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Previous studies have estimated the size, mass, and population of hypothetical unknown animals in a large oligotrophic freshwater loch in Scotland based on biomass and other observational considerations. The “eel hypothesis” proposes that the anthrozoological phenomenon at Loch Ness can be explained in part by observations of large specimens of European eel (

This study expands upon the “eel hypothesis” and related literature by estimating the probability of observing eels at least as large as have been proposed, using catch data from Loch Ness and other freshwater bodies in Europe.

Skew normal and generalized extreme value distributions were fitted to eel body length distributions to estimate cumulative distribution functions from which probabilities were obtained.

The chances of finding a large eel in Loch Ness are around 1 in 50,000 for a 1-meter specimen, which is reasonable given the loch’s fish stock and suggests some sightings of smaller unknown animals may be accounted for by large eels. However, the probability of finding a specimen upward of 6 meters is essentially zero; therefore, eels probably do not account for sightings of larger animals.

The existence of exceedingly large eels in the loch is not likely based on purely statistical considerations. (Reviewed by the Plan P #PeerRef Community).

Loch Ness is a large oligotrophic freshwater loch located along the Great Glen Fault in Scotland. Since the 1930s, purported sightings of unknown animals in the loch have featured prominently in popular media, but to date, no specimen has been obtained despite numerous efforts, making the probability of such animals unlikely.

The authenticity and interpretations of photographs and films allegedly depicting unknown animals in Loch Ness have been seriously doubted [

In the 1970s, a sample of European eels (

Mackal [

An environmental DNA (eDNA) study conducted at the loch in 2018 detected extraordinary amounts of mitochondrial DNA and nuclear DNA from eels [

Simon [

Much larger estimates have been made. Based on their “flipper” photograph, Scott and Rines [

Finally, in an article titled “If there are any, could there be many?” Carl Sagan [

Data on the mass distribution of

Mackal [

_{10}(1000_{10}(100

for mass

Rearranging equation 1 gives:

^{0.316596}

from which the lengths of eels in Mackal’s [

Skew normal and generalized extreme value distributions were fitted to the Loch Ness eel length distribution, and fit parameters were used to estimate the probability density function and cumulative distribution function (CDF).

The probability of finding an eel in Loch Ness at least as long as

For comparison, the above analysis was repeated with publicly available length data on 420 European eels captured in Zeeschelde, Belgium presented in Verhelst et al [

All analyses were performed in Python 3.8.8 (Python Software Foundation) with the packages Numpy 1.20.1, Pandas 1.2.4, Matplotlib 3.3.4, and Scipy 1.6.2. All code and data are available on the web [

This work uses only publicly available secondary data on animal subjects. It did not involve any experiments or interactions with animals and did not compromise their welfare in any manner.

The length distributions for the Loch Ness and Zeeschelde eel samples are shown in the upper plots of

The probabilities of finding an eel at least as big as

While the chance of finding a large eel approximately 1 meter in length in Loch Ness is low (around 1 in 50,000), this is certainly possible given the eel population of the loch: assuming a standing fish stock of 0.55 kg ha^{−1} for Loch Ness [

However, this is not quite the “monster” postulated. Indeed, the probability of finding a 6-meter eel in Loch Ness is essentially zero—too low for the software used to provide a reliable estimate. Thus, while large eels may account for some eyewitness sightings of large animate objects rising to the loch surface, they are unlikely to account for “sightings” of extraordinarily large animals, which may instead be accounted for by wave phenomena, the occasional stray mammal, or other reasons.

Length distributions for European eels (Anguilla anguilla) captured in Loch Ness, Scotland (left) and in Zeeschelde, Belgium (right). The lower plots show the probability of finding an eel at least as long as L. Dotted lines represent skew normal distribution fits. Dashed lines represent generalized extreme value distribution fits. The number of bins follows the rule provided by Freedman and Diaconis [

Probabilities associated with finding a European eel (Anguilla anguilla) at least as large as length (

Length (meters) | Loch Ness ^{a} |
Zeeschelde ^{a} |
Note |

0.505 |
0.238 0.239 |
0.619 0.590 |
Maximum length from sample of 43 European eels in the river Vjosa/Aoos, (Albania/Greece; 2018). Source: Figure 4 of Meulenbroek et al [ |

0.645 |
0.0399 0.0294 |
0.264 0.240 |
Maximum length from sample of 129 European eels in Loch Ness, Scotland (1970-1971). Source: Appendix G of Mackal [ |

0.662 |
0.0307 0.0216 |
0.228 0.206 |
Maximum length from sample of 199 female yellow European eels in the River Havel system, Germany (2001). Source: Table 3 of Simon [ |

0.784 |
0.00348 0.00155 |
0.0592 0.0511 |
Maximum length from sample of 20,108 European eels in the Camargue lagoons, France (1993-2003). Source: Table II of Melia et al [ |

0.932 |
1.20 × 10 1.13 × 10 |
0.00537 0.00443 |
Maximum length from sample of 420 European eels in Zeeschelde, Belgium (2015-2017). Source: Supplemental Information of Verhelst et al [ |

1.30 |
8.18 × 10 ~0 |
2.71 × 10 2.20 × 10 |
Physiologically possible maximum length of female yellow European eel in the River Havel system, Germany. Source: Abstract of Simon [ |

2.40 |
5.55 × 10 ~0 |
2.22 × 10 ~0 |
Upper size estimate for “Surgeon’s Photograph” subject. Source: LeBlond and Collins [ |

6.10 |
6.66 × 10 ~0 |
~0 ~0 |
Size estimate for hypothetical unknown animals in Loch Ness (“up to 20 ft.”). Source: Chapter XIV of Mackal [ |

^{a}The first value in each cell of this column corresponds to the skew normal distribution and the second value corresponds to the generalized extreme value distribution.

This study used data on the distribution of European eel (

However, these analyses suggest that larger eels upward of 6 meters are highly improbable; therefore, “super” eels are an unlikely explanation for eyewitness reports of the very largest alleged animals at Loch Ness. Marine Scotland Science has reported growth rates of eels on the Girnock tributary of the River Dee in Scotland as high as 35.2 mm yr^{−1} [

Though one European eel reportedly (unverified) lived to the grand age of 155 years [

This analysis is limited by several factors. First, the Loch Ness eel sample used was relatively small at 129. Larger samples across longer time periods may provide more accurate estimates. Second, the assumption of a skew normal distribution would not hold if, for example, a larger sample revealed a bimodal distribution of eel lengths with a small peak at higher lengths. Third, this analysis is based on purely statistical considerations; the biological mechanism behind the physiological possibility of much larger eels is beyond the scope of this study. Some authors have suggested one such mechanism as neoteny [

In conclusion, while Sagan [

1.05-meter female silver eel. Image courtesy of Dr Derek W Evans from the Agri-Food and Biosciences Institute.

Academy of Applied Science

cumulative distribution function

environmental DNA

This work was not supported by any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

The author thanks Charles GM Paxton, Dr Don Jellyman, and Dr Derek W Evans for helpful comments and suggestions.

The data and code generated or analyzed during this study are available on OSF [

None declared.

This paper was peer-reviewed by the Plan P Hashtag Community partner #PeerRef.