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Improving the precision of recreational fishing harvest estimates using two-part conditional general linear models
Fisheries Research 110 (2011) 408–414
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Improving the precision of recreational fishing harvest estimates using two-part conditional general linear models Stephen M. Taylor a,∗ , James A.C. Webley a , David G. Mayer b a b
Fisheries Queensland, Department of Employment, Economic Development and Innovation, Primary Industries Building, 80 Ann Street, Brisbane 4001, Australia AgriScience Queensland, Department of Employment, Economic Development and Innovation, Ecosciences Precinct, 41 Boggo Road, Dutton Park, Queensland 4102, Australia
a r t i c l e
i n f o
Article history: Received 25 February 2011 Received in revised form 5 May 2011 Accepted 5 May 2011 Keywords: Survey Precision Right-skewed Gamma distribution Recreational catch Bus route
a b s t r a c t As recreational fishing continues to expand, the need to obtain precise harvest estimates is becoming increasingly important for the sustainable management of fisheries. Recreational fishing data are frequently zero-inflated which can present problems for commonly used analyses that assume a normal distribution. In this study, we analysed zero-inflated recreational fishing data collected from a bus-route access point survey in southeastern Queensland, Australia. Using the Time Interval Count method, we compared estimates of the proportion of boats fishing, fishing effort, harvest per unit effort (HPUE) and harvest using sample mean values and mean values derived from a two-part conditional general linear model (CGLM). The CGLM gave more precise estimates of the proportion of boats fishing, fishing effort and HPUE, which formed the basis of the harvest calculations. Differences in harvest estimates using the two methods ranged from 3 to 28% for the five recreational species examined. Relative standard errors for harvest estimated by the CGLM were 65–84% smaller. The results suggest that CGLMs may deliver more precise outputs in other types of recreational fishing surveys that derive effort and catch from zero-inflated data. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Recreational fishing is an important leisure pursuit for millions of people (Arlinghaus and Cooke, 2005). Recreational fishing also has the potential to reduce the abundance of fish through direct harvesting and the unintended mortality of released fish (Coggins et al., 2007; Cooke and Cowx, 2004). In some regions, the recreational catch forms a considerable component of overall fishing mortality (Henry and Lyle, 2003) and as recreational fishing continues to expand in many countries (McPhee, 2008) the need to obtain accurate (unbiased) and precise (low variance) catch estimates will become increasingly important for the sustainable management of fisheries resources (Steffe et al., 2008). The main purpose of many recreational fishing surveys is to estimate recreational fishing effort, harvest per unit effort (HPUE) and total harvest (or catch) as precisely as possible using a robust sampling design (Malvestuto, 1990; Pollock et al., 1994). Precision is particularly important because confidence in survey results and the ability to infer changes in the fishery often hinge on the precision of these measured variables (Malvestuto, 1990; Pollock et al., 1994). Recreational fishing surveys are typically tailored to management requirements and the spatial scale of the data required
∗ Corresponding author. Tel.: +61 7 3225 1683; fax: +61 7 3224 2804. E-mail address: [email protected] (S.M. Taylor). 0165-7836/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fishres.2011.05.001
frequently dictates the choice of survey method used (Pollock et al., 1994). Irrespective of whether an onsite (e.g. roving creel or busroute access point survey) or offsite (e.g. telephone) survey design is used, there are several ways to improve the precision of harvest estimates. These include increasing the spatial and temporal stratification, increasing the number of replicates within strata and post-stratification (Pollock et al., 1994). Even in well designed surveys, recreational catch data are typically dominated by large numbers of zeroes. This is particularly the case where a small proportion of recreational fishers catch the majority of fish (Henry and Lyle, 2003) or where the capture of certain species requires specialist equipment or access to a fishing location that the majority of fishers do not visit. In onsite recreational fishing surveys, this commonly leads to a high proportion of interviewed fishers reporting no catch. When aggregated, these catch rate data are often positively-skewed thereby violating the assumptions of normality required for many abundance analyses (Lewin et al., 2010; O’Neill and Faddy, 2003). An alternative approach to dealing with zero catches is to use a statistical distribution that allows for zero observations (Maunder and Punt, 2004). For example, two-part conditional general linear models (CGLMs) have been used to model the zero and non-zero components of the data separately (MacNeil et al., 2009; O’Neill and Faddy, 2003; Terceiro, 2003). A binary (presence/absence model) is typically used on the zero component and an appropriate conditional distribution (e.g. truncated Poisson, negative Binomial, or
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Gamma distribution) is used on the non-zero component. Although CGLMs have been widely used on positively-skewed commercial fishing data (Minami et al., 2007; Punt et al., 2000; Stefansson, 1996) few studies have used these models to derive catch and effort estimates from zero-inflated recreational fishing data (O’Neill and Faddy, 2003). We are unaware of any published study that has directly compared harvest and effort from sample means and CGLMs taken from the same onsite recreational fishing survey. This paper directly compares estimates of the proportion of boats fishing, fishing effort, HPUE and total harvest from sample means and CGLM values from the same real data set. Analysis was carried out on the results of a bus-route access point survey conducted in southeastern Queensland, Australia in 2007–2008. Sample mean and CGLM values were estimated at the level of the primary sampling unit (PSU) and scaled up using the Time Interval Count method (outlined in Pollock et al., 1994). Harvest estimates using sample means and CGLM values were compared for five species commonly caught by recreational fishers. These were yellowfin bream (Acanthopagrus australis), sand whiting (Sillago ciliata), dusky flathead (Platycephalus fuscus), snapper (Pagrus auratus) and grass emperor (Lethrinus laticaudis). The comparative nature of this paper provides insight into whether the choice to use a more complex modelling approach or a more traditional approach influences the harvest and effort estimates, and importantly their associated precision. 2. Method 2.1. Survey method A bus-route access point boat ramp survey (as described in Pollock et al., 1994) was conducted at public boat ramps in southeastern Queensland between October 2007 and November 2008. The Time Interval Count method (Pollock et al., 1994) was used to calculate fishing effort because it was expected that few interviews would be obtained from some of the ramps and that most of the trailers counted would be associated with boats that were recreationally fishing. Boat ramps were assigned to one of 15 bus routes and each route had between three and nine ramps. After three months one of the routes was discontinued because it contributed few data and so the analysis was based on the data from 14 bus routes. Each ramp was assigned a specific wait time during which the survey agent counted the number of boat trailers present and recorded the times that boats were launched and retrieved. Wait time at each ramp ranged from 6 to 90 min, with a longer wait time at the busier ramps to maximise the number of interviews obtained. Wait time permitting, all boat occupants returning to the ramps were interviewed to determine whether they had been recreationally fishing and what they had caught. Due to the linear nature of most of the bus routes it was not practical to randomise the order in which ramps within a route were visited. However, the order of the bus route (forwards or backwards) was randomised and shifts commenced at a variety of times within the assumed 11 h fishing day. A full description of the survey method, including information on the number of interviews per stratum, the questionnaires used and all equations and variance estimates is given in Webley et al. (2009).
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strata. We chose ramps as the PSU in this analysis because the coastal boat ramps of southeast Queensland vary in their provision of access to the various marine fishing areas and often attract quite different fishers despite being within a few kilometres of each other. For example within the same route, some ramps are predominantly used by fishers who fish offshore while other ramps are predominantly used by fishers targeting estuarine species. The characteristics of the fishers are different and the activity being measured is independent among ramps within a route. Partitioning this variation at the ramp level allows it to be separated from the random error term, whereas estimating at the route level would pool this with the random error term and hence inflate the standard errors and confidence intervals. Stratifying to the ramp also assists in the uptake and general use of the data as ramp totals are easier to interpret by fisheries managers and other researchers. When scaling up estimates of fishing effort and harvest from the sampled days to the total days in each stratum, the finite population correction factor for the variance was not used because the survey of each ramp was estimated from a snapshot in time and hence could be different to the true population value for that day. By not using the finite population factor, our estimated standard errors will be more conservative, with wider confidence intervals. Two separate estimation approaches were used to derive the total effort and harvest estimates: 1. Established survey approach. We define the established approach as using sample mean values to form the basis of the Time Interval Count method calculations. Given the defined levels of stratification, the means and variances for the raw (untransformed) data were estimated at the stratum level, then scaled-up for the total number of days in each stratum, and finally summed as appropriate. Harvest per unit effort was calculated via the recommended mean of ratios estimator (Hoenig et al., 1997). Standard errors for these values were calculated using the standard variance formulae for products (Goodman, 1960) assuming that the covariance between these variables was zero and that the variables were independent. Detailed calculations are outlined in Pollock et al. (1994) and can be summarised as: H = E × P × HR where H is the harvest for a given species, E is the effort in boat hours (determined from trailer counts at the boat ramps), P is the proportion fishing (determined from returning boats at the boat ramps) and HR is the harvest rate (determined from interviewing recreational fishing boat parties). 2. Conditional general linear models (CGLMs). This approach used CGLM values to form the basis of the Time Interval Count method calculations. These values were scaled up from sampled days to the total number of days in each stratum in the same way as the established method. Boat effort, the proportion of fishers and harvest per unit effort (HPUE) were modelled, as detailed below. Basic calculations are as follows: H = E × P × HR where
2.2. Statistical method
E = pa × a;
The principle sampling unit (PSU) was each survey of a ramp, with randomly selected days providing the replicates. Stratification was based on season (four levels: spring, summer, autumn and winter), day-type (weekday (WD) and weekends and public holidays (WE)) and ramp (94 levels) creating a survey with 752
where Pa and a ∼ f (daytype + season + ramp + daytype × season) H is the harvest for a given species, E is the effort in boat hours (determined from trailer counts at the boat ramps), P is the proportion fishing (determined from returning boats at the boat ramps), HR is the harvest rate (determined from interviewing
P = pa;
HR = pa × a
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Table 1 Harvest per unit effort (HPUE), estimated harvest and relative standard error (RSE) using sample means and a two-part conditional general linear model (CGLM) for five recreationally caught species in a bus-route boat ramp survey in southeastern Queensland in 2007–2008. HPUE is the number of fish per boat party-hour averaged across all ramp, day-type and season strata. Species
Sample means HPUE (SE)
Yellowfin bream Sand whiting Dusky flathead Snapper Grass emperor
0.084 (0.603) 0.081 (0.225) 0.025 (0.125) 0.035 (0.338) 0.009 (0.159)
Two-part GLM Harvest (RSE) 107 631 (16%) 80 261 (17%) 27 302 (17%) 37 299 (25%) 12 616 (46%)
HPUE (SE)
Harvest (RSE)
0.095 (0.164) 0.096 (0.270) 0.028 (0.048) 0.040 (0.093) 0.010 (0.028)
126 550 (3%) 78 194 (6%) 34 887 (5%) 42 633 (4%) 14 128 (10%)
Fig. 1. Frequency distribution for (a) yellowfin bream, (b) dusky flathead, (c) sand whiting, (d) snapper and (e) grass emperor caught in a bus-route access point survey in southeastern Queensland, Australia in 2007–2008.
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Fig. 2. Plots of residuals for recreational fishing effort obtained from a bus-route access point survey in southeastern Queensland, Australia in 2007–2008 from (a) sample mean data and (b) two-part conditional general linear model data. All recreational fishing effort values were included in (a) and >0 recreational fishing effort values were used in (b). Circles represent catch rate values, upper and lower lines represent the empirical confidence intervals.
recreational fishing boat parties), Pa is the presence/absence model and a > 0 values modelled with the gamma GLM. Estimates of boating effort for each stratum were the product of the mean proportion presence (from the presence/absence model) and the mean effort (from the >0 values using the gamma GLM). The mean proportion of boats fishing for each stratum was estimated from the presence absence model. Estimates of harvest rate for each stratum were the product of the presence/absence model and the >0 harvest per unit effort model. Overall harvest was then calculated by multiplying effort by the proportion of boats fishing by the harvest rate. A further description of this CGLM method is given below for each of the variables. 2.3. Boat effort Estimated boat effort was based on trailer counts at each ramp and scaled up to the wait time at each ramp. These data were positively skewed, and at the individual ramp level 17% of all daily observations were zero. It was concluded that no single statistical distribution could adequately model these data. As such, a CGLM was adopted. The first part of this CGLM used a binomial GLM with the logit link to model the zero-class, which corresponds to the proportion of all observations that were zeroes. All higher-order interactions were screened and discarded if not significant. Means and standard errors were estimated at the individual cell level with stable estimates provided for any missing combinations in the sample scheme. The second part of the model considered all values greater than zero. A gamma GLM (Feuerverger, 1979; Ye et al., 2001) with the log link function was adopted. 2.4. Proportion of fishers The proportion of boats that had been fishing was calculated for each stratum level. A binomial GLM with the logit link was used to analyse these data. As with boating effort, all possible interactions were initially fitted and screened for significance. Total fishing effort was then the product of total boat effort multiplied by the proportion of fishers. 2.5. Harvest per unit effort (HPUE) As with the established approach, HPUE was calculated via the mean of ratios estimator (Hoenig et al., 1997). Individual interviews within ramps were considered as sub-samples and averaged within each ramp/season/day-type strata. These data contained many zeros because on many visits to a ramp no fish of a particular
species were harvested. The probability of a zero catch was modelled using a binomial distribution and actual catch numbers (>0) were modelled with a gamma distribution. Overall estimates were again made by integrating these two components. As with the established survey approach, standard errors for boat effort, proportion of fishers and HPUE were calculated using the standard variance formulae for products (Goodman, 1960) assuming that the covariance between these variables was zero and that the variables were independent. All statistical modelling was conducted in GenStat 11 statistical software (VSN International Ltd, 2009). For each of the three variables (boat effort, proportion of fishers, HPUE), all analyses considered the main effects of day-type, season and ramp, along with their interactions. Generally the three-way interaction and two-way interactions involving ramp (all of which had high degrees of freedom) were non-significant and of a lower order of magnitude than the other effects. As a result, these interactions were omitted to arrive at a more parsimonious model. The season by day-type interaction, with only three degrees of freedom, was retained as it was generally significant (p < 0.05). Recreational fishing effort (in boat hours) and associated relative standard error (RSE) were compared between the established and the CGLM approach. Using both approaches, harvest estimates and relative standard error (RSE) were calculated for yellowfin bream, sand whiting, dusky flathead, snapper and grass emperor. The number of fish caught per boat was plotted for each of the five species to compare the catch distribution for each species. To examine the distribution of the residuals from the sample means and CGLM modelled values, half-normal plots were constructed in GenStat 11 for recreational fishing effort. Half-normal plots from both methods were also constructed for yellowfin bream and grass emperor HPUE data. These fish were chosen because they represented the most commonly caught and the least commonly caught of the species examined, respectively. Half-normal plots were constructed for all of the sample mean data and for >0 recreational fishing effort and HPUE values using the gamma model in the CGLM. These graphs were used to visually assess whether the residual harvest rate data from the sample means and the gamma model means aligned closely with the expected residual values. 3. Results In total, 7657 boat crews were interviewed, of which 4559 (60%) had been recreationally fishing. For the five species examined,
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Fig. 3. Plots of residuals for harvest rate values obtained from a bus-route access point survey in southeastern Queensland, Australia in 2007–2008. (a) Sample mean data for yellowfin bream, (b) two-part conditional general linear model (CGLM) data for yellowfin bream, (c) sample mean data for grass emperor and (d) two-part CGLM data for grass emperor. All HPUE values are included in (a) and (c) and >0 HPUE values are shown in (b) and (d). Circles represent catch rate values, upper and lower lines represent the empirical confidence intervals.
the catch distributions were zero-inflated and positively-skewed (Fig. 1). The percentage of trips where no fish were caught ranged from 79% for yellowfin bream to 97% for grass emperor. The percentage of trips where 5 or more fish were caught per boat ranged from 1% for dusky flathead to 6% for yellowfin bream. The established method estimated the mean (se) proportion of boats fishing as 0.546 (0.320) while the binomial GLM estimated the mean (se) proportion of boats fishing as 0.586 (0.138). The established method estimated total recreational fishing effort (RSE) for the year as 1,230,456 (4%) boat hours and the CGLM estimated total recreational fishing effort (RSE) as 1,324,944 (1%) boat hours. The harvest rate (HPUE) from the established method and the CGLM averaged across all ramp, day-type and seasons strata were similar for all five species examined (Table 1). For four of the species, the CGLM delivered more precise estimates of HPUE. Harvest estimates (RSE) for yellowfin bream, sand whiting, dusky flathead, snapper and grass emperor are shown in Table 1. The similarity in harvest estimates from the established method and the CGLM method varied between species. Compared to the former, the difference in harvest between the two methods ranged from 3% for sand whiting to 28% for dusky flathead. For all five species the CGLM delivered more precise estimates of harvest. Relative standard errors estimated from the CGLM were 65–84% smaller.
Half normal plots for fishing effort showed that the sample mean data from the established method showed wide divergence from the expected line, indicating that these fishing effort data were not normally distributed (Fig. 2a). Fishing effort data obtained from the gamma component of the CGLM (>0 fishing effort values) aligned closely with the expected residual values (Fig. 2b) indicating good agreement between the modelled distribution and the underlying gamma distribution. Half-normal plots for both yellowfin bream and grass emperor showed that the sample mean harvest rate data from the established method were nowhere near normally distributed, as shown by the lack of a linear relationship between the actual residual values and the expected normal residuals, and wide divergence from the expected line (Fig. 3a and c). For both species, actual residual >0 HPUE data from the gamma component of the CGLM aligned closely with the expected residual values (Fig. 3b and d). The majority of these residuals fell within the empirical confidence intervals. This indicated good agreement between the CGLM harvest rate data and the underlying statistical distribution. 4. Discussion Although recreational fishing surveys vary in their complexity and scope (Henry and Lyle, 2003), well-designed surveys
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share common goals of minimising bias and maximising precision (Anon, 2006). While the importance of recreational fishing survey design has been highlighted in the literature (Malvestuto, 1990; Pollock et al., 1994; Steffe et al., 2008), this study has shown that the choice of analytical method used to analyse recreational fishing data in onsite surveys can influence the precision of the harvest estimates and to a lesser extent, the estimates of harvest. We applied the Time Interval Count method to zero-inflated recreational fishing data collected during a bus-route access point survey in southeastern Queensland, using sample means and twopart conditional general linear model (CGLM) estimates for the basis of all subsequent scale-up calculations. The CGLM provided more precise estimates of harvest with relative standard errors that were 65–84% smaller for the five species examined. This gain in precision resulted from the CGLM providing more precise estimates of the proportion of boats fishing, fishing effort and harvest per unit effort (HPUE), which formed the basis of the total harvest calculations. The results suggest that CGLMs may improve the precision of harvest estimates in other types of recreational fishing survey when the recreational fishing data are zero-inflated. A proliferation of zero values is not a problem unique to the analysis of recreational fishing data. Elsewhere data sets containing many zero values are common, for example, in commercial fisheries data (refer to Maunder and Punt, 2004 for a detailed review) and in the study of rare terrestrial animals (Welsh et al., 1996). In these fields of research, models have been used to cope with zero-inflated data with the specificity of the model depending on the nature of the data (Maunder and Punt, 2004). The gamma model, used here to model the >0 fishing effort and >0 HPUE values, has also been used in other studies on commercial fisheries data (Punt et al., 2000; Ye et al., 2001) and is considered to be a good fit for highly skewed continuous data. The fact that in the current study, the residuals from the analysis of recreational fishing effort and HPUE aligned closely to the gamma distribution suggests that this model may also provide a good fit for other highly-skewed recreational fishing catch data. The lack of other comparative studies on sample mean vs. CGLM estimates make comparisons of harvest and RSE across a range of situations difficult. However, the magnitude of the difference in the precision of estimates of total harvest between the two methods in this study may be linked to the large number of strata. Gains in precision obtained from the latter approach would have accumulated when the variances for each stratum were summed across the various ramp, day-type and season strata. This study also demonstrates that the CGLM can improve the precision of estimates for recreational fishing effort and HPUE, which form the basis of the overall harvest calculations. For four of the five species examined, the CGLM gave much more precise estimates of HPUE. When estimating recreational fishing effort, the CGLM provided an almost four fold increase in precision. Gains in the precision of estimates of the proportion of boats fishing by the CGLM method also contributed to the overall gain in precision for recreational fishing effort. On some days it was not possible to obtain certain data at a particular ramp. For example, even though the average shift time per ramp was more than double the 15 min recommended by Robson and Jones (1989), on some occasions no boats returned to the ramp and no fisher interviews were completed, providing no data about the proportion of boats fishing on that day at that ramp. In these cases, an arbitrary value of 0.5 was imputed using the sample means approach while the CGLM approach estimated the missing values from the fitted model coefficients. This suggests that modelling approaches may be more robust and improve the precision in other onsite recreational fishing surveys when null values are encountered during sampling.
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Differences in precision of harvest estimates between the two methods were related to differences in the way these methods dealt with the same dataset. The established approach ignored the fact that the underlying HPUE data estimated at the level of the ramp per day and then averaged across day-type and season strata were not normally distributed, while the CGLM approach used the gamma distribution which more closely modelled the underlying data. In reality, even in well-designed surveys with sufficient replication, the catch distribution is unlikely to be normally distributed (O’Neill and Faddy, 2003; Webley et al., 2011). This may be linked to the fact that recreational fishers differ in their motives for fishing and skill levels (Henry and Lyle, 2003; Sutton et al., 2009) which can result in wide variability in catch rates during a sampling session. This issue is confounded when CPUE or HPUE is expressed at the species level as fewer interviews typically report a catch of the species of interest, while a small number of interviewed fishers dominate the catch. This is exemplified by the current study where only 3–11% of boat parties reported a catch of yellowfin bream, sand whiting, dusky flathead, snapper and grass emperor. Numerous steps can be taken in the planning stages of recreational fishing surveys to improve the precision of the results. In onsite recreational fishing surveys this can include increasing the number of sampling days per stratum, stratifying within-days (e.g. morning, afternoon and evening) and/or increasing the sampling intensity during busier periods (Kinloch et al., 1997; Malvestuto, 1990). The use of traffic counters to provide a supplementary measure of effort has also been advocated as a valid method of improving the accuracy and precision of effort and harvest estimates for surveys that derive effort from an access point design (Steffe et al., 2008). In an Australian boat-based estuarine fishery, traffic counters were used to extend the spatial coverage of an access point survey which led to gains in precision for effort and harvest of 76% and 37%, respectively, for little financial cost (Steffe et al., 2008). With the exception of the supplemented access point design (Steffe et al., 2008), these methodological improvements are often costly and gains in precision need to be carefully balanced against the financial limitations faced by many fisheries researchers. Based on the results of this study, CGLMs can be considered a costeffective way of improving the precision of effort, HPUE and harvest in recreational fishing surveys when the underlying data are zeroinflated. However, the potential for bias in this and all other recreational fishing surveys must also be acknowledged. A recent study (Webley et al., 2011) applied six commonly used models in fisheries research to a variety of simulated typical fisheries data sets and examined the mean bias, confidence interval width and actual Type 1 error rates for each of these models. The gamma model used here was included in the Webley et al. (2011) study, the results of which suggested that under certain scenarios this and other complex models tend to be less robust to breaches of their distribution than the sample mean, although the performance of each model did vary as the degree of skewedness in the data changed. Webley et al. (2011) suggested that an assessment of the robustness of a model should be made a priori using pre-existing catch data. Based on the results of both Webley et al. (2011) and this study we advocate further research to examine both the precision and the accuracy of catch estimates from sample mean and conditional modelling values across a range of recreational fishing surveys. As the recreational catch increases, there will be a growing need to use recreational fishing survey data in stock assessments. In areas where competition for resources occurs between the recreational and commercial sector, precise recreational harvest estimates will also be needed to resolve issues of resource allocation. Using CGLMs in other types of recreational fishing survey may also lead to gains in the precision of relevant estimates. Until further comparative research examines the survey outputs derived from sampled means
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and CGLMs across a range of studies we highlight the need for researchers to clearly document the analytical method used to analyse recreational fishing data as the choice of method may influence estimates of precision for harvest. Acknowledgements We are very grateful to all the fishers who agreed to be interviewed during the boat ramp survey. We thank Len Olyott and Kara Dew for their assistance in the design and general running of the boat ramp survey along with the survey agents who collected the data. Dr. Tony Swain provided invaluable statistical advice and we thank Dr. Wayne Sumpton for comments on the manuscript and Dr. Ian Jacobsen for assistance with some of the figures. We also thank the two anonymous reviewers and the associate editor for their insightful comments. References Anon, 2006. Review of Recreational Fisheries Survey Methods. Committee on the Review of Recreational Fisheries Survey Methods. National Research Council, The National Academies Press, Washington, DC. Arlinghaus, R., Cooke, S.J., 2005. Global impact of recreational fisheries. Science 307, 1561–1562. Coggins, L.G., Catalano, M.J., Allen, M.S., Pine, W.E., Walters, C.J., 2007. Effects of cryptic mortality and the hidden costs of using length limits in fishery management. Fish and Fisheries 8, 196–210. Cooke, S.J., Cowx, I.G., 2004. The role of recreational fishing in global fish crises. Bioscience 54, 857–859. Feuerverger, A., 1979. On some methods of analysis for weather experiments. Biometrika 66, 655–658. Goodman, L.A., 1960. On the exact variance of products. Journal of the American Statistical Association 55, 708–713. Henry, G., Lyle, J.M., 2003. The National Recreational and Indigenous Fishing Survey. FRDC project no. 99/158. Australian Government. Department of Agriculture, Fisheries and Forestry. www.daff.gov.au/fisheries/recreational/recfishsurvey. Hoenig, J.M., Jones, C.M., Pollock, K.H., Robson, D.S., Wade, D.L., 1997. Calculation of catch rate and total catch in roving surveys of anglers. Biometrics 53, 306–317. Kinloch, M.A., McGlennon, D., Nicoll, G., Pike, P.G., 1997. Evaluation of the bus-route creel survey method in a large Australian marine recreational fishery. I. Survey design. Fisheries Research 33, 101–121.
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Improving the precision of recreational fishing harvest estimates using two-part conditional general linear models Stephen M. Taylor a,∗ , James A.C. Webley a , David G. Mayer b a b
Fisheries Queensland, Department of Employment, Economic Development and Innovation, Primary Industries Building, 80 Ann Street, Brisbane 4001, Australia AgriScience Queensland, Department of Employment, Economic Development and Innovation, Ecosciences Precinct, 41 Boggo Road, Dutton Park, Queensland 4102, Australia
a r t i c l e
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Article history: Received 25 February 2011 Received in revised form 5 May 2011 Accepted 5 May 2011 Keywords: Survey Precision Right-skewed Gamma distribution Recreational catch Bus route
a b s t r a c t As recreational fishing continues to expand, the need to obtain precise harvest estimates is becoming increasingly important for the sustainable management of fisheries. Recreational fishing data are frequently zero-inflated which can present problems for commonly used analyses that assume a normal distribution. In this study, we analysed zero-inflated recreational fishing data collected from a bus-route access point survey in southeastern Queensland, Australia. Using the Time Interval Count method, we compared estimates of the proportion of boats fishing, fishing effort, harvest per unit effort (HPUE) and harvest using sample mean values and mean values derived from a two-part conditional general linear model (CGLM). The CGLM gave more precise estimates of the proportion of boats fishing, fishing effort and HPUE, which formed the basis of the harvest calculations. Differences in harvest estimates using the two methods ranged from 3 to 28% for the five recreational species examined. Relative standard errors for harvest estimated by the CGLM were 65–84% smaller. The results suggest that CGLMs may deliver more precise outputs in other types of recreational fishing surveys that derive effort and catch from zero-inflated data. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Recreational fishing is an important leisure pursuit for millions of people (Arlinghaus and Cooke, 2005). Recreational fishing also has the potential to reduce the abundance of fish through direct harvesting and the unintended mortality of released fish (Coggins et al., 2007; Cooke and Cowx, 2004). In some regions, the recreational catch forms a considerable component of overall fishing mortality (Henry and Lyle, 2003) and as recreational fishing continues to expand in many countries (McPhee, 2008) the need to obtain accurate (unbiased) and precise (low variance) catch estimates will become increasingly important for the sustainable management of fisheries resources (Steffe et al., 2008). The main purpose of many recreational fishing surveys is to estimate recreational fishing effort, harvest per unit effort (HPUE) and total harvest (or catch) as precisely as possible using a robust sampling design (Malvestuto, 1990; Pollock et al., 1994). Precision is particularly important because confidence in survey results and the ability to infer changes in the fishery often hinge on the precision of these measured variables (Malvestuto, 1990; Pollock et al., 1994). Recreational fishing surveys are typically tailored to management requirements and the spatial scale of the data required
∗ Corresponding author. Tel.: +61 7 3225 1683; fax: +61 7 3224 2804. E-mail address: [email protected] (S.M. Taylor). 0165-7836/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fishres.2011.05.001
frequently dictates the choice of survey method used (Pollock et al., 1994). Irrespective of whether an onsite (e.g. roving creel or busroute access point survey) or offsite (e.g. telephone) survey design is used, there are several ways to improve the precision of harvest estimates. These include increasing the spatial and temporal stratification, increasing the number of replicates within strata and post-stratification (Pollock et al., 1994). Even in well designed surveys, recreational catch data are typically dominated by large numbers of zeroes. This is particularly the case where a small proportion of recreational fishers catch the majority of fish (Henry and Lyle, 2003) or where the capture of certain species requires specialist equipment or access to a fishing location that the majority of fishers do not visit. In onsite recreational fishing surveys, this commonly leads to a high proportion of interviewed fishers reporting no catch. When aggregated, these catch rate data are often positively-skewed thereby violating the assumptions of normality required for many abundance analyses (Lewin et al., 2010; O’Neill and Faddy, 2003). An alternative approach to dealing with zero catches is to use a statistical distribution that allows for zero observations (Maunder and Punt, 2004). For example, two-part conditional general linear models (CGLMs) have been used to model the zero and non-zero components of the data separately (MacNeil et al., 2009; O’Neill and Faddy, 2003; Terceiro, 2003). A binary (presence/absence model) is typically used on the zero component and an appropriate conditional distribution (e.g. truncated Poisson, negative Binomial, or
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Gamma distribution) is used on the non-zero component. Although CGLMs have been widely used on positively-skewed commercial fishing data (Minami et al., 2007; Punt et al., 2000; Stefansson, 1996) few studies have used these models to derive catch and effort estimates from zero-inflated recreational fishing data (O’Neill and Faddy, 2003). We are unaware of any published study that has directly compared harvest and effort from sample means and CGLMs taken from the same onsite recreational fishing survey. This paper directly compares estimates of the proportion of boats fishing, fishing effort, HPUE and total harvest from sample means and CGLM values from the same real data set. Analysis was carried out on the results of a bus-route access point survey conducted in southeastern Queensland, Australia in 2007–2008. Sample mean and CGLM values were estimated at the level of the primary sampling unit (PSU) and scaled up using the Time Interval Count method (outlined in Pollock et al., 1994). Harvest estimates using sample means and CGLM values were compared for five species commonly caught by recreational fishers. These were yellowfin bream (Acanthopagrus australis), sand whiting (Sillago ciliata), dusky flathead (Platycephalus fuscus), snapper (Pagrus auratus) and grass emperor (Lethrinus laticaudis). The comparative nature of this paper provides insight into whether the choice to use a more complex modelling approach or a more traditional approach influences the harvest and effort estimates, and importantly their associated precision. 2. Method 2.1. Survey method A bus-route access point boat ramp survey (as described in Pollock et al., 1994) was conducted at public boat ramps in southeastern Queensland between October 2007 and November 2008. The Time Interval Count method (Pollock et al., 1994) was used to calculate fishing effort because it was expected that few interviews would be obtained from some of the ramps and that most of the trailers counted would be associated with boats that were recreationally fishing. Boat ramps were assigned to one of 15 bus routes and each route had between three and nine ramps. After three months one of the routes was discontinued because it contributed few data and so the analysis was based on the data from 14 bus routes. Each ramp was assigned a specific wait time during which the survey agent counted the number of boat trailers present and recorded the times that boats were launched and retrieved. Wait time at each ramp ranged from 6 to 90 min, with a longer wait time at the busier ramps to maximise the number of interviews obtained. Wait time permitting, all boat occupants returning to the ramps were interviewed to determine whether they had been recreationally fishing and what they had caught. Due to the linear nature of most of the bus routes it was not practical to randomise the order in which ramps within a route were visited. However, the order of the bus route (forwards or backwards) was randomised and shifts commenced at a variety of times within the assumed 11 h fishing day. A full description of the survey method, including information on the number of interviews per stratum, the questionnaires used and all equations and variance estimates is given in Webley et al. (2009).
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strata. We chose ramps as the PSU in this analysis because the coastal boat ramps of southeast Queensland vary in their provision of access to the various marine fishing areas and often attract quite different fishers despite being within a few kilometres of each other. For example within the same route, some ramps are predominantly used by fishers who fish offshore while other ramps are predominantly used by fishers targeting estuarine species. The characteristics of the fishers are different and the activity being measured is independent among ramps within a route. Partitioning this variation at the ramp level allows it to be separated from the random error term, whereas estimating at the route level would pool this with the random error term and hence inflate the standard errors and confidence intervals. Stratifying to the ramp also assists in the uptake and general use of the data as ramp totals are easier to interpret by fisheries managers and other researchers. When scaling up estimates of fishing effort and harvest from the sampled days to the total days in each stratum, the finite population correction factor for the variance was not used because the survey of each ramp was estimated from a snapshot in time and hence could be different to the true population value for that day. By not using the finite population factor, our estimated standard errors will be more conservative, with wider confidence intervals. Two separate estimation approaches were used to derive the total effort and harvest estimates: 1. Established survey approach. We define the established approach as using sample mean values to form the basis of the Time Interval Count method calculations. Given the defined levels of stratification, the means and variances for the raw (untransformed) data were estimated at the stratum level, then scaled-up for the total number of days in each stratum, and finally summed as appropriate. Harvest per unit effort was calculated via the recommended mean of ratios estimator (Hoenig et al., 1997). Standard errors for these values were calculated using the standard variance formulae for products (Goodman, 1960) assuming that the covariance between these variables was zero and that the variables were independent. Detailed calculations are outlined in Pollock et al. (1994) and can be summarised as: H = E × P × HR where H is the harvest for a given species, E is the effort in boat hours (determined from trailer counts at the boat ramps), P is the proportion fishing (determined from returning boats at the boat ramps) and HR is the harvest rate (determined from interviewing recreational fishing boat parties). 2. Conditional general linear models (CGLMs). This approach used CGLM values to form the basis of the Time Interval Count method calculations. These values were scaled up from sampled days to the total number of days in each stratum in the same way as the established method. Boat effort, the proportion of fishers and harvest per unit effort (HPUE) were modelled, as detailed below. Basic calculations are as follows: H = E × P × HR where
2.2. Statistical method
E = pa × a;
The principle sampling unit (PSU) was each survey of a ramp, with randomly selected days providing the replicates. Stratification was based on season (four levels: spring, summer, autumn and winter), day-type (weekday (WD) and weekends and public holidays (WE)) and ramp (94 levels) creating a survey with 752
where Pa and a ∼ f (daytype + season + ramp + daytype × season) H is the harvest for a given species, E is the effort in boat hours (determined from trailer counts at the boat ramps), P is the proportion fishing (determined from returning boats at the boat ramps), HR is the harvest rate (determined from interviewing
P = pa;
HR = pa × a
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Table 1 Harvest per unit effort (HPUE), estimated harvest and relative standard error (RSE) using sample means and a two-part conditional general linear model (CGLM) for five recreationally caught species in a bus-route boat ramp survey in southeastern Queensland in 2007–2008. HPUE is the number of fish per boat party-hour averaged across all ramp, day-type and season strata. Species
Sample means HPUE (SE)
Yellowfin bream Sand whiting Dusky flathead Snapper Grass emperor
0.084 (0.603) 0.081 (0.225) 0.025 (0.125) 0.035 (0.338) 0.009 (0.159)
Two-part GLM Harvest (RSE) 107 631 (16%) 80 261 (17%) 27 302 (17%) 37 299 (25%) 12 616 (46%)
HPUE (SE)
Harvest (RSE)
0.095 (0.164) 0.096 (0.270) 0.028 (0.048) 0.040 (0.093) 0.010 (0.028)
126 550 (3%) 78 194 (6%) 34 887 (5%) 42 633 (4%) 14 128 (10%)
Fig. 1. Frequency distribution for (a) yellowfin bream, (b) dusky flathead, (c) sand whiting, (d) snapper and (e) grass emperor caught in a bus-route access point survey in southeastern Queensland, Australia in 2007–2008.
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Fig. 2. Plots of residuals for recreational fishing effort obtained from a bus-route access point survey in southeastern Queensland, Australia in 2007–2008 from (a) sample mean data and (b) two-part conditional general linear model data. All recreational fishing effort values were included in (a) and >0 recreational fishing effort values were used in (b). Circles represent catch rate values, upper and lower lines represent the empirical confidence intervals.
recreational fishing boat parties), Pa is the presence/absence model and a > 0 values modelled with the gamma GLM. Estimates of boating effort for each stratum were the product of the mean proportion presence (from the presence/absence model) and the mean effort (from the >0 values using the gamma GLM). The mean proportion of boats fishing for each stratum was estimated from the presence absence model. Estimates of harvest rate for each stratum were the product of the presence/absence model and the >0 harvest per unit effort model. Overall harvest was then calculated by multiplying effort by the proportion of boats fishing by the harvest rate. A further description of this CGLM method is given below for each of the variables. 2.3. Boat effort Estimated boat effort was based on trailer counts at each ramp and scaled up to the wait time at each ramp. These data were positively skewed, and at the individual ramp level 17% of all daily observations were zero. It was concluded that no single statistical distribution could adequately model these data. As such, a CGLM was adopted. The first part of this CGLM used a binomial GLM with the logit link to model the zero-class, which corresponds to the proportion of all observations that were zeroes. All higher-order interactions were screened and discarded if not significant. Means and standard errors were estimated at the individual cell level with stable estimates provided for any missing combinations in the sample scheme. The second part of the model considered all values greater than zero. A gamma GLM (Feuerverger, 1979; Ye et al., 2001) with the log link function was adopted. 2.4. Proportion of fishers The proportion of boats that had been fishing was calculated for each stratum level. A binomial GLM with the logit link was used to analyse these data. As with boating effort, all possible interactions were initially fitted and screened for significance. Total fishing effort was then the product of total boat effort multiplied by the proportion of fishers. 2.5. Harvest per unit effort (HPUE) As with the established approach, HPUE was calculated via the mean of ratios estimator (Hoenig et al., 1997). Individual interviews within ramps were considered as sub-samples and averaged within each ramp/season/day-type strata. These data contained many zeros because on many visits to a ramp no fish of a particular
species were harvested. The probability of a zero catch was modelled using a binomial distribution and actual catch numbers (>0) were modelled with a gamma distribution. Overall estimates were again made by integrating these two components. As with the established survey approach, standard errors for boat effort, proportion of fishers and HPUE were calculated using the standard variance formulae for products (Goodman, 1960) assuming that the covariance between these variables was zero and that the variables were independent. All statistical modelling was conducted in GenStat 11 statistical software (VSN International Ltd, 2009). For each of the three variables (boat effort, proportion of fishers, HPUE), all analyses considered the main effects of day-type, season and ramp, along with their interactions. Generally the three-way interaction and two-way interactions involving ramp (all of which had high degrees of freedom) were non-significant and of a lower order of magnitude than the other effects. As a result, these interactions were omitted to arrive at a more parsimonious model. The season by day-type interaction, with only three degrees of freedom, was retained as it was generally significant (p < 0.05). Recreational fishing effort (in boat hours) and associated relative standard error (RSE) were compared between the established and the CGLM approach. Using both approaches, harvest estimates and relative standard error (RSE) were calculated for yellowfin bream, sand whiting, dusky flathead, snapper and grass emperor. The number of fish caught per boat was plotted for each of the five species to compare the catch distribution for each species. To examine the distribution of the residuals from the sample means and CGLM modelled values, half-normal plots were constructed in GenStat 11 for recreational fishing effort. Half-normal plots from both methods were also constructed for yellowfin bream and grass emperor HPUE data. These fish were chosen because they represented the most commonly caught and the least commonly caught of the species examined, respectively. Half-normal plots were constructed for all of the sample mean data and for >0 recreational fishing effort and HPUE values using the gamma model in the CGLM. These graphs were used to visually assess whether the residual harvest rate data from the sample means and the gamma model means aligned closely with the expected residual values. 3. Results In total, 7657 boat crews were interviewed, of which 4559 (60%) had been recreationally fishing. For the five species examined,
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Fig. 3. Plots of residuals for harvest rate values obtained from a bus-route access point survey in southeastern Queensland, Australia in 2007–2008. (a) Sample mean data for yellowfin bream, (b) two-part conditional general linear model (CGLM) data for yellowfin bream, (c) sample mean data for grass emperor and (d) two-part CGLM data for grass emperor. All HPUE values are included in (a) and (c) and >0 HPUE values are shown in (b) and (d). Circles represent catch rate values, upper and lower lines represent the empirical confidence intervals.
the catch distributions were zero-inflated and positively-skewed (Fig. 1). The percentage of trips where no fish were caught ranged from 79% for yellowfin bream to 97% for grass emperor. The percentage of trips where 5 or more fish were caught per boat ranged from 1% for dusky flathead to 6% for yellowfin bream. The established method estimated the mean (se) proportion of boats fishing as 0.546 (0.320) while the binomial GLM estimated the mean (se) proportion of boats fishing as 0.586 (0.138). The established method estimated total recreational fishing effort (RSE) for the year as 1,230,456 (4%) boat hours and the CGLM estimated total recreational fishing effort (RSE) as 1,324,944 (1%) boat hours. The harvest rate (HPUE) from the established method and the CGLM averaged across all ramp, day-type and seasons strata were similar for all five species examined (Table 1). For four of the species, the CGLM delivered more precise estimates of HPUE. Harvest estimates (RSE) for yellowfin bream, sand whiting, dusky flathead, snapper and grass emperor are shown in Table 1. The similarity in harvest estimates from the established method and the CGLM method varied between species. Compared to the former, the difference in harvest between the two methods ranged from 3% for sand whiting to 28% for dusky flathead. For all five species the CGLM delivered more precise estimates of harvest. Relative standard errors estimated from the CGLM were 65–84% smaller.
Half normal plots for fishing effort showed that the sample mean data from the established method showed wide divergence from the expected line, indicating that these fishing effort data were not normally distributed (Fig. 2a). Fishing effort data obtained from the gamma component of the CGLM (>0 fishing effort values) aligned closely with the expected residual values (Fig. 2b) indicating good agreement between the modelled distribution and the underlying gamma distribution. Half-normal plots for both yellowfin bream and grass emperor showed that the sample mean harvest rate data from the established method were nowhere near normally distributed, as shown by the lack of a linear relationship between the actual residual values and the expected normal residuals, and wide divergence from the expected line (Fig. 3a and c). For both species, actual residual >0 HPUE data from the gamma component of the CGLM aligned closely with the expected residual values (Fig. 3b and d). The majority of these residuals fell within the empirical confidence intervals. This indicated good agreement between the CGLM harvest rate data and the underlying statistical distribution. 4. Discussion Although recreational fishing surveys vary in their complexity and scope (Henry and Lyle, 2003), well-designed surveys
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share common goals of minimising bias and maximising precision (Anon, 2006). While the importance of recreational fishing survey design has been highlighted in the literature (Malvestuto, 1990; Pollock et al., 1994; Steffe et al., 2008), this study has shown that the choice of analytical method used to analyse recreational fishing data in onsite surveys can influence the precision of the harvest estimates and to a lesser extent, the estimates of harvest. We applied the Time Interval Count method to zero-inflated recreational fishing data collected during a bus-route access point survey in southeastern Queensland, using sample means and twopart conditional general linear model (CGLM) estimates for the basis of all subsequent scale-up calculations. The CGLM provided more precise estimates of harvest with relative standard errors that were 65–84% smaller for the five species examined. This gain in precision resulted from the CGLM providing more precise estimates of the proportion of boats fishing, fishing effort and harvest per unit effort (HPUE), which formed the basis of the total harvest calculations. The results suggest that CGLMs may improve the precision of harvest estimates in other types of recreational fishing survey when the recreational fishing data are zero-inflated. A proliferation of zero values is not a problem unique to the analysis of recreational fishing data. Elsewhere data sets containing many zero values are common, for example, in commercial fisheries data (refer to Maunder and Punt, 2004 for a detailed review) and in the study of rare terrestrial animals (Welsh et al., 1996). In these fields of research, models have been used to cope with zero-inflated data with the specificity of the model depending on the nature of the data (Maunder and Punt, 2004). The gamma model, used here to model the >0 fishing effort and >0 HPUE values, has also been used in other studies on commercial fisheries data (Punt et al., 2000; Ye et al., 2001) and is considered to be a good fit for highly skewed continuous data. The fact that in the current study, the residuals from the analysis of recreational fishing effort and HPUE aligned closely to the gamma distribution suggests that this model may also provide a good fit for other highly-skewed recreational fishing catch data. The lack of other comparative studies on sample mean vs. CGLM estimates make comparisons of harvest and RSE across a range of situations difficult. However, the magnitude of the difference in the precision of estimates of total harvest between the two methods in this study may be linked to the large number of strata. Gains in precision obtained from the latter approach would have accumulated when the variances for each stratum were summed across the various ramp, day-type and season strata. This study also demonstrates that the CGLM can improve the precision of estimates for recreational fishing effort and HPUE, which form the basis of the overall harvest calculations. For four of the five species examined, the CGLM gave much more precise estimates of HPUE. When estimating recreational fishing effort, the CGLM provided an almost four fold increase in precision. Gains in the precision of estimates of the proportion of boats fishing by the CGLM method also contributed to the overall gain in precision for recreational fishing effort. On some days it was not possible to obtain certain data at a particular ramp. For example, even though the average shift time per ramp was more than double the 15 min recommended by Robson and Jones (1989), on some occasions no boats returned to the ramp and no fisher interviews were completed, providing no data about the proportion of boats fishing on that day at that ramp. In these cases, an arbitrary value of 0.5 was imputed using the sample means approach while the CGLM approach estimated the missing values from the fitted model coefficients. This suggests that modelling approaches may be more robust and improve the precision in other onsite recreational fishing surveys when null values are encountered during sampling.
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Differences in precision of harvest estimates between the two methods were related to differences in the way these methods dealt with the same dataset. The established approach ignored the fact that the underlying HPUE data estimated at the level of the ramp per day and then averaged across day-type and season strata were not normally distributed, while the CGLM approach used the gamma distribution which more closely modelled the underlying data. In reality, even in well-designed surveys with sufficient replication, the catch distribution is unlikely to be normally distributed (O’Neill and Faddy, 2003; Webley et al., 2011). This may be linked to the fact that recreational fishers differ in their motives for fishing and skill levels (Henry and Lyle, 2003; Sutton et al., 2009) which can result in wide variability in catch rates during a sampling session. This issue is confounded when CPUE or HPUE is expressed at the species level as fewer interviews typically report a catch of the species of interest, while a small number of interviewed fishers dominate the catch. This is exemplified by the current study where only 3–11% of boat parties reported a catch of yellowfin bream, sand whiting, dusky flathead, snapper and grass emperor. Numerous steps can be taken in the planning stages of recreational fishing surveys to improve the precision of the results. In onsite recreational fishing surveys this can include increasing the number of sampling days per stratum, stratifying within-days (e.g. morning, afternoon and evening) and/or increasing the sampling intensity during busier periods (Kinloch et al., 1997; Malvestuto, 1990). The use of traffic counters to provide a supplementary measure of effort has also been advocated as a valid method of improving the accuracy and precision of effort and harvest estimates for surveys that derive effort from an access point design (Steffe et al., 2008). In an Australian boat-based estuarine fishery, traffic counters were used to extend the spatial coverage of an access point survey which led to gains in precision for effort and harvest of 76% and 37%, respectively, for little financial cost (Steffe et al., 2008). With the exception of the supplemented access point design (Steffe et al., 2008), these methodological improvements are often costly and gains in precision need to be carefully balanced against the financial limitations faced by many fisheries researchers. Based on the results of this study, CGLMs can be considered a costeffective way of improving the precision of effort, HPUE and harvest in recreational fishing surveys when the underlying data are zeroinflated. However, the potential for bias in this and all other recreational fishing surveys must also be acknowledged. A recent study (Webley et al., 2011) applied six commonly used models in fisheries research to a variety of simulated typical fisheries data sets and examined the mean bias, confidence interval width and actual Type 1 error rates for each of these models. The gamma model used here was included in the Webley et al. (2011) study, the results of which suggested that under certain scenarios this and other complex models tend to be less robust to breaches of their distribution than the sample mean, although the performance of each model did vary as the degree of skewedness in the data changed. Webley et al. (2011) suggested that an assessment of the robustness of a model should be made a priori using pre-existing catch data. Based on the results of both Webley et al. (2011) and this study we advocate further research to examine both the precision and the accuracy of catch estimates from sample mean and conditional modelling values across a range of recreational fishing surveys. As the recreational catch increases, there will be a growing need to use recreational fishing survey data in stock assessments. In areas where competition for resources occurs between the recreational and commercial sector, precise recreational harvest estimates will also be needed to resolve issues of resource allocation. Using CGLMs in other types of recreational fishing survey may also lead to gains in the precision of relevant estimates. Until further comparative research examines the survey outputs derived from sampled means
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and CGLMs across a range of studies we highlight the need for researchers to clearly document the analytical method used to analyse recreational fishing data as the choice of method may influence estimates of precision for harvest. Acknowledgements We are very grateful to all the fishers who agreed to be interviewed during the boat ramp survey. We thank Len Olyott and Kara Dew for their assistance in the design and general running of the boat ramp survey along with the survey agents who collected the data. Dr. Tony Swain provided invaluable statistical advice and we thank Dr. Wayne Sumpton for comments on the manuscript and Dr. Ian Jacobsen for assistance with some of the figures. We also thank the two anonymous reviewers and the associate editor for their insightful comments. References Anon, 2006. Review of Recreational Fisheries Survey Methods. Committee on the Review of Recreational Fisheries Survey Methods. National Research Council, The National Academies Press, Washington, DC. Arlinghaus, R., Cooke, S.J., 2005. Global impact of recreational fisheries. Science 307, 1561–1562. Coggins, L.G., Catalano, M.J., Allen, M.S., Pine, W.E., Walters, C.J., 2007. Effects of cryptic mortality and the hidden costs of using length limits in fishery management. Fish and Fisheries 8, 196–210. Cooke, S.J., Cowx, I.G., 2004. The role of recreational fishing in global fish crises. Bioscience 54, 857–859. Feuerverger, A., 1979. On some methods of analysis for weather experiments. Biometrika 66, 655–658. Goodman, L.A., 1960. On the exact variance of products. Journal of the American Statistical Association 55, 708–713. Henry, G., Lyle, J.M., 2003. The National Recreational and Indigenous Fishing Survey. FRDC project no. 99/158. Australian Government. Department of Agriculture, Fisheries and Forestry. www.daff.gov.au/fisheries/recreational/recfishsurvey. Hoenig, J.M., Jones, C.M., Pollock, K.H., Robson, D.S., Wade, D.L., 1997. Calculation of catch rate and total catch in roving surveys of anglers. Biometrics 53, 306–317. Kinloch, M.A., McGlennon, D., Nicoll, G., Pike, P.G., 1997. Evaluation of the bus-route creel survey method in a large Australian marine recreational fishery. I. Survey design. Fisheries Research 33, 101–121.
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