Journal of Marine Biology

Volume 2019, Article ID 7184634, 6 pages

https://doi.org/10.1155/2019/7184634

## Against Common Assumptions, the World’s Shark Bite Rates Are Decreasing

^{1}Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA^{2}Shark Research Institute, Princeton, NJ 08540, USA

Correspondence should be addressed to Erich Ritter; ude.fwu@rettire

Received 17 February 2019; Accepted 8 May 2019; Published 2 June 2019

Academic Editor: Garth L. Fletcher

Copyright © 2019 Erich Ritter et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The trends of the world’s top ten countries relating to shark bite rates, defined as the ratio of the annual number of shark bites of a country and its resident human population, were analyzed for the period 2000-2016. A nonparametric permutation-based methodology was used to determine whether the slope of the regression line of a country remained constant over time or whether so-called joinpoints, a core feature of the statistical software* Joinpoint*, occurred, at which the slope changes and a better fit could be obtained by applying a straight-line model. More than 90% of all shark bite incidents occurred along the US, Australia, South Africa, and New Zealand coasts. Since three of these coasts showed a negative trend when transformed into bite rates, the overall global trend is decreasing. Potential reasons for this decrease in shark bite rates—besides an increase in the world’s human population, resulting in more beach going people, and a decrease of sharks due to overfishing—are discussed.

#### 1. Introduction

Sharks are at the top of most people’s minds when entering the sea, for seemingly good reasons, considering the still prevalent shark hype stemming from news outlets around the world [1–3]. But the media is not the only source of erroneous shark bite lore [4]. Some of the experts, too, got carried away in the past when elaborating on this phenomenon [5–8]. The overall consensus is that shark bites are on the rise despite that the yearly bite counts range between eighty to a hundred incidents [9–12]. Considering that sharks still represent the most abundant top predators weighing over 50 kg on our planet and that millions of people swim in the seas each day, this yearly bite count remains extremely low when compared to other predators commonly involved in human incidents [13–16]. However, an even more surprising fact about bite count predictions is that the beach visiting populations directly affecting the bite numbers are regularly excluded from predicting long-term tendencies [9]. Such an approach is fallacious because the number of people bitten by sharks directly corresponds to the number of people entering the sea. Hence, trends and predictions must include the respective human population. To that extent, we introduced bite rates [13–16]: the ratio of annually reported shark bites for a given region to the annual estimated beach attendance for that region. The assumption is made that an equal number of these people, at some point, will enter the sea. Since beach attendance populations are not always determined, any population number that can be recognized as akin to the number of people attending a beach can be used as a valid substitute. Therefore, the regional, state, or country populace can be utilized as such a proxy [16].

By creating regression models—using the software package Joinpoint—to analyze the bite rate trends for the top ten countries from 2000 to 2016, we can determine if statistically significant changes in these trends have occurred. A model for the global bite rates was also created to determine the accuracy of the chosen method by predicting the bite rates for 2018 and comparing this number with the actual incident number of that year.

#### 2. Methods

The number of bites for 2000-2016 for the world’s top ten countries was drawn from the “Global Shark Attack File” incident dataset of the Shark Research Institute [17], which lists every encounter that ends in a human injury or damages a surfboard, boat, and so on. Due to the vast variety of what is labeled an “attack,” some of these incidents reflect biased occurrences, thus falsifying the trends, and so they were excluded from this study. Such incidents entailed spearfishing, surf and shark fishing, or shark feeding. Furthermore, all bumps into persons that did not render a wound or lacked any physical evidence of teeth marks on surfboards, kayaks, or boats were also excluded. Additionally, throughout the period, there were also a series of questionable deaths that were likely drowning incidents with later scavenging by sharks [18–20].

##### 2.1. Replacing Bite Counts with Bite Rates

To determine the bite trends for the top ten countries, we used bite rates instead of bite counts [13–15]. A bite rate is defined as the ratio of the annual bite count for a specified region to the corresponding beach going population or any related proxy [13–15]. Here, we used the population numbers of the respective countries to determine the rates.

##### 2.2. Incident Modeling through Time

We decided to employ the software* Joinpoint* 4.6.0.0 because it uses a modern nonparametric permutation-based methodology to test whether the slope of a regression line remains constant over time or whether there are so-called joinpoints at which the slope changes and a straight-line model then obtains a better fit. Such a regression test is used by the National Cancer Institute (NCI) to monitor cancer rates over time. We are using this modern epidemiology-based approach to benefit from the latest developments in this field.

In order to decide whether it is better to use a fixed slope linear model, we used the permutation method in which we randomly permuted residuals from the straight-line model, meaning we shuffled around the distances between the regression line and each observation [21]. We then calculated the test statistic T for the permutation dataset and measured how much evidence the data provides against the null hypothesis by estimating the proportion of the permutation datasets. The corresponding T values are at least as extreme as the one we observed with the original dataset. If the tests were significant, then at least one joinpoint existed at which the true slope has changed. Joinpoints can range from none to several within a single regression.

##### 2.3. Regression Models Used

Since the above-mentioned analysis did not reveal any joinpoints for any country, a fixed slope linear model for the different countries was used where stands for the bite counts in year , stands for the year , a stands for the regression intercept, and b stands for the slope of the regression line.

Although this simple linear regression model was sufficient for the individual countries, it was not adequate to measure the global trend, including predicting the number of bites for 2018. While individual countries show some regularity when it comes to bites, global bites rather fluctuate due to the occasional freak incidents in countries where bites are normally rare or even previously nonexistent. This variation made the simple linear regression model insufficient, and a better fit was needed. The best outcome was reached by transforming the bite counts to their natural log, and dividing these values by the respective population counts. Thus, a new response variable was proposed, following the new model:where ln stands for the natural log function and a and b stand for the (new) intercept and slope, respectively.

In order to predict the bite count for 2018, we obtained the predicted value of the natural log of the bite counts, divided by the matching population count, and retransformed the said value to the original unit for bite counts. For the prediction to obtain the intercept and slope, we used the regression procedure* proc reg* from the Statistical Analysis System (SAS).

During the remainder of the paper, we will refer to the ten countries with the most shark bites as merely the “top ten countries.”

#### 3. Results

The project aimed to determine if the shark bite numbers for the top ten countries were on the increase or not, and if the individual tendencies were linear or if joinpoints existed. In addition, a global model was also created and its accuracy tested by predicting the number of bites for 2018 and comparing that prediction with the actual number for that year.

Between 2000 and 2016, more than 80% of all shark bites occurred along the US and Australian shorelines, whereas the US, including Hawaii, had nearly three times as many bites as Australia for this period (Table 1). When adding South Africa and New Zealand to the top two countries, these top four countries record more than 90% of the world’s shark bites (Table 1).