The origins of postmating reproductive isolation: testing hypotheses in the grasshopper Chorthippus parallelus

Although there are several well-established hypotheses for the origins of postmating isolation during allopatric divergence, there have been very few attempts, to determine their relative importance in nature. We have developed an approach based on knowledge of the differing evolutionary histories of populations within species that allows systematic comparison of the predictions of these hypotheses. In previous work, we have applied this methodology to mating signal variation and premating reproductive isolation between populations of the meadow grasshopper Chorthippus parallelus. Here we review the principles behind our approach and report a study measuring postmating isolation in the same set of populations. The populations have known and differing evolutionary histories and relationships resulting from the colonization of northern Europe following the last glaciation. We use a maximum-likelihood analysis to compare the observed pattern of postmating isolation with the predictions of the hypotheses that isolation primarily evolves either as a result of gradual accumulation of mutations in allopatry, or through processes associated with colonization, such as founder events., We also quantify the extent to which degree of postmating isolation can be predicted by genetic distance. Our results suggest that although there is only a weak correlation between genetic distance and postmating isolation, long periods of allopatry do lead to postmating isolation. In contrast to the pattern of premating isolation described in our previous study, colonization does not seem to be associated with increased postmating isolation

Anti-optimisation for modelling the vibration of locally nonlinear structures: An exploratory study

Modelling the vibration of complex structures with uncertain nonlinearities is a significant challenge. However, nonlinearities are often spatially localised: this enables efficient linear methods to describe the behaviour of the majority of the structure and reduces the size of the nonlinear problem. This paper explores anti-optimisation as an approach to modelling uncertain nonlinearities for this class of system. The ‘worst-case’ output metric is sought by considering nonlinear forces as an external input subject to constraints that capture what is known about the nonlinearity. A systematic sequence of tests is carried out using a mass on spring system within a pair of end-stops: the results show how the anti-optimised solutions become less conservative as the constraints are increasingly restrictive. The method is applied to bending vibration of a beam within a pair of local end-stops. Anti-optimised solutions are found as a function of frequency and are compared with a Monte Carlo set of benchmark simulations. Almost all anti-optimised solutions over-predict the simulations and the overall trend of the simulations is also clearly captured. The method shows significant potential and motivates further research.Tore Butlin is supported by an RAEng/EPSRC Research FellowshipThis is the final published version distributed under a Creative Commons Attribution License, which can also be found on the publisher's website at: http://www.sciencedirect.com/science/article/pii/S0022460X13005683

An efficient model of drillstring dynamics

This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jsv.2015.06.033High amplitude vibration regimes can cause significant damage to oilwell drillstrings: torsional stick-slip oscillation, forward whirl and backward whirl are each associated with different kinds of damage. There is a need for models of drillstring dynamics that can predict this variety of phenomena that are: efficient enough to carry out parametric studies; simple enough to provide insight into the underlying physics, and which retain sufficient detail to correlate to real drillstrings. The modelling strategy presented in this paper attempts to balance these requirements. It includes the dynamics of the full length of the drillstring over a wide bandwidth but assumes that the main nonlinear effects are due to spatially localised regions of strong nonlinearity, for example at the drillbit cutting interface and at stabilisers where the borehole wall clearance is smallest. The equations of motion can be formed in terms of this reduced set of degrees of freedom, coupled to the nonlinear contact laws and solved by time-domain integration. Two implementations of this approach are presented, using (1) digital filters and (2) a Finite Element model to describe the linear dynamics. Choosing a sampling period that is less than the group delay between nonlinear degrees of freedom results in a decoupled set of equations that can be solved very efficiently. Several cases are presented which demonstrate a variety of phenomena, including stick-slip oscillation; forward whirl and backward whirl. Parametric studies are shown which reveal the conditions which lead to high amplitude vibration regimes, and an analytic regime boundary is derived for torsional stick-slip oscillation. The digital filter and Finite Element models are shown to be in good agreement and are similarly computationally efficient. The digital filter approach has the advantage of more intuitive interpretation, while the Finite Element model is more readily implemented using existing software packages.The authors are grateful to industrial support and permission to publish this work, and would like to thank Prof Jim Woodhouse for technical contributions, and Dr Louis Kovalevski for assistance with the Finite Element model

A derivation of the Transient Statistical Energy Analysis (TSEA) equations with benchmark applications to plate systems

Statistical Energy Analysis (SEA) is a well-established method for predicting the response of complex systems to high frequency steady-state harmonic or random excitation. The method has also been applied to transient and shock loading, in which case it is referred to as Transient SEA (TSEA), although the validity of the approach is less certain for this case since the TSEA equations mix time and frequency descriptions of the response in an ad-hoc way. In this paper, the TSEA equations are derived in a new way by employing an analogy of the Priestley description of a non-stationary random process. A key feature is that shock loading is deterministic, so that the random ensemble of responses arises from random structural properties rather than random loading, and this requires a reinterpretation of the Priestley description. The present derivation of TSEA enables the appropriate initial conditions on the equations to be established and bounds on the prediction error are found from Parseval’s theorem. The derived equations are applied to numerical and experimental examples involving plates.Mitsubishi Heavy Industrie

A novel method for predicting the response variability of friction-damped gas turbine blades

Predicting the response of gas turbine blades with underplatform friction dampers is challenging due to the combination of frictional nonlinearity and system uncertainty: a traditional Monte Carlo approach to predicting response distributions requires a large number of nonlinear simulations which is computationally expensive. This paper presents a new approach based on the principle of Maximum Entropy that provides an estimate of the response distribution that is approximately two orders of magnitude faster than Monte Carlo Harmonic Balance Method simulations. The premise is to include the concept of `computational uncertainty': incorporating lack of knowledge of the solution as part of the uncertainty, on the basis that there are diminishing returns in computing precise solutions to an uncertain system. To achieve this, the method uses a describing function approximation of the friction-damped part of the system; chooses an ignorance prior probability density function for the complex value of the describing function based on Coulombs friction law; updates the distribution using an estimate of the mean solution, the admissible domain of solutions, and the principle of Maximum Entropy; then carries out a linear Monte Carlo simulation to estimate the response distribution. The approach is validated by comparison with HBM simulations and experimental tests, using an idealised academic system consisting of a periodic array of beams (with controllable uncertainty) coupled by single-point friction dampers. Comparisons with two- and eight-blade systems show generally good agreement. Predicting the response statistics of the maximum blade amplitude reveals specific well-understood circumstances when the method is less effective. Predictions of the overall blade response statistics agree with Monte Carlo HBM extremely well across a wide range of excitation amplitudes and uncertainty levels. Critically, experimental comparisons reveal the care that is needed in accurately characterising uncertainty in order to obtain agreement of response percentiles. The new method allowed fast iteration of uncertainty parameters and correlations to achieve good agreement, which would not have been possible using traditional methods.Mitsubishi Heavy Industrie

Predicting response bounds for friction-damped gas turbine blades with uncertain friction coupling

Friction dampers are often used to reduce high amplitude vibration within gas turbines: they are a robust solution that are able to withstand extreme operating environments. Although the turbine blades are manufactured to tight tolerances, there can be significant variability in the overall response of the assembly. Uncertainties associated with the frictional contact properties are a major factor contributing to this variability. This paper applies a recently developed method for predicting response bounds to friction-damped gas turbines when the characteristics of the friction dampers are unknown, including uncertainty regarding the underlying functional form of the friction law. The approach taken is to represent the frictional contact using a describing function, and formulate an optimisation problem to seek upper and lower bounds on a chosen response metric, such as displacement amplitude. Constraints are chosen that describe known properties of the frictional nonlinearity, without needing to specify a particular constitutive law. The method was validated by comparison with numerical and experimental results from an idealised test system. The experimental test rig consisted of an array of eight beams coupled by pin-contact friction dampers. A modal description of this test rig formed the basis of a numerical model, which uses the Harmonic Balance Method (HBM) for nonlinear simulations. A set of Monte Carlo tests was carried out numerically and experimentally for both a two-beam sub-assembly as well as for the full eight-beam assembly. Comparisons with numerical results showed excellent agreement providing confident verification of the implementation, and comparisons with experimental results revealed that the bounds became less conservative as the system complexity increased. Overall the results are promising: upper and lower response bounds for an array of friction-damped systems can be computed at similar cost to a single HBM simulation, giving reliable bounds that are valid for both parametric and model uncertainties associated with the friction couplings.Mitsubishi Heavy Industrie

Tissue Culture as a Source of Replicates in Nonmodel Plants: Variation in Cold Response in Arabidopsis lyrata ssp. petraea

While genotype–environment interaction is increasingly receiving attention by ecologists and evolutionary biologists, such studies need genetically homogeneous replicates—a challenging hurdle in outcrossing plants. This could be potentially overcome by using tissue culture techniques. However, plants regenerated from tissue culture may show aberrant phenotypes and “somaclonal” variation. Here, we examined somaclonal variation due to tissue culturing using the response to cold treatment of photosynthetic efficiency (chlorophyll fluorescence measurements for Fv/Fm, Fv9/Fm9, and FPSII, representing maximum efficiency of photosynthesis for dark- and lightadapted leaves, and the actual electron transport operating efficiency, respectively, which are reliable indicators of photoinhibition and damage to the photosynthetic electron transport system). We compared this to variation among half-sibling seedlings from three different families of Arabidopsis lyrata ssp. petraea. Somaclonal variation was limited, and we could detect within-family variation in change in chlorophyll fluorescence due to cold shock successfully with the help of tissue-culture derived replicates. Icelandic and Norwegian families exhibited higher chlorophyll fluorescence, suggesting higher performance after cold shock, than a Swedish family. Although the main effect of tissue culture on Fv/Fm, Fv9/Fm9, and FPSII was small, there were significant interactions between tissue culture and family, suggesting that the effect of tissue culture is genotype-specific. Tissue-cultured plantlets were less affected by cold treatment than seedlings, but to a different extent in each family. These interactive effects, however, were comparable to, or much smaller than the single effect of family. These results suggest that tissue culture is a useful method for obtaining genetically homogenous replicates for studying genotype–environment interaction related to adaptively-relevant phenotypes, such as cold response, in nonmodel outcrossing plants

Experimental validation of variance estimation in the statistical energy analysis of a structural-acoustic system

The Statistical Energy Analysis (SEA) approach has largely been used in vibro-acoustic modelling to predict the averaged energy in coupled vibrating structures and acoustic cavities. The average is performed over an ensemble of nominally identical built-up systems where random responses are observed at high frequencies after excitation. Over the years, this approach has been extended to predict the energy variance employing the statistics of the Gaussian Orthogonal Ensemble, and numerical and experimental evidence has supported the predictions of the mean and variance of energy of coupled vibrating structures. However, little experimental evidence is found to validate the prediction of the variance of energy in coupled structural-acoustic systems. In this work, the mean and variance of energies predicted from a statistical energy analysis model have been validated with experimental measurements on a structural-acoustic system, comprised by a flat thin plate coupled to an enclosed acoustic volume. The structural system has been randomised by adding small masses on arbitrary positions on the plate, whereas the randomisation of the acoustic cavity is achieved by allocating rigid baffles in random positions within the acoustic volume. In general, good agreement is found between the predictions of the model and the experimental results. Bose Cor

A developmentally descriptive method for quantifying shape in gastropod shells

The growth of snail shells can be described by simple mathematical rules. Variation in a few parameters can explain much of the diversity of shell shapes seen in nature. However, empirical studies of gastropod shell shape variation typically use geometric morphometric approaches, which do not capture this growth pattern. We have developed a way to infer a set of developmentally descriptive shape parameters based on three-dimensional logarithmic helicospiral growth and using landmarks from two-dimensional shell images as input. We demonstrate the utility of this approach, and compare it to the geometric morphometric approach, using a large set of Littorina saxatilis shells in which locally adapted populations differ in shape. Our method can be modified easily to make it applicable to a wide range of shell forms, which would allow for investigations of the similarities and differences between and within many different species of gastropods

Genomic architecture of parallel ecological divergence : beyond a single environmental contrast

The study of parallel ecological divergence provides important clues to the operation of natural selection. Parallel divergence often occurs in heterogeneous environments with different kinds of environmental gradients in different locations, but the genomic basis underlying this process is unknown. We investigated the genomics of rapid parallel adaptation in the marine snail Littorina saxatilis in response to two independent environmental axes (crab-predation versus wave-action and low-shore versus high-shore). Using pooled whole-genome resequencing, we show that sharing of genomic regions of high differentiation between environments is generally low but increases at smaller spatial scales. We identify different shared genomic regions of divergence for each environmental axis and show that most of these regions overlap with candidate chromosomal inversions. Several inversion regions are divergent and polymorphic across many localities. We argue that chromosomal inversions could store shared variation that fuels rapid parallel adaptation to heterogeneous environments, possibly as balanced polymorphism shared by adaptive gene flow