North American Journal of Fisheries Management 20:672–682, 2000 q Copyright by the American Fisheries Society 2000
Detecting Fish Population Responses to a Minimum Length Limit: Effects of Variable Recruitment and Duration of Evaluation MICHEAL S. ALLEN*
AND
WILLIAM E. PINE III
Department of Fisheries and Aquatic Sciences, The University of Florida, 7922 Northwest 71st Street, Gainesville, Florida 32653, USA Abstract.—We used a simulation model to evaluate how recruitment variability and evaluation duration would affect fisheries managers’ ability to detect fish population responses to a minimum length limit. Length limits modeled were 254 mm for white crappie Pomoxis annularis and 305, 356, and 457 mm for largemouth bass Micropterus salmoides. Simulations were conducted at recruitment variation (coefficient of variation, CV 5 100 3 SD/mean) of 20–100% for age-1 recruits. We evaluated how population density, population biomass, total catch (fish harvested and released), yield, and proportional stock density (PSD) would differ in response to a single 3-year or 5-year length limit evaluation. For white crappies, simulations suggested that a 254-mm length limit would not provide detectable differences (P . 0.10) in any population parameter if recruitment variability exceeded 90% for either evaluation period. Mean CV in recruits to age 0 or age 1 for empirical white crappie populations was 82% (range 5 55–124, N 5 14). Simulations revealed that largemouth bass populations would not exhibit detectable differences unless recruitment variability was 40% or less for a 305-mm length limit and 65% or less for a 356-mm length limit. Values of CV in recruits to age 0 or age 1 for largemouth bass populations averaged 66% (range 5 11–189, N 5 13). A 457-mm length limit for largemouth bass provided detectable differences in total biomass and PSD up to recruitment variabilities of 100%. Detectable differences were more likely under 5-year evaluations than 3-year evaluations. Proportional stock density was the variable most likely to change in response to the size limit for both white crappies and largemouth bass. However, at recruitment variabilities greater than 90%, detectable differences did not occur in 3-year or 5-year evaluations, unless the size limit was 457 mm for largemouth bass. Fishery managers should consider effects of variable recruitment and duration of evaluation period when evaluating the success of a minimum length limit.
Fishery managers frequently use length limits to modify recreational fisheries. The goals of length limits are to lower fishing mortality, increase the number of large fish in the population, and improve angler catch rates relative to prelength limit conditions (Noble and Jones 1993). Thus, the expectation for length limits is that a fish population response will be evident after implementation of the regulation. However, fish population responses may not be evident after the regulation is initiated. Wilde (1997) reviewed length-limit evaluation studies for largemouth bass Micropterus salmoides and found that length limits often did not significantly alter fish abundance, angler catch rates, harvest, or population size structure. Factors contributing to not observing length limit effects included short length-limit evaluation periods and possible effects of variable recruitment and growth rates. More than 50% of the length limits evaluated were completed with only 2 years of preregulation and no more than 2 years of postregulation data (Wilde
1997). Wilde (1997) concluded that, to assess such outcomes, evaluation periods after implementation of length limits may need to exceed 3 years. However, the number of years required for largemouth bass populations to respond to a length limit were unknown (Wilde 1997). Except for empirical studies (e.g., Redmond 1974; Van Horn et al. 1984; Novinger 1986; Terre and Zerr 1994; Maceina et al. 1998), factors influencing fishery managers’ ability to detect fish population responses to length limits have not been evaluated. Recognizing a need to know how factors such as recruitment variability and evaluation period could affect detection of a fishery response to length limits, we used a simulation model to investigate those responses. We used examples for populations of white crappie Pomoxis annularis and largemouth bass because both species are frequently managed with minimum length limits (Colvin 1991; Webb and Ott 1991; Wilde 1997; Maceina et al. 1998). Methods
* Corresponding author:
[email protected] Received September 20, 1999; accepted February 11, 2000
We used computer simulation to estimate the predicted fishery response (e.g., change in fish bio672
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mass, total catch) after a length limit was initiated; we then introduced random recruitment fluctuations into the population and evaluated how it would affect fishery managers’ ability to detect the predicted population response to the length limit. The model and overall approach were similar to methods described by Allen (1997), but the model used was written for Statistical Analysis Systems (SAS) by M. Costello, Ohio Department of Natural Resources. The age-structured population model was represented by P t11 5
O [P 2 P (u 1 v )] 1 r ; i
i
i
i
(1)
Pt11 5 number of individuals in the population at the end of one year (t), Pi 5 number of fish at each age i at the beginning of year (t), ui 5 age-specific annual exploitation rate (percent; Ricker 1975), vi 5 age-specific annual natural mortality rate (percent; Ricker 1975), and r 5 number of recruits to age 1 each year. The number of fish at each age were determined by u , v , and r (specified below) from equation (1). Fish growth in the model was expressed by an array of length-at-age means, and age-specific rates of u and v were applied. Fish lengths were transformed to fish weights by means of weight– length equations. Numbers of fish and total weights of fish at each age were then summed across ages to obtain total population biomass and density each year. The model simulated length limits by protecting fish from u if they were below the minimum length limit. Growth and mortality rates for white crappie and largemouth bass populations were obtained from the literature. Mean white crappie total length (TL; mm) at age (TL 5 353[1 2 e20.374(age20.197)]), exploitation (u 5 40%), and natural mortality (v 5 30%) from Allen and Miranda (1995) were used for all white crappie simulations. Mean white crappie weights (g) for each age were derived from mean TL by means of the weight–length equation of Neumann and Murphy (1991). We used largemouth bass mean lengths at age (mm) from Beamesderfer and North (1995) for ‘‘high productivity’’ populations (TL 5 643[1 2 e20.260(age10.024)]), which was the 75th percentile of their length-at-age estimates. We used the 75th percentile because studies reviewed by Beamesderfer and North (1995) were concentrated at northern latitudes, whereas largemouth bass fisheries are concentrated at more southern latitudes
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(U.S. Fish and Wildlife Service 1996). We believed mean length at age from Beamesderfer and North (1995) was low, relative to most largemouth bass fisheries where size limits would be recommended, and used the 75th percentile for all simulations. Using the weight–length equation of Wege and Anderson (1978), we estimated mean largemouth bass weight (g) from mean TL for each age. Exploitation and natural mortality rates were obtained from Allen et al. (1998). However, we excluded estimates of u and v collected before 1980 because exploitation rates of largemouth bass may have declined compared with historical rates due to increases in voluntary catch and release (Quinn 1996). A mean u of 31% and v of 33% were used in all largemouth bass simulations. We modeled one minimum length limit for white crappie and three for largemouth bass. A 254-mm TL limit was used for white crappie, and we assumed that fish less than 200 mm were not harvested by anglers when no length limit existed. Length limits modeled for largemouth bass were 305, 356, and 457 mm, and we assumed fish less than 254 mm TL were not harvested by anglers if no length limit existed. Before modeling variable recruitment, we estimated population parameters under no length limit and under constant recruitment for each length limit. The constant recruitment models provided the predicted mean population response to the length limit. A 7-year (i.e., the number of ageclasses) period of instability in population density and age structure occurred when length-limit simulations began. This instability resulted from the stable age distribution adjusting to changes in mortality rates from the length limit. After this period of instability, the populations formed a new, stationary age distribution. Results exclude the 7-year period of instability. Population parameters compared between the no length-limit and length-limit models included total population density (number of fish), total population biomass (kg), total catch (number of fish harvested plus those released), yield (kg), and proportional stock density (PSD 5 100 3 number of fish $ quality size/number of fish $ stock size; Anderson and Neumann 1996). Stock and quality sizes were, respectively, 130 and 200 mm TL for white crappie and 200 and 300 mm TL for largemouth bass (Anderson and Neumann 1996). Constant recruitment models assumed 2,000 fish/ year reached age 1 for both species. We used a random number generator described by Allen (1997) to simulate variation in recruit-
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ment. We modeled population recruitment variabilities (CV 5 100 3 SD/mean) in recruits to age 1 of 20, 40, 60, 70, 80, 90, and 100%. Each standard deviation simulated recruitment variability potentially exhibited by wild populations of white crappie or largemouth bass. Recruitment averaged 2,000 fish/year and was normally distributed among years for all simulations. We modeled length-limit evaluation periods of 3 and 5 years. From each simulated population of variable recruitment under a length limit, we obtained independent (i.e., each group did not contain the same year-class) groups of consecutive years (either groups of 3 or 5 consecutive years). Each selected group was analogous to sampling a population for 3 or 5 consecutive years with a length limit in place and estimating the population parameters (e.g., PSD, total fish density, etc.) each year. We used the mean population parameter across each 3- or 5-year group as the response for the population parameter. For example, the mean PSD across a group of 5 years was used as the response in PSD to a single 5-year length-limit evaluation. We obtained groups of years (3 and 5 years) until the mean population parameter across all groups differed by less than 10% from the predicted population parameter (e.g., PSD, total population density) under the length limit and constant recruitment. The standard deviation of each mean value (e.g., mean PSD, mean population density) was then assumed to be known and was attributed to the specific variation in recruitment and duration of evaluation for each simulated population. We calculated the probability of obtaining one group of consecutive years (3 or 5 years) in which the mean population parameter would differ from the no length-limit model (i.e., effects of the length limit would be detected). To estimate this probability, we used the standard normal distribution where: Z q,critical 5 x¯no length limit, q 2 x¯ q length
limit /SD q
;
(2)
Zq, critical 5 the critical value for rejection of the null hypothesis (Ho: no difference between mean q with no length limit and the mean q with a length limit), q 5 population parameter (parameters included total population density [number of fish], total population biomass [kg], total catch [number of fish harvested and released], yield [kg], and proportional stock density),
TABLE 1.—Model predictions of population parameters for white crappie using no length limit (fish harvestable at 200 mm total length) and under length limit of 254 mm total length with constant recruitment.
Population parameter (q)
No length limit
254-mm length limit (% difference)
Total density (number of fish) Total biomass (kg) Yield (kg) Total catch Proportional stock density (%)
2,316 199 77 343 47
2,586 273 75 470 56
(112%) (137%) (23%) (137%) (119%)
x¯no length limit, q 5 mean population parameter q for no length limit and constant recruitment, x¯ q length limit 5 population parameter q under the length limit and constant recruitment, SDq 5 standard deviation of the mean in population parameter q due to a specific variation in recruitment and duration of evaluation with a length limit in place. The observed change of each population parameter (e.g., total density, PSD) after implementation of the length limit under constant recruitment was the assumed difference between the no length-limit and length-limit models. Equation (2) was repeated for 3-year and 5-year evaluation periods. We compiled crappie and largemouth bass recruitment data from published and unpublished studies. Recruitment variability was expressed as the CV in mean density or catch per effort of age0 or age-1 fish for studies containing at least 5 consecutive years of data. Age-0 fish collected during late summer or fall were used if catch rates of age-1 fish were unavailable. We assessed simulation results relative to variation from empirical data for white crappie and largemouth bass populations. Results The constant recruitment models resulted in changes from 23% to 173% in population parameters after implementation of the various length limits. White crappie models showed that yield would exhibit the least change in response to the 254-mm length limit (23%), and total biomass and total catch showed the most change (both 137%; Table 1). Similarly, the largemouth bass length limits showed the most change with total catch and total biomass and the least with yield (Table 2). Except for yield, population parameters (q) increased as length limits increased from conditions found at no length limit (Table 2). Yield increased
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TABLE 2.—Model predictions of population parameters for largemouth bass under constant recruitment and no length limit (fish harvestable at 254 mm total length) and under various length limits with constant recruitment. Length limit of (% difference)
Population parameter (q)
No length limit
305 mm
Total density (number of fish) Total biomass (kg) Yield (kg) Total catch Proportional stock density (%)
2,583 1,200 335 369 53
2,717 (15%) 1,353 (113%) 350 (14%) 415 (112%) 57 (17%)
from no length limit when a 305-mm or 356-mm length limit was enacted but yield decreased at a 457-mm length limit (Table 2) because delaying harvest until fish reached 457 mm resulted in few (due to natural mortality), albeit large, fish being available for harvest. Required number of simulated evaluations (i.e., the number of 3- or 5-year length-limit evaluations) to approximate the true mean population parameter (q) for each length limit (under constant recruitment) increased with the CV in recruits to age 1. For example, required sample size for white crappies ranged from 279 5-year evaluations at a CV in recruits of 20% to 1,198 3-year evaluations for a CV in recruits to age 1 of 100%. Required samples showed the same trend for largemouth bass, ranging from 200 (20% CV in recruits, 5year evaluation, 457-mm length limit) to 1,600 (100% CV in recruits, 3-year evaluation, 356-mm length limit). Standard deviations in population parameters increased with CV in recruitment to age 1 for both white crappies and largemouth bass (Table 3). Standard deviations for mean q were lowest for PSD and highest for total density for all length limits (Table 3). Variation in q (e.g., total density, PSD) increased about 5–10 times with CV in recruits from 20% to 100%, depending on q. Standard deviations for three-year evaluations exceeded 5-year evaluations for a given recruitment variability in all cases. Thus, the model predicted a positive relation between recruitment variability and SD of population parameters. High recruitment variability precluded detecting predicted differences between no length-limit and the 254-mm length-limit models for white crappie. Detecting the difference in total density, total biomass, PSD, and total catch was unlikely (P . 0.1) if recruitment variability exceeded 90% (Figure 1). Five-year evaluations were more likely to produce significant differences than 3-year evaluations, particularly for PSD (Figure 1). Yield did not differ
356 mm 2,872 1,531 356 454 60
(111%) (128%) (16%) (123%) (113%)
457 mm 3,183 2,076 310 548 66
(123%) (173%) (28%) (148%) (124%)
significantly (all P . 0.2) between no length-limit and 254-mm length-limit models at any recruitment CV but only differed by 3% from the constant recruitment models (Table 1). Significant differences in PSD were more likely to occur than differences in total density, total biomass, and total catch (Figure 1). Thus, the model predicted that changes in white crappie length structure would be most likely to change significantly because of the regulation. Nevertheless, if recruitment variability exceeded 60% or 90%, predicted differences would not be detected in a 3-year or 5-year evaluation period, respectively, after implementing the 254-mm length limit. Observed recruitment variability for white crappie populations often exceeded predicted values required to detect differences from the 254-mm length limit. The CV in recruits for age-0 or age1 crappies averaged 82% (range 55–124, N 5 14; Table 4). At an 82% CV in recruits, detectable differences were only found for PSD with a 5-year evaluation period (Figure 1). Thus, data from white crappie populations suggested that a 254mm length limit would not often yield detectable differences, based on model predictions. Detecting significant differences after implementing largemouth bass length limits depended on recruitment variability and the length limit selected. Using a 305-mm length limit, differences were not detectable in any q if the CV in recruits was 40% or greater (Figure 2). Similarly, the 356mm length limit revealed no detectable differences if recruitment variability was about 65% or greater (Figure 3). Differences in PSD were detectable under a 356-mm length limit up to a CV in recruits of about 65% and a 5-year evaluation period (Figure 3); however, all other population parameters were not significantly different from the no lengthlimit model when the CV in recruits exceeded 40– 60% for either evaluation period (Figure 3). Alternatively, a 457-mm length limit provided detectable differences in total biomass and PSD, even
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at 100% recruitment variability (Figure 4). Total catch differed significantly under a 457-mm length limit for 3-year and 5-year evaluation periods if CV in recruits was less than about 70% or 60%, respectively. Similar to the white crappie simulations, PSD for largemouth bass differed more significantly than any other population parameter in response to the length limit. However, differences in PSD were not likely unless recruitment variability was less than 60% or the length limit was at least 457 mm. Changes in yield were not detectable for all largemouth bass length limits at all CV in recruit values (all P . 0.2). Observed recruitment variability for largemouth bass populations often exceeded predicted values required to detect differences, unless the length limit was 457 mm. The CV in recruits for age-0 or age-1 largemouth bass averaged 66% (range 11– 189, N 5 13; Table 4). At a 66% CV in recruits, detectable differences were only found under a 457-mm length limit for PSD and total biomass (Figure 4). The 305-mm and 356-mm length limits did not provide detectable differences at more than 70% recruitment variability. However, largemouth bass populations exhibiting recruitment variability
less than 50% (Table 4) would allow some detectable differences under a 356-mm length limit, particularly for PSD (Figure 3). Discussion Our simulations found that recruitment variability would often preclude significant differences in fish population density, total biomass, total catch, or PSD in 3-year or 5-year length-limit evaluations. The 457-mm length limit for largemouth bass provided the only detectable differences if recruitment variability exceeded 70%, but the mean CV from largemouth bass populations was 66%. Based on observed recruitment variability for largemouth bass, our model showed few significant differences in response to relatively minor length-limit regulations (e.g., 305 mm, 356 mm). A 254-mm length limit is commonly used for managing white crappie fisheries (Webb and Ott 1991; Maceina et al. 1998), but our simulations suggested no difference from this regulation if CV in recruits exceeded about 70–90% (mean from white crappie populations was 82%). Thus, fish population responses to length limits may be masked by variable recruitment, unless recruitment vari-
TABLE 3.—Standard deviations for white crappie and largemouth bass population parameters resulting from various fluctuations in recruitment to age 1. Values for 5-year evaluation (SD5) and 3-year evaluation periods (SD3) are shown. CV (%) in recruits to age 1: Population parameter
40%
20% SD3
SD3
SD5
SD3
Total density Total biomass (kg) Yield (kg) Total catch (number of fish) PSDa (%)
210 22 6.6 40 1.6
White crappie (254-mm length limit) 242 400 455 591 25 41 47 60 7.4 12 13 17 47 75 86 109 2.4 3.4 5.6 5.3
682 68 20 128 8.9
628 64 19 116 6.3
729 73 22 139 9.5
Total density Total biomass (kg) Yield (kg) Total catch (number of fish) PSD (%)
213 98 27 33 1.8
Largemouth bass (305-mm length limit) 249 403 465 590 106 188 202 270 29 50 54 71 38 63 73 91 2.9 3.6 5.6 5.9
669 292 79 106 8.4
648 299 79 101 6.0
740 322 86 117 9.1
Total density Total biomass (kg) Yield (kg) Total catch (number of fish) PSD (%)
210 104 25 34 1.6
Largemouth bass (356-mm length limit) 239 430 484 583 112 207 226 286 28 51 57 70 39 68 79 95 2.5 3.7 5.5 5.3
663 311 78 110 7.8
691 333 81 111 6.1
775 364 91 128 8.7
Total density Total biomass (kg) Yield (kg) Total catch (number of fish) PSD (%)
224 140 23 39 1.7
Largemouth bass (457-mm length limit) 251 412 467 654 151 259 278 405 26 43 48 66 46 73 85 116 2.4 3.2 4.9 4.8
717 434 74 131 7.4
768 479 79 133 4.6
845 513 85 153 8.4
PSD 5 proportional stock density.
SD3
SD5
70%
SD5
a
SD5
60%
FISH POPULATION RESPONSES TO A LENGTH LIMIT
677
ability is below average or the length limit is a major manipulation (e.g., 457 mm for largemouth bass). Our results correspond well with the empirical analyses of Wilde (1997), who found that many length-limit evaluation studies for largemouth bass yielded nonsignificant results. Most studies (50 of 91) evaluated by Wilde (1997) included data for five or fewer years; generally 2 years of pre- and postregulation implementation. Because environmental factors (including variable recruitment) probably play a role in a fishery’s response to a regulation, longer evaluation periods may be necessary to detect responses to the regulation (Wilde 1997). Our results suggest that a 5-year evaluation period may not be long enough to detect a response, if recruitment variability is more than 60–70%. Because regulation evaluations over 5 years require long-term sampling effort, fishery managers should recognize that highly variable recruitment could confound effects of the length limit. Wilde’s (1997) review of length-limit evaluations for largemouth bass found no significant differences in PSD in response to minimum length limits. Our model predicted that PSD was the var-
TABLE 3.—Extended. CV (%) in recruits to age 1: 90%
80% SD5
100%
SD5
SD3
717 72 23 132 6.5
White crappie (254-mm length limit) 820 790 910 898 82 82 92 90 24 24 27 23 154 150 174 163 9.9 7.2 11 7.9
SD3
SD5
SD3
745 333 88 116 6.9
Largemouth bass (305-mm length limit) 849 823 934 892 1,003 364 376 407 404 435 98 99 110 107 117 134 128 148 138 159 10.2 7.3 10.5 7.8 11.6
754 372 90 122 6.4
Largemouth bass (356-mm length limit) 857 831 947 901 1,032 403 403 441 449 485 101 98 111 109 121 140 132 155 147 170 9.7 6.8 10.5 7.1 11.0
809 508 84 143 6.2
Largemouth bass (457-mm length limit) 910 890 983 968 1,090 545 549 593 611 655 92 89 100 100 111 163 159 178 173 196 9.4 6.3 9.8 7.0 10.2
1,010 100 29 188 11.8
FIGURE 1.—Probability of not detecting a change in (from top to bottom panels) total density (number of fish), total biomass (kg), proportional stock density (PSD), and total catch (fish harvested plus those released) in response to a 254-mm length limit for white crappie during a single 3-year (top curve) and 5-year evaluation period (bottom curve). The horizontal line corresponds to a significant (P , 0.10) effect of the length limit. Percentage change due to the length limit with constant recruitment is indicated.
iable most likely to differ in response to the length limit, but observed recruitment variability for largemouth bass would usually mask differences in PSD, unless the length limit was 457-mm. Improved angler catch rates are among the most common objectives for the use of length limits, but infrequent collection of creel data often negates assessment of these factors (Wilde 1997). Dent (1986) recommended that several years of
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TABLE 4.—Species, lake and state, age-group, gear used for collection, number of consecutive years, and coefficient of variation (CV 5 100 3 SD/mean) in abundance of age-0 or age-1 largemouth bass and crappie populations. All data sets are consecutive years of collection, but lakes listed twice indicate one or more years of missing data between groups of consecutive years. Species labeled as crappies indicate that both black crappies P. nigromaculatus and white crappies were collected. Electrofishing and trap-net catch rates were based on catch per effort (e.g., fish/net day, fish/ min); rotenone samples were expressed as fish/ha for each year. Species Crappies Crappies Crappies Crappies Black crappie Black crappie Black crappie White crappie White crappie White crappie White crappie Crappies Crappies Crappies Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass Largemouth bass a
Lake/state Weiss, Alabama Atkins, Arkansas Nimrod, Arkansas Nimrod, Arkansas Orange Lake, Florida Lochloosa, Florida Rodman, Florida Stockton, Missouri Pomme De Terre, Missouri Lake of the Ozarks, Missouri Wappapello, Missouri Okatibbee, Mississippi Okatibbee, Mississippi Ross Barnett, Mississippi Fayette County, Alabama Walker County, Alabama Bibb, Alabama Marion, Alabama Eufaula, Alabama Kissimmee, Florida Lochloosa, Florida Orange Lake, Florida Rodman, Florida Eufaula, Oklahoma Normandy, Tennessee Kerr, Virginia Smith Mountain, Virginia
Agegroup
Gear
1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0
Trap net Rotenone Rotenone Rotenone Rotenone Rotenone Rotenone Trap net Trap net Trap net Trap net Rotenone Rotenone Rotenone Electrofishing Electrofishing Electrofishing Electrofishing Electrofishing Electrofishing Rotenone Rotenone Rotenone Electrofishing Rotenone Electrofishing Electrofishing
Number of years 5 13 7 6 6 6 5 9 10 11 9 13 6 22 6 7 6 5 10 5 6 9 5 10 6 8 8
CV (%)
Source
67 124 74 61 96 89 91 70 84 55 65 119 88 65 71 91 11 28 67 59 189 55 74 74 40 55 45
Allen (1997) Allen and Miranda (1998) Allen and Miranda (1998) Allen and Miranda (1998) Estes and Myers (1996) Estes and Myers (1996) Estes and Myers (1996) Colvin (1991) Colvin (1991) Colvin (1991) Colvin (1991) Allen and Miranda (1998) Allen and Miranda (1998) Allen (1997) J. Haffner a J. Haffner a J. Haffner a J. Haffner a J. Haffner a Moyer et al. (1993) Estes and Myers (1996) Estes and Myers (1996) Estes and Myers (1996) Wright (1991) Sammons et al. (1999) Duval (1991) Duval (1991)
Alabama Department of Conservation, unpublished data.
creel data before the implementation of a regulation would help set target angler catch rates after the implementation of the regulation. For largemouth bass, our model predicted differences in total catch would not occur unless the length limit was at least 356 mm and recruitment variability was less than 40%. For white crappies, our model predicted that differences in angler catch rates (i.e., total catch) would often not be detected in 3-year or 5-year evaluations, unless recruitment variability was below 60%. Other studies have identified recruitment variability as a potential confounding factor for fishery responses (e.g., yield, population length structure, total catch) to a length limit. Terre and Zerr (1994) found increased catch per effort of largemouth bass 356 mm or longer in 23 of 28 lakes and increased fish length structure in 18 of the 28 lakes after the implementation of a 356-mm length limit (contrary to most studies evaluated by Wilde 1997). However, Terre and Zerr (1994) found that changes in fish abundance and size structure were
largely due to recruitment and growth of largemouth bass already present when the regulation was enacted on the lakes. Colvin (1991) reported difficulty, due to variable recruitment, in assessing the success of length limits for white crappie fisheries. Maceina et al. (1998) found increased angler catch rates and yield of crappies in Weiss Reservoir, Alabama after implementation of a 254-mm length limit. However, high recruitment and rapid fish growth after the length limit was enacted probably increased white crappie catch and yield (Maceina et al. 1998). Thus, successive years of strong or stable recruitment would optimize benefits from a length limit. However, our simulations suggested that highly variable recruitment would result in no detectable difference in fishery characteristics from single 3-year or 5-year evaluation of a lengthlimit regulation (similar to empirical observations reviewed by Wilde 1997). We allowed the age distributions from simulated populations to stabilize before predicting effects of the length limits. In field studies the imple-
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FIGURE 2.—Probability of not detecting a change in (from top to bottom panels) total density (number of fish), total biomass (kg), proportional stock density (PSD), and total catch (fish harvested plus those released) in response to a 305-mm length limit for largemouth bass during a single 3-year (top curve) and 5year evaluation period (bottom curve). The horizontal line corresponds to a significant (P , 0.10) effect of the length limit. Percentage change due to the length limit with constant recruitment is indicated.
FIGURE 3.—Probability of not detecting a change in (from top to bottom panels) total density (number of fish), total biomass (kg), proportional stock density (PSD), and total catch (fish harvested plus those released) in response to a 356-mm length limit for largemouth bass during a single 3-year (top curve) and 5year evaluation period (bottom curve). The horizontal line corresponds to a significant (P , 0.10) effect of the length limit. Percentage change due to the length limit with constant recruitment is indicated.
mentation of a length limit may have less effect than the equilibrium conditions we modeled because of incomplete changes in the population agestructure in response to the length limit. However, natural populations would seldom have a stable age distribution either before or after a length limit is enacted. We believe the value of our simulations was to identify trends in the ability to detect fish population responses. By allowing the models to stabilize, we identified expected trends caused by variable recruitment and duration of evaluation.
Our simulations isolated the confounding effects of variable recruitment on population responses to a length limit, but other factors, such as sampling variability, may even further preclude detection of differences in the postregulation period. Estimates of fish density and biomass, catch and harvest rates, and fish population size structure all have associated sampling variability that may make changes in these variables difficult to detect. Estimates of population biomass or density are usually highly variable (Bettoli and Maceina 1996),
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FIGURE 4.—Probability of not detecting a change in (from top to bottom panels) total density (number of fish), total biomass (kg), proportional stock density (PSD), and total catch (fish harvested plus those released) in response to a 457-mm length limit for largemouth bass during a single 3-year (top curve) and 5year evaluation period (bottom curve). The horizontal line corresponds to a significant (P , 0.10) effect of the length limit. Percentage change due to the length limit with constant recruitment is indicated.
and catch-per-effort estimates (an index of population abundance) also typically have high variability or may be strongly biased (Peterman and Bradford 1987; Hubert 1996). Dent (1986) found that sampling variability yielded imprecise PSD estimates for black basses Micropterus spp. Likewise, estimates of angler catch and harvest from creel surveys often exhibit high variability and may not reveal changes in the fishery (Malvestuto 1996). Thus, sampling variability may impede de-
tecting differences attributable to a length limit more than was indicated by this study. Changes in growth or mortality could also affect the fishery response to a length limit. Depressed growth rates following implementation of a length limit would reduce harvest and yield from values predicted under rapid growth (Webb and Ott 1991; Allen and Miranda 1995; Munger and Kraai 1997; Maceina et al. 1998). Our model assumed constant growth after implementation of the length limits, but reduced growth rates due to increased fish density could negate effects of the length limit on factors such as PSD and total catch. Total mortality is usually expected to decline after implementing a length limit, but compensatory mortality could result in no decline in total mortality (Allen et al. 1998). Additionally, our model used fixed rates of natural mortality and exploitation, except for changes in u due to protection of fish from the length limit; however, changes in mortality could change model predictions. Nevertheless, annual recruitment varies by orders of magnitude for many fishes (Houde 1987), whereas growth and mortality of adult fishes typically exhibit less fluctuation (Carline et al. 1984). Carline et al. (1984) found that recruitment variation influenced variation in estimates of PSD more strongly than changes in growth and mortality. Therefore, we believe recruitment variability would often contribute more variation in response to the regulation than changes in growth or mortality. Nevertheless, factors such as sampling variability and changes in growth and mortality will also contribute to uncertainty regarding population responses to a length limit. Our model identified substantial uncertainty due to recruitment fluctuations, but more studies are needed to evaluate the relative effects of sampling variability and other factors on the ability to detect a response to a length limit. Fisheries managers should consider the reliability of field data and monitor recruitment, growth, and mortality in response to the length limit. One limitation of our study is that the results are simulations from a computer model that may not reflect population parameters in wild populations. Similar to field data, model predictions have associated error and may be unreliable for quantitative predictions (Johnson 1995). Rather than quantitative predictions, models are useful for addressing trends and uncertainty in management decisions (Johnson 1995). The model we used identified trends of uncertainty in length-limit evaluations, but we caution that the model predictions
FISH POPULATION RESPONSES TO A LENGTH LIMIT
may not reflect the response of populations. For example, the populations we simulated were generalized from reviews of growth, fishing, and natural mortalities and may not accurately predict the response of specific populations. Nevertheless, the model allowed simulation of length-limit evaluations across a range of recruitment fluctuations, which would be impractical to conduct using replicated field studies. Management Implications Our simulations indicated that variable recruitment could strongly affect the ability of fishery managers to detect effects of a length limit. Variation in recruitment exceeding 60–70% often precluded detectable effects of minimum length limits for evaluation periods of up to 5 years. Wilde (1997) noted that short evaluation periods contributed to the failure to detect largemouth bass population responses to length limits. Depending on recruitment variability, evaluation periods of over 5 years may be necessary to identify a fishery response to the regulation. Alternatively, highly variable recruitment could cause no difference to occur after implementing a minimum length limit, even with evaluation periods greater than 5 years. Fishery managers should consider that small changes in length limits may not show significant population responses even if recruitment variability is relatively low. We found no differences in response to a 305-mm length limit for largemouth bass at a CV in recruits to age 1 of over 40%. Thus, management scenarios requiring relatively minor length limits may not reveal significant differences, whereas comprehensive (e.g., large length ranges of fish protected) regulations should reveal a more detectable fish population response, assuming stable growth and mortality rates. Wilde (1997) called for well-planned, hypothesis-based studies to evaluate length limits. We also suggest that well-planned studies should be used to assess effects of length limits because factors such as variable recruitment could confound evaluation studies. Fishery managers should monitor recruitment fluctuations before and during length-limit evaluation studies. Occurrence of missing year-classes could falsely indicate that detrimental effects resulted from a length limit, whereas strong year-classes could signify only temporary improvements. By monitoring recruitment during the evaluation period, fishery managers may identify the mechanisms for observed outcomes of the regulation. Fishery managers may need to convey the un-
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certainty associated with the success of length limits to anglers. Anglers may believe that length limits will have an immediate effect on fish populations, when in reality a host of factors including variable recruitment and duration of evaluation combine to determine the outcome. By conveying potential sources of variation and confounding effects to the anglers, fishery managers may avoid conflicts when the outcome of a length limit does not match the expected benefits. Acknowledgments We thank M. Costello for use of the SAS version of the model used in this study, and J. Parkes and D. Roux at the University of Florida for computer assistance. G. Wilde provided helpful insights with our analyses. We thank S. Miranda, R. Myers, and G. Wilde for a review of a previous draft of this manuscript. This manuscript is part of the Florida Agricultural Experiment Station Journal Series R07444. References Allen, M. S. 1997. Effects of variable recruitment on catch-curve analysis for crappie populations. North American Journal of Fisheries Management 17: 202–205. Allen, M. S., and L. E. Miranda. 1995. An evaluation of the value of harvest restrictions in managing crappie fisheries. North American Journal of Fisheries Management 15:766–772. Allen, M. S., L. E. Miranda, and R. E. Brock. 1998. Implications of compensatory and additive mortality to the management of selected sportfish populations. Lakes and Reservoirs: Research and Management 3:67–79. Anderson, R. O., and R. M. Neumann. 1996. Length, weight, and associated structural indices. Pages 447–482 in B. R. Murphy and D. W. Willis, editors. Fisheries techniques, 2nd edition. American Fisheries Society, Bethesda, Maryland. Beamesderfer, R. C. P., and J. A. North. 1995. Growth, natural mortality, and predicted response to fishing for largemouth bass and smallmouth bass in North America. North American Journal of Fisheries Management 15:688–704. Bettoli, P. W., and M. J. Maceina. 1996. Sampling with toxicants. Pages 303–333 in B. R. Murphy and D. W. Willis, editors. Fisheries techniques, 2nd edition. American Fisheries Society, Bethesda, Maryland. Carline, R. F., B. L. Johnson, and T. J. Hall. 1984. Estimation and interpretation of proportional stock density for fish populations in Ohio impoundments. North American Journal of Fisheries Management 4:139–154. Colvin, M. A. 1991. Population characteristics and angler harvest of white crappies in four large Missouri reservoirs. North American Journal of Fisheries Management 11:572–584.
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Dent, R. J., Jr. 1986. Methods and parameters used in evaluating bass length limits on Pomme de Terre Lake, Missouri. Pages 65–72 in G. E. Hall and M. J. Van Den Avyle, editors. Reservoir fisheries management: strategies for the 80’s. American Fisheries Society, Southern Division, Reservoir Committee, Bethesda, Maryland. Duval, M. C. 1991. Factors affecting the apparent differential success of a largemouth bass length regulation at two Virginia reservoirs. Pages 291–295 in J. L. Cooper and R. H. Hamre, editors. Warmwater fisheries symposium 1. U.S. Forest Service, Washington, D.C. Estes, J. R., and R. A. Myers. 1996. Fish population and fishery response to habitat change. Florida Game and Fresh Water Fish Commission, Federal Aid in Sportfish Restoration, Project F-55, Completion Report, Tallahassee. Houde, E. D. 1987. Fish early life dynamics and recruitment variability. Pages 17–29 in E. D. Houde, editor. 10th annual larval fish conference. American Fisheries Society, Symposium 2, Bethesda, Maryland. Hubert, W. A. 1996. Passive capture techniques. Pages 157–192 in B. R. Murphy and D. W. Willis, editors. Fisheries techniques, 2nd edition. American Fisheries Society, Bethesda, Maryland. Johnson, B. L. 1995. Applying computer simulations models as learning tools in fishery management. North American Journal of Fisheries Management 15:736–747. Maceina, M. J., O. Ozen, M. S. Allen, and S. M. Smith. 1998. Use of equilibrium yield models to assess different lengths limits for crappie in Weiss Lake, Alabama. North American Journal of Fisheries Management 18:854–863. Malvestuto, S. P. 1996. Sampling the recreational creel. Pages 591–623 in B. R. Murphy and D. W. Willis, editors. Fisheries techniques, 2nd edition. American Fisheries Society, Bethesda, Maryland. Moyer, E. J., and seven coauthors. 1993. Completion report for Kissimmee chain of lakes studies, study II: Lake Kissimmee investigations (1988–1993). Florida Game and Fresh Water Fish Commission, Tallahassee. Munger, C. R., and J. E. Kraai. 1997. Evaluation of length and bag limits for walleyes in Meredith Reservoir, Texas. North American Journal of Fisheries Management 17:438–445. Neumann, R. M., and B. R. Murphy. 1991. Evaluation of the relative weight (Wr) index for assessment of white crappie and black crappie populations. North American Journal of Fisheries Management 11: 543–555. Noble, R. L., and T. W. Jones. 1993. Managing fisheries with regulations. Pages 383–341 in C. C. Kohler and W. A. Hubert, editors. Inland fisheries management in North America. American Fisheries Society, Bethesda, Maryland. Novinger, G. D. 1986. Effects of a 15-inch length limit on largemouth bass and spotted bass fisheries in
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