Échantillonnage sur le simplexe

Two simple approaches to sampling general probability distributions defined over the simplex, especially with Monte Carlo algorithms and in high dimensions, are presented. The approaches can be generalized to spaces bounded by linear constraints

Soil-borne microorganisms and soil-type affect pyrrolizidine alkaloids in Jacobaea vulgaris

Secondary metabolites like pyrrolizidine alkaloids (PAs) play a crucial part in plant defense. We studied the effects of soil-borne microorganisms and soil-type on pyrrolizidine alkaloids in roots and shoots of Jacobaea vulgaris. We used clones of two genotypes from a dune area (Meijendel), propagated by tissue culture and grown on two sterilized soils and sterilized soils inoculated with 5% of non-sterilized soil of either of the two soil-types. Soil-borne microorganisms and soil-type affected the composition of PAs. By changing the composition rather than the total concentration below and aboveground, plants have a more complex defense strategy than formerly thought. Interestingly, a stronger negative effect on plant growth was found in sterilized soils inoculated with their ‘own’ microbial community suggesting that pathogenic and/or other plant inhibiting microorganisms were adapted to their ‘own’ soil conditions

A relation between log-likelihood and cross-validation log-scores

It is shown that the log-likelihood of a hypothesis or model given some data is equal to an average of all leave-one-out cross-validation log-scores that can be calculated from all subsets of the data. This relation can be generalized to any k-fold cross-validation log-scores

Exceptional Properties of Second and Third Order Ordinary Differential Equations of Maximal Symmetry

AbstractThe Riccati transformation is used in the reduction of order of second and third order ordinary differential equations of maximal symmetry. The sl(2,R) subalgebra is preserved under this transformation. The Riccati transformation is itself associated with the symmetry that is annihilated in the reduction of order. The solution symmetries and the intrinsically contact symmetries become nonlocal symmetries under the Riccati transformation. We investigate the fate and origins of the contact symmetries arising from the Riccati transformation. The exceptional properties of the second and third order equations of maximal symmetry are indicated. In the context of generalised symmetries we express the solution symmetries, contact symmetries, and the sl(2,R) elements in terms of a Jacobian. We show that a basis for the solution set of equations of maximal symmetry is given in terms of the solution set of a second order ordinary differential equation

An integrable SIS model

AbstractWe provide a demonstration of the integrability of a classical model of an infectious disease which neither kills nor induces autoimmunity by means of the Painlevé analysis and use the Lie theory of transformation groups to present an explicit solution

Exceptional Properties of Second and Third Order Ordinary Differential Equations of Maximal Symmetry

AbstractThe Riccati transformation is used in the reduction of order of second and third order ordinary differential equations of maximal symmetry. The sl(2,R) subalgebra is preserved under this transformation. The Riccati transformation is itself associated with the symmetry that is annihilated in the reduction of order. The solution symmetries and the intrinsically contact symmetries become nonlocal symmetries under the Riccati transformation. We investigate the fate and origins of the contact symmetries arising from the Riccati transformation. The exceptional properties of the second and third order equations of maximal symmetry are indicated. In the context of generalised symmetries we express the solution symmetries, contact symmetries, and the sl(2,R) elements in terms of a Jacobian. We show that a basis for the solution set of equations of maximal symmetry is given in terms of the solution set of a second order ordinary differential equation

The Relationship between Structurally Different Pyrrolizidine Alkaloids and Western Flower Thrips Resistance in F2 Hybrids of Jacobaea vulgaros and Jacobaea aquatica

Segregating plant hybrids often have more ecological and molecular variability compared to parental species, and are therefore useful for studying relationships between different traits, and the adaptive significance of trait variation. Hybrid systems have been used to study the relationship between the expression of plant defense compounds and herbivore susceptibility. We conducted a western flower thrips (WFT) bioassay using a hybrid family and investigated the relationship between WFT resistance and pyrrolizidine alkaloid (PA) variation. The hybrid family consisted of two parental (Jacobaea vulgaris and Jacobaea aquatica) genotypes, two F1 genotypes, and 94 F2 hybrid lines. The J. aquatica genotype was more susceptible to thrips attack than the J. vulgaris genotype, the two F1 hybrids were as susceptible as J. aquatica, and susceptibility to WFT differed among F2 hybrid lines: 69 F2 lines were equally susceptible compared to J. aquatica, 10 F2 lines were more susceptible than J. aquatica and 15 F2 lines were as resistant as J. vulgaris or were intermediate to the two parental genotypes. Among 37 individual PAs that were derived from four structural groups (senecionine-, jacobine-, erucifoline- and otosenine-like PAs), the N-oxides of jacobine, jaconine, and jacoline were negatively correlated with feeding damage caused by WFT, and the tertiary amines of jacobine, jaconine, jacoline, and other PAs did not relate to feeding damage. Total PA concentration was negatively correlated with feeding damage. Among the four PA groups, only the total concentration of the jacobine-like PAs was negatively correlated with feeding damage. Multiple regression tests suggested that jacobine-like PAs play a greater role in WFT resistance than PAs from other structural groups. We found no evidence for synergistic effects of different PAs on WFT resistance. The relationship between PA variation and WFT feeding damage in the Jacobaea hybrids suggests a role for PAs in resistance to generalist insects

Size and the Not-So-Single Sex: Disentangling the Effects of Size and Budget on Sex Allocation in Hermaphrodites

Sex allocation theory explains how size-related variations in male and female fitness may favor the evolution of size-dependent sex allocation in hermaphrodites. Although empirical studies show that sex allocation changes gradually with size in many species, theoretical studies tend to predict an abrupt sex reversal from one sex to the other, that is, single-sexed sequential hermaphrodites. We show that this discrepancy between data and theory collapses if one takes into account that size affects male and female fitness through distinct routes. Using the classification of budget (larger individuals spend a greater budget on reproduction) and direct (e.g., larger plants are taller and may disperse pollen more efficiently) effects of size suggested by Klinkhamer et al., we propose a simple general framework appropriately incorporating these two categories of size effects in male and female fitness expressions. Analytical and numerical results show that a gradual sex change is evolutionarily stable for a large set of parameter values. Sex reversal is selected only in the absence of budget effects of size. We provide further predictions on size-dependent sex allocation and assess the relative importance of budget and direct effect for creating different patterns

A different model to explain delayed germination

Goal: To provide an alternative to the usual bet-hedging explanation for delayed germination, one that takes account of known facts about germination in stable, fine-grained environments. Context: Small patches with local environmental conditions (microhabitats) such that seedlings can establish themselves are customarily called safe sites. Key Assumptions: We focus on a single species. Its safe sites become available randomly. Seeds that germinate outside safe sites all die as seedlings. All seeds are equal, i.e. their probability of dying over the year and probabilities to germinate when the right season is there do not depend on their age or any other aspect of their individual history. Moreover, we make the standard assumption of ESS theory that the population is genetically homogeneous but for the occasional mutant 'testing the ESS'. There is a trade-off between the germination probability in safe sites and the probability not to germinate outside safe sites. For germination strategies close to the ESS, the environment does not fluctuate. Procedure: Start with a simple population model, in which the yearly seed survival and the fraction of the area covered by safe sites are fixed quantities. For this model, derive an optimization principle that finds the Evolutionarily Steady Strategy vector consisting of the probabilities to germinate in safe sites and elsewhere. Using this optimization principle, analyse the effect of various trade-offs using Levins' fitness set technique. Analyse how the results extend to ESSs for general life histories and community dynamics subject only to the key assumptions. Conclusion: Seeds in safe sites should not all germinate on the first opportunity if the relationship between the probability to germinate in safe sites and the probability to germinate elsewhere is accelerating and has a sufficiently steep slope at the highest germination probabilities