Peer-Review Report by Derek W Evans: https://bio.jmirx.org/2023/1/e50624/
Peer-Review Report by Don Jellyman: https://bio.jmirx.org/2023/1/e50621/
Authors' Response to Peer-Review Reports: https://bio.jmirx.org/2023/1/e50618/
Background: 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 (Anguilla anguilla), as these animals are most compatible with morphological, behavioral, and environmental considerations.
Objective: 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.
Methods: Skew normal and generalized extreme value distributions were fitted to eel body length distributions to estimate cumulative distribution functions from which probabilities were obtained.
Results: 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.
Conclusions: 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 20th century, systematic searches with submersibles, sector-scanning sonar surveys, hydrophones, underwater photography, long-lining, and trawling undertaken by the Loch Ness Investigation Bureau [ ], the Academy of Applied Science (AAS) [ - ], and the Loch Ness and Morar Project [ ] have returned only ambiguous sonar signals, low-quality photographs, and unidentifiable sound recordings.
In the 1970s, a sample of European eels (Anguilla anguilla) was collected from Loch Ness with baited traps. The distribution of eel masses was skewed, which led biologist Roy Mackal  to conclude that large eels may exist in the loch. Eel body structure and function are characterized by an elongated body form, a single pair of pectoral fins, strong musculature and high-amplitude winding movement, and a durable integument with a thick epidermis and dark chromatophores [ ].
Mackal  noted that large eels would therefore be consistent with eyewitness descriptions of Loch Ness animals including reports of an elongated head-neck, pectoral fins, extreme flexion, and dark integument [ , ]. This explanation has also been reviewed by naturalists Adrian Shine and David Martin of the Loch Ness and Morar Project, who noted that eels migrate via the River Ness and that most “sightings” occur near river mouths [ ].
An environmental DNA (eDNA) study conducted at the loch in 2018 detected extraordinary amounts of mitochondrial DNA and nuclear DNA from eels , prompting principal investigator Neil Gemmell to further suggest the possibility of large eels in the loch [ ]. A large eel-shaped animal was recently filmed in the River Ness by the Ness Fishery Board [ ].
Simon  suggests that the physiologically possible maximum length of A. anguilla is 0.5-1.3 meters, which is not particularly monstrous. Using wave mechanics, LeBlond and Collins [ ] estimated the size of the subject depicted in the infamous “Surgeon’s Photograph” at Loch Ness at 0.6-2.4 meters.
Much larger estimates have been made. Based on their “flipper” photograph, Scott and Rines  estimated a total body length of 15-20 meters for an unknown Loch Ness animal. These estimates seem inconsistent with Loch Ness biomass calculations. Sheldon and Kerr [ , ] estimated a population of 156 if the individual mass of a hypothetical unknown animal in Loch Ness is 100 kilograms and suggested just one individual can exist if its mass is 2000-3000 kilograms. Scheider and Wallis [ ] estimated that the loch may support 157 animals of 100 kilograms each and 10 animals of 1500 kilograms each.
Finally, in an article titled “If there are any, could there be many?” Carl Sagan  used collision physics and suggested that a population of 300 animals that were 10 meters in size each would be consistent with AAS observations. Thus, if there are any, there may be many. If it’s real, could it be an eel? The aim of this study is to estimate the probability of finding various sizes of eel in Loch Ness based on available catch data.
Data on the mass distribution of A. anguilla in Loch Ness were taken from 129 eels caught between 1970 and 1971 under the supervision of the Loch Ness Investigation Bureau and described in Mackal .
Mackal  does not provide the length distribution for the sample nor did Mackal [ ] directly regress length on mass. Mackal [ ] did regress functions of length on mass and maximum circumference but provided only nonlinear equations unsuitable for solving simultaneously. Thus, to convert the mass distribution into a length distribution, the relationship between mass and length in A. anguilla captured in Scottish freshwaters from 1986 to 2008 was taken from Figure 2 of Oliver et al [ ] as:
log10(1000M) = 3.1586 log10(100L) – 3.0076 (1)
for mass M in kilograms and length L in meters. This equation is used over alternatives such as that in Figure 2(b) of Simon  because equation 1 is most relevant to Loch Ness (having been derived from Scottish freshwater).
Rearranging equation 1 gives:
L ≈ 0.797961M0.316596(2)
from which the lengths of eels in Mackal’s  sample were estimated.
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 L was then estimated from the CDF as:
P(l < L) = 1 – CDF(L) (3)
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 . Zeeschelde was selected because raw data were available, whereas this is not the case for other published analyses.
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 . Maps of locations referenced throughout the manuscript in order of reference are also 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 fits were similar for both skew normal and generalized extreme value distributions. The distribution for Loch Ness is evidently skewed toward lower lengths, similar to the length distribution of European eels presented in Figure 2 of Melia et al [ ] for eels captured in the Camargue lagoons of France. The Zeeschelde distribution has notably less skew. The length distribution in a sample of eels in Vistonis Lake, Greece was skewed toward higher lengths (see Figure 2 of Macnamara et al [ ]), suggesting much variability in eel length skew across different environments.
The probabilities of finding an eel at least as big as L in Loch Ness and in Zeeschelde are shown in the lower plots of. Loch Ness has a comparatively low probability of finding larger eels 0.6-0.8 meters in length, and the probability of finding an eel in excess of 1 meter in length is very low for both environments.
contains the estimated probabilities for specific lengths of interest. Results were somewhat similar for skew normal and generalized extreme value fits, and for both Loch Ness and Zeeschelde.
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 [, ] and given a surface area of 5600 hectares, the total standing fish stock of the loch is approximately 3080 kg. Further assuming that half of this stock is eel mass (plausible given the Loch Ness eDNA study [ ]), this would imply 1540 kg of eel in the loch. The average Loch Ness eel mass is 0.1857 kg [ ]; therefore, there are over 8000 eels in Loch Ness at a given time. Over the course of a few generations, an eel 1 meter in length may be expected.
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 (meters)||Loch Ness P (l>L)a||Zeeschelde P (l>L)a||Note|
|0.505||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||Maximum length from sample of 129 European eels in Loch Ness, Scotland (1970-1971). Source: Appendix G of Mackal |
|0.662||Maximum length from sample of 199 female yellow European eels in the River Havel system, Germany (2001). Source: Table 3 of Simon |
|0.784||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||Maximum length from sample of 420 European eels in Zeeschelde, Belgium (2015-2017). Source: Supplemental Information of Verhelst et al |
|1.30||Physiologically possible maximum length of female yellow European eel in the River Havel system, Germany. Source: Abstract of Simon |
|2.40||Upper size estimate for “Surgeon’s Photograph” subject. Source: LeBlond and Collins |
|6.10||Size estimate for hypothetical unknown animals in Loch Ness (“up to 20 ft.”). Source: Chapter XIV of Mackal |
aThe 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 (A. anguilla) masses in an oligotrophic freshwater loch in Scotland to estimate the probability of finding an eel of extraordinary size there. Similar to other eel populations in Europe, the average eel length in Loch Ness is relatively small and highly comparable to biometric data on silver eels (sexually mature A. anguilla) collected in the same decade at the Girnock Burn fish trap on the River Dee in Aberdeenshire, Scotland (see Table 5.3 of Bašić et al ), suggesting Loch Ness eels are similar to those found elsewhere in the country. The findings of this study suggest that the chance of finding a 1-meter eel in the loch (1 in 50,000) is reasonable given the standing fish stock, and so some eels may account for purported sightings of somewhat large animals at the loch surface. For comparative purposes, shows an image of a female silver eel 1.05 meters in length. Other images of European eels in excess of 1 meter in length are provided on the web [ ].
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 . Assuming a linear rate of growth throughout the life cycle of an eel (in reality, the rate of change of an eel’s total length is an exponential decay curve, as described by Tesch and Thorpe [ ]), it would take an eel in Scotland almost 30 years at such a growth rate to reach the 1-meter size. Given that the oldest eels can live for a number of decades [ ], again it seems likely that approximately 1 meter is a realistic maximum length for eels in Loch Ness; a 6-meter specimen would need to live with constant high growth for almost 200 years, an age close to the longest-living fish, the Greenland shark (Somniosus microcephalus).
Though one European eel reportedly (unverified) lived to the grand age of 155 years , that specimen did not grow to a remarkable size because eel growth is nonlinear, slowing in older ages. Furthermore, the “breaching” behavior attributed to unknown Loch Ness animals (swimming upward and out of the water) is not a behavior that is characteristic of eels during migration or otherwise [ ], especially as such behavior would represent unnecessary energy expenditure in a cold environment with relatively little food.
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  (ie, uncontrolled growth of the leptocephalus larva in A. anguilla preceding subsequent stages of development [ ]). Fourth, environmental conditions such as temperature and available biomass impact eel growth and length; therefore, comparisons to other environments such as Zeeschelde may not be appropriate (ie, some of the data cited may not be relevant to the relatively cold waters of Loch Ness).
In conclusion, while Sagan  found that if there are any, there may be many, this study shows that if it’s real, it could be an eel, but not a very large one.
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 .
Conflicts of Interest
This paper was peer-reviewed by the Plan P Hashtag Community partner #PeerRef.
- Martin D, Boyd A. Nessie: The Surgeon's Photograph Exposed. Herts, UK: Twayne Publishers; 1999.
- Shine A. The Dinsdale Loch Ness Film. An Image Analysis. Loch Ness Investigation. 2003. URL: http://www.lochnessinvestigation.com/dinsdale%20paper%202003%20V2.pdf [accessed 2023-07-12]
- Raynor D. Bird effects. Loch Ness Investigation. 2009. URL: https://web.archive.org/web/20090311010529/http://www.lochnessinvestigation.com/Mergansers.html [accessed 2023-07-12]
- Raynor D. Reflections on Tim Dinsdale's 1960 film. Loch Ness Investigation. 2010. URL: https://web.archive.org/web/20220203133626/http://www.lochnessinvestigation.com/Remembered.html [accessed 2023-07-12]
- Campbell S. Monster or boat. Photographic J 1986;126(2):54-58
- Mackal RP. The Monsters of Loch Ness. London, UK: Macdonald and Jane's; 1976.
- Scott P, Rines R. Naming the Loch Ness monster. Nature 1975 Dec;258(5535):466-468 [CrossRef]
- Klein M, Rines R, Dinsdale T, Foster L. Underwater search at Loch Ness. Monograph Acad Appl Sci 1972:1-104
- Rines RH. Summarizing a decade of underwater studies at Loch Ness. Cryptozoology 1982;1:24-32
- Rines R, Curtis H. Loch Ness: the big one that got away- again. Technol Rev 1979;81(7):14-16
- Rines R, Edgerton H, Needleman R. Activities of the Academy of Applied Science related to investigations at Loch Ness, 1984. Cryptozoology 1984;3:71-73
- Edgerton H, Wyckoff C, Rines R, Needleman R, Rines J. AAS underwater elapsed time camera silhouette photography experiments at Loch Ness, 1989. Cryptozoology 1989;8:58-63
- Shine A. Loch Ness. Drumnadrochit, UK: Loch Ness Project; 2006.
- Kloppmann M. Body structure and functions. In: Tesch FW, Thorpe JE, editors. The Eel. Hoboken, NJ: John Wiley & Sons; 2003:1-71
- Gibson J, Heppell D. The search for Nessie in the 1980s - part one. In: The Scottish Naturalist. 1988 Presented at: International Society of Cryptozoology Symposium on the Loch Ness Monster; July 25, 1987; Edinburgh, UK URL: https://archive.org/details/scottishnaturali1002scot
- Gibson J, Heppell D. The search for Nessie in the 1980s - part two. In: The Scottish Naturalist. 1988 Jul 25 Presented at: International Society of Cryptozoology Symposium on the Loch Ness Monster; July 25, 1987; Edinburgh, UK URL: https://archive.org/details/scottishnaturali1003scot
- Shine A. The Loch Ness eDNA Project: super natural history. The Loch Ness Project. 2019. URL: https://web.archive.org/web/20220506012235/https://www.lochnessproject.org/explore_loch_ness/loch%20ness%20eDNA/loch%20ness%20eDNA_index.html [accessed 2023-07-12]
- First eDNA study of Loch Ness points to something fishy. The University of Otago. 2019. URL: https://web.archive.org/web/20220607165452/https://www.otago.ac.nz/news/news/otago717609.html [accessed 2023-07-12]
- Turner R. New footage supports theory Loch Ness Monster is actually an eel. Country Life. 2019. URL: https://tinyurl.com/5n8dz8ef [accessed 2023-07-12]
- Simon J. Age, growth, and condition of European eel (Anguilla anguilla) from six lakes in the River Havel system (Germany). ICES J Marine Sci 2007;64(7):1414-1422 [CrossRef]
- LeBlond P, Collins M. The Wilson Nessie photo: a size determination based on physical principles. Cryptozoology 1987;6:55-64
- Sheldon RW, Kerr SR. The population density of monsters in Loch Ness. Limnology Oceanography 2003 Dec 22;17(5):796-798 [CrossRef]
- Sheldon RW, Kerr SR. The Loch Ness monster: reply to comments of C. H. Mortimer. Limnology Oceanography 2003 Dec 22;18(2):345-346 [CrossRef]
- Scheider W, Wallis P. An alternate method of calculating the population density of monsters in Loch Ness. Limnology Oceanography 2003 Dec 22;18(2):343-345 [CrossRef]
- Sagan C. If there are any, could there be many? Nature 1976 Dec 1;264(5586):497 [CrossRef]
- Oliver IW, Macgregor K, Godfrey JD, Harris L, Duguid A. Lipid increases in European eel (Anguilla anguilla) in Scotland 1986-2008: an assessment of physical parameters and the influence of organic pollutants. Environ Sci Pollut Res Int 2015 May;22(10):7519-7528 [CrossRef] [Medline]
- Verhelst P, De Meyer J, Reubens J, Coeck J, Goethals P, Moens T, et al. Unimodal head-width distribution of the European eel ( L.) from the Zeeschelde does not support disruptive selection. PeerJ 2018;6:e5773 [https://europepmc.org/abstract/MED/30416881] [CrossRef] [Medline]
- Foxon F. Supplemental materials for paper: if it’s real, could it be an eel? OSF. URL: https://osf.io/zmgdj/ [accessed 2023-07-12]
- Melia P, Bevacqua D, Crivelli AJ, De Leo GA, Panfili J, Gatto M. Age and growth of Anguilla anguilla in the Camargue lagoons. J Fish Biol 2006 Mar;68(3):876-890 [CrossRef]
- Macnamara R, Koutrakis ET, Sapounidis A, Lachouvaris D, Arapoglou F, Panora D, et al. Reproductive potential of silver European eels (Anguilla anguilla) migrating from Vistonis Lake (Northern Aegean Sea, Greece). Mediterranean Marine Sci 2014 Jun 19;15(3):539 [CrossRef]
- Freedman D, Diaconis P. On the histogram as a density estimator: L2 theory. Zeitschrift Wahrscheinlichkeitstheorie Verwandte Gebiete 1981 Dec;57(4):453-476 [CrossRef]
- Meulenbroek P, Hammerschmied U, Schmutz S, Weiss S, Schabuss M, Zornig H, et al. Conservation requirements of European Eel (Anquilla anquilla) in a Balkan catchment. Sustainability 2020 Oct 15;12(20):8535 [CrossRef]
- Bašić T, Taylor A, Godfrey J, Evans D, Evans R. Report to ICES on the eel stock, fishery and other impacts in UK, 2020-2021. In: Joint EIFAAC/ICES/GFCM Working Group on Eels (WGEEL) Country Reports 2020-2021. Copenhagen, Denmark: International Council for the Exploration of the Sea; 2021:348-410
- Tesch FW, Thorpe JE. Post-larval ecology and behaviour. In: Tesch FW, Thorpe JE, editors. The Eel. Hoboken, NJ: John Wiley & Sons; 2003:119-212
- Rundquist S. World's oldest eel dies in Swedish well. The Local. 2014. URL: https://www.thelocal.se/20140808/worlds-oldest-eel-dies-in-sweden [accessed 2023-07-12]
- Tesch FW, Thorpe JE. Developmental stages and distribution of the eel species. In: Tesch FW, Thorpe JE, editors. The Eel. Hoboken, NJ: John Wiley & Sons; 2003:73-117
|AAS: Academy of Applied Science|
|CDF: cumulative distribution function|
|eDNA: environmental DNA|
Edited by G Eysenbach; submitted 16.05.23; peer-reviewed by DW Evans, D Jellyman; accepted 22.06.23; published 21.07.23Copyright
©Floe Foxon. Originally published in JMIRx Bio (https://bio.jmirx.org), 21.07.2023.
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