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Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Under certain conditions, that we call the "partial order of adaptation", we can couple these measures. This allows us to construct the central object of this paper, the Λ−asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. Interestingly, the construction also provides a connection to the theory of optimal transport. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Under certain conditions, that we call the ``partial order of adaptation'', we can couple these measures. This allows us to construct the central object of this paper, the Λ−asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. Interestingly, the construction also provides a connection to the theory of optimal transport. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.
Julian/Jutta Schutting, as a self-conscious author, understands the literary activity as a common and democratic act of creation, performed both by the writer as well as by the reader, thus revealing and connecting the multitude of associative meanings of the literary artifact. Until 1989, until her transformation, the writing of Jutta Schutting was a “secret therapy for survival,” by means of which the troubled existence was to be overcome through the creative power and the originality of her work. Back then she described her art as a “hybrid life … neither … nor…, both … and …,” an attempt to transform the personal inner conflict into curative fictional models. This “neither … nor … - both … and …” situation illustrates the androgynous attitude towards this kind of fictionalized models, this tonality being also supported at the stylistic level that escapes any formalist framework of the genre literature. “Gralslicht. Ein Theaterlibretto” [“The Grail’s Light. A TheatreLibretto“] was published in 1989 by Residenz-Publishing House and is explicitly “composed” as a modern interpretation of Wagner’s “Parsifal” in the typical manner of Schutting. The language ceases to be referential and becomes almost exclusively self-referential, because the dialogues do not rely on a situation of communication [communication situation], but are to be regarded as an interactive exchange of monologues. The female character “Kundry” is almost completely absent from the stage [at the level of the stage] and becomes evident only in the dramatic game between the two male characters that regard her and her duality as the principle of the eternal feminine. Kundry remains active only at the textual level and becomes a life example and a pretext in the love-chastity debate between Parsifal and Don Giovanni.