A Comparison of Automatically Extracted Quantitative EEG Features for Seizure Risk Stratification in Neonatal Encephalopathy.

PURPOSE: Seizures occur in up to 40% of neonates with neonatal encephalopathy. Earlier identification of seizures leads to more successful seizure treatment, but is often delayed because of limited availability of continuous EEG monitoring. Clinical variables poorly stratify seizure risk, and EEG use to stratify seizure risk has previously been limited by need for manual review and artifact exclusion. The goal of this study is to compare the utility of automatically extracted quantitative EEG (qEEG) features for seizure risk stratification. METHODS: We conducted a retrospective analysis of neonates with moderate-to-severe neonatal encephalopathy who underwent therapeutic hypothermia at a single center. The first 24 hours of EEG underwent automated artifact removal and qEEG analysis, comparing qEEG features for seizure risk stratification. RESULTS: The study included 150 neonates and compared the 36 (23%) with seizures with those without. Absolute spectral power best stratified seizure risk with area under the curve ranging from 63% to 71%, followed by range EEG lower and upper margin, median and SD of the range EEG lower margin. No features were significantly more predictive in the hour before seizure onset. Clinical examination was not associated with seizure risk. CONCLUSIONS: Automatically extracted qEEG features were more predictive than clinical examination in stratifying neonatal seizure risk during therapeutic hypothermia. qEEG represents a potential practical bedside tool to individualize intensity and duration of EEG monitoring and decrease time to seizure recognition. Future work is needed to refine and combine qEEG features to improve risk stratification.

Fine scale diversity in the lava: genetic and phenotypic diversity in small populations of Arctic charr Salvelinus alpinus.

BACKGROUND: A major goal in evolutionary biology is to understand the processes underlying phenotypic variation in nature. Commonly, studies have focused on large interconnected populations or populations found along strong environmental gradients. However, studies on small fragmented populations can give strong insight into evolutionary processes in relation to discrete ecological factors. Evolution in small populations is believed to be dominated by stochastic processes, but recent work shows that small populations can also display adaptive phenotypic variation, through for example plasticity and rapid adaptive evolution. Such evolution takes place even though there are strong signs of historical bottlenecks and genetic drift. Here we studied 24 small populations of the freshwater fish Arctic charr (Salvelinus alpinus) found in groundwater filled lava caves. Those populations were found within a few km2-area with no apparent water connections between them. We studied the relative contribution of neutral versus non-neutral evolutionary processes in shaping phenotypic divergence, by contrasting patterns of phenotypic and neutral genetic divergence across populations in relation to environmental measurements. This allowed us to model the proportion of phenotypic variance explained by the environment, taking in to account the observed neutral genetic structure. RESULTS: These populations originated from the nearby Lake Mývatn, and showed small population sizes with low genetic diversity. Phenotypic variation was mostly correlated with neutral genetic diversity with only a small environmental effect. CONCLUSIONS: Phenotypic diversity in these cave populations appears to be largely the product of neutral processes, fitting the classical evolutionary expectations. However, the fact that neutral processes did not explain fully the phenotypic patterns suggests that further studies can increase our understanding on how neutral evolutionary processes can interact with other forces of selection at early stages of divergence. The accessibility of these populations has provided the opportunity for long-term monitoring of individual fish, allowing tracking how the environment can influence phenotypic and genetic divergence for shaping and maintaining diversity in small populations. Such studies are important, especially in freshwater, as habitat alteration is commonly breaking populations into smaller units, which may or may not be viable.

The missing fraction problem as an episodes of selection problem.

In evolutionary quantitative genetics, the missing fraction problem refers to a specific kind of bias in parameters estimated later in life that occurs when nonrandom subsets of phenotypes are missing from the population due to prior viability selection on correlated traits. The missing fraction problem thus arises when the following hold: (a) viability selection and (b) correlation between later-life traits and traits important for early-life survival. Although it is plausible that these conditions are widespread in wild populations, this problem has received little empirical attention. This may be natural: the problem could appear intractable, given that it is impossible to measure phenotypes of individuals that have previously died. However, it is not impossible to correctly measure lifetime selection, or correctly predict evolutionary trajectories, of later-life traits in the presence of the missing fraction. Two basic strategies are available. First, given phenotypic data on selected early life traits, well established but underused episodes of selection theory can yield correct values of evolutionary parameters throughout life. Second, when traits subjected to early-life viability selection are not known and/or measured, it is possible to use the genetic association of later-life traits with early-life viability to correctly infer important information about the consequences of prior viability selection for later-life traits. By carefully reviewing the basic nature of the missing fraction problem, and describing the tractable solutions to the problem, we hope that future studies will be able to be better designed to cope with the (likely pervasive) consequences of early-life viability selection.

Macroperiodic Oscillations: A Potential Novel Biomarker of Outcome in Neonatal Encephalopathy.

PURPOSE: Neonatal encephalopathy (NE) is a common cause of neurodevelopmental morbidity. Tools to accurately predict outcomes after therapeutic hypothermia remain limited. We evaluated a novel EEG biomarker, macroperiodic oscillations (MOs), to predict neurodevelopmental outcomes. METHODS: We conducted a secondary analysis of a randomized controlled trial of neonates with moderate-to-severe NE who underwent standardized clinical examination, magnetic resonance (MR) scoring, video EEG, and neurodevelopmental assessment with Bayley III evaluation at 18 to 24 months. A non-NE cohort of neonates was also assessed for the presence of MOs. The relationship between clinical examination, MR score, MOs, and neurodevelopmental assessment was analyzed. RESULTS: The study included 37 neonates with 24 of whom survived and underwent neurodevelopmental assessment (70%). The strength of MOs correlated with severity of clinical encephalopathy. MO strength and spread significantly correlated with Bayley III cognitive percentile (P = 0.017 and 0.046). MO strength outperformed MR score in predicting a combined adverse outcome of death or disability (P = 0.019, sensitivity 100%, specificity 77% vs. P = 0.079, sensitivity 100%, specificity 59%). CONCLUSIONS: MOs are an EEG-derived, quantitative biomarker of neurodevelopmental outcome that outperformed a comprehensive validated MRI injury score and a detailed systematic discharge examination in this small cohort. Future work is needed to validate MOs in a larger cohort and elucidate the underlying pathophysiology of MOs.

Causation, not collinearity: Identifying sources of bias when modelling the evolution of brain size and other allometric traits.

Many biological traits covary with body size, resulting in an allometric relationship. Identifying the evolutionary drivers of these traits is complicated by possible relationships between a candidate selective agent and body size itself, motivating the widespread use of multiple regression analysis. However, the possibility that multiple regression may generate misleading estimates when predictor variables are correlated has recently received much attention. Here, we argue that a primary source of such bias is the failure to account for the complex causal structures underlying brains, bodies, and agents. When brains and bodies are expected to evolve in a correlated manner over and above the effects of specific agents of selection, neither simple nor multiple regression will identify the true causal effect of an agent on brain size. This problem results from the inclusion of a predictor variable in a regression analysis that is (in part) a consequence of the response variable. We demonstrate these biases with examples and derive estimators to identify causal relationships when traits evolve as a function of an existing allometry. Model mis-specification relative to plausible causal structures, not collinearity, requires further consideration as an important source of bias in comparative analyses.

Detecting slow narrowband modulation in EEG signals.

BACKGROUND: We observed an unusual modulatory phenomenon in the electroencephalogram (EEG) of pediatric patients with acquired brain injury. The modulation is orders of magnitude slower than the fast EEG background activity, necessitating new analysis procedures to systematically detect and quantify the phenomenon. NEW METHOD: We propose a method for analyzing spatial and temporal relationships associated with slow, narrowband modulation of EEG. We extract envelope signals from physiological frequency bands of EEG. Then, we construct a sparse representation of the spectral content of the envelope signal across sliding windows. For the latter, we use an augmented LASSO regression to incorporate spatial and temporal filtering into the solution. The method can be applied to windows of variable length, depending on the desired frequency resolution. RESULTS: The sparse estimates of the envelope power spectra enable the detection of narrowband modulation in the millihertz frequency range. Subsequently, we are able to assess non-stationarity in the frequency and spatial relationships across channels. The method can be paired with unsupervised anomaly detection to identify windows with significant modulation. We validated such findings by applying our method to a control set of EEGs. COMPARISON WITH EXISTING METHODS: To our knowledge, no methods have been previously proposed to quantify second order modulation at such disparate time-scales. CONCLUSIONS: We provide a general EEG analysis framework capable of detecting signal content below 0.1 Hz, which is especially germane to clinical recordings that may contain multiple hours worth of continuous data.

Genetic variance in fitness indicates rapid contemporary adaptive evolution in wild animals.

The rate of adaptive evolution, the contribution of selection to genetic changes that increase mean fitness, is determined by the additive genetic variance in individual relative fitness. To date, there are few robust estimates of this parameter for natural populations, and it is therefore unclear whether adaptive evolution can play a meaningful role in short-term population dynamics. We developed and applied quantitative genetic methods to long-term datasets from 19 wild bird and mammal populations and found that, while estimates vary between populations, additive genetic variance in relative fitness is often substantial and, on average, twice that of previous estimates. We show that these rates of contemporary adaptive evolution can affect population dynamics and hence that natural selection has the potential to partly mitigate effects of current environmental change.

Analytical results for directional and quadratic selection gradients for log-linear models of fitness functions.

Log-linear models are widely used for assessing determinants of fitness in empirical studies, for example, in determining how reproductive output depends on trait values or environmental conditions. Similarly, theoretical works of fitness and natural selection employ log-linear models, often with a negative quadratic term, generating Gaussian fitness functions. However, in the specific application of regression-based analysis of natural selection, such models are rarely employed. Rather, OLS regression is the predominant means of assessing the form of natural selection. OLS regressions allow specific evolutionary quantitative parameters, selection gradients, to be estimated, and benefit from the fact that the associated statistical models are easily applied. We examine whether selection gradients can be directly expressed in terms of the coefficients of models using exponential fitness functions with linear or quadratic arguments. Such models can be easily fitted with generalized linear models (GLMs). The expressions we obtain coincide with those for Gaussian functions, but relax the major constraint that the (log) fitness function is concave (downwardly curved). Additionally these results lead to univariate and multivariate analyses of both linear and quadratic selection that potentially incorporate pragmatic and interpretable models of fitness functions, where the parameters can be related analytically to selection gradients, and that can be operationalized using widely available statistical tools.

Resolving and characterizing the incidence of millihertz EEG modulation in critically ill children.

OBJECTIVE: We analyze a slow electrographic pattern, Macroperiodic Oscillations (MOs), in the EEG from a cohort of young critical care patients (n = 43) with continuous EEG monitoring. We construct novel quantitative methods to quantify and understand MOs. METHODS: We applied a nonparametric bilevel spectral analysis to identify MOs, a millihertz (0.004-0.01 Hz) modulation of 5-15 Hz activity in two separate ICU patient cohorts (n = 195 total). We also developed a rigorous measure to quantify MOs strength and spatial expression, which was validated against surrogate noise data. RESULTS: Strong or spatially widespread MOs appear in both high clinical suspicion and a general ICU population. In the former, patients with strong or spatially widespread MOs tended to have worse clinical outcomes. Intracranial pressure and heart rate data from one patient provide insight into a potential broader physiological mechanism for MOs. CONCLUSIONS: We quantified millihertz EEG modulation (MOs) in cohorts of critically ill pediatric patients. We demonstrated high incidence in two patient populations. In a high suspicion cohort, MOs are associated with poor outcome, suggesting future potential as a diagnostic and prognostic aid. SIGNIFICANCE: These results support the existence of EEG dynamics across disparate time-scales and may provide insight into brain injury physiology in young children.

A synthesis of senescence predictions for indeterminate growth, and support from multiple tests in wild lake trout.

Senescence-the deterioration of functionality with age-varies widely across taxa in pattern and rate. Insights into why and how this variation occurs are hindered by the predominance of laboratory-focused research on short-lived model species with determinate growth. We synthesize evolutionary theories of senescence, highlight key information gaps and clarify predictions for species with low mortality and variable degrees of indeterminate growth. Lake trout are an ideal species to evaluate predictions in the wild. We monitored individual males from two populations (1976-2017) longitudinally for changes in adult mortality (actuarial senescence) and body condition (proxy for energy balance). A cross-sectional approach (2017) compared young (ages 4-10 years) and old (18-37 years) adults for (i) phenotypic performance in body condition, and semen quality-which is related to fertility under sperm competition (reproductive senescence)-and (ii) relative telomere length (potential proxy for cellular senescence). Adult growth in these particular populations is constrained by a simplified foodweb, and our data support predictions of negligible senescence when maximum size is only slightly larger than maturation size. Negative senescence (aka reverse senescence) may occur in other lake trout populations where diet shifts allow maximum sizes to greatly exceed maturation size.

Transcriptomic Determinants of Response to Pembrolizumab Monotherapy across Solid Tumor Types.

PURPOSE: To explore relationships between biological gene expression signatures and pembrolizumab response. EXPERIMENTAL DESIGN: RNA-sequencing data on baseline tumor tissue from 1,188 patients across seven tumor types treated with pembrolizumab monotherapy in nine clinical trials were used. A total of 11 prespecified gene expression signatures [18-gene T-cell-inflamed gene expression profile (TcellinfGEP), angiogenesis, hypoxia, glycolysis, proliferation, MYC, RAS, granulocytic myeloid-derived suppressor cell (gMDSC), monocytic myeloid-derived suppressor cell (mMDSC), stroma/epithelial-to-mesenchymal transition (EMT)/TGFß, and WNT] were evaluated for their relationship to objective response rate (per RECIST, version 1.1). Logistic regression analysis of response for consensus signatures was adjusted for tumor type, Eastern Cooperative Oncology Group performance status, and TcellinfGEP, an approach equivalent to evaluating the association between response and the residuals of consensus signatures after detrending them for their relationship with the TcellinfGEP (previously identified as a determinant of pembrolizumab response) and tumor type. Testing of the 10 prespecified non-TcellinfGEP consensus signatures for negative association [except proliferation (hypothesized positive association)] with response was adjusted for multiplicity. RESULTS: Covariance patterns of the 11 signatures (including TcellinfGEP) identified in Merck-Moffitt and The Cancer Genome Atlas datasets showed highly concordant coexpression patterns in the RNA-sequencing data from pembrolizumab trials. TcellinfGEP was positively associated with response; signatures for angiogenesis, mMDSC, and stroma/EMT/TGFß were negatively associated with response to pembrolizumab monotherapy. CONCLUSIONS: These findings suggest that features beyond IFNγ-related T-cell inflammation may be relevant to anti-programmed death 1 monotherapy response and may define other axes of tumor biology as candidates for pembrolizumab combinations. See related commentary by Cho et al., p. 1479.

Macroperiodic Oscillations Are Associated With Seizures Following Acquired Brain Injury in Young Children.

PURPOSE: Seizures occur in 10% to 40% of critically ill children. We describe a phenomenon seen on color density spectral array but not raw EEG associated with seizures and acquired brain injury in pediatric patients. METHODS: We reviewed EEGs of 541 children admitted to an intensive care unit between October 2015 and August 2018. We identified 38 children (7%) with a periodic pattern on color density spectral array that oscillates every 2 to 5 minutes and was not apparent on the raw EEG tracing, termed macroperiodic oscillations (MOs). Internal validity measures and interrater agreement were assessed. We compared demographic and clinical data between those with and without MOs. RESULTS: Interrater reliability yielded a strong agreement for MOs identification (kappa: 0.778 [0.542-1.000]; P < 0.0001). There was a 76% overlap in the start and stop times of MOs among reviewers. All patients with MOs had seizures as opposed to 22.5% of the general intensive care unit monitoring population ( P < 0.0001). Macroperiodic oscillations occurred before or in the midst of recurrent seizures. Patients with MOs were younger (median of 8 vs. 208 days; P < 0.001), with indications for EEG monitoring more likely to be clinical seizures (42 vs. 16%; P < 0.001) or traumatic brain injury (16 vs. 5%, P < 0.01) and had fewer premorbid neurologic conditions (10.5 vs. 33%; P < 0.01). CONCLUSIONS: Macroperiodic oscillations are a slow periodic pattern occurring over a longer time scale than periodic discharges in pediatric intensive care unit patients. This pattern is associated with seizures in young patients with acquired brain injuries.

Multivariate analysis of morphology, behaviour, growth and developmental timing in hybrids brings new insights into the divergence of sympatric Arctic charr morphs.

BACKGROUND: Studying the development of fitness related traits in hybrids from populations diverging in sympatry is a fundamental approach to understand the processes of speciation. However, such traits are often affected by covariance structures that complicate the comprehension of these processes, especially because the interactive relationships between traits of different nature (e.g. morphology, behaviour, life-history) remain largely unknown in this context. In a common garden setup, we conducted an extensive examination of a large suit of traits putatively involved in the divergence of two morphs of Arctic charr (Salvelinus alpinus), and investigated the consequences of potential patterns of trait covariance on the phenotype of their hybrids. These traits were measured along ontogeny and involved growth, yolk sac resorption, developmental timing (hatching and the onset of exogeneous feeding), head morphology and feeding behaviour. RESULTS: Growth trajectories provided the strongest signal of phenotypic divergence between the two charr. Strikingly, the first-generation hybrids did not show intermediate nor delayed growth but were similar to the smallest morph, suggesting parental biases in the inheritance of growth patterns. However, we did not observe extensive multivariate trait differences between the two morphs and their hybrids. Growth was linked to head morphology (suggesting that morphological variations in early juveniles relate to simple allometric effects) but this was the only strong signal of covariance observed between all the measured traits. Furthermore, we did not report evidence for differences in overall phenotypic variance between morphs, nor for enhanced phenotypic variability in their hybrids. CONCLUSION: Our study shed light on the multivariate aspect of development in a context of adaptive divergence. The lack of evidence for the integration of most traits into a single covariance structure suggested that phenotypic constraints may not always favour nor impede divergence toward ecological niches differing in numerous physical and ecological variables, as observed in the respective habitats of the two charr. Likewise, the role of hybridization as a disruptive agent of trait covariance may not necessarily be significant in the evolution of populations undergoing resource polymorphism.

Re-identification of individuals from images using spot constellations: a case study in Arctic charr (Salvelinus alpinus).

The ability to re-identify individuals is fundamental to the individual-based studies that are required to estimate many important ecological and evolutionary parameters in wild populations. Traditional methods of marking individuals and tracking them through time can be invasive and imperfect, which can affect these estimates and create uncertainties for population management. Here we present a photographic re-identification method that uses spot constellations in images to match specimens through time. Photographs of Arctic charr (Salvelinus alpinus) were used as a case study. Classical computer vision techniques were compared with new deep-learning techniques for masks and spot extraction. We found that a U-Net approach trained on a small set of human-annotated photographs performed substantially better than a baseline feature engineering approach. For matching the spot constellations, two algorithms were adapted, and, depending on whether a fully or semi-automated set-up is preferred, we show how either one or a combination of these algorithms can be implemented. Within our case study, our pipeline both successfully identified unmarked individuals from photographs alone and re-identified individuals that had lost tags, resulting in an approximately 4% increase in our estimate of survival rate. Overall, our multi-step pipeline involves little human supervision and could be applied to many organisms.

Horn growth appears to decline under intense trophy hunting, but biases in hunt data challenge the interpretation of the evolutionary basis of trends.

A recent article in Evolutionary Applications by LaSharr et al. reports on trends in the size of horns of bighorn sheep (Ovis canadensis) throughout much of the species' range. The article concludes that there are "... stable or increasing trends in horn growth over nearly 3 decades in the majority of hunt areas throughout the western U.S. and Canada." However, the article equates nonsignificance of predominantly negative trends in the areas with the most selective harvest as evidence for the null hypothesis of no trends and also fails to consider well-known and serious biases in the use of data collected in size-regulated hunts. By applying meta-analysis to the estimates reported by LaSharr et al., we show that there has been a pervasive overall trend of declining horn sizes in Alberta, where the combination of horn size-based legality, combined with unrestricted hunter numbers are understood to generate the greatest selective pressures. Given the nature of the biases in the underlying data, the magnitudes of the trends resulting from our re-analysis of LaSharr et al.'s (Evolutionary Applications, 2019, 12, 1823) trend estimates are probably underestimated.

Fluctuating optimum and temporally variable selection on breeding date in birds and mammals.

Temporal variation in natural selection is predicted to strongly impact the evolution and demography of natural populations, with consequences for the rate of adaptation, evolution of plasticity, and extinction risk. Most of the theory underlying these predictions assumes a moving optimum phenotype, with predictions expressed in terms of the temporal variance and autocorrelation of this optimum. However, empirical studies seldom estimate patterns of fluctuations of an optimum phenotype, precluding further progress in connecting theory with observations. To bridge this gap, we assess the evidence for temporal variation in selection on breeding date by modeling a fitness function with a fluctuating optimum, across 39 populations of 21 wild animals, one of the largest compilations of long-term datasets with individual measurements of trait and fitness components. We find compelling evidence for fluctuations in the fitness function, causing temporal variation in the magnitude, but not the direction of selection. However, fluctuations of the optimum phenotype need not directly translate into variation in selection gradients, because their impact can be buffered by partial tracking of the optimum by the mean phenotype. Analyzing individuals that reproduce in consecutive years, we find that plastic changes track movements of the optimum phenotype across years, especially in bird species, reducing temporal variation in directional selection. This suggests that phenological plasticity has evolved to cope with fluctuations in the optimum, despite their currently modest contribution to variation in selection.

Quantifying the causal pathways contributing to natural selection.

The consequences of natural selection can be understood from a purely statistical perspective. In contrast, an explicitly causal approach is required to understand why trait values covary with fitness. In particular, key evolutionary constructs, such as sexual selection, fecundity selection, and so on, are best understood as selection via particular fitness components. To formalize and operationalize these concepts, we must disentangle the various causal pathways contributing to selection. Such decompositions are currently only known for linear models, where they are sometimes referred to as "Wright's rules." Here, we provide a general framework, based on path analysis, for partitioning selection among its contributing causal pathways. We show how the extended selection gradient-which represents selection arising from a trait's causal effects on fitness-can be decomposed into path-specific selection gradients, which correspond to distinct causal mechanisms of selection. This framework allows for nonlinear effects and nonadditive interactions among variables, which may be estimated using standard statistical methods (e.g., generalized linear [mixed] models or generalized additive models). We thus provide a generalization of Wright's path rules that accommodates the nonlinear and nonadditive mechanisms by which natural selection commonly arises.

Herbivore-mediated negative frequency-dependent selection underlies a trichome dimorphism in nature.

Negative frequency-dependent selection (NFDS) has been shown to maintain polymorphism in a diverse array of traits. The action of NFDS has been confirmed through modeling, experimental approaches, and genetic analyses. In this study, we investigated NFDS in the wild using morph-frequency changes spanning a 20-year period from over 30 dimorphic populations of Datura wrightii. In these populations, plants either possess glandular (sticky) or non-glandular (velvety) trichomes, and the ratio of these morphs varies substantially among populations. Our method provided evidence that NFDS, rather than drift or migration, is the primary force maintaining this dimorphism. Most populations that were initially dimorphic remained dimorphic, and the overall mean and variance in morph frequency did not change over time. Furthermore, morph-frequency differences were not related to geographic distances. Together, these results indicate that neither directional selection, drift, or migration played a substantial role in determining morph frequencies. However, as predicted by negative frequency-dependent selection, we found that the rare morph tended to increase in frequency, leading to a negative relationship between the change in the frequency of the sticky morph and its initial frequency. In addition, we found that morph-frequency change over time was significantly correlated with the damage inflicted by two herbivores: Lema daturaphila and Tupiochoris notatus. The latter is a specialist on the sticky morph and damage by this herbivore was greatest when the sticky morph was common. The reverse was true for L. daturaphila, such that damage increased with the frequency of the velvety morph. These findings suggest that these herbivores contribute to balancing selection on the observed trichome dimorphism.

The role of selection and evolution in changing parturition date in a red deer population.

Changing environmental conditions cause changes in the distributions of phenotypic traits in natural populations. However, determining the mechanisms responsible for these changes-and, in particular, the relative contributions of phenotypic plasticity versus evolutionary responses-is difficult. To our knowledge, no study has yet reported evidence that evolutionary change underlies the most widely reported phenotypic response to climate change: the advancement of breeding times. In a wild population of red deer, average parturition date has advanced by nearly 2 weeks in 4 decades. Here, we quantify the contribution of plastic, demographic, and genetic components to this change. In particular, we quantify the role of direct phenotypic plasticity in response to increasing temperatures and the role of changes in the population structure. Importantly, we show that adaptive evolution likely played a role in the shift towards earlier parturition dates. The observed rate of evolution was consistent with a response to selection and was less likely to be due to genetic drift. Our study provides a rare example of observed rates of genetic change being consistent with theoretical predictions, although the consistency would not have been detected with a solely phenotypic analysis. It also provides, to our knowledge, the first evidence of both evolution and phenotypic plasticity contributing to advances in phenology in a changing climate.

A note on simulating null distributions for G matrix comparisons.

Genetic variances and covariances, summarized in G matrices, are key determinants of the course of adaptive evolution. Consequently, understanding how G matrices vary among populations is critical to answering a variety of questions in evolutionary biology. A method has recently been proposed for generating null distributions of statistics pertaining to differences in G matrices among populations. The general approach facilitated by this method is likely to prove to be very important in studies of the evolution of G. We have identified an issue in the method that will cause it to create null distributions of differences in G matrices that are likely to be far too narrow. The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on G matrices estimated from data, randomizing these vectors across populations, and then calculating null values of statistics from G matrices that are calculated directly from the variances and covariances among randomized vectors. This calculation treats breeding values as quantities that are directly measurable, instead of predicted from G matrices that are themselves estimated from patterns of covariance among kin. The existing method thus neglects a major source of uncertainty in G matrices, which renders it anti-conservative. We first suggest a correction to the method. We then apply the original and modified methods to a very simple instructive scenario. Finally, we demonstrate the use of both methods in the analysis of a real data set.