TY - JOUR A1 - Pielström, Steffen A1 - Roces, Flavio T1 - Sequential Soil Transport and Its Influence on the Spatial Organisation of Collective Digging in Leaf-Cutting Ants JF - PLoS ONE N2 - The Chaco leaf-cutting ant Atta vollenweideri (Forel) inhabits large and deep subterranean nests composed of a large number of fungus and refuse chambers. The ants dispose of the excavated soil by forming small pellets that are carried to the surface. For ants in general, the organisation of underground soil transport during nest building remains completely unknown. In the laboratory, we investigated how soil pellets are formed and transported, and whether their occurrence influences the spatial organisation of collective digging. Similar to leaf transport, we discovered size matching between soil pellet mass and carrier mass. Workers observed while digging excavated pellets at a rate of 26 per hour. Each excavator deposited its pellets in an individual cluster, independently of the preferred deposition sites of other excavators. Soil pellets were transported sequentially over 2 m, and the transport involved up to 12 workers belonging to three functionally distinct groups: excavators, several short-distance carriers that dropped the collected pellets after a few centimetres, and long-distance, last carriers that reached the final deposition site. When initiating a new excavation, the proportion of long-distance carriers increased from 18% to 45% within the first five hours, and remained unchanged over more than 20 hours. Accumulated, freshly-excavated pellets significantly influenced the workers' decision where to start digging in a choice experiment. Thus, pellets temporarily accumulated as a result of their sequential transport provide cues that spatially organise collective nest excavation. KW - animal behavior KW - ants KW - confidence interval KW - decision making KW - foraging KW - fungal structure KW - fungi KW - hormone transport Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-96275 ER - TY - THES A1 - Wisheckel, Florian T1 - Some Applications of D-Norms to Probability and Statistics T1 - Einige Anwendungen von D-Normen in Wahrscheinlichkeitstheorie und Statistik N2 - This cumulative dissertation is organized as follows: After the introduction, the second chapter, based on “Asymptotic independence of bivariate order statistics” (2017) by Falk and Wisheckel, is an investigation of the asymptotic dependence behavior of the components of bivariate order statistics. We find that the two components of the order statistics become asymptotically independent for certain combinations of (sequences of) indices that are selected, and it turns out that no further assumptions on the dependence of the two components in the underlying sample are necessary. To establish this, an explicit representation of the conditional distribution of bivariate order statistics is derived. Chapter 3 is from “Conditional tail independence in archimedean copula models” (2019) by Falk, Padoan and Wisheckel and deals with the conditional distribution of an Archimedean copula, conditioned on one of its components. We show that its tails are independent under minor conditions on the generator function, even if the unconditional tails were dependent. The theoretical findings are underlined by a simulation study and can be generalized to Archimax copulas. “Generalized pareto copulas: A key to multivariate extremes” (2019) by Falk, Padoan and Wisheckel lead to Chapter 4 where we introduce a nonparametric approach to estimate the probability that a random vector exceeds a fixed threshold if it follows a Generalized Pareto copula. To this end, some theory underlying the concept of Generalized Pareto distributions is presented first, the estimation procedure is tested using a simulation and finally applied to a dataset of air pollution parameters in Milan, Italy, from 2002 until 2017. The fifth chapter collects some additional results on derivatives of D-norms, in particular a condition for the existence of directional derivatives, and multivariate spacings, specifically an explicit formula for the second-to-last bivariate spacing. N2 - Diese kumulative Dissertation ist wie folgt aufgebaut: Nach der Einleitung wird im zweiten Kapitel, welches auf “Asymptotic independence of bivariate order statistics” (2017) von Falk und Wisheckel beruht, die asymptotische Abhängigkeitsstruktur von bivariaten Ordnungsstatistiken untersucht. Dazu wird eine explizite Darstellung der bedingten Verteilung einer bivariaten Ordnungsstatistik hergeleitet. Kapitel 3, basierend auf “Conditional tail independence in archimedean copula models” (2019) von Falk, Padoan und Wisheckel, zeigt, dass unter schwachen Anforderungen an den Generator einer Archimedischen Copula die übrigen Komponenten unabhängig werden, wenn man auf eine davon bedingt. Das insbesondere auch dann, wenn die Komponenten ohne die Bedingung abhängig waren. Die theoretischen Erkenntnisse werden anhand von Simulationsergebnissen verdeutlicht. “Generalized pareto copulas: A key to multivariate extremes” (2019) von Falk, Padoan und Wisheckel liefert Kapitel 4. Es wird ein nichtparametrischer Ansatz vorgestellt um die Überschreitungswahrscheinlichkeit eines Zufallsvektors über einen festen, hohen Schwellenwert zu schätzen, wenn dieser einer verallgemeinerten Pareto Copula folgt. Das Verfahren wird in den theoretischen Rahmen eingebettet, anhand einer Simulation validiert und auf Luftverschmutzungsdaten in Mailand, Italien, von 2002 bis 2017 angewendet. Im fünften Kapitel werden einige weitere Ergebnisse gesammelt: es geht um Ableitungen von D-Normen, insbesondere um eine Bedingung, die die Existenz der Richtungsableitungen sicherstellt. Außerdem werden multivariate Spacings thematisiert. KW - Kopula KW - Bedingte Unabhängigkeit KW - Extremwertstatistik KW - D-Norms KW - Multivariate order statistics KW - Archimedean copula KW - Extreme value copula KW - Exceedance Stability KW - Generalized Pareto copula KW - Asymptotic independence KW - multivariate generalized Pareto distribution KW - confidence interval KW - Pareto-Verteilung KW - Copula Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-212140 ER -