Evolved polygenic herbicide resistance in Lolium rigidum by low-dose herbicide selection within standing genetic variation

The interaction between environment and genetic traits under selection is the basis of evolution. In this study, we have investigated the genetic basis of herbicide resistance in a highly characterized initially herbicide-susceptible Lolium rigidum population recurrently selected with low (below recommended label) doses of the herbicide diclofop-methyl. We report the variability in herbicide resistance levels observed in F1 families and the segregation of resistance observed in F2 and back-cross (BC) families. The selected herbicide resistance phenotypic trait(s) appear to be under complex polygenic control. The estimation of the effective minimum number of genes (NE), depending on the herbicide dose used, reveals at least three resistance genes had been enriched. A joint scaling test indicates that an additive-dominance model best explains gene interactions in parental, F1, F2 and BC families. The Mendelian study of six F2 and two BC segregating families confirmed involvement of more than one resistance gene. Cross-pollinated L. rigidum under selection at low herbicide dose can rapidly evolve polygenic broad-spectrum herbicide resistance by quantitative accumulation of additive genes of small effect. This can be minimized by using herbicides at the recommended dose which causes high mortality acting outside the normal range of phenotypic variation for herbicide susceptibility

Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions

We present Monte Carlo simulations of the spanning-forest model (q \to 0 limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show that, in contrast to the two-dimensional case, the model has a "ferromagnetic" second-order phase transition at a finite positive value w_c. We present numerical estimates of w_c and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.Comment: LaTex2e, 4 pages; includes 6 Postscript figures; Version 2 has expanded title as published in PR

Grassmann Integral Representation for Spanning Hyperforests

Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff's matrix-tree theorem. Furthermore, we show that the class of integrals describing unrooted spanning (hyper)forests is induced by a theory with an underlying OSP(1|2) supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J. Phys.

Cluster simulations of loop models on two-dimensional lattices

We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard O(n) loop models at n \ge 1. We show that our algorithm has little or no critical slowing-down when 1 \le n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop model, for which we determine several new critical exponents, and a square-lattice O(n) loop model, for which we obtain new information on the phase diagram.Comment: LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten in version 2, with new theory and new data. Version 3 as published in PR

Social Effects in Science: Modelling Agents for a Better Scientific Practice

Science is a fundamental human activity and we trust its results because it has several error-correcting mechanisms. Its is subject to experimental tests that are replicated by independent parts. Given the huge amount of information available, scientists have to rely on the reports of others. This makes it possible for social effects to influence the scientific community. Here, an Opinion Dynamics agent model is proposed to describe this situation. The influence of Nature through experiments is described as an external field that acts on the experimental agents. We will see that the retirement of old scientists can be fundamental in the acceptance of a new theory. We will also investigate the interplay between social influence and observations. This will allow us to gain insight in the problem of when social effects can have negligible effects in the conclusions of a scientific community and when we should worry about them.Comment: 14 pages, 5 figure

Critical speeding-up in a local dynamics for the random-cluster model

We study the dynamic critical behavior of the local bond-update (Sweeny) dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2,3, by Monte Carlo simulation. We show that, for a suitable range of q values, the global observable S_2 exhibits "critical speeding-up": it decorrelates well on time scales much less than one sweep, so that the integrated autocorrelation time tends to zero as the critical point is approached. We also show that the dynamic critical exponent z_{exp} is very close (possibly equal) to the rigorous lower bound \alpha/\nu, and quite possibly smaller than the corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.Comment: LaTex2e/revtex4, 4 pages, includes 5 figure

Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies

Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX. If the $d$ tests are dependent, $d_{MAX} < d$. The second parameter is the fractional degrees of freedom $k$ of the chi-square distribution $\chi^2_k$ that fits the MAX null distribution. These two parameters, $d_{MAX}$ and $k$, can be independently defined, and $k$ can be non-integer even if $d_{MAX}$ is an integer. We illustrate these two parameters using the example of MAX2 and MAX3 statistics in genetic case-control studies. We speculate that $k$ is related to the amount of ambiguity of the model inferred by the test. In the case-control genetic association, tests with low $k$ (e.g. $k=1$) are able to provide definitive information about the disease model, as versus tests with high $k$ (e.g. $k=2$) that are completely uncertain about the disease model. Similar to Heisenberg's uncertain principle, the ability to infer disease model and the ability to detect significant association may not be simultaneously optimized, and $k$ seems to measure the level of their balance