Habitat light sets the boundaries for the rapid evolution of cichlid fish vision, while sexual selection can tune it within those limits

Cichlid fishes’ famous diversity in body coloration is accompanied by a highly diverse and complex visual system. Although cichlids possess an unusually high number of seven cone opsin genes, they express only a subset of these during their ontogeny, accounting for their astonishing interspecific variation in visual sensitivities. Much of this diversity is thought to have been shaped by natural selection as cichlids inhabit a variety of habitats with distinct light environments. Also, sexual selection might have contributed to the observed visual diversity, and sexual dimorphism in coloration potentially co‐evolved with sexual dimorphism in opsin expression. We investigated sex‐specific opsin expression of several cichlids from Africa and the Neotropics and collected and integrated datasets on sex‐specific body coloration, species‐specific visual sensitivities, lens transmission and habitat light properties for some of them. We comparatively analyzed this wide range of molecular and ecological data, illustrating how integrative approaches can address specific questions on the factors and mechanisms driving diversification, and the evolution of cichlid vision in particular. We found that both sexes expressed opsins at the same levels ‐ even in sexually dimorphic cichlid species – which argues against coevolution of sexual dichromatism and differences in sex‐specific visual sensitivity. Rather, a combination of environmental light properties and body coloration shaped the diversity in spectral sensitivities among cichlids. We conclude that although cichlids are particularly colorful and diverse and often sexually dimorphic, it would appear that natural rather than sexual selection is a more powerful force driving visual diversity in this hyper‐diverse lineage

Evolutionary Dynamics of Structural Variation at a Key Locus for Color Pattern Diversification in Cichlid Fishes

Color patterns in African cichlid fishes vary spectacularly. Although phylogenetic analysis showed already 30 years ago that many color patterns evolved repeatedly in these adaptive radiations, only recently have we begun to understand the genomic basis of color variation. Horizontal stripe patterns evolved and were lost several times independently across the adaptive radiations of LakeVictoria, Malawi, and Tanganyika and regulatory evolution of agouti-related peptide 2 (agrp2/asip2b) has been linked to this phenotypically labile trait. Here, we asked whether the agrp2 locus exhibits particular characteristics that facilitate divergence in color patterns. Based on comparative genomic analyses, we discovered several recent duplications, insertions, and deletions. Interestingly, one of these events resulted in a tandem duplication of the last exon of agrp2. The duplication likely precedes the EastAfrican radiations that started 8-12 Ma, is not fixed within any of the radiations, and is found to vary even within some species. Moreover, we also observed variation in copy number (two to five copies) and secondary loss of the duplication, illustrating a surprising dynamic at this locus that possibly promoted functional divergence of agrp2. Our work suggests that such instances of exon duplications are a neglected mechanism potentially involved in the repeated evolution and diversification that deserves more attention.Peer reviewe

Generating Functions for Coherent Intertwiners

We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for different choices of combinatorial weights. Moreover, we identify one choice of weight distinguished thanks to its geometric interpretation. As an example of dynamics, we consider the simple case of SU(2) flatness and describe the corresponding Hamiltonian constraint whose quantization on coherent intertwiners leads to partial differential equations that we solve. Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2) flatness on coherent spin networks for arbitrary graphs.Comment: 31 page

Spin foams with timelike surfaces

Spin foams of 4d gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this article, we express the associated partition function in terms of vertex amplitudes and integrals over coherent states. The coherent states are characterized by unit 3--vectors which represent normals to surfaces and lie either in the 2--sphere or the 2d hyperboloids. In the case of timelike surfaces, a new type of coherent state is used and the associated completeness relation is derived. It is also shown that the quantum simplicity constraints can be deduced by three different methods: by weak imposition of the constraints, by restriction of coherent state bases and by the master constraint.Comment: 22 pages, no figures; v2: remarks on operator formalism added in discussion; correction: the spin 1/2 irrep of the discrete series does not appear in the Plancherel decompositio

Euclidean three-point function in loop and perturbative gravity

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of gamma<1. We find results consistent with Regge calculus in the limit gamma->0 and j->infinity. We also compute the tree-level three-point function of perturbative quantum general relativity in position space, and discuss the possibility of directly comparing the two results.Comment: 16 page

Asymptotics of 4d spin foam models

We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary data. For some classes of geometrical boundary data, the asymptotic formulae are given, in all three cases, by simple functions of the Regge action for the four-simplex geometry.Comment: 10 pages, Proceedings for the 2nd Corfu summer school and workshop on quantum gravity and quantum geometry, talk given by Winston J. Fairbair

Lorentzian spin foam amplitudes: graphical calculus and asymptotics

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.Comment: 30 pages. v2: references now appear. v3: presentation greatly improved (particularly diagrammatic calculus). Definition of "Regge state" now the same as in previous work; signs change in final formula as a result. v4: two references adde

A spin foam model for general Lorentzian 4-geometries

We derive simplicity constraints for the quantization of general Lorentzian 4-geometries. Our method is based on the correspondence between coherent states and classical bivectors and the minimization of associated uncertainties. For spacelike geometries, this scheme agrees with the master constraint method of the model by Engle, Pereira, Rovelli and Livine (EPRL). When it is applied to general Lorentzian geometries, we obtain new constraints that include the EPRL constraints as a special case. They imply a discrete area spectrum for both spacelike and timelike surfaces. We use these constraints to define a spin foam model for general Lorentzian 4-geometries.Comment: 27 pages, 1 figure; v4: published versio

A new look at loop quantum gravity

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems.Comment: 15 pages, 5 figure