# Risk assessment of radioisotope contamination for aquatic living resources in and around Japan

^{a}Research Center for Fisheries Management, National Research Institute of Fisheries Science, Fisheries Research Agency, Kanagawa 236-8648, Japan;^{b}Department of Mathematical Analysis and Statistical Inference, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan;^{c}Research Center for Fisheries Oceanography and Marine Ecosystem, National Research Institute of Fisheries Science, Fisheries Research Agency, Kanagawa 236-8648, Japan

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Edited by David Cox, Nuffield College, Oxford, United Kingdom, and approved January 26, 2016 (received for review October 6, 2015)

## Significance

Quantification of contamination risk caused by radioisotopes released from the Fukushima Dai-ichi nuclear power plant is useful for excluding or reducing groundless rumors about food safety. Our new statistical approach made it possible to evaluate the risk for aquatic food and showed that the present contamination levels of radiocesiums are low overall. However, some freshwater species still have relatively high risks. We also suggest the necessity of refining data collection plans to reduce detection limits in the future, because a small number of precise measurements are more valuable than many measurements that are below detection limits.

## Abstract

Food contamination caused by radioisotopes released from the Fukushima Dai-ichi nuclear power plant is of great public concern. The contamination risk for food items should be estimated depending on the characteristics and geographic environments of each item. However, evaluating current and future risk for food items is generally difficult because of small sample sizes, high detection limits, and insufficient survey periods. We evaluated the risk for aquatic food items exceeding a threshold of the radioactive cesium in each species and location using a statistical model. Here we show that the overall contamination risk for aquatic food items is very low. Some freshwater biota, however, are still highly contaminated, particularly in Fukushima. Highly contaminated fish generally tend to have large body size and high trophic levels.

The Fukushima Dai-ichi Nuclear Power Plant (FDNPP) accident caused by the catastrophic earthquake and tsunami on 11 March 2011 caused immense damage to human society in and around Japan by releasing large amounts of radioisotopes to the environment (1⇓⇓⇓–5). This accident has raised great public concern about food safety. The government of Japan has therefore been monitoring intensively the γ-emitting radioisotopes in various foods since March 2011, to prevent highly contaminated foods from being distributed in the market. The current monitoring targets are two cesium isotopes (radiocesiums),

Because of the continual leakage of contaminated water with traces of radioisotopes into the ocean from FDNPP after the accident, as reported by the Tokyo Electric Power Company (TEPCO) in August 2013 (6), concerns about radioisotope contamination of aquatic foods are being raised. Some reports have indicated that demersal fish off Fukushima are at the highest risk of all aquatic foods. Some researchers have reported that contamination levels in demersal fish had not decreased even a year after the accident (7), and the decrease was much slower than predicted at the end of 2012 (8). In contrast, others have reported that the concentration in most marine organisms, even including demersal fish in the Fukushima coastal waters, had decreased exponentially, although the radiocesium introduced into the ocean was rapidly transferred to marine organisms (9). These contradictory statements must confuse the general public.

The Ministry of Health, Labor, and Welfare (MHLW) in Japan has reported the inspection results of radioisotope contamination in various foods every month since the FDNPP accident (10). We extracted radiocesium measurement data for aquatic foods from the MHLW database. In addition to pairs of *Materials and Methods* for details). We used the data collected from 1April 2011 to 31 March 2015. Overall, we have 1,646 combinations of species and prefectures. However, the analysis of the radiocesium measurement data is not straightforward. Many measurement results have “N.D.” (not detected). This N.D. information does not mean that the item is free from contamination but that any radiocesium concentration is below the detection limit. The limit depends on the measurement conditions but is typically defined as the concentration that gives counts within 3 SDs of the counting error (9). These N.D. measurements are, in fact, missing data and do not occur at random. Therefore, when the contamination is low, they not only reduce precision, but also cause bias (11). In the most extreme case, all measurements for a specific species in a specific prefecture are N.D. Then it is more difficult to evaluate the contamination risk.

We developed a statistical method for quantifying the spatial and temporal contamination risk for foods. This method can handle missing data caused by detection limits. When parameter estimation was difficult because of small sample size, missing data, and shortage of data contrasts, a random-effects model was used, in which the data of similar species with similar sample locations (i.e., prefectures) are used to increase the amount of information available. The risk is defined as the probability that the sum of *D* Bq/kg (*D* = 20, 50, and 100)—that is, *Materials and Methods* for a full exposition of methods.

## Results and Discussion

The simple regression analysis for the difference between *Materials and Methods* and Fig. S1). Our statistical model generally fitted the data quite well (Dataset S1). The predicted species-specific and prefecture-specific risks [i.e.,

The risk of cesium contamination in Fukushima has steadily decreased from 1 April 2011 to 1 September 2015 (Fig. 1). The contamination risks of marine species are much smaller than those of freshwater species. The median

For the contamination risk map, we predicted the probability of aquatic foods with *Materials and Methods*). The number of groups with relatively high risk is largest in Fukushima, and the prefectures to the south of Fukushima generally tend to have higher risks than the northern prefectures (Fig. 2 and Figs. S2 and S3). This relatively high risk in the southern prefectures would result from the higher radioactive deposition accompanied by radioactive plume transport during mid-March 2011 (1, 16) and the polluted water mass transport southward from the FDNPP (17). Contamination risk tends to decrease as the distance from Fukushima increases. The risks for freshwater fish and freshwater crustaceans are high compared with those for other species groups such as marine fish. As expected from previous studies (7, 8), the contamination risk of demersal fish is highest in marine fish and much higher than that for pelagic fish. However, the conspicuous risk for demersal fish is limited to Fukushima (Fig. 2). The spatial and temporal risk transition indicates that the contamination of marine fish has rapidly dispersed even at the bottom of the sea since 11 March 2011 (Fig. 1, Dataset S1, and Figs. S2 and S3).

The predicted contamination risk higher than *Salvelinus leucomaenis leucomaenis* (whitespotted char) was higher than *Anguilla japonica* (Japanese eel) was higher than *Eisenia bicyclis*) showed slightly higher risk (

Table 1 shows the risks for representative fish in Fukushima. We selected those species somewhat subjectively. *Sebastes cheni* (Japanese white seaperch) and *Hexagrammos otakii* (fat greenling) are well known as highly contaminated demersal fish (7, 9, 18). *Salvelinus leucomaenis leucomaenis* and *Anguilla japonica* are highly contaminated freshwater and diadromous fish from our analysis. *Salvelinus leucomaenis leucomaenis* and *Anguilla japonica* in Fukushima have high risks compared with the highly contaminated demersal fish in Fukushima. Finally, *Trachurus japonicus* (Japanese jack mackerel) is a typical pelagic fish and selected as a reference. The information for all species in all prefectures is provided in Dataset S2.

We conducted multiple regression for the parameters [*ρ*, and *Materials and Methods*). We used trophic level (TL), the logarithm of asymptotic length [*ρ* and *A*), this suggests that the initial contamination was not significantly different among fish with different TLs, although there are differences in the species and prefectures probably caused by the massive explosion. The dispersion rates are different for different TLs or body sizes, probably because of bioaccumulation (13, 21). In fact, *S. leucomaenis leucomaenis* and *A. japonica* have relatively large asymptotic body sizes and high trophic levels (Dataset S2). We also performed the model selection using the Bayesian information criterion (BIC) and the AIC with small-sample bias adjustment (AICc) (20). In either case, the two variables, *ρ* and TL for

The contamination risks of freshwater fish, freshwater crustaceans, and diadromous fish are relatively high, as indicated in earlier studies (22). However, freshwater fish used as food in Japan are usually not wild but cultured. Thus, because the radiocesium concentration of cultured fish tends to be low (10), the high contamination risk of wild freshwater fish around Fukushima should not be a serious food concern but is a vital problem for recreational fisheries and tourism industries because even leisure fishing is restricted or prohibited if a fish exceeding the limit (100 Bq/kg) is caught. Although the Japanese freshwater system is very complex with many short rivers with small flows, continuing careful monitoring and increasing sample sizes for these species is important as an indicator of environmental contamination (22).

In conclusion, our analysis showed that the present contamination levels of radiocesiums were low overall, even for demersal fish, although some freshwater species still have relatively high risks. Although many N.D. data have made radiocesium risk assessment of foods difficult, our method made it possible to evaluate the risk for each food item and to produce a big picture of contamination risk. Our methodology could contribute greatly to decision-making for quick and effective recovery from the FDNPP accident. Whereas our method can quantify risks even when all data are N.D., high detection limits tend to cause biased results. We therefore recommend data collection plans with lower detection limits in the future.

## Materials and Methods

### Aquatic Food Data.

The radioisotope contamination data published by the MHLW in Japan come from monthly inspections and contain various food items including drinking water, farm products, dairy products, stock farm products, and seafood. Each observation in the data has species name, prefecture, date of official announcement of measurement, and measured values of

The sampling was carried out by research ships and commissioned fishing boats of the Japanese and prefectural governments for major fishery items, including 472 species on major fishery sites (23). The numbers of species for main prefectures are shown in Dataset S3. The researchers selected the sampled species based on their habitats, including the surface layer, middle layer, deep layer, and seaweed, in each fishery season. Consequently, the sampling covered the relevant geographical areas of sea. The area of sea for each prefecture was defined by the area enclosed between the extended boundaries of the prefecture and the line marking 200 nautical miles off the Japanese main islands.

The data used in this article were collected from 1 April 2011 to 31 March 2015. We set the starting date in our analysis to 1 April 2011 because the peak ocean discharge occurred 1 mo after the earthquake (1, 24). We then excluded aquacultured fish and processed foods like fried fish before analysis. As a result, the data consist of 68,894 measurements with independent inspections. We have 1,646 combinations of species and prefectures.

The measurements of radiocesiums were sometimes recorded as less than a threshold value (detection limit), for instance,

Before the risk analysis, we regressed the difference between

### Basic Model Structure.

The probability distribution for contamination of radiocesium was modeled by a Weibull distribution, a two-parameter extension of the exponential distribution that allows flexible modeling. This distribution is widely used in survival analysis (26)

where *x* is the contamination level for either *μ* is the scale parameter, and *k* is the shape parameter. To take into account the temporal change of contamination level, the scale parameter *μ* of the Weibull distribution was modeled using

Here, *m* is the parameter related to the initial contamination level on 1 April 2011 {the mean of a Weibull distribution is *t* is the cumulative days from 1 April 2011. This variable was calculated using sampling dates obtained by subtracting 7 d from the announcement dates to adjust for the delay between announcement and measurement. The coefficient *λ* is the dispersion rate caused by radioactive decay, which is calculated by *ρ* is the dispersion rate caused by ecological processes, which includes all decays other than physical decay, including biological and environmental factors, and is calculated by

where *c* is an indicator variable that represents whether the observation is above the detection limit or not (above:

Because the physical half-life is known, the parameters to be estimated are *m*, *ρ*, and *k*. Estimation of parameters is done using a maximum likelihood method (26). Although *m* values can be different between

### Risk Assessment.

After the parameters— *m*, *ρ*, and *k*—have been estimated by maximizing the log-likelihood function, the probability that the sum of *D* Bq/kg on a specific date is calculated using the convolution operation for summation of random variables (28)

where *D* is set to 20, 50, or 100. The limit of radiocesium concentration in Japan was reduced to 100 from 500 Bq/kg on 1 April 2012. Currently, 100 Bq/kg is the standard limit for general foods where food safety is basically secured (29, 30); 20 Bq/kg is the maximum detection limit of the sum of radiocesiums recommended by the Japanese government (25), and 50 Bq/kg is the standard limit for infant foods (30).

### Extrapolation Through the Random-Effects Model for the Data Poor Cases.

The parameter estimation using the Weibull model did not always converge and sometimes produced extremely unrealistic time trends when the number of parameters was greater than the number of observed data values and/or the time span of the data were short, making it difficult to estimate *ρ*. For those cases, we first estimated the *ρ* parameter depending on species group and prefecture group using the random-effects model with a multivariate normal distribution for the converged outcomes, and then substituted the estimated *ρ* in the model and estimated *k* and *m*. Here we used 13 species groups based on similarities of biological and ecological characteristics. The groups are freshwater fish, diadromous fish, demersal fish, pelagic fish, sharks and rays, freshwater crustaceans, marine crustaceans, freshwater molluscs, marine molluscs, cephalopods, aquatic mammals, aquatic invertebrates, and seaweeds. The prefectures were also divided into 13 groups based on their closeness to Fukushima and the sample sizes. The groups are Hokkaido, Aomori, Iwate, Miyagi, Fukushima, Ibaraki, Tochigi, Gunma, Chiba, Saitama, Tokyo, Kanagawa, and Others (Fig. 2 and Dataset S2). The probability model is given by

where *i* corresponds to species group, and *j* corresponds to prefecture group. *ρ* for observations that cannot estimate *ρ* by themselves. If the parameter estimation does not converge even when *ρ* is given, we estimated the *k* parameter depending on species group and prefecture group using the random-effects model with a multivariate normal distribution for the converged outcomes, and then substituted the estimated *k* in the model and estimated only *m*. The probability model for *ρ*. Thus, we could estimate the parameters for all datasets except those in which all data are N.D., in which case the minimum replacement method that follows was used.

### Minimum Replacement Method.

Here we focus on the situation where all of the data are reported as detection limit values. The maximum likelihood estimate for the mean *μ* is then always 0 because the likelihood function is strictly monotone decreasing. This case is known as an improper problem for maximum likelihood. However, the inference would lead to severe bias if we disregarded such data. We therefore propose a reasonable method for estimating *μ*. We hypothetically assume that the minimum of detection limit values, say *μ* because the censored observation, or the interval data

When applying this method to our data, we must make the data revert to the hypothetical measurement on a common specific date. Using the estimate *ρ* or *t* is the cumulative days from 1 April 2011. We then assume that the minimum in the transformed data was an observed value. Given *ρ* and *k* from the random-effects models, we can estimate *m* using the maximum likelihood method.

### The Risk Map of Radioisotope Contamination.

The risk map of radioisotope contamination was generated using a binomial regression model for binary outcomes with 1 if *y*) is given by

where *ω* is the expected value of binary outcomes, *i* corresponds to species group, and *j* corresponds to prefecture group. *ω*) is the expected value of risk that

### Multiple Linear Regression Between the Weibull Parameters and Trophic Level.

To examine the relationship between radiocesium contamination and biological characteristics, we performed a multiple linear regression between the Weibull parameters (*m*, *ρ*, and *k*) and trophic level or asymptotic body length (

where *α*s are regression parameters, and

and

The variable selection for each model was done using AIC (20). As a sensitivity test, we also used BIC or AICc. When the coefficients for TL and

All statistical analyses and figures were made using the programs R (version 3.20) and AD Model Builder, version 2.11.1 (33, 34). We provided the SEs for the risks when we could estimate all three parameters—*m*, *ρ*, and *k*—from data without depending on the random-effects model. The SEs were evaluated using the Hessian matrix and the delta method (26) whenever possible (Dataset S2). However, when we could not estimate *ρ* and/or *k* without the random-effects model, we were not able to evaluate the SEs for the risks. Because we put more importance on the overall assessment of radiocesium contamination, estimation uncertainty was ignored in the overall assessment of contamination risk because most estimations are based on extrapolation and the minimum replacement method. In fact, estimation uncertainty has been ignored in many post hoc analyses; nevertheless, such analyses have continued to provide important knowledge for us (35). However, ignoring estimation errors can result in an inadequate recognition of the uncertainty and may compromise the soundness of results and confidence in them (36). Therefore, developing a new approach to incorporate estimation uncertainty into our method appropriately will be a first priority in the future.

## Acknowledgments

We thank Drs. Fumihito Muto and Kouichi Hoshino for advice on scientific names. This research was partly supported by Japan Science and Technology Agency (JST), CREST.

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. Email: okamura{at}fra.affrc.go.jp.

Author contributions: H.O. designed research; H.O. performed research; H.O., S.I., T.M., and S.E. contributed new reagents/analytic tools; H.O. analyzed data; and H.O., S.I., T.M., and S.E. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

See Commentary on page 3720.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1519792113/-/DCSupplemental.

Freely available online through the PNAS open access option.

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