Application of the Records Method to Identify the Sporadicity of Percnon gibbesi Distribution in Greece

Aims/Objectives: Mediterranean Sea is one of the most severely affected by alien marine invasions regions worldwide. The reported alien species in the Mediterranean Sea represent approximately 6% of the known biodiversity which is estimated to approximately 17000 species. The number of species increases with a rate of one new record every 1.5 weeks. The Sally Light-foot crab, Percnon gibbesi (H. Milne Edwards, 1853) is a primarily algivorous crab of the shallow infra-littoral rocky shores. Percnon gibbesi increased rapidly its distribution in the Mediterranean Sea. In this paper, we will use a mathematical framework based on the theory of records to identify if Percnon gibbesi is sporadic. A record is a result or some measurement in a given chain of events that exceeds everything that has been encountered previously. Then, we first describe the distribution of Percnon gibbesi on site in the Mediterranean Sea, Greece, and after we perform a test to identify if the specie is rare
Study Design: Number of records.
Place and Duration of Study: Department of Applied Mathematics and Department of Biology, Institute of Applied and Computational Mathematics, between February 2013 and November 2013.
Methodology: We apply a new statistical method in marine ecology to study the evolution of some new marine species for which few information are available. We would determine if some species are isolated (sporadic) based on record method. A specie is recorded or have a record if the number of occurrence of this specie exceeds the last registered number. The observations can be presented with a high variability that may come from some random phenomena such as the transfer, the environment or others.
Results: We consider the inverse of the waiting time between two observed successive species, Percnon gibbesi in the Mediterranean Sea Greece. The first case is founded in Greece in 2001 and the last in 2012. Based on the record method we can easily check the evolution of Percnon gibbesi in Greece is a species that spreads with the time.
Conclusion: We presented a new method of detection of the beginning of a species marine based on the number of observed records from the first observations. The properties of this method consist first on its convenience for any number n of observations since the distribution of the number of records is exactly calculated for each n, and its robustness since this distribution is independent of the cumulative distribution function involved in the distribution of {∆Sn}.