Fitting competing models and evaluation of model parameters of the abundance distribution of the land snail Vallonia pulchella (Pulmonata, Valloniidae)
AbstractThis paper summarizes the mechanisms behind the patterning of the intra-population abundance distribution of the land snail Vallonia pulchella (Müller, 1774). The molluscs were collected in recultivated soil formed on red-brown clays (Pokrov, Ukraine). Data obtained in this study reveal that V. pulchella population abundance ranges from 1 to 13 individuals per 100 g of soil sample. To obtain estimates of the mean, three models were used: the model of the arithmetic mean, the Poisson model and a log-normal model. The arithmetic mean of the occurrence of this species during the study period was 1.84 individuals/sample. Estimation of the average number of molluscs in one sample calculated using the Poisson model is lower and equals 1.40 individuals/sample. The distribution of the number of individuals in a population was described by the graphics "rank – abundance". The individual sample plot sites with molluscs may be regarded as equivalents of individual species in the community. For the analysis, the following models were used: broken sticks model, niche preemption model, log-normal model, Zipf model, and Zipf-Mandelbrot model. Applying the log-normal distribution gives a lower estimate of the mean density at 1.28 individuals/sample. Median value and mode is estimated at 1.00 individuals/sample. The Zipf-Mandelbrot model was shown as the most adequate to describe distribution of the V. pulchella population within the study area. The Zipf-Mandelbrot model belongs to the family of so-called non-Gaussian distributions. This means that the sample statistics do not possess asymptotic properties and by increasing the sample size, they tend to infinity, and are not close to the values of the general population. Therefore, the average value of the random variable that describes the non-Gaussian distribution has no statistical meaning. From an environmental point of view, this means that within the study area the capacity of the habitat is large, and for some combination of environmental conditions the rapid growth of the abundance of a given species is possible.
Bohan, D. A., Glen, D. M., Wiltshire, C. W., & Hughes, L. (2000). Parametric in tensity and the spatial arrangement of the terrestrial mollusc herbivores Deroceras reticulatum and Arion intermedius. Journal of Animal Ecology, 69(6), 1031–1046.
Brygadyrenko, V. V. (2015a). Influence of moisture conditions and mineralization of soil solution on structure of litter macrofauna of deciduous forests of Ukraine’s steppe zone. Visnyk of Dnipropetrovsk University. Biology, Ecology, 23(1), 50–65 (in Ukrainian).
Brygadyrenko, V. V. (2015b). Influence of tree crown density and density of the herbaceous layer on the structure of litter macrofauna of deciduous forests of Ukraine’s steppe zone. Visnyk of Dnipropetrovsk University. Biology, Ecology 23(2), 134–148 (in Ukrainian).
Čejka, T., & Hamerlik, L. (2009). Land snails as indicators of soil humidity in Da nubian woodland (SW Slovakia). Polish Journal of Ecology, 57(4), 741–747.
Evans, J. G. (1972). Land snails in archaeology. Seminar Press, London and New York.
Faly, L. I., & Brygadyrenko, V. V. (2014). Patterns in the horizontal structure of litter invertebrate communities in windbreak plantations in the steppe zone of the Ukraine. Journal of Plant Protection Research, 54(4), 414–420.
Fisher, R. A., Corbert, A. S., & Williams, C. B. (1943). The relation between the number of species and the number of individuals in a random sample of animal population. The Journal of Animal Ecology, 12, 42–58.
Gerber, J. (1996). Revision der Gattung Vallonia Risso 1826 (Mollusca: Gastro poda: Valloniidae). Hemmen, Wiesbaden (Schriften zur Malakozoologie aus dem Haus der Natur-Cismar, Haus der Natur Cismar. Issue 8).
Gural-Sverlova, N. V., & Gural, R. I. (2012). Vyznachnyk nazemnyh moljuskiv Ukrai'ny [Guide to the terrestrial mollusks of Ukraine]. Lviv (in Ukrainian).
Hall, L. S., Krausman, P. R., & Morrison, M. L. (1997). The habitat concept and a plea for standard terminology. Wildlife Society Bulletin, 25(1), 173–182.
Hermida, J., Ondina, M. P., & Rodriguez, T. (2000). The relative importance of edaphic factors on the distribution of some terrestrial gastropod species: Aut ecological and synecological approaches. Acta Zoologica Academiae Scien tiarum Hungaricae, 46, 265–274.
Hermida, J., Outeiro, A., & Rodriguez, T. (1993). Aspectos ecologicos de Vallo nia pulchella (Muller, 1774) (Gastropoda, Pulmonata). Nova Acta Cientifica Compostelana (Bioloxia), 4, 129–135.
Horsák, M. (2003). How to sample mollusc communities in mires easily. Malaco logica Bohemoslovaca, 2, 11–14.
IUSS Working Group WRB (2007). World reference base for soil resources 2006, first update 2007. World Soil Resources Reports No 103. FAO, Rome.
Juřičková, L., Horsák, M., Cameron, R., Hylander, K., Míkovcová, A., Hlaváč, J. Č., & Rohovec, J. (2008). Land snail distribution patterns within a site: The role of different calcium sources. European Journal of Soil Biology, 44(2), 172–179.
Kearney, M. P., & Cameron, R. A. D. (1979). A field guide to the land snails of Britain and North West Europe. William Collins Sons and Company, Ltd., London.
Khalafyan, A. A. (2007). Statistica 6: Statisticheskij analiz dannyh [Statistica 6: Statistical Analysis of the Data]. Bean-Pres, Moscow (in Russian).
Khaytun, S. D. (2005). Kolichestvennyy analiz sotsial'nykh yavleniy. Problemy i perspektivy [Quantitative analysis of social phenomena. Problems and prospect]. KomKniga Publisher, Moscow (in Russian).
Kul’bachko, Y. L., & Unkovs’ka, S. I. (2008). Kharakteristika fauny nazemnykh bryu khonogikh mollyuskov iskusstvennykh drevesnykh nasazhdeniy i rekul'tiviro vannykh territoriy v g. Zheltye Vody [Characteristic of terrestrial snails fauna of artificial stands and rehabilitated territories in the town of Zhovti Vody]. Visnyk of Dnipropetrovsk University. Biology, Ecology, 16(1), 128–132 (in Russian).
Magurran, A. E. (2004). Measuring biological diversity. Blackwell Publishing, Oxford.
Mandelbrot, B. B. (1983). The fractal geometry of nature. W. H. Freeman and Company, New York.
May, R. M. (1975). Patterns of species abundance and diversity. In: Cody, M. L., & Diamond, J. M. (Eds.). Ecology and evolution of communities. Harvard University Press, Cambridge.
McClain, C. R., & Nekola, J. C. (2008). The role of local-scale processes on ter restrial and deep-sea gastropod body size distributions across multiple scales. Evolutionary Ecology Research, 10(1), 129–146.
Millar, A. J., & Waite, S. (1999). Mollusks in coppice woodland. Journal of Con chology, 36, 25–48.
Motomura, I. (1932). On the statistical treatment of communities. Zoological Ma gazine, 44, 379–383.
Müller, J., Strätz, C., & Hothorn, T. (2005). Habitat factors for land snails in Euro pean beech forests with a special focus on coarse woody debris. European Journal of Forest Research, 124(3), 233–242.
Myšák, J., Horsák, M., Svobodová, E., & Cernohorsky, N. (2013). Small-scale distribution of terrestrial snails: Patterns of species richness and abundance related to area. Journal of Molluscan Studies, 79(2), 118–127.
Nekola, J. C., & Smith, T. M. (1999). Terrestrial gastropod richness patterns in Wisconsin carbonate cliff communities. Malacologia, 41(1), 253–270.
Oksanen, J., Blanchet, F. G., Kindt, R., Legendre, P., Minchin, P. R., O’Hara, R. B., Simpson, G. L., Solymos, P., Stevens, M. H. H., & Wagner, H. (2017). Community Ecology Package. R package version 2.4-5.
Pielou, E. C. (1975). Ecological diversity. Wiley, New York.
Puzachenko, Y. G. (2004). Matematicheskie metody v ekologicheskikh i geogra ficheskikh issledovaniyakh [Mathematical Methods in Ecological and Geo graphical Studies]. Academy, Moscow (in Russian).
Schenková, V., Horsák, M., Hájek, M., Hájková, P., & Dítě, D. (2015). Mollusc assemblages of Scandinavian fens: Species composition in relation to envi ronmental gradients and vegetation. Annales Zoologici Fennici, 52, 1–16.
Schenková, V., Horsák, M., Plesková, Z., & Pawlikowski, P. (2012). Habitat pre ferences and conservation of Vertigo geyeri (Gastropoda: Pulmonata) in Slo vakia and Poland. Journal of Molluscan Studies, 78(1), 105–111.
Shebanin, V. S., Melnik, S. I., Kramarenko, S. S., & Ganganov, V. M. (2008). Analіz strukturi populyatsіy [Analysis of population structure]. MSAU Publishing House, Mykolayiv (in Ukrainian).
Szybiak, K., Błoszyk, J., Koralewska-Batura, E., & Gołdyn, B. (2009). Small-scale distribution of wintering terrestrial snails in forest site: relation to habitat con ditions. Polish Journal of Ecology, 57(3), 525–535.
Uvalieva, K. K. (1990). Nazemnye mollyuski Kazakhstana i sopredel'nykh territo riy [Terrestrial mollusks of Kazakhstan and adjacent territories]. Science, Alma-Ata (in Russian).
Weaver, K. F., Anderson, T., & Guralnick, R. (2006). Combining phylogenetic and ecological niche modeling approaches to determine distribution and historical biogeography of Black Hills mountain snails (Oreohelicidae). Diversity and Distributions, 12(6), 756–766.
Whitney, M. E. (1937). Some observations on the reproductive cycle of a com mon land snail, Vallonia pulchella Mull.; influence of environmental factors. Proceedings of the Indiana Academy of Science, 47, 299–307.
Whitney, M. E. (1941). The hermaphrodite gland and germ cells of Vallonia pul chella. Michigan Academy of Science, Arts and Letters, 26, 311–338.
Yorkina, N., Maslikova, K., Kunah, O., & Zhukov, O. (2018). Analysis of the spatial organization of Vallonia pulchella (Muller, 1774) ecological niche in Technosols (Nikopol manganese ore basin, Ukraine). Ecologica Monteneg rina, 17, 29–45.
Zemoglyadchuk, K. V. (2005). Vidovoy sostav nazemnykh mollyuskov Berezin skogo gosudarstvennogo biosfernogo zapovednika [Species composition of terrestrial mollusks of the Berezinsky state biosphere reserve]. Proceedings of the National Academy of Sciences of Belarus, Biological Series, 5(1), 87–90 (in Russian).
Zhukov, A. V., Zadorozhnaya, G. O., Bets, T. U., & Lyadskaya, I. V. (2013). Dy namika usadky dernovo-litogennyh g'runtiv na chervono-buryh glynah za sharamy [Dynamics of the shrinkage of the sod-lithogenic soils on the red-brown clays over the layers]. Scientific Herald of Chernivtsi University. Bio logy (Biological Systems), 5(3), 425–430 (in Ukrainian).
Zhukov, O. V., Zadorozhnaya, G. O., Maslikova, K. P., Andrusevich, K. V., & Lyadskaya, I. V. (2017). Ekologija tehnozemiv [Ecology of Technosoils]. Zhurfond, Dnipro (in Ukrainian).
Zipf, G. K. (1949). Human behavior and the principle of least effort. Addison-Wesley, Cambridge.
Zverkovskyi, V. M., Sytnyk, S. A., Lovynska, V. M., Kharytonov, M. M., & Mykolenko, S. Y. (2017). Remediation potential of forest-forming species in the reclamation planting. Ukrainian Journal of Ecology, 7(3), 64–72.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons «Attribution» 4.0 License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.