An evaluation of the effects of sample size on estimating length composition of catches from tuna longline fisheries using computer simulations

Jiaqi Wang,Luoliang Xu,Bai Li,Siquan Tian,Yong Chen

aCollege of Marine Sciences,Shanghai Ocean University,Shanghai,201306,China

bSchool of Marine Sciences,University of Maine,Orono,ME,04469,USA

cNational Distant-water Fisheries Engineering Research Center,Shanghai Ocean University,Shanghai,201306,China

dKey Laboratory of Sustainable Exploitation of Oceanic Fisheries Resources,Ministry of Education,Shanghai Ocean University,Shanghai,201306,China

ABSTRACT

Keywords:

Length composition

Sample size

Onboard observer

Accuracy and precision

WCPO and computer simulation

1.Introduction

Length composition analysis is a common practice in fish stock assessment and can provide insights into the dynamics of a fish population(Vokoun,Rabeni,&Stanovick,2001).The combination of length data with abundance or catch per unit effort and key life-history parameters can provide key information on year-class strength,growth,or mortality(Miranda,2007).Thus,accurate quantification of the size structure of a population,which can only be achieved by developing effective monitoring programs,is critical to understand the status of afishery and how the population may respond to environmental stressors and management(Adams,Crumby,Greeley,Ryon,&Schilling,1992;Schaefer,1957).It is important to develop a sampling program and estimate what kind of sample size is sufficient to build a reliable lengthfrequency estimate.

Statistic resampling of simulated and empirical data sets have been used to estimate the suitable sample sizes for estimating length composition(Miranda,2007;Vokoun et al.,2001).The required sample size for describing length composition tends to be related to life history processes such as growth,mortality,and movement,and is affected by estimation methods.Commonly used methods include length-frequency distributions(LFD),mean length(ML),proportional stock density or length interval of LFD(Miranda,2007;Schultz,Mayfield,&Whitlock,2016;Vokoun et al.,2001).For small fishes(i.e.,those with maximum length≤30cm),300-400 individuals are often an appropriate sample size for describing LFD,and smaller sample sizes may be suitable for smaller fishes.Many large(i.e.,maximum length＞1m)pelagic fishes are highly migratory species with wider spatial distribution.Small samples for them often fail to capture the true length composition of the whole population or of the total catches within a limited spatio-temporal range(Schultz et al.,2016).

Table 1Classify of the species selected in the study.

Fig.1.Map showing the research area and the observed sets of tuna longline fishery in the WCPO in 2016.

Fig.2.Flowchart of the simulation study summarizing the simulation framework for the evaluation.

Table 2Summary of the items used in the simulation.

For tuna regional fisheries management organizations(tRFMOs),length composition data are critical information required in stock assessment and management(WCPFC,2007;Williams,2018).The length composition of catches for both target and non-target species could be estimated in various monitoring programs such as port sampling,onboard observer programs and/or logbooks.It is generally accepted that the most accurate,reliable and representative way to get the information is through onboard observer programs(Gilman,Weijerman,&Suuronen,2017;Kennelly,1999).Regional Observer Programs(ROPs)of Regional Fisheries Management Organizations(RFMOs)play an important role in ensuring the integrity of the fisheries management system,and one of their main responsibility is to describe the characteristics of the catch(Lawson,2006).All the five tRFMOs now have ROPs.But in most cases,the required coverage rate(CR)is not above 5%and the extent of coverage was defined differently as a percentage of catch,fishing days,sets or trips(Anderson et al.,2013).At a coverage of 5%or less,bycatch estimates are likely to remain highly imprecise for low occurrence species,although it may be still better than no coverage at all(Gilman,Passfield,&Nakamura,2012).

In most regional observer programs,only one observer can be allocated to a vessel because of the financial and logistic limits.Most of the times,not all hooks of each set selected by an observer can be recorded because of hard work and sea conditions,thus observation ratio(OR),which is the percentage of the hooks observed in a set,is often less than 100%.To some extent,the observer has the ability to record the occurrence of all the catches.

One of the most important tasks for observers is to record the size compositions of catches for target species like bigeye tuna(Thunnus obseus,BET),yellow fin tuna(Thunnus albacares,YFT)or Albacore(Thunnus alalunga,ALB).Information about the sample size required to adequately estimate length distributions is often vague(Miranda,1993).Sampling more individuals than necessary is inefficient and adds undue handling stress,particularly for an observer working along on a tuna longline fishing vessel.The objective of this study is to evaluate impacts of sample sizes on the accuracy of size composition for catches in tuna longline fisheries in western and central Pacific Ocean(WCPO)to found the relationships between the accuracy and precision of the estimates and the sample size.We developed a computer simulation method to evaluate how sample size(the number of individuals being measured,CR or OR)could affect the quantitative estimation of the length distribution.This study can provide an important reference for sampling design in regional observer programs with a limited coverage rate.

2.Materials and methods

2.1.Fishery observer data

Fig.3.The distribution of the observation ratio.(The bar is the frequency distribution of TRUE ORs,the dashed line in the middle is the mean value of ORs,and other two dashed line are the range of ORs in the simulation).

Data were collected by observers aboard tuna LL vessel target on BET or ALB during 15 trips and 1335 sets in WCPO in 2016.In accordance with CMM 2007-01(WCPFC,2007),the scientific observers were rigorously trained for collecting the fishery data of tunas and other pelagic fish stocks,including size-frequency data of all pelagic fishes and other marine animals.The data we used in this study include set information(including position,date,target species,the number of sets being observed and the OR for each set)and length data by species.The allocation of observed sets varied among months or target species.Nine fish species,including 3 target tuna species,4 bycatch fish species,and 2 key bycatch sharks with different body shapes(fusiform and elongated)were selected for the analysis(Table 1)(Fig.1).

2.2.Simulation procedure

In order to determine the relationship between sample size and accuracy and precision of estimated size composition,we developed a simulation framework(Fig.2).We started with estimating the indices(LFD and ML)with original data as the true value,and then resampled original data at a defined length interval and sample size 500 times with replacement randomly.The estimates of indices with the resample data and comparison indices were then calculated.At last,the performance of different scenarios were compared(Fig.2).For different species,length-frequency distributions(LFD)(4 kinds of length interval)and mean length(ML)were selected as indices.Mean square difference(MSD),relative estimate error(REE)and relative bias(RB)were used to measure the performance of each sampling scenario.We defined the sample size as the number of individuals,CR or OR and selected simple random sampling(SRS)as the sampling method.The CR in the simulation was defined as a percentage of sets.Six types of OR were selected for the simulation and each set was randomly selected from a normal distribution with the mean and standard deviation from the original observation ratio.Taking into account the actual situation,the random OR was limited at a reasonable range(0.2≥OR≥1)(Table 2 and Fig.3).

2.3.Measure for evaluating performance

Three indices were used to measure the performance of each sampling scheme.MSD was used to quantify the performance of estimated LFD(Vokoun et al.,2001),

Fig.4.Original length frequency distribution of 9 species with 5cm length interval.

where j is the selected CR,N is the number of length intervals,fiis the original length frequency,andis the sample length frequency of the ith length interval.REE was used to quantify the accuracy and precision of estimated mean length(Chen,1996)

We also calculated RB for the estimated mean as

whereYiextimateis the estimated mean in the ith simulated survey,Ytrueis the true mean,N is the number of simulation runs.The REE reflects both bias and variation in the estimation while the RB measures the estimation bias.A smaller REE or RB value suggests a better performance.RB indicates whether the sampling design tends to underestimate or overestimate the population mean(Paloheimo et al.,1996).

3.Results

3.1.Observed data

The number of individuals,means and CVs of length data(fork length from upper jaw to fork)and LFDs with 5cm length interval were different among species as shown in Fig.4.These results were considered to be true in this study.The number of individuals ranged from 467(FAL)to 20,800(ALB).ALB had the largest CV among these 9 species and BSH had the largest ML.All of the LFDs were close to normal distributions(Fig.4).

3.2.Resampling analysis

Overall,the mean MSD or REE decreased with sample sizes(the number of individuals,CR or OR),and the estimated length composition data became increasingly similar to the reference for all the species with sample sizes.The required sample size for achieving the same level of accuracy and precision or the optimal sample size differed among species(Figs.5 and 6).

3.2.1.Effect of the number of individuals

We calculated the mean MSD values of LFD estimates for different species with the same length intervals.The accuracy and precision of the estimated LFD increased with length intervals,increasing from 1 to 10cm.This was more obvious when the sample size was around 500(Fig.5a).This shows that LFD with larger length intervals was more likely to approach to the true length distribution in the simulation when only a small sample size was available because of constraints.The MSD values of LFD with different length intervals had similar breakpoints(around 1000)over which there was only little change in MSD with the increased number of individuals in sampling(Fig.5a).The mean values of MSD and REE for different species were also calculated to find the relationship between the performance indices and the sample size.For most species,the breakpoints were also at around 1000 individuals except ALB.The relationship between MSD and the number of sampled individuals for ALB was different compared with other species in this study(Fig.5b).The breakpoint was larger than 1000 for ALB,implying that more individuals should be measured to achieve the same level of accuracy and/or precision(The upper two panels in Fig.5).The performance measured in MSD had the following ranking(from the best to worst)for the 9 species:FAL,BSH,LEC,WAH,ALX,BET,SKJ,YFT,and ALB.Three groups could be identified according to their performance:the best performance group included five species(FAL,BSH,LEC,WAH and ALX),followed by the median three-species group(BET,SKJ and YFT),and ALB was the worst in performance(Fig.5b).

Fig.5.The performance(MSD,REE and RB)of the estimates of LFD and mean length with different sample size(number of individuals).

The performance for estimating the mean value of length was relatively good because the largest value of REE was less than 4%(Fig.5c).The breakpoints were also at around 1000.The difference still existed among species,although the difference in REE values among species was not the same as that for MSD.For example,to achieve the same value of REE,the smallest number of individuals was required for ALB.The REE ranking of ML estimates for different species from small to large was ALB,SKJ,WAH,YFT,BSH,BET,LEC,ALX,and FAL,suggesting that the species with the lower CV of length composition could perform better at the same level of sample sizes when the index was ML.At a given level of accuracy,the required number of individuals for estimating ML might be smaller than that for estimating LFD because of very low REE values.There was no positive or negative trend of the RB values for all the species.The RB was smaller and had more stable trends when the sample size was larger than 1000(Fig.5d).

3.2.2.Effect of the coverage rate and observation ratio

Based on the analysis above,only the length interval of 5cm was selected for the following analyses.Obviously,no matter what the index is and the OR or the species was,the performance was all improved with the CR although there were some differences among those scenarios(Fig.6).We calculated the mean performance indices(MSD and REE)values for the estimates for different species with the same observation ratio.As we know,a lower OR could lead to a higher value of MSD or REE.However,to some extents the differences among ORs were small when the OR was larger than 70%or a random one,which means there is no need to have 100%OR(Fig.6a and c).As the results shown above,the REEs also had lower values.The performance ranking for LFD was BET＞LEC＞YFT＞ALX＞BSH≈WAH＞FAL＞SKJ＞ALB and ALB＞BET＞YFT≈SKJ＞W(wǎng)AH＞LEC＞BSH≈ALX ＞ FAL for ML of which both were different with the ranking above(Fig.6b and d).

All of the RB values were small(most of the bias was less than 0.5%).But the bias of ML for some species had a tendency to be positive(BET,FAL,LEC,WSH,and YFT)or negative(WAH)when the OR was less than 100%or randomly selected(Fig.7).This indicates that the estimated ML tended to be larger or smaller than the true values.After further analysis,we found that if the deviations of the mean length for the sets with fewer catches were significantly positive for a specific species,this species tended to have positive biases,vice versa.There was no tendency when that pattern was not significant(Figs.7 and 8).

4.Discussion

Ignoring other factors,the larger the sample size could be the more representative the data are.We have to consider the constraints in fisheries-dependent surveys.Thus,optimal sample sizes should be able to balance the constraints.According to the analysis,we found that the indices for describing size compositions,length interval,the characteristics of species and acceptable accuracy and precision of the estimates are all potential factors that might affect the selection of optimal sample sizes.And also,observers may not be able to measure all the catches that are caught because of other priorities,or because they may not observe an entire haul if it continues beyond the end of a 12-h day.If large tallied catches represent schools of a particular size group of catches,failure to measure them may result in the under-estimation of the ML and the LFD of that size group as shown(Francis,2013).Thus,the sampling methods could also be an important factor.Other factors such as observer effects,inaccurate recording of data by observers,and inappropriate stratification may lead to bias in bycatch estimates(Babcock,Pikitch,&Hudson,2003).In this study,we focused on the relationship between the accuracy and precision of the estimates and the sample size.Thus,these observation processes were assumed to be unbiased.

For a given sample size,the smaller length interval is less accurate the estimates are(Vokoun et al.,2001).Although the difference was not that large sometimes,length intervals should be considered in determining the suitable sample size.Compared with previous studies(Vokoun et al.,2001),for fishes of large sizes in this study,around 1000 individual fish could be appropriate to effectively estimate LFDs.For estimating MLs,fewer individuals are required.Indices that require low sample sizes may be suitable for monitoring population status.When large changes in length are evident,additional sampling effort may be allocated to more precisely define length status with more informative estimators(Miranda,2007).Thus,both LFDs and MLs can be an effective index to indicate the status of different species by considering the limited observation effort and management priorities.But,for species with high priority,more detailed information(like the spatiotemporal structure of population)was necessary for reducing the uncertainties in stock assessment and management(Guan,Cao,Chen,&Cieri,2013).For the purpose,more samples should be collected from the whole fishery.The dataset from a well-designed sampling method with a rational CR could largely meet the requirement(Gilman et al.,2017).In this study,20%of CR seems to be an optimal sample size as shown in other similar studies(Allen et al.,2002;Conquest,Burr,Donnelly,Chavarria,&Gallucci,1996);but with a defined accuracy and precision,the required CR could be less than 10%or 5%for some species.

Fig.7.The relationship between RB of the estimates of ML and CR.

A non-random sample could be biased in representing the sampled populations(Cochran,1977).In theory,the observer should be randomly allocated to fishing vessels in the fishery.Previous studies showed that the observation efficiency could be improved by using an appropriate stratification scheme(Allen et al.,2002;Cotter,Course,Buckland,&Garrod,2002;Faunce,2015;Miller,Skalski,&Ianelli,2006).Also,the process to decide which catches should be measured must be unbiased if not all catches of each set could be measured.In practice,however,both of these two processes are unlikely random.The allocation of observer is largely based on the ability and opportunity of a vessel to accept an observer.If only a few catches(include both target and non-target species)were caught on one set,the observer tended to measure all the catches because of small workloads.Thus,the possibility of being measured for all the sampled individuals would not be the same.Small catch per set could lead to a higher possibility of being measured for the individuals on that set.If we randomly choose a certain percentage of baskets in one set,there could be no bias.In our simulation,the process of considering the OR was close to the reality because we randomly selected the individuals which should be measured from all catches in one set.Statistically,less catch means a higher possibility of being selected.Thus,if most of the individuals in the sets which had a few catches belonged to the large or small size group,the ML or the frequency of that group would be overestimated or underestimated(Figs.7 and 8).

In WCPFC,a number of shark species were designated as“key shark species”to support informed management decisions,ensure sound data reporting,and support members' obligations to other conventions and agreements(Tremblay-Boyer et al.,2016;WCPFC,2010).BSH and FAL are on the initial list.As the key sharks,the catch and effort information and relevant research efforts are required for those species.In our bycatch data,BSH and FAL were the two most common sharks,but the individuals were both less than 1000.Based on the analysis above,we don't expect any reduction in the number of individuals required to be measured by an observer for such species.Information such as trophic level,sex and maturity are also needed to be recorded for the ecosystem-based management.

5.Conclusion

We argue that the allocation of observation efforts among baskets,sets,and species should be carefully evaluated.In the process of determining measurement priorities of species or indices,the suitability of sample size also should be considered.For example,not each individual of a given species that have high catches(e.g.,the number of fish individuals captured is larger than 1000)are needed to be measured but the individuals that are expected to be measured should be sampled randomly,the OR should be larger than 70%,and the required CR is no more than 10%for most species if it is acceptable for the MSD values less than 5 or REE values less than 5%.

Because of limited data,we may not find the factors causing the difference in the optimal sample size for estimating LFD among species.We did not analyze sample sizes essential to capture the information about the spatio-temporal change in length composition and optimal sampling design.The optimal sample size should be carefully evaluated and determined.This study provides a good reference for the effective improvement of the observation efficiency to acquire reliable information about the fishery.

Acknowledgments

Fig.8.Comparisons of the mean deviation of ML for different species among sets with different number of catches.

The work was supported by the scientific observer program of the distant-water fishery of the Agriculture Ministry of China(08-25).We thank the National Data Centre for Distant-water Fisheries of China for providing the observer data(2006).We also thank the observers,the captains,and the crew who contributed to the collection of data.Libin Dai and many other colleagues have contributed to the discussion,for which we appreciate.The paper is written while the senior author studied in Dr.Chen's Lab at the University of Maine.