Journal of Marine Science and Technology, Vol. 24, No. 2, pp. 303-310 (2016 ) 303 DOI: 10.6119/JMST-015-0428-1

BAYESIAN HIERARCHICAL ANOVA MODEL OF STOCHASTIC SEASONALITY FOR Diodon holocanthus IN NORTHERN

TAIWAN

Hungyen Chen1, 2, Kwang-Tsao Shao3, and Hirohisa Kishino2

Key words: Bayesian inference, impingement sampling, nuclear power plant, spiny puffer, stochastic seasonality.

ABSTRACT

Detecting seasonal variation in ecological phenomena is not always possible by use of traditional methods. The pattern of seasonality fluctuates because of the stochasticity of environ-mental factors, correlations among organisms, and human activity. Here, we propose a Bayesian hierarchical analysis of variance (ANOVA) model of stochastic seasonality for de-tecting the annual fluctuation of seasonality. Using 11-year data recorded monthly at 2 nuclear power plants in northern Taiwan, we examined monthly fluctuations in fish species. To illustrate the performance of the proposed model, we conducted a sim-ulation that reflects the varying seasonality of species. The most dominant species, Diodon holocanthus, exhibited a shift in peak abundance from March to July that the traditional ANOVA model failed to detect. Our results suggest that im-pingement data obtained from the intakes of power plants are useful in studying the long-term temporal variation of fish spe-cies. The proposed model provides an in-depth examination of temporal variation for ecological analysis.

I. INTRODUCTION

Monitoring long-term marine species diversity patterns in fish communities is receiving increasing attention from ecologists and other researchers (Boyce et al., 2008; Kaschner et al., 2011; Trebilco et al., 2011). The impingement of living organisms

on power plant cooling water intakes in rivers, lakes, estuaries, and coasts provides valuable time-series information on aquatic communities (Love et al., 1998; Maes et al., 1998; Barnthouse, 2013; Lohner and Dixon, 2013; Seegert et al., 2013). Power plant intake screens are ideal locations for monitoring fish populations: when large volumes of water are drawn into a plant for cooling purposes, fish are impinged along with the incoming current. Impingement investigations have been conducted widely to assess fishery production and aquatic biodiversity losses (Hadderingh and Jager, 2002; Liao et al., 2004; Green-wood, 2008; Azila and Chong, 2010), and countermeasures have subsequently been implemented to reduce such impacts (Maes et al., 2004). Obtaining long-term biological monitor-ing data is difficult, and only a few studies have analyzed impingement data for monitoring purposes, and even fewer studies have elucidated temporal changes in biological commu-nities (Liao et al., 2004; Lohner and Dixon, 2013) or the effects of climate change (Henderson et al., 2011). Impingement sur-veys provide informative data for detecting community varia-tion (Greenwood, 2008), have low sampling error, and can be conducted over long periods. The selectivity of the filtering screen in water intakes has limited the range of fish collected through power plant impingement. However, the high consis-tency and efficiency of collecting schemes combined with long- term sampling efforts evince the usefulness of impingement data. To obtain long-term time series data and detect temporal changes in nearshore fish, we monitored impinged fish at nuclear power plants in northern Taiwan on a monthly basis during 2000-2011.

On the northern Taiwanese coast, two nuclear power plants, Jinshan Nuclear Power Plant (the first plant) and Kuosheng Nuclear Power Plant (the second plant), have been operated since 1977 and 1981, respectively, satisfying the massive electricity needs of the 6 million people in the nearby Taipei metropolitan area. The average generating capacity and com-bined water flow velocity of the first plant are 650 2 MW/h and 1.096 × 106 gal/min, respectively, and those of the second plant are 980 2 MW/h and 1.271 106 gal/min, respectively. These two power plants take over 6,000,000 tons of water monthly from the near-shore waters off northeastern Taiwan.

Paper submitted 01/19/15; revised 03/17/15; accepted 04/28/15. Authors for correspondence: Hungyen Chen and Kwang-Tsao Shao (e-mails: chen@lbm.ab.a.u-tokyo.ac.jp; zoskt@gate.sinica.edu.tw). 1 National Research Institute of Fisheries Science, Fisheries Research Agency,Kanagawa, Japan.

2 Graduate School of Agricultural and Life Sciences, University of Tokyo, Tokyo, Japan.

3 Biodiversity Research Center, Academia Sinica, Taipei, Taiwan, R.O.C.

304 Journal of Marine Science and Technology, Vol. 24, No. 2 (2016 )

The seasonal variation of fish species composition and abundance was observed in this study. Unlike economic and geophysical phenomena, fish species composition and abun-dance fluctuate seasonally because environmental factors are stochastic and different fish have different spawning seasons. The most abundant species in the assemblages of impinged fish in northern Taiwan, Diodon holocanthus, the spiny puffer, was used to test the annual seasonality of abundance during the sampling period. The monthly fluctuation of spiny puffer abun-dance by year was observed. The spiny puffer is not a com-mercially targeted fish species, and the adults are less subject to predation because of the long sharp spines that lie flat on their body surface. It generally ranges in length from 20 to 35 cm and may grow to 50 cm. Adults prefer shallow reefs and soft bottoms near the shore, whereas juveniles remain pelagic until reaching 6-9 cm in length (Froese and Pauly, 2013).

The sea floor around the intakes of both plants is a mixture of coral reefs, gravel, large boulders, and sandy patches. The shelf of northern Taiwan is highly dynamic because the Ku-roshio Current flows along its eastern side and frequently in-trudes on the shelf. The complex seafloor topography, geology, and substratum composition (such as sand, mud, gravel, rock, and coral reef) in the offshore areas, combined with the warm Kuroshio Current, have engendered a rich and highly diverse biota. This area is a crucial fishing ground used by local vil-lagers. Fish impingement data may provide a valuable re-source for elucidating long-term trends in fish communities in this area. Moreover, tractable statistical analysis of these data can facilitate identifying key driving forces responsible for the observed temporal variations in fish communities in this cru-cial fishing ground.

In this study, we examined monthly fluctuations in the abundance of the most dominant species, spiny puffer, in fish assemblages at nuclear reactor intakes in northern Taiwan during 2000-2011. To detect seasonal changes in the abun-dance of the spiny puffer during this period, we developed a Bayesian hierarchical ANOVA model with a stochastic sea-sonal component. To illustrate the performance of the model, we conducted a simulation that reflects the varying seasonality of species. The proposed model accurately described the yearly trend and monthly variation adjusted by shifting the abundance peak among years. Finally, we discuss the strengths and weaknesses of using impingement data in fish species and community studies.

II. MATERIALS AND METHODS

1. Impingement Fish Sampling

The long-term abundance data on the spiny puffer used in this study were collected from nuclear power plants at Shihman (the first plant, 25° 17′ 9″ N, 121 35′ 10″ E) and Yehliu (the second plant, 25° 12′ 10″ N, 121 39′ 45″ E), both situated in northern Taiwan. The coast on which the intake of the first plant was built is straighter than the coast adjacent to the second plant, which is located in an open bay along

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Fig. 1. Schematic figure explaining the second layer latent variable, wy,k,

in our model. Beginning with the second year, each year has a set of latent variable with nine elements, wy,k = 1 or 0 (y > 1, k = -4, …, 4, ∑kwy,k = 1 for each y). wy,j = 1 indicates that the state of the m-th month of the y-th year corresponds to the state of the (m + j)-th month of the first year. When (m + j) is larger than 12, the m-th month of the y-th year corresponds to the state of the (m + j - 12)-th month of the first year; when (m + j) is smaller than 1, it corresponds to the state of the (m + j + 12)-th month of the first year. Large circles indicate the month with the largest value in each year.

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Fig. 2. Monthly variation in spiny puffer abundance. Each open circle

represents a year from 2001 to 2011. The 12 radials represent 12 months in each year. Filled circles indicate the value in a given month. The diameter of each circle is proportional to the number of individuals.

Yehliu Cape. Fish samples were collected monthly from in-take screens at both plants from September 2000 to August 2011 (except for December 2006 and 2007 at both plants and January 2007 at the first plant). All samples were collected once every 30 days from the cooling water intake for 24 h from 9 AM to 9 AM on dates chosen using a systematic sampling

H. Chen et al.: Stochastic Seasonality of Diodon holocanthus 305

Diodon holocanthus

Hypoatherina woodwardi

Sardinella lemuru

Apogon cookii

Ostracion cubicus

Chaetodon auripes Kyphosus vaigiensis Lobotes surinamensis Trachurus japonicus Chanos chanos

Secutor insidiator Chromis notata Alectis ciliaris Petroscirtes breviceps

Fistularia petimba Mugil cephalus Plotosus lineatus Gazza minuta

Sardinella gibbosa Aluterus monoceros Stephanolepis cirrhifer Aluterus scriptus

Pempheris oualensis Liza macrolepis Apogon doederleini Abudefduf septemfasciatus

Abudefduf vaigiensis Trichiurus lepturus Siganus fuscescens Tylosurus crocodilus

Fig. 3. Yearly trend and monthly variation of abundance in 30 dominant species. Each open circle represents a year from 2001 to 2011. The 12 radials

represent 12 months in each year. Filled circles indicate the value in a given month. The area of each circle is proportional to the number of individuals. Yearly trend is represented by the gray line.

306 Journal of Marine Science and Technology, Vol. 24, No. 2 (2016 )

method (Cochran, 1977). The impinged fish on the finest mesh (1 cm2, fish smaller than this size, i.e., fish eggs and larval fish, may pass through the mesh and become entrained) were flushed into a sluiceway and then collected in a trash basket suspended outside the pumping house.

2. Bayesian Hierarchical ANOVA Model of Stochastic Seasonality

To incorporate stochastic seasonal variation, we propose the following Bayesian two-way ANOVA model for the latent variable zy,m for the m-th month of the y-th year:

zy,m = + y + m + y,m (1)

In the above equation, is the mean; αy is the year factor; m is the month factor, and the error term, y,m, follows N(0, 2) with mean = 0 and variance = 2. Given the value of wy, the abundance, ny,m, in the m-th month of the y-th year is as-sumed to follow a negative binomial distribution, NB(ezy,m, ), with mean = ezy,m and size = .

,

, ~ ( , )y m yz wy m yn w NB e

The second-layer latent variable, wy (-4 < wy < 4, the ob-served shifting is in the interval of 4 months), follows a Dirichlet compound multivariate distribution with the size being 1 and the parameter (1, 1, 1, 1, 1, 1, 1, 1, 1), describes the variability in seasonal patterns compared with the reference year (Fig. 1). The prior of 2 followed a normal distribution with a mean of 0 and a variance of 100,000. The prior of followed a gamma distribution with a shape parameter of 0.001 and a scale parameter of 1,000. Ten thousand runs (100,000 iterations with burn-in number 10) were performed using a Bayesian Markov chain Monte Carlo (MCMC) method as implemented in the software program WinBUGS (Lunn et al. 2000). All calculations and data analyses were performed using R program (R Development Core Team, 2014).

III. RESULTS

1. Monthly Fluctuations of Seasonality for the Spiny Puffer

The most abundant species in the assemblages, the spiny puffer, was the only species sufficiently abundant for testing the seasonality of abundance in each year during the sampling period. Fig. 2 shows the monthly fluctuations of spiny puffer abundance by year. The month with the highest number of individuals was March in 2001 and 2002 and shifted to April during 2004-2008. Finally, the peaks in the number of indi-viduals were observed in summer during 2009-2011. Fig. 3 illustrates the 11-year temporal variation of the 30 most domi-nant species (frequently observed species) in the assemblages of impinged fish, showing that seasonality of monthly abun-dance by year was clearly observed only for the spiny puffer.

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dance of results of traditional two-way ANOVA.

2. Traditional Two-Way ANOVA Failed to Detect the Stochastic Seasonality

The traditional 2-way ANOVA model failed to describe the stochastic seasonal variation of spiny puffer abundance by year. Fig. 4 shows the yearly trend and monthly variation determined using the traditional 2-way ANOVA model. In Fig. 4(b), the monthly effects are large in spring and summer and small in autumn and winter. In other words, the results ob-tained using the 2-way ANOVA model show vague seasonal variation of spiny puffer abundance because of the monthly fluctuations of seasonality. When the abundance peak is not fixed, the traditional 2-way ANOVA model can be used only to calculate the mean of each month among the years. Conse-quently, the true peak of the seasonality and yearly shift of the seasonality are difficult to observe.

3. Verification of Bayesian Hierarchical ANOVA Model of Stochastic Seasonality

To verify the effectiveness of our seasonal adjustment method, we simulated 11 years of data that exhibited distinct seasonality for each year (Fig. 5). In each year, the peak of abundance was set as 100 times greater than the abundance in other months. The peaks in each year varied from January to May among the 11 years. The yearly trend was included in the simulated data by setting the abundance as 4 times greater in Years 5, 6, 7, and 10 than that in the other years. The results obtained by analyzing the simulated data by using the trade tional 2-way ANOVA model do not describe the stochastic seasonal variation (Fig. 6(a)). By contrast, the results obtained using the Bayesian hierarchical ANOVA model reveal definite seasonality (the peak is clearly evident in March, Fig. 6(b)) throughout all years. Our Bayesian hierarchical ANOVA model accurately described the stochastic seasonality of the simulated data, which cannot be detected using the traditional 2-way ANOVA model.

H. Chen et al.: Stochastic Seasonality of Diodon holocanthus 307

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Fig. 5. Monthly variation of simulation data. Each open circle repre-

sents a year from the first to the eleventh year, and the 12 radials represent 12 months in each year. Filled circles indicate the value in each month. The diameter of each circle is proportional to the number of individuals.

Fig. 7. Yearly trend and monthly variation in spiny puffer abundance adjusted by the Bayesian hierarchical ANOVA model of stochas-tic seasonality. (a) Predicted seasonal component in each month. (b) Yearly trend. Each open circle in (a) represents a year from 2001 to 2011. The 12 radials represent 12 months in each year. Filled circles indicate the value in a given month. The diameter of each circle is proportional to the number of individuals.

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mixing and convergence to the posterior distributions (Fig. 8). Instead of the fixed monthly effect determined using the tra-ditional 2-way ANOVA, the predicted seasonal component of each month in each year is shown in Fig. 7(a). The seasonal component of the Bayesian examination of the spiny puffer indicates fluctuations in the peak of abundance from March to July over the 11 years and monthly variation within each year. Fig. 7(b) illustrates the yearly trend in 2002-2011 ob-tained using the Bayesian hierarchical ANOVA model. The yearly change of the second layer latent variable of spiny puffer abundance shows the variation of the peak in each year and its pattern of delay from March to summer throughout all years (Fig. 9).

Fig. 6. Monthly effect of simulation data (a) using traditional two-way ANOVA model and (b) adjusted by the varying seasonality using Bayesian hierarchical ANOVA model.

4. Bayesian Hierarchical ANOVA Model of Stochastic Seasonality for the Spiny Puffer

Our results clearly describe the yearly trend and monthly variation in spiny puffer abundance adjusted using the Bayes- ian hierarchical ANOVA model of stochastic seasonality (Fig. 7). The traces of the MCMC samples show thorough

IV. DISCUSSION

In In this study, we observed the stochastic seasonality of spiny puffer abundance in northern Taiwan over 11 years. The

308 Journal of Marine Science and Technology, Vol. 24, No. 2 (2016 )

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Fig. 9. The second layer latent variable of spiny puffer abundance from 2002-2011. Each panel represents the posterior mean of the second layer latent

variable, wy,k, k (month) = 4 (Nov), 3 (Dec), 2 (Jan), 1 (Feb), 0 (Mar), -1 (Apr), -2 (May), -3 (Jun), -4 (Jul), in each year from 10000 MCMC samples. The month with the largest number of individuals in 2001 is March (the 3rd month). In each MCMC sample, wy,j = 1 indicates that the state of the (3 - j)-th month of the y-th year corresponds to the state of the 3rd month of the first year. When (3 - j) is smaller than 1, wy,k proceeds in the reverse direction into the previous year. The varying seasonality compared with 2001 is described by the mean of each wy,k in each year.

seasonality cannot be detected using the traditional 2-way ANOVA model because the peak of abundance shifts by year. Therefore, we propose a Bayesian hierarchical ANOVA model in which the abundance peak in each year is fixed as the same month to describe the stochastic seasonality of spiny puffer abundance.

In the simulation study, we showed that when the abun-

dance peak shifts to different months throughout all years and the traditional 2-way ANOVA model is applied, the effect in each month is averaged and the abundance peak is lowered throughout all years. Consequently, observing the seasonality becomes difficult. Our Bayesian hierarchical ANOVA model enables fixing the month of the abundance peak in the second and subsequent years as the month of the abundance peak in

H. Chen et al.: Stochastic Seasonality of Diodon holocanthus 309

the first year. Thus, we can ensure that the ANOVA model does not reduce the monthly effects in the month of the abundance peak throughout all years. In addition, the pro-posed model can describe the variation of the peak by year (Fig. 9), which is crucial in studying temporal variation for ecological analysis. Our model provides an in-depth exami-nation for detecting seasonal variation in ecological phe-nomena.

The results showed a shift in the peak abundance of the spiny puffer from March to summer over the 11 years. Because the seasonality of spiny puffer abundance is due to the migra-tion of juveniles and young fish from open water to the coast, the observed changes in seasonality may be due to a change in environmental conditions caused by sea current and tempera-ture variations. In Taiwan, fish stocks that normally migrate southward with the China Coastal Current to Taiwan waters for spawning and wintering have been retreating northward, and warm-water species are being carried northward by the Kuroshio and South China Sea Currents (Hsieh et al., 2009).

According to our results and those of previous studies, the advantages and disadvantages of using impingement data in fish species and community studies are summarized here. Regarding the advantages, first, impingement is an efficient tool for collecting fish specimens because collecting fish in baskets is easy, fast, and simple. Second, impingement sam-pling can be conducted 24 h per day, 365 days per year during which a reactor is in operation. Third, no cost is involved be-cause impinged fish are an unavoidable byproduct of water cooling by power plants. Fourth, sampling is not affected by sea conditions. Thus, periodically collecting impingement samples and designing experiments involving these samples are easy. Finally, many varieties of benthic and pelagic mi-gratory fish that cannot be observed through traditional scuba diving can be caught (Shao and Kuo, 1988; Shao et al., 1990).

Regarding the disadvantages, many fish species cannot be collected through impingement, particularly deep water and coral reef fish with small home ranges. Only surface, mid-water pelagic species and coral reef fish that swim close to the shoreline can be impinged at intakes. Healthy fish with strong swimming abilities are unlikely to be impinged (Shao et al., 1990). Furthermore, the reliability and representativeness of qualitative impingement data are higher than those of quanti-tative impingement data because factors such as the intake velocity, wave or tidal cycle, typhoons, design of the intake bay, and chlorination may bias the quantity of impinged fish. All of these factors, in addition to normal seasonal migration, can affect fish impingement variation (Wyman and Dischel, 1984). Nevertheless, impingement data are useful in studying local fish communities if the 2 following assumptions are considered before any conclusions are drawn. First, the spe-cies composition determined using impingement data repre-sents only a portion of the local fish fauna. Second, unpre-dictable factors such as typhoons occasionally cause massive impingements, leading to poor time series estimates. To minimize the effect of massive impingements, increasing the

sample size by either increasing the sampling time or length-ening the study period is recommended (Shao et al., 1990). Alternatively, data obtained during massive impingements could be excluded.

For many ecological phenomena, seasonal patterns are caused by environmental variation and other effects such as the annual migration of animals and flowering of perennial plants. Detecting seasonal variation is not always possible by using traditional methods. The proposed model can describe yearly trends and monthly variation adjusted by shifting the peak of abundance throughout all years and provides an in-depth examination of temporal variation for ecological analysis.

ACKNOWLEDGMENTS

This work was supported in part by funding from the Japan Society for the Promotion of Science to H. Kishino. (Grant No. 22300095) and funding by Taiwan Power Company for a long- term monitoring project to K.-T. Shao. We thank Y.-C. Liao and J.-I. Tsai for assisting with the impinged fish monitoring survey and C.-Y. Chen for data management.

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