Myocardial flow reserve by Rb-82 cardiac PET improves the selection of patients eligible for invasive coronary angiography

Aim: We asked whether myocardial flow reserve (MFR) by Rb-82 cardiac PET improve the selection of patients eligible for invasive coronary angiography (ICA). Material and Methods: We enrolled 26 consecutive patients with suspected or known coronary artery disease who performed dynamic Rb-82 PET/CT and (ICA) within 60 days; 4 patients who underwent revascularization or had any cardiovascular events between PET and ICA were excluded. Myocardial blood flow at rest (rMBF), at stress with adenosine (sMBF) and myocardial flow reserve (MFR=sMBF/rMBF) were estimated using the 1-compartment Lortie model (FlowQuant) for each coronary arteries territories. Stenosis severity was assessed using computer-based automated edge detection (QCA). MFR was divided in 3 groups: G1:MFR<1.5, G2:1.5≤MFR<2 and G3:2≤MFR. Stenosis severity was graded as non-significant (<50% or FFR ≥0.8), intermediate (50%≤stenosis<70%) and severe (≥70%). Correlation between MFR and percentage of stenosis were assessed using a non-parametric Spearman test. Results: In G1 (44 vessels), 17 vessels (39%) had a severe stenosis, 11 (25%) an intermediate one, and 16 (36%) no significant stenosis. In G2 (13 vessels), 2 (15%) vessels presented a severe stenosis, 7 (54%) an intermediate one, and 4 (31%) no significant stenosis. In G3 (9 vessels), 0 vessel presented a severe stenosis, 1 (11%) an intermediate one, and 8 (89%) no significant stenosis. Of note, among 11 patients with 3-vessel low MFR<1.5 (G1), 9/11 (82%) had at least one severe stenosis and 2/11 (18%) had at least one intermediate stenosis. There was a significant inverse correlation between stenosis severity and MFR among all 66 territories analyzed (rho= -0.38, p=0.002). Conclusion: Patients with MFR>2 could avoid ICA. Low MFR (G1, G2) on a vessel-based analysis seems to be a poor predictor of severe stenosis severity. Patients with 3-vessel low MFR would benefit from ICA as they are likely to present a significant stenosis in at least one vessel.

Genetic team composition and level of selection in the evolution of cooperation

In cooperative multiagent systems, agents interac to solve tasks. Global dynamics of multiagent teams result from local agent interactions, and are complex and difficult to predict. Evolutionary computation has proven a promising approach to the design of such teams. The majority of current studies use teams composed of agents with identical control rules ("geneti- cally homogeneous teams") and select behavior at the team level ("team-level selection"). Here we extend current approaches to include four combinations of genetic team composition and level of selection. We compare the performance of genetically homo- geneous teams evolved with individual-level selection, genetically homogeneous teams evolved with team-level selection, genetically heterogeneous teams evolved with individual-level selection, and genetically heterogeneous teams evolved with team-level selection. We use a simulated foraging task to show that the optimal combination depends on the amount of cooperation required by the task. Accordingly, we distinguish between three types of cooperative tasks and suggest guidelines for the optimal choice of genetic team composition and level of selection

An ultra performance liquid chromatography-tandem MS assay for tamoxifen metabolites profiling in plasma: first evidence of 4'-hydroxylated metabolites in breast cancer patients.

There is increasing evidence that the clinical efficacy of tamoxifen, the first and most widely used targeted therapy for estrogen-sensitive breast cancer, depends on the formation of the active metabolites 4-hydroxy-tamoxifen and 4-hydroxy-N-desmethyl-tamoxifen (endoxifen). Large inter-individual variability in endoxifen plasma concentrations has been observed and related both to genetic and environmental (i.e. drug-induced) factors altering CYP450s metabolizing enzymes activity. In this context, we have developed an ultra performance liquid chromatography-tandem mass spectrometry method (UPLC-MS/MS) requiring 100 μL of plasma for the quantification of tamoxifen and three of its major metabolites in breast cancer patients. Plasma is purified by a combination of protein precipitation, evaporation at room temperature under nitrogen, and reconstitution in methanol/20 mM ammonium formate 1:1 (v/v), adjusted to pH 2.9 with formic acid. Reverse-phase chromatographic separation of tamoxifen, N-desmethyl-tamoxifen, 4-hydroxy-tamoxifen and 4-hydroxy-N-desmethyl-tamoxifen is performed within 13 min using elution with a gradient of 10 mM ammonium formate and acetonitrile, both containing 0.1% formic acid. Analytes quantification, using matrix-matched calibration samples spiked with their respective deuterated internal standards, is performed by electrospray ionization-triple quadrupole mass spectrometry using selected reaction monitoring detection in the positive mode. The method was validated according to FDA recommendations, including assessment of relative matrix effects variability, as well as tamoxifen and metabolites short-term stability in plasma and whole blood. The method is precise (inter-day CV%: 2.5-7.8%), accurate (-1.4 to +5.8%) and sensitive (lower limits of quantification comprised between 0.4 and 2.0 ng/mL). Application of this method to patients' samples has made possible the identification of two further metabolites, 4'-hydroxy-tamoxifen and 4'-hydroxy-N-desmethyl-tamoxifen, described for the first time in breast cancer patients. This UPLC-MS/MS assay is currently applied for monitoring plasma levels of tamoxifen and its metabolites in breast cancer patients within the frame of a clinical trial aiming to assess the impact of dose increase on tamoxifen and endoxifen exposure.

Determination of oseltamivir and oseltamivir carboxylate in human plasma by liquid chromatography-tandem mass spectrometry

Introduction: Oseltamivir phosphate (OP), the prodrug of oseltamivir carboxylate (OC; active metabolite), is marketed since 10 years for the treatment of seasonal influenza flu. It has recently received renewed attention because of the threat of avian flu H5N1 in 2006-7 and the 2009-10 A/H1N1 pandemic. However, relatively few studies have been published on OP and OC clinical pharmacokinetics. The disposition of OC and the dosage adaptation of OP in specific populations, such as young children or patients undergoing extrarenal epuration, have also received poor attention. An analytical method was thus developed to assess OP and OC plasma concentrations in patients receiving OP and presenting with comorbidities or requiring intensive care. Methods: A high performance liquid chromatography coupled to tandem mass spectrometry method (HPLC-MS/MS) requiring 100-µL aliquot of plasma for quantification within 6 min of OP and OC was developed. A combination of protein precipitation with acetonitrile, followed by dilution of supernant in suitable buffered solvent was used as an extraction procedure. After reverse phase chromatographic separation, quantification was performed by electro-spray ionization-triple quadrupole mass spectrometry. Deuterated isotopic compounds of OP and OC were used as internal standards. Results: The method is sensitive (lower limit of quantification: 5 ng/mL for OP and OC), accurate (intra-/inter-assay bias for OP and OC: 8.5%/5.5% and 3.7/0.7%, respectively) and precise (intra-/inter-assay CV%: 5.2%/6.5% and 6.3%/9.2%, respectively) over the clinically relevant concentration range (upper limits of quantification 5000 ng/mL). Of importance, OP, as in other previous reports, was found not to be stable ex vivo in plasma on standard anticoagulants (i.e. EDTA, heparin or citrate). This poor stability of OP has been prevented by collecting blood samples on commercial fluoride/oxalate tubes. Conclusions: This new simple, rapid and robust HPLC-MS/MS assay for quantification of OP and OC plasma concentrations offers an efficient tool for concentration monitoring of OC. Its exposure can probably be controlled with sufficient accuracy by thorough dosage adjustment according to patient characteristics (e.g. renal clearance). The usefulness of systematic therapeutic drug monitoring in patients appears therefore questionable. However, pharmacokinetic studies are still needed to extend knowledge to particular subgroups of patients or dosage regimens.

How accurate is the current picture of human genetic variation?

Our understanding of the distribution of worldwide human genomic diversity has greatly increased over recent years thanks to the availability of large data sets derived from short tandem repeats (STRs), insertion deletion polymorphisms (indels) and single nucleotide polymorphisms (SNPs). A concern, however, is that the current picture of worldwide human genomic diversity may be inaccurate because of biases in the selection process of genetic markers (so-called 'ascertainment bias'). To evaluate this problem, we first compared the distribution of genomic diversity between these three types of genetic markers in the populations from the HGDP-CEPH panel for evidence of bias or incongruities. In a second step, using a very relaxed set of criteria to prevent the intrusion of bias, we developed a new set of unbiased STR markers and compared the results against those from available panels. Contrarily to recent claims, our results show that the STR markers suffer from no discernible bias, and can thus be used as a baseline reference for human genetic diversity and population differentiation. The bias on SNPs is moderate compared to that on the set of indels analysed, which we recommend should be avoided for work describing the distribution of human genetic diversity or making inference on human settlement history.

Comparative genomics of chemosensory protein genes reveals rapid evolution and positive selection in ant-specific duplicates.

Gene duplications can have a major role in adaptation, and gene families underlying chemosensation are particularly interesting due to their essential role in chemical recognition of mates, predators and food resources. Social insects add yet another dimension to the study of chemosensory genomics, as the key components of their social life rely on chemical communication. Still, chemosensory gene families are little studied in social insects. Here we annotated chemosensory protein (CSP) genes from seven ant genomes and studied their evolution. The number of functional CSP genes ranges from 11 to 21 depending on species, and the estimated rates of gene birth and death indicate high turnover of genes. Ant CSP genes include seven conservative orthologous groups present in all the ants, and a group of genes that has expanded independently in different ant lineages. Interestingly, the expanded group of genes has a differing mode of evolution from the orthologous groups. The expanded group shows rapid evolution as indicated by a high dN/dS (nonsynonymous to synonymous changes) ratio, several sites under positive selection and many pseudogenes, whereas the genes in the seven orthologous groups evolve slowly under purifying selection and include only one pseudogene. These results show that adaptive changes have played a role in ant CSP evolution. The expanded group of ant-specific genes is phylogenetically close to a conservative orthologous group CSP7, which includes genes known to be involved in ant nestmate recognition, raising an interesting possibility that the expanded CSPs function in ant chemical communication.

KIT mutations and dose selection for imatinib in patients with advanced gastrointestinal stromal tumours.

A recent randomized EORTC phase III trial, comparing two doses of imatinib in patients with advanced gastrointestinal stromal tumours (GISTs), reported dose dependency for progression-free survival. The current analysis of that study aimed to assess if tumour mutational status correlates with clinical response to imatinib. Pre-treatment samples of GISTs from 377 patients enrolled in phase III study were analyzed for mutations of KIT or PDGFRA by combination of D-HPLC and direct sequencing of tumour genomic DNA. Mutation types were correlated with patients' survival data. The presence of exon 9-activating mutations in KIT was the strongest adverse prognostic factor for response to imatinib, increasing the relative risk of progression by 171% (P&lt;0.0001) and the relative risk of death by 190% (P&lt;0.0001) when compared with KIT exon 11 mutants. Similarly, the relative risk of progression was increased by 108% (P&lt;0.0001) and the relative risk of death by 76% (P=0.028) in patients without detectable KIT or PDGFRA mutations. In patients whose tumours expressed an exon 9 KIT oncoprotein, treatment with the high-dose regimen resulted in a significantly superior progression-free survival (P=0.0013), with a reduction of the relative risk of 61%. We conclude that tumour genotype is of major prognostic significance for progression-free survival and overall survival in patients treated with imatinib for advanced GISTs. Our findings suggest the need for differential treatment of patients with GISTs, with KIT exon 9 mutant patients benefiting the most from the 800 mg daily dose of the drug.

Local selection rules that can determine specific pathways of DNA unknotting by type II DNA topoisomerases.

We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of inter-segmental juxtapositions at sites of inter-segmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules, type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand-passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.

Autoreactive T cells that bypass negative selection are not tolerant and respond to self-antigen stimulation during infection

Le répertoire cellulaire Τ a pour but d'être tolérant aux antigènes du soi afin d'éviter l'induction de maladies autoimmunes. C'est pourquoi les lymphocytes Τ autoréactifs sont éliminés dans le thymus lors de leur développement par le processus de sélection négative. La plupart des recherches étudient les lymphocytes Τ de haute avidité. Ces lymphocytes Τ de haute avidité sont très sensibles et réagissent fortement à un antigène du soi. En conséquence, ces cellules induisent le développement de maladies autoimmunes lorsqu'elles ciblent des organes exprimant l'antigène du soi. Plusieurs études ont montré que les lymphocytes Τ qui réagissent faiblement aux antigènes spécifiques à un tissu, nommé lymphocytes Τ de faible avidité, peuvent contourner les mécanismes de tolérance centrale et périphérique. J'ai utilisé des souris Rip-mOva qui expriment l'Ovalbumine comme antigène du soi spécifique à un tissu. Dans ces souris transgéniques Rip-mOva, les lymphocytes Τ de faible avidité survivent à la sélection négative. Une fois stimulés à la périphérie, ces lymphocytes Τ CD8+ de faible avidité ont la capacité d'infiltrer les organes qui expriment l'antigène du soi chez les souris Rip-mOva et peuvent induire une destruction tissulaire. L'objectif principal de mon projet de thèse était de comprendre les caractéristiques phénotypiques et fonctionnelles de ces lymphocytes Τ dans un état d'équilibre et dans un contexte infectieux. Pour étudier ces cellules dans un modèle murin bien défini, nous avons généré des souris exprimant un récepteur de cellule Τ transgénique appelé OT-3. Ces souris transgéniques OT-3 ont des lymphocytes Τ CD8+ de faible avidité spécifiques à l'épitope SIINFEKL de l'antigène Ovalbumine. Nous avons démontré qu'un grand nombre de lymphocytes Τ CD8+ OT-3 ne sont pas éliminés lors de la sélection négative dans le thymus après avoir rencontré l'antigène du soi. Par conséquent, les lymphocytes Τ OT-3 de faible avidité sont présents dans une fenêtre de sélection comprise entre la sélection positive et négative. Cette limite se définie comme le seuil d'affinité et est impliquée dans l'échappement de certains lymphocytes Τ OT- 3 autoréactifs. A la périphérie, ces cellules sont capables d'induire une autoimmunité après stimulation au cours d'une infection, ce qui nous permet de les définir comme étant non tolérante et non dans un état anergique à la périphérie. Nous avons également étudié le seuil d'activation des lymphocytes Τ OT-3 à faible avidité à la périphérie et avons constaté que des ligands peptidiques plus faibles que l'épitope natif SIINFEKL sont capables de les activer au cours d'une infection ainsi que de les différencier en lymphocytes Τ effecteurs et mémoires. Les données illustrent une déficience lors de la sélection négative dans le thymus de lymphocytes Τ CD8+ autoréactifs de faible avidité contre un antigène du soi spécifique à tissu et montrent que ces cellules sont entièrement compétentes lors d'une infection. - The diverse Τ cell repertoire needs to be tolerant to self-antigen to avoid the induction of autoimmunity. This is why autoreactive developing Τ cells are deleted in the thymus. The deletion of self-reactive Τ cells occurs through the process of negative selection. Most studies investigated high avidity Τ cells. These high avidity Τ cells are very sensitive and strongly react to a self-antigen. As a consequence, these cells induce the development of autoimmunity when they target organs which express the self-antigen. High avidity autoreactive CD8+ Τ cells are deleted in the thymus. However, several studies have shown Τ cells that weakly respond to tissue-restricted antigen, referred to as low avidity Τ cells, can bypass central and peripheral tolerance mechanisms. I used Rip-mOva mice that expressed Ovalbumin as a neo self-antigen in a tissue-restricted fashion. In these transgenic Rip-mOva mice low avidity CD8+ Τ cells survive negative selection. Upon stimulation in the periphery, these low avidity CD8+ Τ cells have the ability to infiltrate organs that express the self-antigen in the Rip-mOva mice and can also induce the destruction of the tissue. The major aim of my PhD project was to understand the phenotypic and functionality characteristics of these Τ cells in a steady-state condition and in a context of an infection. To study these cells in a well-defined mouse model, we generated OT-3 Τ cell receptor transgenic mice that express low avidity CD8+ Τ cells that are specific for the SIINFEKL epitope of the Ovalbumin antigen. We have been able to demonstrate that a large number of OT-3 CD8+ Τ cells survive negative selection in the thymus after encountering the self-antigen. Thus, low avidity OT-3 Τ cells are present in a window of selection comprised between positive and negative selection. This boundary defined as the affinity threshold is involved in the escape of some autoreactive low avidity OT-3 Τ cells. Once they circulate in the periphery, they are able to induce autoimmunity after stimulation during an infection, allowing us to allocate these cells as being non-tolerant and not in an anergic state in the periphery. We have also looked at the threshold of activation of low avidity OT-3 CD8+ Τ cells in the periphery and found that peptide ligands that are weaker than the native SIINFEKL epitope are able to activate OT-3 Τ cells during an infection and to differentiate them into effector and memory Τ cells. The data illustrate the impairment of negatively selecting low avidity autoreactive CD8+ Τ cells against a tissue-restricted antigen in the thymus and shows that these cells are fully competent upon an infection.

Dissociation of thymic positive and negative selection in transgenic mice expressing major histocompatibility complex class I molecules exclusively on thymic cortical epithelial cells.

Thymic positive and negative selection of developing T lymphocytes confronts us with a paradox: How can a T-cell antigen receptor (TCR)-major histocompatibility complex (MHC)/peptide interaction in the former process lead to transduction of signals allowing for cell survival and in the latter induce programmed cell death or a hyporesponsive state known as anergy? One of the hypotheses put forward states that the outcome of a TCR-MHC/peptide interaction depends on the cell type presenting the selecting ligand to the developing thymocyte. Here we describe the development and lack of self-tolerance of CD8(+) T lymphocytes in transgenic mice expressing MHC class I molecules in the thymus exclusively on cortical epithelial cells. Despite the absence of MHC class I expression on professional antigen-presenting cells, normal numbers of CD8(+) cells were observed in the periphery. Upon specific activation, transgenic CD8(+) T cells efficiently lysed syngeneic MHC class I(+) targets in vitro and in vivo, indicating that thymic cortical epithelium (in contrast to medullary epithelium and antigen-presenting cells of hematopoietic origin) is incapable of tolerance induction. Thus, compartmentalization of the antigen-presenting cells involved in thymic positive selection and tolerance induction can (at least in part) explain the positive/negative selection paradox.

1st radiometric dating of a paleontologically dated Bathonian level from Georgia (USSR) - Use of the cathodoluminescence for selection of suitable plagioclases

Jurassic volcanic formations interlayered with (ammonite-bearing) sediments are common in the Caucasus area; this situation is of interest for the numerical calibration of the poorly documented Jurassic portion of the time scale. However, following petrographic study on thin sections no whole-rocks can be considered reliable geochronometers due to subsequent alteration; from about 20 samples, two were selected for plagioclase dating; one (V134) is probably early Kimmeridgian in age; the other (V136) is probably located in the Lower Bathonian stage according to diagnostic ammonites. Cathodoluminescence (CTL) study has shown that sample V136 was similar to usual volcanic feldspars (blue to green colour); however, the lack of CTL of the V134 plagioclase is a character common to diagenetic feldspars; consequently, in spite of a good optical preservation, this geo-chronometer cannot give an age representative of the time of emplacement of the lava flow. We have combined CTL observation with microprobe analysis in order to document the poorly known CTL behaviour of volcanic feldspars; cations Ti4+ and Fe2+ play a major role in the CTL colour of plagioclases and are able to document the growing history of these feldspars ; phenocrysts are initially rich in Fe2+ (core of the crystals, green in colour), then richer in Ti toward the exterior; microcrysts are even richer in Ti (blue to bright blue). We have also observed that natural CTL colour was modified resulting from acid ``cleaning'' of the separated feldspars : the initial blue or green colour tends to change to yellow or violet, respectively, after acid treatment probably due to oxydation of Fe2+ toward Fe3+. X-ray and microprobe analyses both indicated that plagioclases from sample V134 was near the sodic end member (albite) suggesting a diagenetic origin in this andesitic basalt; In contrast, sample V136 contains a calcic plagioclase of common composition for a doleritic basalt. The K-Ar conventional technique was applied as a preliminary tool for radiometric analysis. The Kimmeridgian Na-plagioclase sample gave a ``rejuvenated'' (85 Ma) apparent age which confirms a late genesis for the separated plagioclase phase; this interpretation is based on CTL observation, X-ray analysis, and microprobe analysis ; these techniques are able to distinguish samples which have been submitted to diagenetic alteration from those which have not. An age consistent with the stratigraphic location has been obtained from sample V136. This age of 161 +/- 3 (2-sigma) Ma, is the first one available from a sample palaeontologically located with reasonable precision within the mid Jurassic time.

TCR-alpha CDR3 loop audition regulates positive selection.

How positive selection molds the T cell repertoire has been difficult to examine. In this study, we use TCR-beta-transgenic mice in which MHC shapes TCR-alpha use. Differential AV segment use is directly related to the constraints placed on the composition of the CDR3 loops. Where these constraints are low, efficient selection of alphabeta pairs follows. This mode of selection preferentially uses favored AV-AJ rearrangements and promotes diversity. Increased constraint on the alpha CDR3 loops leads to inefficient selection associated with uncommon recombination events and limited diversity. Further, the two modes of selection favor alternate sets of AJ segments. We discuss the relevance of these findings to the imprint of self-MHC restriction and peripheral T cell activation.

EEG alpha activity reflects motor preparation rather than the mode of action selection

Alpha-band activity (8-13 Hz) is not only suppressed by sensory stimulation and movements, but also modulated by attention, working memory and mental tasks, and could be sensitive to higher motor control functions. The aim of the present study was to examine alpha oscillatory activity during the preparation of simple left or right finger movements, contrasting the external and internal mode of action selection. Three preparation conditions were examined using a precueing paradigm with S1 as the preparatory and S2 as the imperative cue: Full, laterality instructed by S1; Free, laterality freely selected and None, laterality instructed by S2. Time-frequency (TF) analysis was performed in the alpha frequency range during the S1-S2 interval, and alpha motor-related amplitude asymmetries (MRAA) were also calculated. The significant MRAA during the Full and Free conditions indicated effective external and internal motor response preparation. In the absence of specific motor preparation (None), a posterior alpha event-related desynchronization (ERD) dominated, reflecting the main engagement of attentional resources. In Full and Free motor preparation, posterior alpha ERD was accompanied by a midparietal alpha event-related synchronization (ERS), suggesting a concomitant inhibition of task-irrelevant visual activity. In both Full and Free motor preparation, analysis of alpha power according to MRAA amplitude revealed two types of functional activation patterns: (1) a motor alpha pattern, with predominantly midparietal alpha ERS and large MRAA corresponding to lateralized motor activation/visual inhibition and (2) an attentional alpha pattern, with dominating right posterior alpha ERD and small MRAA reflecting visuospatial attention. The present results suggest that alpha oscillatory patterns do not resolve the selection mode of action, but rather distinguish separate functional strategies of motor preparation.

The stationary distribution of a continuously varying strategy in a class-structured population under mutation-selection-drift balance.

Many traits and/or strategies expressed by organisms are quantitative phenotypes. Because populations are of finite size and genomes are subject to mutations, these continuously varying phenotypes are under the joint pressure of mutation, natural selection and random genetic drift. This article derives the stationary distribution for such a phenotype under a mutation-selection-drift balance in a class-structured population allowing for demographically varying class sizes and/or changing environmental conditions. The salient feature of the stationary distribution is that it can be entirely characterized in terms of the average size of the gene pool and Hamilton's inclusive fitness effect. The exploration of the phenotypic space varies exponentially with the cumulative inclusive fitness effect over state space, which determines an adaptive landscape. The peaks of the landscapes are those phenotypes that are candidate evolutionary stable strategies and can be determined by standard phenotypic selection gradient methods (e.g. evolutionary game theory, kin selection theory, adaptive dynamics). The curvature of the stationary distribution provides a measure of the stability by convergence of candidate evolutionary stable strategies, and it is evaluated explicitly for two biological scenarios: first, a coordination game, which illustrates that, for a multipeaked adaptive landscape, stochastically stable strategies can be singled out by letting the size of the gene pool grow large; second, a sex-allocation game for diploids and haplo-diploids, which suggests that the equilibrium sex ratio follows a Beta distribution with parameters depending on the features of the genetic system.