On the mean path length invariance property for random walks of animals in open environment
Abstract Random walks are common in nature and are at the basis of many different phenomena that span from neutrons and light scattering to the behaviour of animals. Despite the evident differences among all these phenomena, theory predicts that they all share a common fascinating feature known as I...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-24361-9 |
| _version_ | 1811217772164677632 |
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| author | Federico Tommasi Lorenzo Fini Stefano Focardi Fabrizio Martelli Giacomo Santini Stefano Cavalieri |
| author_facet | Federico Tommasi Lorenzo Fini Stefano Focardi Fabrizio Martelli Giacomo Santini Stefano Cavalieri |
| author_sort | Federico Tommasi |
| collection | DOAJ |
| description | Abstract Random walks are common in nature and are at the basis of many different phenomena that span from neutrons and light scattering to the behaviour of animals. Despite the evident differences among all these phenomena, theory predicts that they all share a common fascinating feature known as Invariance Property (IP). In a nutshell, IP means that the mean length of the total path of a random walker inside a closed domain is fixed by the geometry and size of the medium. Such a property has been demonstrated to hold not only in optics, but recently also in the field of biology, by studying the movement of bacteria. However, the range of validity of such a universal property, strictly linked to the fulfilment of equilibrium conditions and to the statistical distributions of the steps of the random walkers, is not trivial and needs to be studied in different contexts, such as in the case of biological entities occupied in random foraging in an open environment. Hence, in this paper the IP in a virtual medium inside an open environment has been studied by using actual movements of animals recorded in nature. In particular, we analysed the behaviour of a grazer mollusc, the chiton Acanthopleura granulata. The results depart from those predicted by the IP when the dimension of the medium increases. Such findings are framed in both the condition of nonequilibrium of the walkers, which is typical of animals in nature, and the characteristics of actual animal movements. |
| first_indexed | 2024-04-12T06:59:58Z |
| format | Article |
| id | doaj.art-0a4845fc046c407caa34eb4867dce318 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-12T06:59:58Z |
| publishDate | 2022-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-0a4845fc046c407caa34eb4867dce3182022-12-22T03:43:01ZengNature PortfolioScientific Reports2045-23222022-11-011211710.1038/s41598-022-24361-9On the mean path length invariance property for random walks of animals in open environmentFederico Tommasi0Lorenzo Fini1Stefano Focardi2Fabrizio Martelli3Giacomo Santini4Stefano Cavalieri5Dipartimento di Fisica e Astronomia, Università di FirenzeDipartimento di Fisica e Astronomia, Università di FirenzeIstituto dei Sistemi Complessi, Consiglio Nazionale delle RicercheDipartimento di Fisica e Astronomia, Università di FirenzeDipartimento di Biologia, Università di FirenzeDipartimento di Fisica e Astronomia, Università di FirenzeAbstract Random walks are common in nature and are at the basis of many different phenomena that span from neutrons and light scattering to the behaviour of animals. Despite the evident differences among all these phenomena, theory predicts that they all share a common fascinating feature known as Invariance Property (IP). In a nutshell, IP means that the mean length of the total path of a random walker inside a closed domain is fixed by the geometry and size of the medium. Such a property has been demonstrated to hold not only in optics, but recently also in the field of biology, by studying the movement of bacteria. However, the range of validity of such a universal property, strictly linked to the fulfilment of equilibrium conditions and to the statistical distributions of the steps of the random walkers, is not trivial and needs to be studied in different contexts, such as in the case of biological entities occupied in random foraging in an open environment. Hence, in this paper the IP in a virtual medium inside an open environment has been studied by using actual movements of animals recorded in nature. In particular, we analysed the behaviour of a grazer mollusc, the chiton Acanthopleura granulata. The results depart from those predicted by the IP when the dimension of the medium increases. Such findings are framed in both the condition of nonequilibrium of the walkers, which is typical of animals in nature, and the characteristics of actual animal movements.https://doi.org/10.1038/s41598-022-24361-9 |
| spellingShingle | Federico Tommasi Lorenzo Fini Stefano Focardi Fabrizio Martelli Giacomo Santini Stefano Cavalieri On the mean path length invariance property for random walks of animals in open environment Scientific Reports |
| title | On the mean path length invariance property for random walks of animals in open environment |
| title_full | On the mean path length invariance property for random walks of animals in open environment |
| title_fullStr | On the mean path length invariance property for random walks of animals in open environment |
| title_full_unstemmed | On the mean path length invariance property for random walks of animals in open environment |
| title_short | On the mean path length invariance property for random walks of animals in open environment |
| title_sort | on the mean path length invariance property for random walks of animals in open environment |
| url | https://doi.org/10.1038/s41598-022-24361-9 |
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