditions passed over the sluice at a rate approximately three times faster than that of those exposed to the highest flow. Residual analysis suggested that the assumption of proportionality might not have been met in these models, however, specifically that passage rates of hatchery smolts were substantially greater than those of wild smolts
147
during the period from 7 to 18 hours after release (P = 0.009). This effect did not substantially change the values of the main effects, however, and we have excluded this result from Table 4.2 for clarity.
The logistic models (Table 4.4) demonstrate that, omitting data from censored individuals, the probability of turbine passage increases with delay. Probability of turbine passage was likewise increased by greater turbine flow, but was reduced by greater sluice gate depth.
Discussion
The results of this study highlight some important differences among the event-time analysis techniques, as well as their relative strengths. Life tables and survivorship curves are simple to construct, and their significance is readily interpreted. Survivorship curves can be generated using either the Kaplan-Meier or life-table approach; the former is the preferred method when time is measured continuously, and is helpful in analyzing appropriateness of parametric models. However, when sample sizes are large, tables generated using Kaplan-Meier can become cumbersome. Life tables, on the other hand, can be used to summarize data concisely, and interval width can be increased as sample size declines (as in this study) to improve function estimates. Both methods show that, while the first half of the fish pass fairly quickly, passage rate declines with time, and the slowest fish take several days to pass the project. Reporting only median passage time masks this important feature (Venditti 2000), a fact that should be of some concern to restoration efforts. Likewise, comparison of Ŝ(t) with Ŝ*(t) shows how omitting censored data can substantially influence estimates of delay time. In our example, such omission
148
would suggest that 88% of the fish passed in less than 24 h, when in fact only 70% had passed by that time.
The survivorship curves also provide graphical representation of the effects of sluice gate depth setting, and provide evidence to support the requirement that censoring be noninformative. Delay times were least for the May-19 release (1.52 m gate depth), and greatest for the last three releases (0.76 m gate depth). Those fish that delayed passage until after the gate was set to a greater depth show a correspondingly greater rate of passage at that time. Although more censoring was observed for later release dates and shallower gate settings, it appears to be dispersed randomly with time: no clustering occurs to suggest that censoring was due to covariate values. The exact cause of censoring was not determined, however, and may have been due to mortality, tag failure or expulsion, or undetected passage.
The Wilcoxon and log-rank tests tend to emphasize different parts of the distribution: the Wilcoxon test is most sensitive to differences early in the distribution, while the log-rank test is more sensitive to differences in the right-hand tail; divergent results can be used to draw inference on which fish are most affected by covariates (Lee 1992). Thus, while the effects of release date and gate depth apply to all smolts, the effect of turbine flow may be most important for those that do not experience large delays, especially among sluice passers. Both methods are limited, however, in that they do not simultaneously account for multiple covariate effects.
149
Both the parametric and Cox’s proportional hazard models simultaneously account for all covariate effects (Type III hypotheses (SAS 1999)), but they differ in important ways. First, since the parametric models describe covariate effects on delay time, we are able to generate predictions of those effects on specific proportions of the population, a useful tool for managers and those interested in understanding population-level implications of delay. The proportional hazards models, by contrast, describe covariate effects on passage rate (hence the reversed sign of the βˆ ’s) and cannot be used to directly estimate delay time (but see Hosmer and Lemeshow (1999) for methods by which indirect estimates can be extrapolated from the baseline hazard function).
The parametric models can also be used to draw important inferences on the shape of the hazard. Here, the numerical and graphical goodness-of-fit tests both suggest that the lognormal models provide a reasonable fit to the data. This implies that the log delay times are approximately normally distributed; observed scale values greater than unity indicate passage rates (i.e. hazard) are initially low, but rapidly increase to a maximum value, then decline with time -- a characteristic also described by the life table. This inverted U-shape in the hazard may have some biological significance, as it implies both initial delay (as might be expected from post-handling and release stress, or delay in locating the passage route), and reduced passage rates for fish that do not subsequently pass quickly. Thus, the risks of delay include increased likelihood of further delay, a pattern one would predict if delay resulted in loss of migratory motivation.
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Although the proportional hazards models do not yield parametric descriptions of the hazard, their independence from specific distributions make them robust against fluctuating passage rate, e.g., due to diel migratory patterns, requiring only that covariate effects on hazard ratios be consistent across these patterns. With either approach, extrapolations far beyond observed values of covariates or delay times should be used with caution.
A further distinction is that proportional hazards models allow ready computation of effects of covariates that change over time, while the parametric models assume that each fish is exposed to fixed covariate conditions. This feature has important implications for the interpretation of the effects of release date and gate depth. Since the shallowest gate settings were applied at the end of the experiment, the experimental design was unbalanced, and variability due to this factor is wrongly apportioned between gate depth and release date under the fully parametric model. By including gate depth as a timedependent covariate, potentially confounding effects between the two variables are reduced. Under this less biased interpretation of the data, delay is appropriately attributed to gate depth and not to date.
Inclusion of time-dependent covariates can also be used to control for deviations from the proportional hazards assumption. The observed difference in passage rate between hatchery and wild smolts is an example of this, with hatchery smolts passing more rapidly between 7 and 18 h after release. Inclusion of such post-hoc model adjustments can lead to biased interpretations of data, and should be used with care when they are not
151
part of the initial experimental design. In this case, the effect did not substantially influence results for the other covariates, but it does imply some difference in the behavior of hatchery and wild smolts. Esophageal implants have been shown to affect behavior of tagged smolts (Adams et al. 1998a;Adams et al. 1998b), and it may be that the smaller, wild fish took more time to recover from the tagging and release procedure than did hatchery fish.
Turbine flow also varied over the course of the experiment. Unfortunately, flow was only logged at time of passage, so we were unable to include this as a time-dependent covariate, assuming instead that flow at time of passage was characteristic of the entire delay time (an assumption that is less reasonable for longer delay times). Significant effects were observed among all three classes of models, however, suggesting that turbine flow did influence passage rate. The opposing signs of the coefficients for turbine and sluice passage models, combined with the nonparametric results suggest that increased turbine flow may distract fish from the bypass sluice, with correspondingly greater and lower rates of turbine and sluice passage.
Each of the techniques described above has specific advantages and can provide unique information on passage rate. The most appropriate approach will depend on sample size, time resolution, shape of the hazard function, and research objectives. None of the above techniques, however, addresses the question of why fish select one route over another. Logistic regression does just this, and therefore complements event-time analysis. Bearing in mind that data from 14 individuals are missing, logistic regression reveals a
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significant time effect, with greater delays associated with increased risk of turbine passage. This result alone is a powerful argument for trying to maximize passage rates. Also significant in the logistic model are effects of turbine flow and gate depth, with greater flow and shallower gate settings associated with increased risk of turbine passage. Thus, combining the logistic and event-time approach, we conclude that greater turbine flow and shallower gate depth not only increase delay, but also simultaneously (perhaps in part due to the delay) increase the likelihood of turbine passage.
The bulk of current fish passage research work focuses on proportions of fish passing through various routes, primarily because this is thought to have the greatest relevance to survival and recruitment (Burnham et al. 1987; Skalski 1998; Skalski et al. 1998). While the importance of delays to migration is not well understood, it is bound to vary by species, river system, and life history (McCormick et al. 1996; Zabel et al. 1998; Zydlewski and McCormick 1997b). Our understanding of the effect of delay is limited at the outset by our ability to quantify it. Event-time analysis provides a powerful set of tools for developing just such descriptions, as well as for evaluating effects of structural and operational modifications on passage rates. Because they afford continuous monitoring of individuals, radio and acoustic telemetry are particularly well suited to these analyses. Other forms of telemetry and monitoring (e.g., from PIT tags) may also be useful, however it is important that time to passage or censoring is known. Since PIT tags tend to have relatively short read ranges (Prentice et al. 1990; Castro-Santos et al. 1996), it may not be possible to identify censoring times using this technology, although the competing risks approach could still be applied to some data.
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While this study focuses on the application of event time analysis to a radio telemetry study of downstream fish passage, the techniques have much broader potential. Analogous applications include quantifying attraction of upstream migrants to fishway entrances, monitoring progress up fishways (where height can be substituted for time as the dependent variable, and successfully exiting the top of the fishway constitutes censoring), and quantifying timing of movements of other migratory species: in short, any application where censoring and competing risks confound the use of standard techniques.
References
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Table 4.1. Life table of telemetry data, pooled across passage routes and treatments, with estimates of probability functions: survivorship function ( S (ti ) ), probability density function (PDF: fˆ (t ) ), and hazard function ( hˆ(t ) ). Time, denoted ti, is reported in mi
mi
hours and refers to the beginning of each interval; bi is the interval width, in hours; ni is the number available to pass at the start of the interval; ci is the number censored; and ri is the risk set. Passers only ( Sˆ *(ti ) ) is equivalent to S (ti ) calculated using uncensored data only, and is included for comparison. Note that S (t ) is calculated at the start of each i
interval, while fˆ (tmi ) and hˆ(tmi ) are calculated at the midpoint. Any fish that did not pass before a change in gate depth are censored at 46 h. Time
Duration
Entered
Passed
Censored
Risk Set ri
PDF ˆt ) f( mi
Hazard hˆ(tmi )
Survivorship S(ti )
Passers only Sˆ*(ti )
ti
bi
ni
pi
ci
0
1
158
8
0
158.0
0.051
0.052
1.000
1.000
1
1
150
36
2
149.0
0.229
0.275
0.949
0.934
2
1
112
12
1
111.5
0.078
0.114
0.720
0.636
3
3
99
10
2
98.0
0.022
0.036
0.643
0.537
6
3
87
6
1
86.5
0.013
0.024
0.577
0.455
9
3
80
15
1
79.5
0.034
0.069
0.537
0.405
12
6
64
12
1
63.5
0.014
0.035
0.436
0.281
18
6
51
7
1
50.5
0.008
0.025
0.353
0.182
24
12
43
12
1
42.5
0.007
0.027
0.304
0.124
36
12
30
3
27
16.5
0.003
0.017
0.218
0.025
158
Table 4.2. Results from various event-time analysis methods. The competing risks approach was applied to each passage route, where censored individuals include those passing through the alternate route. Sample sizes are presented as completed passage (censored). Life table results are from nonparametric tests of individual covariates; all other tests are for complete models. Coefficients for the parametric models indicate effect of each variable on the log of delay (ln T). Coefficients for the proportional hazards models indicate their effect on the log of the hazard (ln h(t)).
Life Table P-value Variables
Wilcoxon
Combined data: N T (c T ) Intercept
Log-Rank
121 (37)
Parametric
βˆ
P-value
Proportional Hazards
βˆ
121 (37)
P-value 144 (14)
---
---
-843.871
0.001
---
---
0.260
0.947
-0.243
0.242
0.068
0.696
