- Email: [email protected]
Simple application of using residuals from catch-curve regressions to assess year-class strength in fish
ELSEVIER
Fisherjes Research 32 (1997) 115-121
Simple application of using residuals from catch-curve regressions to assess year-class strength in fish M.J. Maceina Department of Fisheries and Allied Aquacultures,
*
Auburn Universin’, Auburn, AL 36849, USA
Accepted 26 May I997
Abstract Residuals associated with catch-curve regressions can represent variable recruitment in fish populations. Catch curves are used to estimate steady-state mortality and assume relatively constant recruitment, but this assumption is rarely met. I documented the presence of abundant year classes of largemouth bass (Micropterus saltnoides), from earlier sampling and these dominant year classes persisted over time in two reservoirs. I expanded simple linear catch-curve regressions that used age (in years) as an independent regressor to multiple regression models each of which incorporated an additional independent environmental variable (ENVIR) that was measured when fish were age 0. The age term in the regression was proportionally weighted to the sample size at each age which deflated the influence of older and rarer fish in the analysis. This generalized regression equation: log, (NUMBER) = b,-b, (AGE) + b, (ENVIR); explained variable abundance-at-age (NUMBER) and the environmental term was related to the formation of weak and strong year classes after accounting for the effects of age. Typically, age will explain the majority (r* 2 0.5) of the variation in abundance-at-age. For two largemouth bass populations, environmental hydraulic variables were significant (P < 0.10) terms in this equation and explained an additional 12 and 16% of the variation in number after accounting for the variation explained by age. For data collected in one population 2 yrs after the initial analysis, the same strong and weak year classes persisted, residuals from these catch curves were correlated (r = 0.86, P < 0.05, N = 6), and the influence of hydrology on year class formation was duplicated. This approach can provide savings in labor and funds as abundance of young fish or recruitment indices do not have to be measured each year. 0 1997 Elsevier Science B.V. Keywords:
Age; Catch-curve;
Multiple regression;
Residuals
1. Introduction Determination tive success
of factors
and recruitment
the understanding,
assessment,
that influence
reproduc-
of fish is paramount and management
’ Corresponding author. Tel.: + l-334-844-93 844-9208; e-mail: [email protected]
any population.
Estimates
for many
usually
species
of year-class involves
enumer-
ation
of juveniles
to
some
instances,
of
such as for striped bass (Murane suxitulis) from the Roanoke River, NC (Rulifson and Manooch, 19901, or annual density and biomass of young fish was determined over time (Ploskey et al., 1996). However, collections need to
19; fax: + l-334-
young
0165.7836/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO165-7836(97)00051-9
fish were
or young
abundance
the direct
long-term developed
adults
via sampling.
In
indices
of abundance
of
116
M.J. Maceina/ Fisheries Research 32 (1997) 115-121
be taken every year and the compilation of a continuous long-term data base is costly and cannot always be accomplished. Fishery biologists estimate total annual mortality using catch-curve regressions (Ricker, 1975). A random sample of fish is collected from a population, aged, and then the natural log of the number of fish at each age (dependent variable) is regressed against age or year class (independent variable) for the descending limb of the curve. The slope of the regression is the instantaneous annual mortality rate (Z>, and the estimate of survival (S) is equal to emZ. An assumption of this analysis is that relatively constant recruitment to the population occurs each year. Guy and Willis (1995) used catch curves to identify missing year classes and developed a qualitative recruitment variability index based on the frequency of missing year classes to describe stability in annual cohort production. In this paper, I built upon this concept by expanding simple linear catch-curve regression to a multiple regression by including an environmental variable. This term explained some of the additional error (residuals) in the simple catchcurve regression. I present examples from two populations of largemouth bass ( Microprerus su2moides), and examined the relations between environmental or reservoir hydraulics and the residuals (regression error) associated with catch-curve regressions. Computation of the instantaneous mortality rate was not of interest. Positive and negative residuals associated with catch-curve regressions represented strong and weak year classes in these populations. I verified this method by documenting the persistence of strong year classes in these exploited populations and was able to duplicate the results in one population for data collected 2 yrs later. I also determined if spatial differences in catch-curve analyses were present in both populations to assess the potential of sampling location bias.
2. Methods 2. I. Fish collection In March-April 1993, 1007 largemouth bass were collected with electrofishing from Lake Guntersville,
a 28,500-ha impoundment of the Tennessee River, AL with a catch-depletion technique in coves to determine abundance (Maceina et al., 1995). Three downstream and three upstream coves were sampled and the minimum distance between downstream and upstream sites was 35 km. In March-April 1995, 727 largemouth bass were collected with electrofishing from 12 lower and 13 upper stations in Weiss Lake, a 11,200-ha impoundment of the Coosa River, AL. Otoliths were removed from a sample of 20 fish from successive 25-mm total length (TL) size groups, although this sample size was not achieved for all size groups in Lake Guntersville. In Weiss Lake, all fish greater than 400 mm TL were sacrificed for aging. A total of 190 and 313 fish were aged from Lakes Guntersville and Weiss, respectively. Otolith preparation and examination followed Hoyer et al. (1985) and age-length keys estimated the age-structure for the entire sample. In Lakes Guntersville and Weiss, no minimum size limits were in effect for largemouth bass and I assumed that age-2 and older fish were vulnerable to exploitation. At age 2, these fish averaged 26 and 28 cm in Lakes Guntersville and Weiss, respectively. For each population, catch-curve analysis (Ricker, 1975) was computed by regressing the loge of abundance-at-age against age for largemouth bass 2 to 9-11 yrs old. The age term in the regression was proportionally weighted to the sample size at each age (log, values were used) which deflated the influence of older and rarer fish in the analysis (Montgomery and Peck, 1982). To verify the use of residuals from catch-curve regressions to quantify year class strength, I examined the persistence of strong year classes in these populations from previous sampling. Possibly, strong year classes could suffer greater density-dependent mortality from natural causes or compensatory mortality from angler exploitation. In 1990, the Alabama Department of Conservation and Natural Resources (ADCNR) collected 106 and 111 largemouth bass from Lakes Guntersville and Weiss and aged fish using otoliths. Percent composition by age in 1990 was compared to residuals from catch-curve regressions computed for Lakes Guntersville and Weiss for data collected in 1993 and 1995. In Lake Guntersville, I examined the influence of retention time (reservoir volume/discharge) during
M.J. Maceina/ Fisheries Research 32 (1997) 115-121
different time periods on the error or residuals associated with the catch-curve regressions. A multiple regression equation was computed that included both age (weighted for sample size) and retention time as independent variables. Similar procedures were used in Weiss Lake, and I compared the production of weak and strong year classes of largemouth bass to retention time, water level fluctuations, and changes in reservoir area during different time periods. I attempted to duplicate the results obtained from Lake Guntersville for data collected in 1993 with data collected 2 yrs later. In spring 1995, the Tennessee Valley Authority (TVA) and the ADCNR collected 604 largemouth bass that ranged in age from 2 to 9 yrs old as part of their reservoir monitoring program. From these catch-curve regressions, ‘student’ residuals (residual/standard error of the residuals) were computed and compared with correlation analysis to determine if detection of strong and weak year classes could be repeated. ‘Student’ residuals display a t distribution, where for example, about 95% of ‘student’ residuals will fall between - 1.96 and + 1.96 regardless of sample size or the fit ( between the dependent and independent variable(s). Thus, comparison of individual data points can be made between regression equations. Catch-curve regressions were derived for fish collected from the lower and upper sections of each reservoir. Corresponding student residuals for each year-class were computed and compared using correlation analysis to determine if weak and strong year classes existed in each reservoir section.
r*>
3. Results 3.1. Catch-curue
analysis and oerification
of strong
and weak year classes
Inspection of catch-curve plots of loge number-atage against respective year classes showed variation about the regression line and suggested that annual recruitment was not homogenous in these populations (Fig. I>. In Lake Guntersville, strong largemouth bass year classes were evident in 1985, 1986, 1988, and 1990 while weak year-class production seemed apparent in 1982, 1983, 1987, 1989, and
500.
’
117
’
1
’
’
1
’
’
’
‘-
GUNTERSVILLE
0
\
IOO50
\@ \
l
l
.’
1.
105 -
‘*, l
1 -
tY ; E
2 = -0.481 12= 0.74 P < 0.01
o-1 91 500
100
I 0
I, 90
/ 88
a9 /
/
I a7
I, a6
I
IJ a4
a5
I
I
a3 I
a2 I
WEISS
‘\
50
.‘q \ \ \
10 5
2 = -0.574 ? = 0.69 P < 0.05
0 \@
0
0
4
\ \O \
I
I
/
I
I
I
,
I
93
92
91
90
a9
88
a7
a6
YEAR CLASS
./
Fig. 1. Catch-curves and corresponding regressions (dashed lines) for largemouth bass collected from lakes Guntersville and Weiss. 2 is the instantaneous mortality rate. The regression equations were weighted proportionally for sample sizes at each age.
1991. In Weiss Lake, strong largemouth bass year classes were evident in 1986, 1987, and 1993, while weaker year classes were produced in 1989, 1990, and 1992. Sampling prior to the computation of catch-curves suggested the presence of strong and weak year classes of largemouth bass in both lakes Guntersville and Weiss. In Lake Guntersville, age 2 and older largemouth bass comprised six year classes that were collected in spring 1990. Of these fish, the 1988 cohort was the predominant year class and comprised 50% of the catch. In 1993, this year class was five yrs old and still appeared as a strong year class in the catch curve plot (Fig. 1). In Weiss Lake, age 2 and older largemouth bass represented nine year
M.J. Maceina/Fisheries
118
classes that were collected in spring 1990. Of these fish, the 1987 year class was the dominant year class and comprised 52% of all fish collected. From inspection of the catch-curve plot in 1995, this cohort of 8-yr-old fish still appeared as a strong year class 5 yrs later. Exploitation and natural mortality undoubtedly reduced the abundance of largemouth bass, but strong year classes still persisted in both populations.
Research 32 (1997) 115-121
“”j-i--GE \ [r.
loo-
\
i.% f
\ 50.
v
2
\
a
a
\ -P
3.2. Hydrological variables related to variation in catch-curve regressions
For largemouth bass from Lake Guntersville, residuals from the catch-curve regression were plotted against the mean retention time from April to July and a positive relation was evident (Fig. 2). The relation appeared curvilinear, so log 10 transformed values of April to July retention time (RET) were
I
1.5 :
0.5 1.0
Z 2
0.0
$
-0.5
2
-1 .o
I
I
I
I
I
!
I
93
92
91
90
\-
I
I
I
/
a9
aa
a7
a6
YEAR CLASS Fig. 3. Catch-curve for largemouth bass data collected in spring 1995 from Lake Guntersville. The regression equations were weighted proportionally for sample sizes at each age.
log, (Number) = 3.987 - 0.528 (AGE)
I
+ 2.027(log,, RET).
84 ---------91 90 a7 a2
88861
30
40
RETENTION (days)
g2
89
I go9
-2000
h l
entered into the catch-curve regression (Fig. 1) to produce a multiple regression:
I
a5
20
-1.5
\
-0.410 ? = 0.61 lo - P < 0.05 z =
I
I
I
-1000
0
1000
i 2000
CHANGE IN AREA (ha) FROM MARCH TO JUNE Fig. 2. Residual values derived from catch-curve regression of log, number versus age (from Fig. 1) plotted against April to July retention time for largemouth bass collected from Lake Guntersville (top). The residuals of the catch-curve regression of loge number versus age (from Fig. 1) plotted against the change in area from 1 March to 30 June from Weiss Lake (bottom). Numbers represent year classes.
(1)
This equation explained an additional 12.5% of the variation in number-at-age (R* = 0.869) and retention time was a significant (P < 0.05) term in the equation after accounting for the effects of age. Thus, stronger largemouth bass year class production in 1985, 1986, 1988, and 1990 was associated with retention times of about 18 days or longer, while the weak year classes produced in 1987, 1989, and 1991, were typically related to retention times less than 18 days (Fig. 2). A similar pattern of weak and strong year classes was evident in Lake Guntersville in 1995 compared to data collected in 1993 (Fig. 3). Student residuals for six common year classes (1986 to 1991) were correlated (r = 0.86, P < 0.05) which indicated the detection of strong and weak year classes was repeated even though two years had elapsed between sampling periods. Eq. (1) was recomputed using 1995 data: log, (Number) = 2.562 - 0.548 (AGE) + 3.094( log 1oRET) .
(2) The equation (P < 0.01) explained 85.2% of the variation in number-at-age and both terms were sig-
h4.J. Maceina / Fisheries Research 32 (1997) 115-121
nificant (P < 0.05) regressors in the model. Retention explained an additional 24.4% of the variation in number-at-age after accounting for the effects of age. Analysis of covariance indicated the regression slope coefficients for both age and retention did not differ (P > 0.10) between 1993 and 1995. The same procedures were used to examine potential factors related to variation in the catch curve for largemouth bass in Weiss Lake. I found that the change in reservoir area between 1 March and 30 June from 1986 to 1993 was associated with the formation of strong and weak cohorts of largemouth bass. Reservoir area changes during this four-month period ranged from a decline of 1708 ha in 1990 to an increase of 1542 ha in 1993. Adding the change in reservoir area (AREA) to the catch-curve regression in Fig. 1 for Weiss Lake yielded:
119
,
I
,
/
1
I
r
I
GUNTERSVILLE
g
0
z f
A
91
90
/
300
89 I
88 I
07
86
I
a5
84
a3
a2
IT-
WEISS t
\
100 50 30
log,(Number)
= 5.583 - 0.503 (AGE) + 0.000611 (AREA);
10
(3) 5
and this equation explained an additional 16.4% (R2 = 0.852, P < 0.01) of the variation in numberat-age above that explained by age alone. The change in area was a significant (P = 0.07) independent variable. A plot of the residuals from the log, (numher)-at-age to year class regression against the change in area showed a positive relation, with the 1990 year class as an influential data point (Fig. 2).
3.3. Spatial r:ariation in catch-curve
analysis
In lakes Guntersville and Weiss, the formation of weak and strong year classes of largemouth bass was generally consistent in lower and upper regions of each reservoirs (Fig. 4). In Lake Guntersville, the presence of aquatic macrophytes enhanced recruitment of the 1991 year class in the upper region (Wrenn et al., 1996). A positive residual for this year class was computed for the catch-curve regression in this region, but a negative value was evident in the unvegetated lower region. Deleting the 1991 year class, a positive correlation (r = 0.70, N = 9, P < 0.05) was computed between corresponding student residual values. Similarly in Weiss Lake, student residuals computed for each year class from catch curves from the lower and upper section of the
3
1 93
92
91
90
89
88
a7
86
YEAR CLASS Fig. 4. Number-at-age of largemouth bass plotted against year classes for largemouth bass collected from lower (circles-solid lines) and upper (squares-dashed lines) regions of lakes Guntersville and Weiss. Corresponding straight lines represent regression lines. The regression equations were weighted proportionally for sample sizes at each age.
reservoir
were highly
correlated
(r = 0.95,
N = 8,
P < 0.01).
4. Discussion For these data, the addition of an independent environmental variable in the catch-curve regression was related to the formation of weak and strong year classes in fish populations. This approach is best suited for longer-lived species. Using this technique for shorter-lived fish will reduce sample size and statistical power. This will decrease the likelihood to reject the null hypothesis and conclude that an environmental term is a significant regressor of abundance-at-age after accounting for the effects of age.
120
M.J. Maceina/ Fisheries Research 32 (1997) 115-121
Because a small number of observations will usually be associated with this type of analysis, the use of more than one environmental term in the multiple regression equation may also confound the analysis. Collinearity among variables can be a problem and by using principal component analysis, a group of related variables can be quantified into one term (Ploskey et al., 1996) which then can be used as an independent variable in the analysis. This technique suggested that year-class strength in these two populations was achieved during the first year of life, but this does not always occur. Density-dependent natural mortality undoubtedly affects populations, particularly at young ages. This would contribute to error using this technique, but the recognition of a significant environmental term that is related to the variation about catch curves can provide useful insights. Compensatory fishing mortality (i.e., high angler exploitation due to the production of a strong year class) could also affect the results, but I did not find this to occur in the two populations that I examined. Harvest does not target a specific cohort of fish, but all fish would be vulnerable to harvest unless restrictions protected certain ages (sizes). In support to this, I identified the formation of strong year classes at younger ages and these cohorts persisted in these exploited populations. In Lake Guntersville, strong largemouth bass year class production was associated with retention times of I8 days or longer. Maceina et al. (1996) found that for a given level of phosphorus, full expression of algal biomass was achieved when retention times in Alabama reservoirs exceeded 30 days. Lower age-0 largemouth bass production may have been associated with lower primary production that caused a reduction in other trophic food web resources. In Weiss Lake, largemouth bass year class strength was positively related to greater areas of the reservoir that was inundated with higher water after the spawn when fish were age-O. Enumeration of daily growth rings showed that largemouth bass spawn from midApril to early June in Weiss Lake (Greene, 1995). Thus, rising water that inundated more area prior to and during largemouth bass spawning was associated with strong cohort production, while a reduction in reservoir area especially in 1990 was related to poor recruitment. Rising water levels inundating more
area is typically associated with greater recruitment of littoral nest spawners such as largemouth bass (Ploskey, 1986). Because the residuals about a catch curve and some environmental term are statistically related, this does not infer a direct cause and effect relation. The environmental term related to recruitment may instead be strongly related to some unmeasured variable that is the true factor affecting reproductive success. Mechanistic approaches would be needed to verify if a variable is directly related to cohort production. I found the error or residuals about catch-curves to be useful indicators of variable recruitment in fish populations. This technique can provide savings in labor and funds as data on juvenile abundances do not need to be collected every year as relative yearclass abundances can be estimated with a single sample. In addition, this method can be used to verify the persistence of strong and weak year classes when other data are available for comparison. Identification of environmental terms related to recruitment that can be manipulated could enhance reproductive success.
Acknowledgements
Funding for this work was provided by the Alabama Department of Conservation and Natural Resources (ADCNR) through Federal Aid in Sport Fish Restoration Project F-40, and the Tennessee Valley Authority (TVA). D. Lowery (TVA) and W. Reeves (ADCNR) ki ndly provided some of the data. Technical insights were provided by S. Miranda and M. van den Avyle. M. Allen, P. Bettoli, V. DiCenzo, J. Slipke, S. Szedlmayer, M. Stimpert, and V. Travnichek provided comments to improve this paper. This is journal paper 8-955141 the Alabama Agricultural Experiment Station.
References Greene, C.J., 1995. Factors Influencing Spawning Periodicity and Growth of Young-of-Year Largemouth Bass and Spotted Bass in Alabama Reservoirs. MS. Thesis. Auburn University, AL, USA.
M.J. Maceina/ Fisheries Research 32 (1997) 115-121 Guy, C.S., Willis, D.M., 1995. Population characteristics of black crappie in South Dakota waters: a case for ecosystem-specific management. No. Am. J. Fish. Manage. 15, 754-765. Hoyer, M.V.. Shireman, J.V., Maceina, M.J., 1985. Use of otoliths to determine age and growth of largemouth bass in Florida. Trans. Am. Fish. Sot. 114, 307-309. Maceina, M.J., Wrenn, W.B., Lowery, D.R., 1995. Estimating harvestable largemouth bass abundance in a reservoir using an electrofishing catch-depletion technique. No. Am. J. Fish. Manage. 15, 103-109. Maceina, M.J., Bayne, D.R., Hendricks, A.S., Reeves, W.C., Black, W.P., DiCenzo, V.J., 1996. Compatibility between water clarity and black bass and crappie fisheries in Alabama. Multidimensional approaches to reservoir fisheries management. Am. Fish. Sot. Spec. Publ. 16, 296-305. Montgomery, D.C., Peck, E.A., 1982. Introduction to Linear Regression Analysis. Wiley, New York. Ploskey,
G.R., 1986. Effects of water-level
changes
on reservoir
121
ecosystems. In: Hall, G.E., van den Avyle, M.J. (Eds.), Reservoir Fisheries Management: Strategies for the 80’s. South. Div. Am. Fish. Sot., Bethesda, MD, USA, pp. 86-97. Ploskey, G.R., Nestler, J.M., Biven, W.M., 1996. Predicting black bass reproductive success from reservoir hydrology. Multidimensional approaches to reservoir fisheries management. Am. Fish. Sot. Spec. Publ. 16, 422-444. Ricker, W.E., 1975. Computation and interpretation of biological statistics of fish populations. Fish. Res. Bd. Canada Bull. 191. Rulifson, B.L., Manooch, C.S. III, 1990. Recruitment of juvenile striped bass in the Roanoke River, North Carolina, as related to reservoir discharge. No. Am. J. Fish. Manage 10, 397-407. Wrenn, W.B., Lowery, D.R., Maceina, M.J., Reeves, W.C., 1996. Largemouth bass and aquatic plant abundance in Guntersville Reservoir, Alabama. Multidimensional approaches to reservoir fisheries management. Am. Fish. Sot. Spec. Publ. 16, 382393.
Fisherjes Research 32 (1997) 115-121
Simple application of using residuals from catch-curve regressions to assess year-class strength in fish M.J. Maceina Department of Fisheries and Allied Aquacultures,
*
Auburn Universin’, Auburn, AL 36849, USA
Accepted 26 May I997
Abstract Residuals associated with catch-curve regressions can represent variable recruitment in fish populations. Catch curves are used to estimate steady-state mortality and assume relatively constant recruitment, but this assumption is rarely met. I documented the presence of abundant year classes of largemouth bass (Micropterus saltnoides), from earlier sampling and these dominant year classes persisted over time in two reservoirs. I expanded simple linear catch-curve regressions that used age (in years) as an independent regressor to multiple regression models each of which incorporated an additional independent environmental variable (ENVIR) that was measured when fish were age 0. The age term in the regression was proportionally weighted to the sample size at each age which deflated the influence of older and rarer fish in the analysis. This generalized regression equation: log, (NUMBER) = b,-b, (AGE) + b, (ENVIR); explained variable abundance-at-age (NUMBER) and the environmental term was related to the formation of weak and strong year classes after accounting for the effects of age. Typically, age will explain the majority (r* 2 0.5) of the variation in abundance-at-age. For two largemouth bass populations, environmental hydraulic variables were significant (P < 0.10) terms in this equation and explained an additional 12 and 16% of the variation in number after accounting for the variation explained by age. For data collected in one population 2 yrs after the initial analysis, the same strong and weak year classes persisted, residuals from these catch curves were correlated (r = 0.86, P < 0.05, N = 6), and the influence of hydrology on year class formation was duplicated. This approach can provide savings in labor and funds as abundance of young fish or recruitment indices do not have to be measured each year. 0 1997 Elsevier Science B.V. Keywords:
Age; Catch-curve;
Multiple regression;
Residuals
1. Introduction Determination tive success
of factors
and recruitment
the understanding,
assessment,
that influence
reproduc-
of fish is paramount and management
’ Corresponding author. Tel.: + l-334-844-93 844-9208; e-mail: [email protected]
any population.
Estimates
for many
usually
species
of year-class involves
enumer-
ation
of juveniles
to
some
instances,
of
such as for striped bass (Murane suxitulis) from the Roanoke River, NC (Rulifson and Manooch, 19901, or annual density and biomass of young fish was determined over time (Ploskey et al., 1996). However, collections need to
19; fax: + l-334-
young
0165.7836/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO165-7836(97)00051-9
fish were
or young
abundance
the direct
long-term developed
adults
via sampling.
In
indices
of abundance
of
116
M.J. Maceina/ Fisheries Research 32 (1997) 115-121
be taken every year and the compilation of a continuous long-term data base is costly and cannot always be accomplished. Fishery biologists estimate total annual mortality using catch-curve regressions (Ricker, 1975). A random sample of fish is collected from a population, aged, and then the natural log of the number of fish at each age (dependent variable) is regressed against age or year class (independent variable) for the descending limb of the curve. The slope of the regression is the instantaneous annual mortality rate (Z>, and the estimate of survival (S) is equal to emZ. An assumption of this analysis is that relatively constant recruitment to the population occurs each year. Guy and Willis (1995) used catch curves to identify missing year classes and developed a qualitative recruitment variability index based on the frequency of missing year classes to describe stability in annual cohort production. In this paper, I built upon this concept by expanding simple linear catch-curve regression to a multiple regression by including an environmental variable. This term explained some of the additional error (residuals) in the simple catchcurve regression. I present examples from two populations of largemouth bass ( Microprerus su2moides), and examined the relations between environmental or reservoir hydraulics and the residuals (regression error) associated with catch-curve regressions. Computation of the instantaneous mortality rate was not of interest. Positive and negative residuals associated with catch-curve regressions represented strong and weak year classes in these populations. I verified this method by documenting the persistence of strong year classes in these exploited populations and was able to duplicate the results in one population for data collected 2 yrs later. I also determined if spatial differences in catch-curve analyses were present in both populations to assess the potential of sampling location bias.
2. Methods 2. I. Fish collection In March-April 1993, 1007 largemouth bass were collected with electrofishing from Lake Guntersville,
a 28,500-ha impoundment of the Tennessee River, AL with a catch-depletion technique in coves to determine abundance (Maceina et al., 1995). Three downstream and three upstream coves were sampled and the minimum distance between downstream and upstream sites was 35 km. In March-April 1995, 727 largemouth bass were collected with electrofishing from 12 lower and 13 upper stations in Weiss Lake, a 11,200-ha impoundment of the Coosa River, AL. Otoliths were removed from a sample of 20 fish from successive 25-mm total length (TL) size groups, although this sample size was not achieved for all size groups in Lake Guntersville. In Weiss Lake, all fish greater than 400 mm TL were sacrificed for aging. A total of 190 and 313 fish were aged from Lakes Guntersville and Weiss, respectively. Otolith preparation and examination followed Hoyer et al. (1985) and age-length keys estimated the age-structure for the entire sample. In Lakes Guntersville and Weiss, no minimum size limits were in effect for largemouth bass and I assumed that age-2 and older fish were vulnerable to exploitation. At age 2, these fish averaged 26 and 28 cm in Lakes Guntersville and Weiss, respectively. For each population, catch-curve analysis (Ricker, 1975) was computed by regressing the loge of abundance-at-age against age for largemouth bass 2 to 9-11 yrs old. The age term in the regression was proportionally weighted to the sample size at each age (log, values were used) which deflated the influence of older and rarer fish in the analysis (Montgomery and Peck, 1982). To verify the use of residuals from catch-curve regressions to quantify year class strength, I examined the persistence of strong year classes in these populations from previous sampling. Possibly, strong year classes could suffer greater density-dependent mortality from natural causes or compensatory mortality from angler exploitation. In 1990, the Alabama Department of Conservation and Natural Resources (ADCNR) collected 106 and 111 largemouth bass from Lakes Guntersville and Weiss and aged fish using otoliths. Percent composition by age in 1990 was compared to residuals from catch-curve regressions computed for Lakes Guntersville and Weiss for data collected in 1993 and 1995. In Lake Guntersville, I examined the influence of retention time (reservoir volume/discharge) during
M.J. Maceina/ Fisheries Research 32 (1997) 115-121
different time periods on the error or residuals associated with the catch-curve regressions. A multiple regression equation was computed that included both age (weighted for sample size) and retention time as independent variables. Similar procedures were used in Weiss Lake, and I compared the production of weak and strong year classes of largemouth bass to retention time, water level fluctuations, and changes in reservoir area during different time periods. I attempted to duplicate the results obtained from Lake Guntersville for data collected in 1993 with data collected 2 yrs later. In spring 1995, the Tennessee Valley Authority (TVA) and the ADCNR collected 604 largemouth bass that ranged in age from 2 to 9 yrs old as part of their reservoir monitoring program. From these catch-curve regressions, ‘student’ residuals (residual/standard error of the residuals) were computed and compared with correlation analysis to determine if detection of strong and weak year classes could be repeated. ‘Student’ residuals display a t distribution, where for example, about 95% of ‘student’ residuals will fall between - 1.96 and + 1.96 regardless of sample size or the fit ( between the dependent and independent variable(s). Thus, comparison of individual data points can be made between regression equations. Catch-curve regressions were derived for fish collected from the lower and upper sections of each reservoir. Corresponding student residuals for each year-class were computed and compared using correlation analysis to determine if weak and strong year classes existed in each reservoir section.
r*>
3. Results 3.1. Catch-curue
analysis and oerification
of strong
and weak year classes
Inspection of catch-curve plots of loge number-atage against respective year classes showed variation about the regression line and suggested that annual recruitment was not homogenous in these populations (Fig. I>. In Lake Guntersville, strong largemouth bass year classes were evident in 1985, 1986, 1988, and 1990 while weak year-class production seemed apparent in 1982, 1983, 1987, 1989, and
500.
’
117
’
1
’
’
1
’
’
’
‘-
GUNTERSVILLE
0
\
IOO50
\@ \
l
l
.’
1.
105 -
‘*, l
1 -
tY ; E
2 = -0.481 12= 0.74 P < 0.01
o-1 91 500
100
I 0
I, 90
/ 88
a9 /
/
I a7
I, a6
I
IJ a4
a5
I
I
a3 I
a2 I
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2 = -0.574 ? = 0.69 P < 0.05
0 \@
0
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4
\ \O \
I
I
/
I
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,
I
93
92
91
90
a9
88
a7
a6
YEAR CLASS
./
Fig. 1. Catch-curves and corresponding regressions (dashed lines) for largemouth bass collected from lakes Guntersville and Weiss. 2 is the instantaneous mortality rate. The regression equations were weighted proportionally for sample sizes at each age.
1991. In Weiss Lake, strong largemouth bass year classes were evident in 1986, 1987, and 1993, while weaker year classes were produced in 1989, 1990, and 1992. Sampling prior to the computation of catch-curves suggested the presence of strong and weak year classes of largemouth bass in both lakes Guntersville and Weiss. In Lake Guntersville, age 2 and older largemouth bass comprised six year classes that were collected in spring 1990. Of these fish, the 1988 cohort was the predominant year class and comprised 50% of the catch. In 1993, this year class was five yrs old and still appeared as a strong year class in the catch curve plot (Fig. 1). In Weiss Lake, age 2 and older largemouth bass represented nine year
M.J. Maceina/Fisheries
118
classes that were collected in spring 1990. Of these fish, the 1987 year class was the dominant year class and comprised 52% of all fish collected. From inspection of the catch-curve plot in 1995, this cohort of 8-yr-old fish still appeared as a strong year class 5 yrs later. Exploitation and natural mortality undoubtedly reduced the abundance of largemouth bass, but strong year classes still persisted in both populations.
Research 32 (1997) 115-121
“”j-i--GE \ [r.
loo-
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i.% f
\ 50.
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3.2. Hydrological variables related to variation in catch-curve regressions
For largemouth bass from Lake Guntersville, residuals from the catch-curve regression were plotted against the mean retention time from April to July and a positive relation was evident (Fig. 2). The relation appeared curvilinear, so log 10 transformed values of April to July retention time (RET) were
I
1.5 :
0.5 1.0
Z 2
0.0
$
-0.5
2
-1 .o
I
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I
I
I
!
I
93
92
91
90
\-
I
I
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/
a9
aa
a7
a6
YEAR CLASS Fig. 3. Catch-curve for largemouth bass data collected in spring 1995 from Lake Guntersville. The regression equations were weighted proportionally for sample sizes at each age.
log, (Number) = 3.987 - 0.528 (AGE)
I
+ 2.027(log,, RET).
84 ---------91 90 a7 a2
88861
30
40
RETENTION (days)
g2
89
I go9
-2000
h l
entered into the catch-curve regression (Fig. 1) to produce a multiple regression:
I
a5
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-1.5
\
-0.410 ? = 0.61 lo - P < 0.05 z =
I
I
I
-1000
0
1000
i 2000
CHANGE IN AREA (ha) FROM MARCH TO JUNE Fig. 2. Residual values derived from catch-curve regression of log, number versus age (from Fig. 1) plotted against April to July retention time for largemouth bass collected from Lake Guntersville (top). The residuals of the catch-curve regression of loge number versus age (from Fig. 1) plotted against the change in area from 1 March to 30 June from Weiss Lake (bottom). Numbers represent year classes.
(1)
This equation explained an additional 12.5% of the variation in number-at-age (R* = 0.869) and retention time was a significant (P < 0.05) term in the equation after accounting for the effects of age. Thus, stronger largemouth bass year class production in 1985, 1986, 1988, and 1990 was associated with retention times of about 18 days or longer, while the weak year classes produced in 1987, 1989, and 1991, were typically related to retention times less than 18 days (Fig. 2). A similar pattern of weak and strong year classes was evident in Lake Guntersville in 1995 compared to data collected in 1993 (Fig. 3). Student residuals for six common year classes (1986 to 1991) were correlated (r = 0.86, P < 0.05) which indicated the detection of strong and weak year classes was repeated even though two years had elapsed between sampling periods. Eq. (1) was recomputed using 1995 data: log, (Number) = 2.562 - 0.548 (AGE) + 3.094( log 1oRET) .
(2) The equation (P < 0.01) explained 85.2% of the variation in number-at-age and both terms were sig-
h4.J. Maceina / Fisheries Research 32 (1997) 115-121
nificant (P < 0.05) regressors in the model. Retention explained an additional 24.4% of the variation in number-at-age after accounting for the effects of age. Analysis of covariance indicated the regression slope coefficients for both age and retention did not differ (P > 0.10) between 1993 and 1995. The same procedures were used to examine potential factors related to variation in the catch curve for largemouth bass in Weiss Lake. I found that the change in reservoir area between 1 March and 30 June from 1986 to 1993 was associated with the formation of strong and weak cohorts of largemouth bass. Reservoir area changes during this four-month period ranged from a decline of 1708 ha in 1990 to an increase of 1542 ha in 1993. Adding the change in reservoir area (AREA) to the catch-curve regression in Fig. 1 for Weiss Lake yielded:
119
,
I
,
/
1
I
r
I
GUNTERSVILLE
g
0
z f
A
91
90
/
300
89 I
88 I
07
86
I
a5
84
a3
a2
IT-
WEISS t
\
100 50 30
log,(Number)
= 5.583 - 0.503 (AGE) + 0.000611 (AREA);
10
(3) 5
and this equation explained an additional 16.4% (R2 = 0.852, P < 0.01) of the variation in numberat-age above that explained by age alone. The change in area was a significant (P = 0.07) independent variable. A plot of the residuals from the log, (numher)-at-age to year class regression against the change in area showed a positive relation, with the 1990 year class as an influential data point (Fig. 2).
3.3. Spatial r:ariation in catch-curve
analysis
In lakes Guntersville and Weiss, the formation of weak and strong year classes of largemouth bass was generally consistent in lower and upper regions of each reservoirs (Fig. 4). In Lake Guntersville, the presence of aquatic macrophytes enhanced recruitment of the 1991 year class in the upper region (Wrenn et al., 1996). A positive residual for this year class was computed for the catch-curve regression in this region, but a negative value was evident in the unvegetated lower region. Deleting the 1991 year class, a positive correlation (r = 0.70, N = 9, P < 0.05) was computed between corresponding student residual values. Similarly in Weiss Lake, student residuals computed for each year class from catch curves from the lower and upper section of the
3
1 93
92
91
90
89
88
a7
86
YEAR CLASS Fig. 4. Number-at-age of largemouth bass plotted against year classes for largemouth bass collected from lower (circles-solid lines) and upper (squares-dashed lines) regions of lakes Guntersville and Weiss. Corresponding straight lines represent regression lines. The regression equations were weighted proportionally for sample sizes at each age.
reservoir
were highly
correlated
(r = 0.95,
N = 8,
P < 0.01).
4. Discussion For these data, the addition of an independent environmental variable in the catch-curve regression was related to the formation of weak and strong year classes in fish populations. This approach is best suited for longer-lived species. Using this technique for shorter-lived fish will reduce sample size and statistical power. This will decrease the likelihood to reject the null hypothesis and conclude that an environmental term is a significant regressor of abundance-at-age after accounting for the effects of age.
120
M.J. Maceina/ Fisheries Research 32 (1997) 115-121
Because a small number of observations will usually be associated with this type of analysis, the use of more than one environmental term in the multiple regression equation may also confound the analysis. Collinearity among variables can be a problem and by using principal component analysis, a group of related variables can be quantified into one term (Ploskey et al., 1996) which then can be used as an independent variable in the analysis. This technique suggested that year-class strength in these two populations was achieved during the first year of life, but this does not always occur. Density-dependent natural mortality undoubtedly affects populations, particularly at young ages. This would contribute to error using this technique, but the recognition of a significant environmental term that is related to the variation about catch curves can provide useful insights. Compensatory fishing mortality (i.e., high angler exploitation due to the production of a strong year class) could also affect the results, but I did not find this to occur in the two populations that I examined. Harvest does not target a specific cohort of fish, but all fish would be vulnerable to harvest unless restrictions protected certain ages (sizes). In support to this, I identified the formation of strong year classes at younger ages and these cohorts persisted in these exploited populations. In Lake Guntersville, strong largemouth bass year class production was associated with retention times of I8 days or longer. Maceina et al. (1996) found that for a given level of phosphorus, full expression of algal biomass was achieved when retention times in Alabama reservoirs exceeded 30 days. Lower age-0 largemouth bass production may have been associated with lower primary production that caused a reduction in other trophic food web resources. In Weiss Lake, largemouth bass year class strength was positively related to greater areas of the reservoir that was inundated with higher water after the spawn when fish were age-O. Enumeration of daily growth rings showed that largemouth bass spawn from midApril to early June in Weiss Lake (Greene, 1995). Thus, rising water that inundated more area prior to and during largemouth bass spawning was associated with strong cohort production, while a reduction in reservoir area especially in 1990 was related to poor recruitment. Rising water levels inundating more
area is typically associated with greater recruitment of littoral nest spawners such as largemouth bass (Ploskey, 1986). Because the residuals about a catch curve and some environmental term are statistically related, this does not infer a direct cause and effect relation. The environmental term related to recruitment may instead be strongly related to some unmeasured variable that is the true factor affecting reproductive success. Mechanistic approaches would be needed to verify if a variable is directly related to cohort production. I found the error or residuals about catch-curves to be useful indicators of variable recruitment in fish populations. This technique can provide savings in labor and funds as data on juvenile abundances do not need to be collected every year as relative yearclass abundances can be estimated with a single sample. In addition, this method can be used to verify the persistence of strong and weak year classes when other data are available for comparison. Identification of environmental terms related to recruitment that can be manipulated could enhance reproductive success.
Acknowledgements
Funding for this work was provided by the Alabama Department of Conservation and Natural Resources (ADCNR) through Federal Aid in Sport Fish Restoration Project F-40, and the Tennessee Valley Authority (TVA). D. Lowery (TVA) and W. Reeves (ADCNR) ki ndly provided some of the data. Technical insights were provided by S. Miranda and M. van den Avyle. M. Allen, P. Bettoli, V. DiCenzo, J. Slipke, S. Szedlmayer, M. Stimpert, and V. Travnichek provided comments to improve this paper. This is journal paper 8-955141 the Alabama Agricultural Experiment Station.
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M.J. Maceina/ Fisheries Research 32 (1997) 115-121 Guy, C.S., Willis, D.M., 1995. Population characteristics of black crappie in South Dakota waters: a case for ecosystem-specific management. No. Am. J. Fish. Manage. 15, 754-765. Hoyer, M.V.. Shireman, J.V., Maceina, M.J., 1985. Use of otoliths to determine age and growth of largemouth bass in Florida. Trans. Am. Fish. Sot. 114, 307-309. Maceina, M.J., Wrenn, W.B., Lowery, D.R., 1995. Estimating harvestable largemouth bass abundance in a reservoir using an electrofishing catch-depletion technique. No. Am. J. Fish. Manage. 15, 103-109. Maceina, M.J., Bayne, D.R., Hendricks, A.S., Reeves, W.C., Black, W.P., DiCenzo, V.J., 1996. Compatibility between water clarity and black bass and crappie fisheries in Alabama. Multidimensional approaches to reservoir fisheries management. Am. Fish. Sot. Spec. Publ. 16, 296-305. Montgomery, D.C., Peck, E.A., 1982. Introduction to Linear Regression Analysis. Wiley, New York. Ploskey,
G.R., 1986. Effects of water-level
changes
on reservoir
121
ecosystems. In: Hall, G.E., van den Avyle, M.J. (Eds.), Reservoir Fisheries Management: Strategies for the 80’s. South. Div. Am. Fish. Sot., Bethesda, MD, USA, pp. 86-97. Ploskey, G.R., Nestler, J.M., Biven, W.M., 1996. Predicting black bass reproductive success from reservoir hydrology. Multidimensional approaches to reservoir fisheries management. Am. Fish. Sot. Spec. Publ. 16, 422-444. Ricker, W.E., 1975. Computation and interpretation of biological statistics of fish populations. Fish. Res. Bd. Canada Bull. 191. Rulifson, B.L., Manooch, C.S. III, 1990. Recruitment of juvenile striped bass in the Roanoke River, North Carolina, as related to reservoir discharge. No. Am. J. Fish. Manage 10, 397-407. Wrenn, W.B., Lowery, D.R., Maceina, M.J., Reeves, W.C., 1996. Largemouth bass and aquatic plant abundance in Guntersville Reservoir, Alabama. Multidimensional approaches to reservoir fisheries management. Am. Fish. Sot. Spec. Publ. 16, 382393.