Do invasive species show higher phenotypic plasticity than native species and,if so,is it adaptive? A meta‐analysis

Do invasive plant species have greater phenotypic plasticity than non-invasive species? And, if so, how does this affect their fitness relative to native, non-invasive species? What role might this play in plant invasions? To answer these long-standing questions, we conducted a meta-analysis using data from 75 invasive/non-invasive species pairs. Our analysis shows that invasive species demonstrate significantly higher phenotypic plasticity than non-invasive species. To examine the adaptive benefit of this plasticity, we plotted fitness proxies against measures of plasticity in several growth, morphological and physiological traits to test whether greater plasticity is associated with an improvement in estimated fitness. Invasive species were nearly always more plastic in their response to greater resource availability than non-invasives but this plasticity was only sometimes associated with a fitness benefit. Intriguingly, non-invasive species maintained greater fitness homoeostasis when comparing growth between low and average resource availability. Our finding that invasive species are more plastic in a variety of traits but that non-invasive species respond just as well, if not better, when resources are limiting, has interesting implications for predicting responses to global change.     

Delta blue intensity vs. maximum density: A case study using Pinus uncinata in the Pyrenees

We explore the potential of the delta blue intensity (DBI) parameter as a proxy of past summer temperatures using a well replicated (85 trees) chronology of Pinus uncinata from upper treeline in the Spanish Pyrenees. Principal component analysis, correlation response function analysis and Superposed Epoch Analysis show definitively that the DBI data are indistinguishable to other MXD datasets in the region and that DBI expresses a similarly “pure” time-stable climate signal as MXD when compared to their RW counterparts. Calibration r² values > 0.5 are attainable depending on period used. The signal strength of DBI data is weaker than MXD and behave more like RW data with ca. 19 trees being needed to attain an EPS value > 0.85. However, as the generation of DBI data is cheaper than MXD, this limitation is not deemed to be a serious issue. This pilot study suggests that robust reconstructions of past summer temperatures could be gained using DBI data at a much-reduced cost than relying on MXD. Future dendroclimatic efforts in the region therefore should focus on the measurement of this parameter and the expansion of the pinus ring-density network.     

Reliability of parameter estimates from models applied to respiratory impedance data

Many previous studies have fit lumped parameter models to respiratory input (Zin) and transfer (Ztr) impedance data. For frequency ranges higher than 4-32 Hz, a six-element model may be required in which an airway branch (with a resistance and inertance) is separated from a tissue branch (with a resistance, inertance, and compliance) by a shunt compliance. A sensitivity analysis is applied to predict the effects of frequency range on the accuracy of parameter estimates in this model obtained from Zin or Ztr data. Using a parameter set estimated from experimental data between 4 and 64 Hz in dogs, both Zin and Ztr were simulated from 4 to 200 Hz. Impedance sensitivity to each parameter was also calculated over this frequency range. The simulation predicted that for Zin a second resonance occurs near 80 Hz and that the impedance is considerably more sensitive to several of the parameters at frequencies surrounding this resonance than at any other frequencies. Also, unless data is obtained at very high frequencies (where the model is suspect), Zin data provides more accurate estimates than Ztr data. After adding random noise to the simulated Zin data, we attempted to extract the original parameters by using a nonlinear regression applied to three frequency ranges: 4-32, 4-64, and 4-110 Hz. Estimated parameters were substantially incorrect when using only 4- to 32-Hz or 4- to 64-Hz data, but nearly correct when fitting 4- to 110-Hz data. These results indicate that respiratory system parameters can be more accurately extracted from Zin than Ztr, and to make physiological inferences from parameter estimates based on Zin impedance data in dogs, the data must include frequencies surrounding the second resonance.     

Quantitative analysis of biological responses to ionizing radiation, including dose, irradiation time, and dose rate

Because biological responses to radiation are complex processes that depend on both irradiation time and total dose, consideration of both dose and dose rate is necessary to predict the risk from long-term irradiations at low dose rates. Here we mathematically and statistically analyzed the quantitative relationships between dose, dose rate and irradiation time using micronucleus formation and inhibition of proliferation of human osteosarcoma cells as indicators of biological response. While the dose-response curves did not change with exposure times of less than 20 h, at a given dose, both biological responses clearly were reduced as exposure time increased to more than 8 days. These responses became dependent on dose rate rather than on total dose when cells were irradiated for 20 to 27 days. Mathematical analysis demonstrates that the relationship between effective dose and dose rate is well described by an exponential function when the logarithm of effective dose is plotted as a function of the logarithm of dose rate. These results suggest that our model, the modified exponential (ME) model, can be applied to predict the risk from exposure to low-dose/low-dose-rate radiation.     

The spatial frequency discrimination function at low contrasts

Spatial frequency difference thresholds for sinewave gratings near contrast threshold were measured using a two-alternative forced-choice technique, and the threshold frequency differences were plotted as a proportion of standard frequency for standards from 2 to 7 cycles/degree. This function shows reliable local maxima and minima, and these features are more pronounced than they are when stimuli of 30% contrast are used. This result is consistent with the notion that at low contrasts, fewer spatial frequency channels are above threshold in the area of the visual field covered by the stimulus than when the stimulus is at high contrast.     

On robustness and model flexibility in survival analysis: transformed hazard models and average effects

Yin and Ibrahim (2005a, Biometrics 61, 208-216) use a Box-Cox transformed hazard model to acknowledge uncertainty about how a linear predictor acts upon the hazard function of a failure-time response. Particularly, additive and proportional hazards models arise for particular values of the transformation parameter. As is often the case, however, this added model flexibility is obtained at the cost of lessened parameter interpretability. Particularly, the interpretation of the coefficients in the linear predictor is intertwined with the value of the transformation parameter. Moreover, some data sets contain very little information about this parameter. To shed light on the situation, we consider average effects based on averaging (over the joint distribution of the explanatory variables and the failure-time response) the partial derivatives of the hazard, or the log-hazard, with respect to the explanatory variables. First, we consider fitting models which do assume a particular form of covariate effects, for example, proportional hazards or additive hazards. In some such circumstances, average effects are seen to be inferential targets which are robust to the effect form being misspecified. Second, we consider average effects as targets of inference when using the transformed hazard model. We show that in addition to being more interpretable inferential targets, average effects can sometimes be estimated more efficiently than the corresponding regression coefficients.     

Temperature dependence of the functional response

The Arrhenius equation has emerged as the favoured model for describing the temperature dependence of consumption in predator-prey models. To examine the relevance of this equation, we undertook a meta-analysis of published relationships between functional response parameters and temperature. We show that, when plotted in lin-log space, temperature dependence of both attack rate and maximal ingestion rate exhibits a hump-shaped relationship and not a linear one as predicted by the Arrhenius equation. The relationship remains significantly downward concave even when data from temperatures above the peak of the hump are discarded. Temperature dependence is stronger for attack rate than for maximal ingestion rate, but the thermal optima are not different. We conclude that the use of the Arrhenius equation to describe consumption in predator-prey models requires the assumption that temperatures above thermal optima are unimportant for population and community dynamics, an assumption that is untenable given the available data.     

A new statistic for detecting genetic differentiation

A new statistic for detecting genetic differentiation of subpopulations is described. The statistic can be calculated when genetic data are collected on individuals sampled from two or more localities. It is assumed that haplotypic data are obtained, either in the form of DNA sequences or data on many tightly linked markers. Using a symmetric island model, and assuming an infinite-sites model of mutation, it is found that the new statistic is as powerful or more powerful than previously proposed statistics for a wide range of parameter values.     

When does parameter drift decrease the uncertainty in extinction risk estimates?

Halley (2003) proposed that parameter drift decreases the uncertainty in long‐range extinction risk estimates, because drift mitigates the extreme sensitivity of estimated risk to estimated mean growth rate. However, parameter drift has a second, opposing effect: it increases the uncertainty in parameter estimates from a given data set. When both effects are taken into account, parameter drift can increase, sometimes substantially, the uncertainty in risk estimates. The net effect depends sensitively on the type of drift and on which model parameters must be estimated from observational data on the population at risk. In general, unless many parameters are estimated from independent data, parameter drift increases the uncertainty in extinction risk. These findings suggest that more mechanistic PVA models, using long‐term data on key environmental variables and experiments to quantify their demographic impacts, offer the best prospects for escaping the high data requirements when extinction risk is estimated from observational data.     

Expert elicitation and data noise learning for material flow analysis using Bayesian inference

Bayesian inference allows the transparent communication and systematic updating of model uncertainty as new data become available. When applied to material flow analysis (MFA), however, Bayesian inference is undermined by the difficulty of defining proper priors for the MFA parameters and quantifying the noise in the collected data. We start to address these issues by first deriving and implementing an expert elicitation procedure suitable for generating MFA parameter priors. Second, we propose to learn the data noise concurrent with the parametric uncertainty. These methods are demonstrated using a case study on the 2012 US steel flow. Eight experts are interviewed to elicit distributions on steel flow uncertainty from raw materials to intermediate goods. The experts' distributions are combined and weighted according to the expertise demonstrated in response to seeding questions. These aggregated distributions form our model parameters' informative priors. Sensible, weakly informative priors are adopted for learning the data noise. Bayesian inference is then performed to update the parametric and data noise uncertainty given MFA data collected from the United States Geological Survey and the World Steel Association. The results show a reduction in MFA parametric uncertainty when incorporating the collected data. Only a modest reduction in data noise uncertainty was observed using 2012 data; however, greater reductions were achieved when using data from multiple years in the inference. These methods generate transparent MFA and data noise uncertainties learned from data rather than pre-assumed data noise levels, providing a more robust basis for decision-making that affects the system.     

Frailty models with missing covariates

We present a method for estimating the parameters in random effects models for survival data when covariates are subject to missingness. Our method is more general than the usual frailty model as it accommodates a wide range of distributions for the random effects, which are included as an offset in the linear predictor in a manner analogous to that used in generalized linear mixed models. We propose using a Monte Carlo EM algorithm along with the Gibbs sampler to obtain parameter estimates. This method is useful in reducing the bias that may be incurred using complete-case methods in this setting. The methodology is applied to data from Eastern Cooperative Oncology Group melanoma clinical trials in which observations were believed to be clustered and several tumor characteristics were not always observed.     

Neurons in the inferior colliculus of the big brown bat show maximal amplitude sensitivity at the best duration

The big brown bats, Eptesicus fuscus, emit ultrasonic signals and analyze the returning echoes in multi-parametric domains to extract target features. The variation of different pulse parameters during hunting predicts that analysis of an echo parameter by bats is inevitably affected by other co-varying echo parameters. In this study, we presented data to show that the bat inferior collicular (IC) neurons have maximal amplitude sensitivity at the best duration (BD). A family of rate-amplitude function (RAF) of each IC neuron is plotted with the BD and non-BD sound pulses. The RAF plotted with BD pulses has sharper slope (SL) and smaller dynamic range (DR) than the RAF plotted with non-BD pulses has. All RAFs can be described as monotonic, saturated or non-monotonic. IC neurons with monotonic RAF are mostly recorded at deeper IC and they have the largest average BD, best amplitude (BA) and DR. Conversely, IC neurons with non-monotonic RAF are mostly recorded at upper IC and they have the smallest average BD, BA and DR. Low best frequency (BF) neurons at upper IC have shorter BD, smaller BA and DR than high BF neurons at deeper IC have. These data suggest that IC neurons that tune to an echo duration also have the greatest sensitivity to echo amplitude. These data also suggest that sensitivity in frequency, duration and amplitude appears to be orderly represented along the dorso-ventral axis of the IC.     

Is southern Africa different? An investigation of the relationship between leaf physiognomy and climate in southern African mesic vegetation

Leaves from 24 South African vegetation sites, including 3 Fynbos sites, exhibiting high levels of endemism, were assessed by both LMA (Leaf Margin Analysis) and CLAMP (Climate Leaf Multivariate Program) to determine the effect of endemism on these palaeoclimate proxies. We examined whether existing calibrations using either locally recorded climate data or globally gridded climate data are appropriate for South Africa, or whether new calibrations specific to the region provide more accurate results. The results suggest that calibrations using gridded data yield slightly cooler estimates using LMA when the percentage of entire margined species is over 25. Overall, however, the differences are small and both gridded and local climate station calibration data can be used with equal accuracy. Xeric sites differ from mesic sites regarding the relationship between leaf margin proportion (LMP) and MAT, but with the exception of Fynbos sites, the differences are small when the percentage of entire margined species is < 65. Fynbos sites plot up to 8 °C cooler for a given leaf margin percentage (LMP) than do other sites. LMA was also sensitive to the number of taxa scored and in general should not be attempted on less than 15 leaf morphotypes per site. For CLAMP, the African non-Fynbos sites plotted within the parameters characterized by the existing PHYSG3BRC data set, indicating that they had a leaf physiognomic response to climate consistent with that of the rest of the world. However, the African non-Fynbos sites did fill a previously unoccupied void within that space, indicating the existence of a regional variance from the global pattern. This suggests that endemism per se does not prevent CLAMP from yielding reliable climate predictions. The inclusion of African non-Fynbos sites into the calibration improved the ability of CLAMP to predict Fynbos site climate, although this remained poor for non-coastal xeromorphic Fynbos vegetation. The addition of the African non-Fynbos vegetation did not degrade significantly the PHYSG3BRC calibration, particularly regarding key climatic variables such as enthalpy. Enthalpy appears to be a particularly robust variable with which to test climate model performance against CLAMP palaeoclimate predictions.     

Smoothing noisy data using dynamic programming and generalized cross-validation

Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.     

A method for the analysis of biological transduction phenomena

Biological transduction can be defined as the triggering of a cellular response by the binding of molecules of effector substances to specific cellular sites. An example of biological transduction, analyzed in this report, is the triggering of T-cell proliferation by the binding of T-cell growth factor (TCGF) to specific TCGF-binding sites on responsive T-cells. Sigmoidal or S-shaped curves often result when measurements of biological response are plotted as a function of concentration of effector substance. Such curves suggest that effector molecules must bind a critical number of cellular sites, and this critical number of bound complexes must undergo secondary events (cross-linking, association, internalization, second messenger release, etc.) in order to initiate the biological response. The method described here estimates the critical number of cellular sites (R) and the probability of these secondary events (PS/B) as follows: (1) The total number of cellular sites (N) is estimated from binding data, and the probabilities (PB) of effector molecules binding to a site are estimated from response data. (2) The response data are assumed to follow the summed binomial distribution function, which is equated to the incomplete beta function. (3) R and PS/B are estimated by applying nonlinear regression to the incomplete beta function. The T-cell data to which the method was applied gave N = 15,000, R = 5, and PS/B = 7.22 x 10(-4). These results show that the binding of very few TCGF molecules is required for activation of T-cells and that the probability of the secondary events leading to cell proliferation is much smaller than the probability of TCGF binding to T-cells. The method described can be used to analyze any biological transduction experiments where both binding and biological response data are available.     

Usefulness of single nucleotide polymorphism data for estimating population parameters

Single nucleotide polymorphism (SNP) data can be used for parameter estimation via maximum likelihood methods as long as the way in which the SNPs were determined is known, so that an appropriate likelihood formula can be constructed. We present such likelihoods for several sampling methods. As a test of these approaches, we consider use of SNPs to estimate the parameter Theta = 4N(e)micro (the scaled product of effective population size and per-site mutation rate), which is related to the branch lengths of the reconstructed genealogy. With infinite amounts of data, ML models using SNP data are expected to produce consistent estimates of Theta. With finite amounts of data the estimates are accurate when Theta is high, but tend to be biased upward when Theta is low. If recombination is present and not allowed for in the analysis, the results are additionally biased upward, but this effect can be removed by incorporating recombination into the analysis. SNPs defined as sites that are polymorphic in the actual sample under consideration (sample SNPs) are somewhat more accurate for estimation of Theta than SNPs defined by their polymorphism in a panel chosen from the same population (panel SNPs). Misrepresenting panel SNPs as sample SNPs leads to large errors in the maximum likelihood estimate of Theta. Researchers collecting SNPs should collect and preserve information about the method of ascertainment so that the data can be accurately analyzed.     

The effect of end-point adjustments on smoothing splines used for tree-ring standardization

The cubic smoothing spline has been a popular method for detrending tree-ring data since the 1980s. The common implementation of this procedure (e.g., ARSTAN, dplR) uses a unique method for determining the smoothing parameter that is widely known as the %n criterion. However, this smoothing parameter selection method carries the assumption that end point effects are ignorable. In this paper, we complete the mathematical derivation and show how the original method differs from the complete version, both in the interpretation of the smoothing parameter and in the spline fit. Frequency response curves (FRC) demonstrate how the smoothing parameter is affected by the original assumption. For example, the FRC results indicate that a tree core of 250-year length has a 14% difference in the cut-off frequency when looking at the 67%n criterion. The FRC analysis shows that the existing approach produces a more flexible fit than anticipated, i.e., it is removing more variance than previously thought. For example, a 67%n spline under the existing approach corresponds to a 53%n spline fit. By using both simulated tree-core sequences and a dataset from a Midwest forest, we discuss which conditions result in greater differences between the spline fits and which conditions will have small differences. Tree-core sequences that have more curvature, such as a large-amplitude growth release, will lead to greater differences. Finally, we provide approximations to the end-point effect procedure. For example, using an 83%n criterion under the original approach produces a spline fit approximating the 67%n fit under the complete approach. These approximations could be easily implemented within existing programs like ARSTAN.     

Penalized spline smoothing using Kaplan–Meier weights with censored data

In this paper, we consider the problem of nonparametric curve fitting in the specific context of censored data. We propose an extension of the penalized splines approach using Kaplan–Meier weights to take into account the effect of censorship and generalized cross‐validation techniques to choose the smoothing parameter adapted to the case of censored samples. Using various simulation studies, we analyze the effectiveness of the censored penalized splines method proposed and show that the performance is quite satisfactory. We have extended this proposal to a generalized additive models (GAM) framework introducing a correction of the censorship effect, thus enabling more complex models to be estimated immediately. A real dataset from Stanford Heart Transplant data is also used to illustrate the methodology proposed, which is shown to be a good alternative when the probability distribution for the response variable and the functional form are not known in censored regression models.