Global models of planet formation and evolution

Despite the strong increase in observational data on extrasolar planets, the processes that led to the formation of these planets are still not well understood. However, thanks to the high number of extrasolar planets that have been discovered, it is now possible to look at the planets as a population that puts statistical constraints on theoretical formation models. A method that uses these constraints is planetary population synthesis where synthetic planetary populations are generated and compared to the actual population. The key element of the population synthesis method is a global model of planet formation and evolution. These models directly predict observable planetary properties based on properties of the natal protoplanetary disc, linking two important classes of astrophysical objects. To do so, global models build on the simplified results of many specialized models that address one specific physical mechanism. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disc (of gas and solids), those that describe one (proto)planet (its solid core, gaseous envelope and atmosphere), and finally those that describe the interactions (orbital migration and N-body interaction). We compare the approaches taken in different global models, discuss the links between specialized and global models, and identify physical processes that require improved descriptions in future work. We then shortly address important results of planetary population synthesis like the planetary mass function or the mass-radius relationship. With these statistical results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Owing to their nature as meta models, global models depend on the results of specialized models, and therefore on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that the global models will in future undergo significant modifications. Despite these limitations, global models can already now yield many testable predictions. With future global models addressing the geophysical characteristics of the synthetic planets, it should eventually become possible to make predictions about the habitability of planets based on their formation and evolution.

Mechano-Chemical Aspects of Organ Formation in Arabidopsis thaliana: The Relationship between Auxin and Pectin

How instructive signals are translated into robust and predictable changes in growth is a central question in developmental biology. Recently, much interest has centered on the feedback between chemical instructions and mechanical changes for pattern formation in development. In plants, the patterned arrangement of aerial organs, or phyllotaxis, is instructed by the phytohormone auxin; however, it still remains to be seen how auxin is linked, at the apex, to the biochemical and mechanical changes of the cell wall required for organ outgrowth. Here, using Atomic Force Microscopy, we demonstrate that auxin reduces tissue rigidity prior to organ outgrowth in the shoot apex of Arabidopsis thaliana, and that the de-methyl-esterification of pectin is necessary for this reduction. We further show that development of functional organs produced by pectin-mediated ectopic wall softening requires auxin signaling. Lastly, we demonstrate that coordinated localization of the auxin transport protein, PIN1, is disrupted in a naked-apex produced by increasing cell wall rigidity. Our data indicates that a feedback loop between the instructive chemical auxin and cell wall mechanics may play a crucial role in phyllotactic patterning.

Pattern and process: competition causes regular spacing of individuals within plant populations

1 We used simulated and experimental plant populations to analyse mortality-driven pattern formation under size-dependent competition. Larger plants had an advantage under size-asymmetric but not under symmetric competition. Initial patterns were random or clumped. 2 The simulations were individual-based and spatially explicit. Size-dependent competition was modelled with different rules to partition overlapping zones of influence. 3 The experiment used genotypes of Arabidopsis thaliana with different morphological plasticity and hence size-dependent competition. Compared with wild types, transgenic individuals over-expressed phytochrome A and had decreased plasticity because of disabled phytochrome-mediated shade avoidance. Therefore, competition among transgenics was more asymmetric compared with wild-types. 4 Density-dependent mortality under symmetric competition did not substantially change the initial spatial pattern. Conversely, simulations under asymmetric competition and experimental patterns of transgenic over-expressors showed patterns of survivors that deviated substantially from random mortality independent of initial patterns. 5 Small-scale initial patterns of wild types were regular rather than random or clumped. We hypothesize that this small-scale regularity may be explained by early shade avoidance of seedlings in their cotyledon stage. 6 Our experimental results support predictions from an individual-based simulation model and support the conclusion that regular spatial patterns of surviving individuals should be interpreted as evidence for strong, asymmetric competitive interactions and subsequent density-dependent mortality.

Site-Specific Expression of Gelatinolytic Activity during Morphogenesis of the Secondary Palate in the Mouse Embryo

Morphogenesis of the secondary palate in mammalian embryos involves two major events: first, reorientation of the two vertically oriented palatal shelves into a horizontal position above the tongue, and second, fusion of the two shelves at the midline. Genetic evidence in humans and mice indicates the involvement of matrix metalloproteinases (MMPs). As MMP expression patterns might differ from sites of activity, we used a recently developed highly sensitive in situ zymography technique to map gelatinolytic MMP activity in the developing mouse palate. At embryonic day 14.5 (E14.5), we detected strong gelatinolytic activity around the lateral epithelial folds of the nasopharyngeal cavity, which is generated as a consequence of palatal shelf elevation. Activity was concentrated in the basement membrane of the epithelial fold but extended into the adjacent mesenchyme, and increased in intensity with lateral outgrowth of the cavity at E15.5. Gelatinolytic activity at this site was not the consequence of epithelial fold formation, as it was also observed in Bmp7-deficient embryos where shelf elevation is delayed. In this case, gelatinolytic activity appeared in vertical shelves at the exact position where the epithelial fold will form during elevation. Mmp2 and Mmp14 (MT1-MMP), but not Mmp9 and Mmp13, mRNAs were expressed in the mesenchyme around the epithelial folds of the elevated palatal shelves; this was confirmed by immunostaining for MMP-2 and MT1-MMP. Weak gelatinolytic activity was also found at the midline of E14.5 palatal shelves, which increased during fusion at E15.5. Whereas MMPs have been implicated in palatal fusion before, this is the first report showing that gelatinases might contribute to tissue remodeling during early stages of palatal shelf elevation and formation of the nasopharynx.

The bovine aristaless-like homeobox 4 (ALX4) as a candidate gene for syndactyly

The ALX4 (aristaless-like homeobox 4) gene encodes a paired-type homeodomain transcriptional activator and plays a major role in anterior-posterior pattern formation during limb development. Here, the cloning, genomic structure and expression of the bovine ortholog of the ALX4 gene are reported. The bovine ALX4 gene consists of four exons and is located on BTA15q28-->q29 in a region syntenic to HSA11p11.2. The transcribed ALX4 mRNA encodes a 397-amino-acid protein showing a paired-type homeodomain and a C-terminal stretch of amino acids known as the OAR- or aristaless domain. The predicted protein shares 92.5% identity to human and mouse ALX4 proteins and all three species share almost complete identity in the conserved domains. ALX4 expression was detected by reverse transcriptase polymerase chain reaction in bovine fetal limb bones. The ALX4 gene was evaluated as a candidate gene for bovine syndactyly which has been mapped on the telomeric region of cattle chromosome 15. Sequencing of the four exons with flanking sequences of the bovine ALX4 gene from a panel of 14 affected animals belonging to German Holstein, German Fleckvieh and crossbreds, and 27 unaffected individuals from German Holstein revealed five silent SNPs within the coding region out of eleven SNPs in total. Four SNPs were polymorphic in the affected animals, but in comparison to the genotyped unaffected individuals the genotype distribution showed no evidence for an association to the phenotype. Therefore our data indicate that the ALX4 gene can probably be excluded as candidate gene for bovine syndactyly in the examined animals.

Stereological Modelling of Random Particles

Stochastic models for three-dimensional particles have many applications in applied sciences. Lévy–based particle models are a flexible approach to particle modelling. The structure of the random particles is given by a kernel smoothing of a Lévy basis. The models are easy to simulate but statistical inference procedures have not yet received much attention in the literature. The kernel is not always identifiable and we suggest one approach to remedy this problem. We propose a method to draw inference about the kernel from data often used in local stereology and study the performance of our approach in a simulation study.

Selection and influence effects in defending a victim of bullying: The moderating effects of school context

In this paper we examined whether defenders of victims of school bullying befriended similar peers, and whether the similarity is due to selection or influence processes or both. We examined whether these processes result in different degrees of similarity between peers depending on teachers’ self-efficacy and the school climate. We analyzed longitudinal data of 478 Swiss school students employing actor-based stochastic models. Our analyses showed that similarity in defending behavior among friends was due to selection rather than influence. The extent to which adolescents selected peers showing similar defending behavior was related to contextual factors. In fact, lower self-efficacy of teachers and positive school climate were associated with increased selection effects in terms of defending behavior.

Saddlepoint approximations

The saddlepoint method provides accurate approximations for the distributions of many test statistics, estimators and for important probabilities arising in various stochastic models. The saddlepoint approximation is a large deviations technique which is substantially more accurate than limiting normal or Edgeworth approximations, especially in presence of very small sample sizes or very small probabilities. The outstanding accuracy of the saddlepoint approximation can be explained by the fact that it has bounded relative error.

Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

Hotshots, hot spots, and female preference: exploring lek formation models with a bower-building cichlid fish

In many animals, males congregate in leks that females visit for the sole purpose of mating. We observed male and female behavior on 3 different-sized leks of the bower-building cichlid fish Nyassachromis cf. microcephalus to test predictions of 3 prominent lek models: the "hotshot," "hot spot," and "female preference" models. In this system, we were able to refine these predictions by distinguishing between indirect mate choice, by which females restrict their set of potential mates in the absence of individual male assessment, and direct mate choice, by which females assess males and their territories through dyadic behavioral interactions. On no lek were males holding central territories favored by indirect or direct mate choice, contrary to the prediction of the hotshot model that leks form because inferior males establish territories surrounding hotshot males preferred by females. Average female encounter rate of males increased with lek size, a pattern typically interpreted as evidence that leks form through female preference for lekking males, rather than because males congregate in hot spots of high female density. Female propensity to engage in premating behavior once courted did not increase with lek size, suggesting female preference for males on larger leks operated through indirect choice rather than direct choice based on individual assessment. The frequency of male-male competitive interactions increased with lek size, whereas their foraging rate decreased, implying a cost to males maintaining territories on larger leks. Together these data most strongly support the female preference model, where females may benefit through indirect mate choice for males able to meet the competitive cost of occupying larger leks.