Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities

The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive systems. For well-mixed systems where interactions result in fitness reductions of the losers exceeding fitness gains of the winners, classical theory predicts that two strategies go extinct. The effects of spatial heterogeneity and dispersal rates on this outcome are analyzed using a general framework for evolutionary games in patchy landscapes. The analysis reveals that coexistence is determined by the rates at which dominant strategies invade a landscape occupied by the subordinate strategy (e.g. rock invades a landscape occupied by scissors) and the rates at which subordinate strategies get excluded in a landscape occupied by the dominant strategy (e.g. scissor gets excluded in a landscape occupied by rock). These invasion and exclusion rates correspond to eigenvalues of the linearized dynamics near single strategy equilibria. Coexistence occurs when the product of the invasion rates exceeds the product of the exclusion rates. Provided there is sufficient spatial variation in payoffs, the analysis identifies a critical dispersal rate $d^*$ required for regional persistence. For dispersal rates below $d^*$, the product of the invasion rates exceed the product of the exclusion rates and the rock-paper-scissor metacommunities persist regionally despite being extinction prone locally. For dispersal rates above $d^*$, the product of the exclusion rates exceed the product of the invasion rates and the strategies are extinction prone. These results highlight the delicate interplay between spatial heterogeneity and dispersal in mediating long-term outcomes for evolutionary games.Comment: 31pages, 5 figure

Investigations on the haploid specificity of the t-complex responder in non- Mendelian inheritance in the mouse

Die nicht-Mendelsche Vererbung des t-Haplotyps von heterozygoten Mausmännchen an ihre Nachkommen ist unter der Bezeichnung Transmission Ratio Distortion bekannt. Der t-Haplotyp, eine abweichende Form des t-Komplexes, erstreckt sich über fast ein Drittel des Mauschromosoms 17 und codiert mehrere Distortergene und ein Respondergen, die in der Spermatogenese zur Ausbildung von zwei verschiedenen Spermienpopulationen führen. Die früh exprimierten Distorter wirken auf Signalkaskaden einer Spermienmotilitätskinase, Smok1, und haben eine negative Wirkung auf die Motilität aller Spermien, während der Responder diese Situation nur in Spermien, die das Respondergen tragen, wieder ausgleicht. Dies verschafft den sogenannten t-Spermien einen Vorteil bei der Befruchtung und führt zu der ungewöhnlich hohen Vererbung. Vorangegangene Arbeiten haben gezeigt, dass ein responderbasiertes Transgen haploidspezifische Transkriptexpression aufweist, das heißt, die mRNA ist haploidspezifisch auf die Hälfte der runden Spermatiden begrenzt, obwohl diese Zellen durch Zellbrücken miteinander verbunden sind und ein Austausch von Genprodukten stattfinden kann. Außerdem ist das Responderprotein nur im Flagellum elongierter Spermien detektierbar, das heißt, die Translation findet erst in späten Spermatogenesestadien statt. Dies zeigt, dass translationelle Regulation in der Expression des Respondergens involviert ist und eine datenbankbasierte Analyse konnte bereits mögliche, regulatorische Elemente der translationellen Kontrolle in der 5’- untranslatierten Region (5’-UTR) des Respondertranskripts aufdecken. Im Rahmen dieser Arbeit wurden verschiedene, responderbasierte Transgene kloniert, aus denen transgene Mäuse generiert wurden, um die Haploidspezifität der t-Komplex Responders in vivo auf Transkript- und Proteinebene durch in situ Hybridisierung und Immunhistochemie sowie funktionell in einem Vererbungstest zu untersuchen. Um die Bedeutung von regulatorischen Elementen der 5’-UTR für die Responderexpression zu klären, wurden unterschiedliche Deletionskonstrukte generiert und die Expressionsanalyse in vivo zeigte, dass die 5’-UTR tatsächlich in der Transkriptlokalisation involviert war. Sobald die selben 5’-UTR-Deletionen in Kombination mit der codierenden Region des Responders verwendet wurden, konnte gezeigt werden, dass die codierende Sequenz für die Transkriptstabilität und erfolgreiche Translation wichtig war, allerdings nur zusammen mit mindestens dem letzten Drittel der 5’-UTR. Schließlich konnte bei Untersuchungen der spezifischen Subdomänen innerhalb der codierenden Region des Responders durch Verwendung von Deletionskonstrukten in dieser Region verdeutlicht werden, dass eine erfolgreiche Translation des Gens von dem Vorhandensein der regulatorischen Subdomäne in der codierenden Sequenz abhängig war. Um das Ergebnis der Deletionsuntersuchungen auch funktionell zu bestätigen, wurden transgene Mäuse mit den Deletionen in der codierenden Region in einem Transmissionstest eingesetzt, bei dem die jeweilige Vererbungsrate des Transgens in Anwesenheit von Distortern erfasst wurde. Im Hinblick auf Transmission Ratio Distortion war dieser Vererbungstest nicht sehr aussagekräftig und damit nicht ausreichend, um zu beantworten, welche Responderuntereinheit allein ausreichende Responderaktivität hat. Zusätzlich offenbarte der Test, dass die gewählte Integrationsstrategie für Transgene möglicherweise Defizite aufweist. Zur Generierung von transgenen Mäusen wurde ein Rekombinase vermittelter Kassettenaustausch transgener Konstrukte als Einzelkopie in den ColA1 -Locus von embryonalen Stammzellen verwendet, aber der Integrationsort selbst zeigte im Verlauf dieser Arbeit jedoch unerwartete Positionseffekte, die zu niedriger oder komplett abwesender Expression der Transgene führten und die Ergebnisse der in situ Hybridisierung, der Immunhistochemie und des Transmissionstests beeinflussten. Das Vorhaben der Arbeit war die regulatorischen Elemente des Respondertranskripts zu identifizieren, die bedeutsam für die spezielle Expression diese Gens sind, um diese bei der Manipulation der Expression anderer Gene in der Maus oder anderen Spezies einsetzen zu können. Diese Arbeit konnte zeigen, dass die 5’-UTR des Respondergens in der Transkriptlokalisation involviert ist, während die codierende Region, allerdings nur in Kombination mit der 5’-UTR, die Transkriptstabilität und Translation kontrolliert. Somit verdeutlichen die Ergebnisse dieser Arbeit, dass die posttranskriptionelle Regulation des Responders sehr komplex ist und auf verschiedene regulatorische Elemente innerhalb des Transkripts angewiesen ist und dies erschwert eine mögliche Anwendung deutlich.Non-Mendelian inheritance of the t-haplotype from heterozygous male mice to their offspring is also known as transmission ratio distortion. The t-haplotype, a variant form of the t-complex, spans nearly one third of mouse chromosome 17 and encodes several distorter genes and one responder gene, which lead to formation of two different sperm populations during spermatogenesis. Early expressed distorters activate signalling cascades of the sperm motility kinase, smok1, resulting in a negative effect on the motility of all sperm, while the responder counterbalances this situation only in sperm carrying the responder gene. This gives these so called t-sperm an advantage during fertilisation, and leads to an abnormally high inheritance. Previous work has demonstrated that a responder-based transgene shows haploid- specific transcript expression, which means that the mRNA is restricted to only half of all round spermatids, although these cells are connected via cellular bridges and thus exchange of gene products can occur. Furthermore, the responder protein is detectable only in the flagellum of elongated sperm, which means its translation takes place during late stages of spermatogenesis. This shows that translational regulation might be involved in responder gene expression and in silico analysis revealed already possible regulatory elements for translational control of the responder within the 5’-untranslated region (5’UTR) of the responder transcript. In the context of this work different responder-based transgenes were cloned to generate transgenic mice and to investigate the haploid specificity of the t-complex responder in vivo on transcript and protein level by using in situ hybridization and immunohistochemistry and functionally in a transmission ratio distortion test. In order to address the importance of regulatory elements of the 5’-UTR in responder expression several deletion constructs were generated and expression analyses in vivo revealed that the 5’-UTR was indeed involved in transcript localisation. When the same 5’-UTR deletions were examined in combination with the responder coding sequence, it was demonstrated that the coding region was necessary for transcript stability and successful translation, along with at least the last third of the 5’-UTR region. Additionally, analysis of specific subdomains within the coding region of the responder using deletion constructs within this region, revealed that successful translation of this gene was dependent on the presence of at least the regulatory subdomain in the coding sequence. In order to functionally verify observations from the deletion studies, transgenic mice harbouring the coding region deletions were used in a transmission ratio distortion test, which measured the rate of transgene inheritance in the presence of distorters. In terms of transmission ratio distortion this test was inconclusive, and was thus insufficient to answer the question of which responder subdomain has adequate responder activity. The test further revealed possible shortfalls in the transgene integration strategy chosen. A strategy using recombinase-mediated cassette exchange of transgenic constructs integrated as a single copy in the ColA1 locus was used to generate mice, but within this work the locus itself revealed some unexpected positional effects resulting in low or completely absent expression, thereby impacting the outcome of in situ hybridization analyses, immunohistochemistry, and of the transmission test. The intention of this work was to identify regulatory elements in the responder transcript which are important for the special expression of this gene and which might be used to manipulate other genes in the mouse or in other species. This work demonstrated that the 5’-UTR of the responder is involved in transcript localization while the coding region only in combination with the 5’-UTR is controlling transcript stability and translation. Therefore the results of this work revealed that post-transcriptional regulation of the responder is quite complex and depends on different regulatory elements within the transcript and this makes a possible application significantly difficult

Quantifying strain in analogue models simulating fold-and-thrust belts using magnetic fabric analysis

Applying the anisotropy of magnetic susceptibility to analogue models provides detailed insights into the strain distribution and quantification of deformation within contractional tectonic settings like fold-and-thrust belts (FTBs). Shortening in FTBs is accommodated by layer-parallel shortening, folding, and thrusting. The models in this research reflect the different deformation processes and the resulting magnetic fabric can be attributed to thrusting, folding and layer-parallel shortening. Thrusting develops a magnetic foliation parallel to the thrust surface, whereas folding and penetrative strain develop a magnetic lineation perpendicular to the shorting direction but parallel to the bedding. These fabric types can be observed in the first model of this study, which simulated a FTB shortened above two adjacent décollements with different frictional properties. The different friction coefficients along the décollements have not only an effect on the geometric and kinematic evolution of a FTB, but also on the strain distribution and magnitude of strain within the belt.  The second series of models performed in this study show the development of a thrust imbricate and the strain distribution across a single imbricate in more detail. Three models, with similar setup but different magnitudes of bulk shortening, show strain gradients by gradual changes in principal axes orientations and decrease in degree of anisotropy with decreasing distance to thrusts and kinkzones. These models show that at the beginning of shortening, strain is accommodated mainly by penetrative strain. With further shortening, formation of thrusts and kinkzones overprint the magnetic fabric locally and the degree of anisotropy is decreasing within the deformation zones. At thrusts, an overprint of the magnetic fabric prior deformation towards a magnetic foliation parallel to the thrust surfaces can be observed. A rather complex interplay between thrusting and folding can be analysed in the kinkzones. In general, this thesis outlines the characteristics of magnetic fabric observed in FTBs, relates different types of magnetic fabric to different processes of deformation and provides insights into the strain distribution of FTBs

Revealing invisible strain : Magnetic Fabric Analysis as Strain Indicator in Analogue Models and Nature

Strain is accommodated by folding, thrusting and an “invisible” component, known as penetrative strain. Magnetic fabric analysis allows for identification and quantification of this imperceivable strain. In this thesis, magnetic fabric analysis is applied to quantify strain in analogue sandbox models. Several cases are simulated by the outlined models, such as the development of fold-and-thrust belts, single thrust-imbricates and a basin with subsequent inversion. These models developed characteristic sets of magnetic fabric that are comparable with observations from nature. The main results observed in the models can be summarized as follows. The initial fabric is affected by model preparation and subsequent deformation is accommodated by penetrative strain, folding and thrusting. Pouring and scraping the model material creates a horizontal magnetic lineation (axis of maximum susceptibility) parallel to the scraping direction. In contrast, sieving produces a fabric similar to a sedimentary fabric in nature, with a random magnetic lineation in the bedding plane. Penetrative strain overprints the initial magnetic fabric and compensates initial differences that are created during model preparation. The observed penetrative strain-induced fabric is classified by a clustering of the principal axes of magnetic susceptibility with magnetic lineation oriented mainly horizontally, perpendicular to the shortening direction. With the development of faults, the magnetic foliation aligns parallel to the fault surface. It is noted that thrusting is more efficient in aligning the magnetic foliation in contrast to normal faulting. However, the development of such a magnetic fabric depends on the maturity of a thrust. Moreover, with increasing strain, the magnetic fabric shows gradual changes in reorientation of the principal axes and degree of anisotropy. In detail, such gradual changes are observed from the foreland towards the hinterland and correlate with distance to a thrust within a thrust imbricate. This thesis demonstrates the use of magnetic fabric analysis as strain indicator in analogue models and provides insights in the development of magnetic fabric in nature. In fact, the results presented in the thesis barely scratches the surface of a potential rich research subject, which could be extended to tackle various questions in structural geology, tectonics and geodynamics.

Revealing invisible strain : Magnetic Fabric Analysis as Strain Indicator in Analogue Models and Nature

Strain is accommodated by folding, thrusting and an “invisible” component, known as penetrative strain. Magnetic fabric analysis allows for identification and quantification of this imperceivable strain. In this thesis, magnetic fabric analysis is applied to quantify strain in analogue sandbox models. Several cases are simulated by the outlined models, such as the development of fold-and-thrust belts, single thrust-imbricates and a basin with subsequent inversion. These models developed characteristic sets of magnetic fabric that are comparable with observations from nature. The main results observed in the models can be summarized as follows. The initial fabric is affected by model preparation and subsequent deformation is accommodated by penetrative strain, folding and thrusting. Pouring and scraping the model material creates a horizontal magnetic lineation (axis of maximum susceptibility) parallel to the scraping direction. In contrast, sieving produces a fabric similar to a sedimentary fabric in nature, with a random magnetic lineation in the bedding plane. Penetrative strain overprints the initial magnetic fabric and compensates initial differences that are created during model preparation. The observed penetrative strain-induced fabric is classified by a clustering of the principal axes of magnetic susceptibility with magnetic lineation oriented mainly horizontally, perpendicular to the shortening direction. With the development of faults, the magnetic foliation aligns parallel to the fault surface. It is noted that thrusting is more efficient in aligning the magnetic foliation in contrast to normal faulting. However, the development of such a magnetic fabric depends on the maturity of a thrust. Moreover, with increasing strain, the magnetic fabric shows gradual changes in reorientation of the principal axes and degree of anisotropy. In detail, such gradual changes are observed from the foreland towards the hinterland and correlate with distance to a thrust within a thrust imbricate. This thesis demonstrates the use of magnetic fabric analysis as strain indicator in analogue models and provides insights in the development of magnetic fabric in nature. In fact, the results presented in the thesis barely scratches the surface of a potential rich research subject, which could be extended to tackle various questions in structural geology, tectonics and geodynamics.

Sieving vs Scraping - AMS dataset from Analogue Sandbox Models

Model preparation has a great impact on the rheology of the model and model development. Here, a sand-magnetite mixture is used to study the effect of model preparation on magnetic fabric and on the deformation of analogue sandbox models. The AMS datasets of each model are uploaded here. The datasets include next to the magnetic measurement parameters, the location (x and z coordinates), and the distance to the closest thrust (if applicable). Please, see the associated publication for further discussion (in preparation).In detail:- Two datasets show AMS data from the initial state of a scraped and sieved model (labelled: "initial")- Two datasets show AMS data from a deformed scraped and sieved modelNote, that the new version of the datasets from the deformed models contain a correction of the orientation of the principal axes. This correction is due to a sampling issue and is discussed in the associated main article.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

2frictionalDecollementModel_AMSdataset

AMS (anisotropy of magnetic susceptibility) dataset of an analogue model simulating a fold-and-thrust belt above two adjacent décollements. Samples from the model are measured with the MFK1-FA Kappabridge (Agico Inc.) using an AC field strength of 200 A/m with a frequency of 976 Hz. For each sample the location within the model is given (x,y, in local coordinate system). Note, that the dataset is divided into surface and deep samples. This dataset is used in following publication: 'Influence of décollement friction on anisotropy of magnetic susceptibility in a fold-and-thrust belt model' by Schöfisch, T. et al. 202

Magnetic Fabric Distribution in inverted Basin Sandbox Models

Three sandbox models represent different stages of basin inversion. After modelling, samples are taken throughout the models for AMS (Anisotropy of Magnetic Susceptibility) measurements with a MFK1-FA Kappabridge from Agico Inc. The AMS datasets of each model are uploaded here. The datasets include next to the magnetic measurement parameters, the location (x,y, coordinate), depth (which is different to y coordinate), closest distance to next thrust or normal fault, as well as if associated with a fault, how much structure is captured in a sample. Please, see associated publication for further discussion and explanation: Schöfisch et al., "Magnetic Fabric Analyses of Basin Inversion: A Sandbox Modelling approach", in Special Issue of Solid Earth.Some details:Model I shows extension only with two main magnetic fabrics; one is associated with normal faulting, whereas away from the faults the magnetic fabrics remains as initially sieved. Model II and Model III are shortened after extension, but to different degrees respectively. Both have magnetic fabrics that show an overprint towards penetrative-strain induced fabric at areas away from faults, some persistent initial fabric, an overprinted fabric at the normal faults, and finally, thrust-induced fabrics. The reference North in the data is the modelling north, which is the backstop of the sandbox models. The Excel file contains three tabs, one for each model.THIS DATASET IS ARCHIVED AT DANS/EASY, BUT NOT ACCESSIBLE HERE. TO VIEW A LIST OF FILES AND ACCESS THE FILES IN THIS DATASET CLICK ON THE DOI-LINK ABOV

2frictionalDecollementModel_AMSdataset

AMS (anisotropy of magnetic susceptibility) dataset of an analogue model simulating a fold-and-thrust belt above two adjacent décollements. Samples from the model are measured with the MFK1-FA Kappabridge (Agico Inc.) using an AC field strength of 200 A/m with a frequency of 976 Hz. For each sample the location within the model is given (x,y, in local coordinate system). Note, that the dataset is divided into surface and deep samples. This dataset is used in following publication: 'Influence of décollement friction on anisotropy of magnetic susceptibility in a fold-and-thrust belt model' by Schöfisch, T. et al. 202