Evolution of size-dependent flowering in Onopordum illyricum: A quantitative assessment of the role of stochastic selection pressures

We explore the evolution of delayed, size-dependent reproduction in the monocarpic perennial Onopordum illyricum, using a range of mathematical models, parameterized with long-term field data. Analysis of the long-term data indicated that mortality, flowering, and growth were age and size dependent. Using mixed models, we estimated the variance about each of these relationships and also individual-specific effects. For the held populations, recruitment was the main density-dependent process, although there were weak effects of local density on growth and mortality Using parameterized growth models, which assume plants grow along a deterministic trajectory, we predict plants should flower at sizes approximately 50% smaller than observed in the field. We then develop a simple criterion, termed the "1-yr look-ahead criterion," based on equating seed production now with that of next year, allowing for mortality and growth, to determine at what size a plant should flower. This model allows the incorporation of variance about the growth function and individual-specific effects. The model predicts flowering at sizes approximately double that observed, indicating that variance about the growth curve selects for larger sizes at flowering. The 1-yr look-ahead approach is approximate because it ignores growth opportunities more than 1 yr ahead. To assess the accuracy of this approach, we develop a more complicated dynamic state variable model. Both models give similar results indicating the utility of the 1-yr look-ahead criterion. To allow for temporal variation in the model parameters, we used an individual-based model with a generic algorithm. This gave very accurate prediction of the observed flowering strategies. Sensitivity analysis of the model suggested that temporal variation in the parameters of the growth equation made waiting to flower more risky, so selected for smaller sizes at flowering. The models clearly indicate the need to incorporate stochastic variation in life-history analyses

An evaluation of roasteak procedure and modifications of the procedure for cooking bottom round of beef

"Publication authorized August 2, 1964

Reflection tomography of time-lapse GPR data for studying dynamic unsaturated flow phenomena

Ground-penetrating radar (GPR) reflection tomography algorithms allow non-invasive monitoring of water content changes resulting from flow in the vadose zone. The approach requires multi-offset GPR data that are traditionally slow to collect. We automate GPR data collection to reduce the survey time significantly, thereby making this approach to hydrologic monitoring feasible. The method was evaluated using numerical simulations and laboratory experiments that suggest reflection tomography can provide water content estimates to within 5 % vol vol−1–10 % vol vol−1 for the synthetic studies, whereas the empirical estimates were typically within 5 %–15 % of measurements from in situ probes. Both studies show larger observed errors in water content near the periphery of the wetting front, beyond which additional reflectors were not present to provide data coverage. Overall, coupling automated GPR data collection with reflection tomography provides a new method for informing models of subsurface hydrologic processes and a new method for determining transient 2-D soil moisture distributions

The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance

We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a breakdown of symmetry (if present). The exit trajectory bifurcates, and the exit location distribution may become `skewed' (non-Gaussian). The weak-noise asymptotics of the mean escape time are strongly affected. Our methods extend to the study of skewed exit location distributions in stochastic models without symmetry.Comment: REVTEX macros (latest version). Two accompanying PS figures, one of which is large (over 600K unpacked

Unstable decay and state selection II

The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are occupied to be calculated by finding optimal paths, and fluctuations about them, in the weak noise limit. The method is illustrated on a system described by two coupled Langevin equations, which are found in the study of instabilities in fluid dynamics and superconductivity. The problem involves a subtle interplay between non-linearities and noise, and a naive approximation scheme which does not take this into account is shown to be unsatisfactory. The use of optimal paths is briefly reviewed and then applied to finding the conditional probability of ending up in one of the metastable states, having begun in the unstable state. There are several aspects of the calculation which distinguish it from most others involving optimal paths: (i) the paths do not begin and end on an attractor, and moreover, the final point is to a large extent arbitrary, (ii) the interplay between the fluctuations and the leading order contribution are at the heart of the method, and (iii) the final result involves quantities which are not exponentially small in the noise strength. This final result, which gives the probability of a particular state being selected in terms of the parameters of the dynamics, is remarkably simple and agrees well with the results of numerical simulations. The method should be applicable to similar problems in a number of other areas such as state selection in lasers, activationless chemical reactions and population dynamics in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.

Recent models for adaptive personality differences: a review

In this paper we review recent models that provide adaptive explanations for animal personalities: individual differences in behaviour (or suites of correlated behaviours) that are consistent over time or contexts. We start by briefly discussing patterns of variation in behaviour that have been documented in natural populations. In the main part of the paper we discuss models for personality differences that (i) explain animal personalities as adaptive behavioural responses to differences in state, (ii) investigate how feedbacks between state and behaviour can stabilize initial differences among individuals and (iii) provide adaptive explanations for animal personalities that are not based on state differences. Throughout, we focus on two basic questions. First, what is the basic conceptual idea underlying the model? Second, what are the key assumptions and predictions of the model? We conclude by discussing empirical features of personalities that have not yet been addressed by formal modelling. While this paper is primarily intended to guide empiricists through current adaptive theory, thereby stimulating empirical tests of these models, we hope it also inspires theoreticians to address aspects of personalities that have received little attention up to now

A Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem

We consider the overdamped limit of two-dimensional double well systems perturbed by weak noise. In the weak noise limit the most probable fluctuational path leading from either point attractor to the separatrix (the most probable escape path, or MPEP) must terminate on the saddle between the two wells. However, as the parameters of a symmetric double well system are varied, a unique MPEP may bifurcate into two equally likely MPEP's. At the bifurcation point in parameter space, the activation kinetics of the system become non-Arrhenius. In this paper we quantify the non-Arrhenius behavior of a system at the bifurcation point, by using the Maslov-WKB method to construct an approximation to the quasistationary probability distribution of the system that is valid in a boundary layer near the separatrix. The approximation is a formal asymptotic solution of the Smoluchowski equation. Our analysis relies on the development of a new scaling theory, which yields `critical exponents' describing weak-noise behavior near the saddle, at the bifurcation point.Comment: LaTeX, 60 pages, 24 Postscript figures. Uses epsf macros to include the figures. A file in `uufiles' format containing the figures is separately available at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/figures.uu and a Postscript version of the whole paper (figures included) is available at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/paperF.p

Pericellular activation of hepatocyte growth factor by the transmembrane serine proteases matriptase and hepsin, but not by the membrane-associated protease uPA

HGF (hepatocyte growth factor) is a pleiotropic cytokine homologous to the serine protease zymogen plasminogen that requires canonical proteolytic cleavage to gain functional activity. The activating proteases are key components of its regulation, but controversy surrounds their identity. Using quantitative analysis we found no evidence for activation by uPA (urokinase plasminogen activator), despite reports that this is a principal activator of pro-HGF. This was unaffected by a wide range of experimental conditions, including the use of various molecular forms of both HGF and uPA, and the presence of uPAR (uPA receptor) or heparin. In contrast the catalytic domains of the TTSPs (type-II transmembrane serine proteases) matriptase and hepsin were highly efficient activators (50% activation at 0.1 and 3.4 nM respectively), at least four orders of magnitude more efficient than uPA. PS-SCL (positional-scanning synthetic combinatorial peptide libraries) were used to identify consensus sequences for the TTSPs, which in the case of hepsin corresponded to the pro-HGF activation sequence, demonstrating a high specificity for this reaction. Both TTSPs were also found to be efficient activators at the cell surface. Activation of pro-HGF by PC3 prostate carcinoma cells was abolished by both protease inhibition and matriptase-targeting siRNA (small interfering RNA), and scattering of MDCK (Madin–Darby canine kidney) cells in the presence of pro-HGF was abolished by inhibition of matriptase. Hepsin-transfected HEK (human embryonic kidney)-293 cells also activated pro-HGF. These observations demonstrate that, in contrast with the uPA/uPAR system, the TTSPs matriptase and hepsin are direct pericellular activators of pro-HGF, and that together these proteins may form a pathway contributing to their involvement in pathological situations, including cancer