Flying snails.

In this study, probable maximum flight distances for airborne transport of loose specimens of Truncatellina land snails from Greece were calculated. The results suggest that minute snails could be blown over the sea for several kilometers in heavy storms.
Truncatellina is a minute land snail of the family Vertiginidae, not exceeding 2 mm in size. In central Europe, T. cylindrica (same size) is known quite well (click here for its range in Slovenia). In 1995 two new Truncatellina species from Croatia were described (click here and search for paper 17). In our study we chose T. rothi from Greece.
In the internet there are some descriptions of current ideas and research interests in aeolian sand transport (algorithmic analysis, electrostatic effects, wind erosion problems).

 This page is managed by Francisco Welter-Schultes.

 Last modified 2.10.2002.

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Here is the text of our Flying-snails paper, with tables but without most of the figures.

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FLYING SNAILS - HOW FAR CAN TRUNCATELLINA (PULMONATA: VERTIGINIDAE) BE BLOWN OVER THE SEA ?
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CH. KIRCHNER, R. KRÄTZNER¹ & F. W. WELTER-SCHULTES²

Max-Planck-Institut für Biophysikalische Chemie, Abteilung Molekulare Entwicklungsbiologie, Am Fassberg, D-37077 Göttingen, Germany.
(Current address: Charlotte Kirchner, Max-Planck-Institut für Züchtungsforschung, Abt. Molekulare Pflanzengenetik, Carl-von-Linné-Weg 10, D-50829 Köln, Germany)
¹ Institut für Molekulare Genetik der Universität, Grisebachstr. 8, D-37075 Göttingen, Germany.
² Zoologisches Institut der Universität, Berliner Str. 28, D-37073 Göttingen, Germany
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 INTRODUCTION

The smallest pulmonate inhabitants of the Greek islands belong to the genus Truncatellina (Vertiginidae). A widespread species in the South Aegean is Truncatellina rothi (Reinhardt) (Fig. 1). The systematics in the Southeast European Truncatellina has not been thoroughly studied yet. Maybe T. rothi is a species complex.
The area of dispersal of T. rothi is not well known, presumably due to its small size. It has been found at several sites in Northern Greece and Albania (Fig. 2) (Frank, 1987; Klemm, 1962; Maassen, 1984; Dhora & Welter-Schultes, 1996). It is reported to live in the southwestern and southern parts of Turkey (Schütt, 1993), and is also known from Attikí (Reinhardt, 1916) and several Greek islands: Lefkáda (Klemm, 1962), Thásos (Reischütz, 1983), Límnos (Reischütz, 1986), Chíos (Bar & Butot, 1986), Náxos (Mylonas, 1982), Léros (Reischütz, 1985), Kálimnos (Reischütz, 1986), Ródos (Maassen, 1981), Crete, Kíthira and Andikíthira (Vardinoyannis, 1994) and some surrounding islands of Crete.
During investigations on the small surrounding islands of Crete by F. Welter-Schultes in 1987-1994, Truncatellina was found for the first time in ground-litter samples of Koufonísi Island (South of Crete) in 1991. After 1991, Truncatellina was found in similar habitats on almost every island investigated (Gávdos, Gavdopoúla, Chrisí, Grándes, different sites in Crete). T. rothi was found on the island of Gávdos and in Albania, in the altitude of 200 m and 400 m respectively.
If there was a probability for Truncatellina to be dispersed by wind for some kilometers flying from one island to another, the probability of genetic interchange between island populations would increase. Wind-borne transport is regarded as an important factor for the dispersal of small species of land snails. Most of the information available about dispersal ability in land snails are deductions from distribution patterns (Baur & Bengtsson, 1987). The relatively quick dispersal of small species northwards and to the tops of mountains in the Late and Post Glacial Period in Europe is considered to have been wind-borne (Ant, 1963). There is also strong evidence that the land snail fauna of the Pacific islands originated primarily through aerial dispersal (Valvolgyi, 1975), at least for small species.
Mechanisms of airborne dispersal of snails have never been studied under experimental conditions, as has been the wind-borne transport of sand in desert sand storms (Anderson, Sørensen & Willets, 1990). The wind-borne translocation behavior of particles like sand or snow has also been studied under field conditions (Jensen, Rasmussen, Sørensen & Willetts, 1984; Takeuchi, 1980).
Wind blowing over a surface will, under certain conditions, impart momentum to any available loose small particles, causing them to skip along the surface. As each particle impacts the surface, yet more particles are ejected into the wind, and eventually a distinct layer forms consisting of particles in flight across the surface. This phenomenon is known as saltation. Very light particles, for which the force of gravity is small compared to that of aerodynamic origin, travel downwind at the mercy of turbulent fluctuations without undergoing impact with the surface. There is no particle-bed-interaction. These particles are in suspension. We suppose that saltation plays an important role in aerial snail dispersal on land, in the same way as it does in the case of wind-borne continental dispersal of sand (Bagnold, 1941; Barndorff-Nielsen, Blæsild, Jensen & Sørensen, 1983; Sørensen, 1988). Saltation on the sea surface is impossible for the snails. They have to travel in suspension.
The values of sand, silt and clay when travelling long distances in suspension are known. A grain of sand (diameter 0.1 mm, fall velocitiy 0.824 m s-1) may be dispersed by wind (15 m s-1) for 0.3 to 3 s reaching a distance of 46-460 m. For silt grains (diameter 0.01 mm, fall velocity 0.00824 m s-1), a maximum flight distance in suspension (wind 15 m s-1) of 400-4000 km is calculated (Pettijohn, Potter & Siever, 1987). For these calculations the sand particle density is generally assumed to be 2.65 g cm-3 (Iversen & White, 1982).
For calculations of possible flight distances, one of the most important factors is the fall velocity (Bagnold, 1941). The request of the present study is to find out the fall velocity of Truncatellina rothi.

MATERIALS AND METHODS

Two random samples of 50 empty shells of Truncatellina rothi from two different ground litter samples which have been collected on Gávdos Island (UTM KU3559 and KU3460, for the 1x1 km UTM map of Gávdos see Welter-Schultes, 1995) have been measured (shell height and shell diameter) under microscope. The shells of the sample KU3460 have been filled with paraffin jelly (Vaseline) to simulate approximately the live weight of Truncatellina. The weight of the specimens was determined using an analytical balance of 0.00001 g accuracy (calculated error ± 20 mg).
Each individual of the two samples was dropped from 5.1 m and from 10.9 m altitude above base level. The time between dropping, from release to landing was measuered with a stop watch (accuracy 0.01 s, calculated error of this method ± 0.15 s). The terminal fall velocity has been obtained in evaluating the results of the experiments.
The photo was taken using an SEM Zeiss Novoscan 30 microscope.

RESULTS

Measurements and weight of the specimens

The diameter of the shells (D) is between 0.70 and 0.95 mm (ø = 0.83 mm, sigma x = 0.04 mm, n = 100), the height of the shells (H) varies between 1.1 and 1.8 mm (ø = 1.47 mm, sigma x = 0.12 mm, n = 100) for the specimens of Gávdos (Fig. 3). There is obviously no correlation between diameter and height of the shell of Truncatellina rothi.

Living snails of Truncatellina rothi have not been found on Gávdos. In 1995, some living individuals of Truncatellina cylindrica (Férussac), a species which is very similar to T. rothi in size, have been collected in San Marino. The weight of these snails had an average value of 350-400 micg. The weight of empty adult shells of Truncatellina rothi was between 100 and 300 micg (ø = 151 micg, sigma x = 34 micg, n = 50). After being filled with paraffin jelly, the weight of the specimens of sample KU3460 reached values between 250 and 550 micg (ø = 375 micg, sigma x = 69 micg, n = 50). The weight differences were principally due to the different size of the shells and to dust particles in the interior space of the empty shells and on the shell surface (Fig. 1).
The density of shells filled with Vaseline varied between 0.6 and 0.9 g cm^-3 (ø = 0.72
g cm^-3, sigma x = 0.14 g cm^-3, n = 50, fitting well with the few values we had for living snails), the density of empty shells 0.2-0.4 g cm^-3 (ø = 0.306 g cm^-3, sigma x = 0.054 g cm^-3, n = 50). These values have been obtained in dividing the weight of the specimens by their volume. The approximate volume of Truncatellina can be obtained by the equation

V = 4/3 × pi × H/2 × (D/2)²  =  0.5236 × H × D × D

V = volume (mm³); H = height of the shell (mm); D = diameter of the shell (mm).

which is the volume of an ellipsoid. For Truncatellina an average volume of 0.525 mm³ was calculated. The density of living Truncatellina is lower than that of water because the body of the living snail does not occupy the entire space inside the shell.
The height of the ribs of Truncatellina rothi is approximate 15 micm, the mean rib distance varies between 50 and 80 micm.

Fall velocity

The results of the experiments are shown in Fig. 4. The fall velocity values of a grain of sand of the same dimensions as Truncatellina and the values of the empty shells are included in the diagram in order to be compared with the fall velocity values of the "living" snails. The figures show the degree to which living Truncatellina and shells may be expected to vary as regards to their wind resistance. The fall velocity depends on the g cm^-2 values of the specimens. For living Truncatellina a mean value of 0.28-0.32 g cm^-2 is calculated. The more important factor influencing this value is the weight since differences in shell size are small and can be ignored. Table 1 shows the average terminal fall velocity values for snails of approximate life weight, which have been obtained in the experiments. For living Truncatellina of mean weight, regularly grown and free of any large adherent objects on their shell surface, an average fall velocity of 2.6-2.7 m s^-1 was determined.

 Theoretical flight distances

The simple addition of the two vectors of the terminal forward velocity, which is assumed to be close to the wind velocity, and the terminal downward velocity, which is assumed to be close to the fall velocity of the snails, results in a theoretical flight distance at laminar wind conditions (Fig. 5B). We base our calculations of flight distances on the assumption that the snail will start from an island from a certain altitude above sea level (100 m). Due to the slower particle response as a result of drag conditions (Anderson, 1987), particles of the size of Truncatellina will not immediately follow the trajectories of the wind turbulences on the lee side of an island. The terminal forward vector as shown in Fig. 5B principally does not describe an unreal situation.

Turbulent wind conditions

Particles in suspension follow two parameters. Suspension is the balance between downward advective flux as a result of the settling of grains (Table 2), and their upward diffusive flux as a result of turbulence (Anderson & Hallet, 1986).
As shown in Anderson (1987), it is possible to incorporate turbulent wind conditions in statistical approaches on trajectories of particles in suspension, allowing calculations of probable maximum flight distances under natural conditions. Grains of sand (diameter 0.1 mm, fall velocity 0.824 m s^-1) are able to reach a maximum flight distance of 46-460 m in 15 m s^-1 wind. The maximum height reached by the particles is 0.61-6.1 m respectively (Pettijohn et al., 1987). The theoretical flight distance (as applied in Table 2, taken into account the different fall velocity and wind velocity of the given example), neglecting the upward movement of the grains and setting them to start at an altitude of 0.61-6.1 m, would be of 11.10-111.0 m.
In our calculations, the upward diffusive flux as a result of turbulent wind conditions can be included as a turbulence factor, comparing the theoretical flight distances of sand grains used in the example with their actual maximum flight distances as given in Pettijohn et al. (1987). This factor 460/111 = 4.14 could be applied to approximate probable maximum flight distances under natural conditions.
The point at which a particle in saltation is at the top of its trajectory can be calculated (Sørensen, 1990). Suspension is an extreme kind of modified saltation, and eolian suspension can be modelled in the same way as modified saltation (Anderson et al., 1990). The relation between the mean rising periods and the mean falling periods of the trajectories is 24:76 % (Anderson, 1987). This relation gives good fits for the suspension profiles and can be applied for the example in Pettijohn et al. (1987). When only the mean falling periods of the trajectories are considered the turbulence factor is reduced from 4.14 to 3.15.
The maximum flight distance for one specimen of Truncatellina rothi in a storm of a wind velocity of 100 km h^-1, when starting at an altitude of 100 m above sea level, is calculated to be approximately 3300 m. If wind velocity is reduced to 50 km h^-1, the distance is halved. Setting the snails to start at an altitude of 200 m enables them to reach a distance of 6600 m in 100 km h^-1 wind. The probable maximum flight distance of snails living in 500 m altitude is 16.5 km.

DISCUSSION AND CONCLUSIONS

Outline of the study

The present study has been carried out in order to ascertain whether it is theoretically possible for Truncatellina to overcome distances of several kilometers continuously over sea. The study has not been carried out in order to simulate field conditions, or to calculate exactly possible flight distances of Truncatellina rothi between two Greek islands under natural circumstances. Passive dispersal by wind in general and suspension trajectories in particular are stochastic rather than deterministic. We have also avoided the question of how the snails may be dislodged and lifted into the air. Our studies are thought to give an answer to what is possible once they are airborne.

Neglected influences

Considering the mere fall velocity in our experiments and calculations, we neglect possible influences originated not only in variation of aerodynamic forces, but also in the existence of inter-particle forces due to moisture, electrostatic effects, and other forces of cohesion. These forces are known to be greater for small particles and relatively independent of particle density (Iversen, Pollack, Greenley & White, 1976). In comparison to the sand grains usually dealt with in the sedimentological studies, Truncatellina does not belong to the small particle fractions.
We also neglect probable changes in wind velocity, and assume that the forward velocity of the snails equals the velocity of the wind. The wind is faster when striking over the top of an island (Fig. 5A), but at the same moment the snails will not yet have reached their terminal forward velocity, due to drag conditions.

Biogeographical implications

Direct passive dispersal by wind is not the only method of airborne translocation for Truncatellina. There are many other means for living land snails to be tranported over the sea. Dispersal of land snails by birds and insects is considered as fact (Rees, 1965; Valvolgyi, 1975). Furthermore, minute snails are able to stick on leaves, single bird feathers or other inter-island flight agencies, which can be transported by wind much more easily. In our research, direct dispersal has been studied because of the presumably increased probability for single snails to be dislodged by wind.
Initiation of Truncatellina populations does not necessarily require more than one individual landing on the next island, as Vertiginidae are self-fertile in many instances (Falkner, 1990). Our results are important concerning probabilities of genetic interchange, and hence questions of systematics and taxonomy. Relatively frequent genetic interchange between island populations of minute snail species are not provided by changing sea levels combined with tectonic movements, though for explaining the distribution of the Aegean land snails, these events may be of importance (Heller, 1976).

Flying to islands around Crete

100 km h^-1 is probably about the maximum wind velocity in the Aegean. At this velocity a flight from Andikíthira to Crete or back is not probable, and Crete could not be reached by Kárpathos snails. So Crete is isolated from the rest of Greece. The island of Gávdos could be reached by snails starting their trajectory in 1500 m altitude in Western Crete. So genetic interchange is possible, but only one-way. Gávdos does not exceed 400 m altitude, so they are not able to fly back to Crete. Chrisí and Koufonísi could be reached from various sites from Eastern Crete. In Eastern Crete the snails would also be able to be transported to Grándes, Elása and the Dionisádes. The island of Día could probably be reached by snails starting from the top of Mount Gioúchtas (700-800 m), and from the tops of the mountains of Ródia west of Día.
We base our calculations on the assumption that Truncatellina lives on the highest points of the islands at the start of the trajectory. Of course, the greatest distances would not be travelled frequently, but they appear to be theoretically possible.

ACKNOWLEDGEMENTS

We wish to express our gratitude to W. Zarnack (Göttingen) for helpful comments and kindly placing at our disposal the wind channels of the I. Zoological Institute of Göttingen University, for further experiments which helped to ascertain the results of the presented study. L. Bull (Freetown) and P. Mordan (London) are acknowledged for the linguistic revision and correction of the english manuscript.

 REFERENCES

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ANDERSON, R. S., SØRENSEN, M. & WILLETTS, B. B. 1990. A review of recent progress in our understanding of aeolian sediment transport. Research Reports, Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus, 213: 1-48.
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BAGNOLD, R. A. 1941. The physics of blown sand and desert dunes. Methuen & Co., London.
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 FIGURE CAPTIONS

Figure 1. Truncatellina rothi, with dust particles in the mouth of the empty shell. Scale bar = 0.20 mm.

Figure 2. Truncatellina rothi has been found at sites in Northern Greece and Albania (dots) and on several Greek islands.

Figure 3. Size and dimensions of the specimens of Truncatellina rothi used in the experiments.

Figure 4. Terminal fall velocity of Truncatellina rothi. A. Relation between fall velocity and the g cm^-2 values of the specimens. B. Relation between fall velocity and weight of the specimens. For living Truncatellina of an average weight of 350-400 micg, fall velocity values of 2.4-2.9 m s^-1 have been determined.

Figure 5. A. Probable natural wind conditions. The velocity of wind is approximately reflected in the length of the arrows. B. Addition of the two vectors of wind velocity and fall velocity. The dashed arrow describes the theoretic trajectory of the snail neglecting turbulent wind conditions.
 

 Table 1. Mean terminal fall velocity for Truncatellina of approximate life weight.

weight          g cm^-2 values          fall velocity
                   (± 0.01 g cm^-2)        (± 0.3 m s^-1)

300 micg      0.27 g cm-2               2.5 m s-1
350 micg      0.29 g cm-2               2.6 m s-1
400 micg      0.31 g cm-2               2.7 m s-1
450 micg      0.33 g cm-2               2.8 m s-1
 

 Table 2. Theoretical flight distances for living Truncatellina rothi, as result of the addition of the two velocity vectors shown in Fig. 5B. Start of the snails 100 m above sea level, laminar horizontal wind 27.8 m s^-1.

weight              fall velocity          theoretical
                                                  flight distance
                       (± 0.3 m s^-1)          (± 93 m)

300 micg          2.5 m s-1              1111 m
350 micg          2.6 m s-1              1068 m
400 micg          2.7 m s-1              1029 m
450 micg          2.8 m s-1               992 m

 Table 3. Maximum flight distances for living Truncatellina rothi under turbulent wind conditions. Two different calculations are suggested, the most probable values are assumed to be close to the factor 3.15 values. Start of the snails 100 m above sea level, turbulent wind 27.8 m s^-1.

weight              flight distance         flight distance
                       applying                  applying
                       factor 4.14              factor 3.15
                       (± 385 m)              (± 293 m)

300 micg          4600 m              3500 m
350 micg          4422 m              3364 m
375 micg          4342 m              3304 m
400 micg          4260 m              3241 m
450 micg          4107 m              3125 m
 
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