Predictive margins with survey data

In the analysis of covariance, the display of adjusted treatment means allows one to compare mean (treatment) group outcomes controlling for different covariate distributions in the groups. Predictive margins are a generalization of adjusted treatment means to nonlinear models. The predictive margin for group r represents the average predicted response if everyone in the sample had been in group r. This paper discusses the use of predictive margins with complex survey data, where an important consideration is the choice of covariate distribution used to standardize the predictive margin. It is suggested that the textbook formula for the standard error of an adjusted treatment mean from the analysis of covariance may be inappropriate for applications involving survey data. Applications are given using data from the 1992 National Health Interview Survey (NHIS) and the Epidemiologic Followup Study to the first National Health and Nutrition Examination Survey (NHANES I).     

Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift

Abstract. Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variance-covariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding G-matrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time.     

Reduction of ecosystem productivity and respiration during the European summer 2003 climate anomaly: a joint flux tower, remote sensing and modelling analysis

The European CARBOEUROPE/FLUXNET monitoring sites, spatial remote sensing observations via the EOS‐MODIS sensor and ecosystem modelling provide independent and complementary views on the effect of the 2003 heatwave on the European biosphere's productivity and carbon balance. In our analysis, these data streams consistently demonstrate a strong negative anomaly of the primary productivity during the summer of 2003. FLUXNET eddy‐covariance data indicate that the drop in productivity was not primarily caused by high temperatures (‘heat stress’) but rather by limitation of water (drought stress) and that, contrary to the classical expectation about a heat wave, not only gross primary productivity but also ecosystem respiration declined by up to more than to 80 gC m⁻² month⁻¹. Anomalies of carbon and water fluxes were strongly correlated. While there are large between‐site differences in water‐use efficiency (WUE, 1–6 kg C kg⁻¹ H₂O) here defined as gross carbon uptake divided by evapotranspiration (WUE=GPP/ET), the year‐to‐year changes in WUE were small (<1 g kg⁻¹) and quite similar for most sites (i.e. WUE decreased during the year of the heatwave). Remote sensing data from MODIS and AVHRR both indicate a strong negative anomaly of the fraction of absorbed photosynthetically active radiation in summer 2003, at more than five standard deviations of the previous years. The spatial differentiation of this anomaly follows climatic and land‐use patterns: Largest anomalies occur in the centre of the meteorological anomaly (central Western Europe) and in areas dominated by crops or grassland. A preliminary model intercomparison along a gradient from data‐oriented models to process‐oriented models indicates that all approaches are similarly describing the spatial pattern of ecosystem sensitivity to the climatic 2003 event with major exceptions in the Alps and parts of Eastern Europe, but differed with respect to their interannual variability.     

Environmental controls over carbon exchange of three forest ecosystems in eastern China

Net ecosystem productivity (NEP) was continuously measured using the eddy covariance (EC) technique from 2003 to 2005 at three forest sites of ChinaFLUX. The forests include Changbaishan temperate mixed forest (CBS), Qianyanzhou subtropical coniferous plantation (QYZ), and Dinghushan subtropical evergreen broad‐leaved forest (DHS). They span wide ranges of temperature and precipitation and are influenced by the eastern Asian monsoon climate to varying extent. In this study, we estimated ecosystem respiration (RE) and gross ecosystem productivity (GEP). Comparison of ecosystem carbon exchange among the three forests shows that RE was mainly determined by temperature, with the forest at CBS exhibiting the highest temperature sensitivity among the three ecosystems. The RE was highly dependent on GEP across the three forests, and the ratio of RE to GEP decreased along the North–South Transect of Eastern China (NSTEC) (i.e. from the CBS to the DHS), with an average of 0.77 ± 0.06. Daily GEP was mainly influenced by temperature at CBS, whereas photosynthetic photon flux density was the dominant factor affecting the daily GEP at both QYZ and DHS. Temperature mainly determined the pattern of the interannual variations of ecosystem carbon exchange at CBS. However, water availability primarily controlled the interannual variations of ecosystem carbon exchange at QYZ. At DHS, NEP attained the highest values at the beginning of the dry seasons (autumn) rather than the rainy seasons (summer), probably because insufficient radiation and frequent fog during the rainy seasons hindered canopy photosynthesis. All the three forest ecosystems acted as a carbon sink from 2003 to 2005. The annual average values of NEP at CBS, QYZ, and DHS were 259 ± 19, 354 ± 34, and 434 ± 66 g C m⁻² yr⁻¹, respectively. The slope of NEP that decreased with increasing latitude along the NSTEC was markedly different from that observed on the forest transect in the European continent. Long‐term flux measurements over more forest ecosystems along the NSTEC will further help verify such a difference between the European forest transect and the NSTEC and provide insights into the responses of ecosystem carbon exchange to climate change in China.     

Offsetting high water demands with high productivity: Sorghum as a biofuel crop in a high irradiance arid ecosystem

High irradiance arid environments are promising, yet understudied, areas for biofuel production. We investigated the productivity and environmental trade‐offs of growing sorghum (Sorghum bicolor) as a biofuel feedstock in the low deserts of California (CA). Using a 5.3 ha experimental field in the Imperial Valley, CA, we measured aboveground biomass production and net ecosystem exchange of CO₂ and H₂O via eddy covariance over three growing periods between February and November 2012. Environmental conditions were extreme, with high irradiance, vapor pressure deficit (VPD), and air temperature throughout the growing season. Air temperature peaked in August with a maximum of 45.7 °C. Sorghum produced an annual aboveground biomass yield of 43.7 Mg per hectare. Net ecosystem exchange (NEE) was highest during the summer growth period and reached a maximum of ?68 μmol CO₂ m^?2 s^?1. Water use efficiency, or biomass water ratio (BWR), was high (4.0 g dry biomass kg^?1 H₂O) despite high seasonal evapotranspiration (1094 kg H₂O m^?2). The BWR of sorghum surpassed that of many C4 biofuel candidate crops in the United States, as well as that of alfalfa which is currently widely grown in the Imperial Valley. Sorghum also outperformed many US biofuel crops in terms of radiation use efficiency (RUE), achieving 1.5 g dry biomass MJ^?1. We found no evidence of saturation of NEE at high levels of photosynthetically active radiation (PAR) (up to 2250 μmol m^?2 s^?1). In addition, we found no evidence that NEE was inhibited by either high VPD or air temperature during peak photosynthetic phases. The combination of high productivity, high BWR, and high RUE suggests that sorghum is well adapted to this extreme environment. The biomass production rates and efficiency metrics spanning three growing periods provide fundamental data for future Life Cycle Assessments (LCA), which are needed to assess the sustainability of this sorghum biofuel feedstock system.     

Are we underestimating the genetic variances of dimorphic traits?

Populations often contain discrete classes or morphs (e.g., sexual dimorphisms, wing dimorphisms, trophic dimorphisms) characterized by distinct patterns of trait expression. In quantitative genetic analyses, the different morphs can be considered as different environments within which traits are expressed. Genetic variances and covariances can then be estimated independently for each morph or in a combined analysis. In the latter case, morphs can be considered as separate environments in a bivariate analysis or entered as fixed effects in a univariate analysis. Although a common approach, we demonstrate that the latter produces downwardly biased estimates of additive genetic variance and heritability unless the quantitative genetic architecture of the traits concerned is perfectly correlated between the morphs. This result is derived for four widely used quantitative genetic variance partitioning methods. Given that theory predicts the evolution of genotype‐by‐environment (morph) interactions as a consequence of selection favoring different trait combinations in each morph, we argue that perfect correlations between the genetic architectures of the different morphs are unlikely. A sampling of the recent literature indicates that the majority of researchers studying traits expressed in different morphs recognize this and do estimate morph‐specific quantitative genetic architecture. However, ca. 16% of the studies in our sample utilized only univariate, fixed‐effects models. We caution against this approach and recommend that it be used only if supported by evidence that the genetic architectures of the different morphs do not differ.     

Differential condition dependence among morphological traits inferred from responses to heat stress is predicted by sexual selection theory

Secondary sexual traits that are condition‐dependent are expected to reveal the physiological state and/or genetic quality of individuals, and therefore, should more often be found to be under sexual selection than (1) secondary sexual traits not currently condition‐dependent, and (2) nonsecondary sexual traits. In the present study, we contrasted the degree of condition dependence in three morphological traits of male Drosophila bipectinata: two secondary sexual traits (distinct components of the sex comb), one of which significantly predicts mating success in nature (segment 2), whereas the other does not (segment 1), and a nonsecondary sexual trait (sternopleural bristle number). As predicted, comb segment 2 decreased significantly in size, in response to increasing temperature during development, whereas comb segment 1 and sternopleural bristle number either did not change significantly, or increased with increasing temperature. These results support the hypothesis that condition‐dependence, inferred from stress‐induced reductions in trait expression, engenders a trait to sexual selection. Small‐combed genotypes did not exhibit disproportionate reductions in larva‐to‐adult survivorship and adult body size compared to large‐combed genotypes, suggesting that comb size does not reveal genotypic quality, at least as revealed by sensitivity in body size and juvenile survivorship to thermal stress. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 566–574.     

Seasonal variability in net ecosystem carbon dioxide exchange over a young Switchgrass stand

Understanding carbon dynamics of switchgrass ecosystems is crucial as switchgrass (Panicum virgatum L.) acreage is expanding for cellulosic biofuels. We used eddy covariance system and examined seasonal changes in net ecosystem CO₂ exchange (NEE) and its components – gross ecosystem photosynthesis (GEP) and ecosystem respiration (ER) – in response to controlling factors during the second (2011) and third (2012) years of stand establishment in the southern Great Plains of the United States (Chickasha, OK). Larger vapor pressure deficit (VPD > 3 kPa) limited photosynthesis and caused asymmetrical diurnal NEE cycles (substantially higher NEE in the morning hours than in the afternoon at equal light levels). Consequently, rectangular hyperbolic light–response curve (NEE partitioning algorithm) consistently failed to provide good fits at high VPD. Modified rectangular hyperbolic light–VPD response model accounted for the limitation of VPD on photosynthesis and improved the model performance significantly. The maximum monthly average NEE reached up to ?33.02 ± 1.96 μmol CO₂ m^?2 s^?1 and the highest daily integrated NEE was ?35.89 g CO₂ m^?2 during peak growth. Although large differences in cumulative seasonal GEP and ER were observed between two seasons, total seasonal ER accounted for about 75% of GEP regardless of the growing season lengths and differences in aboveground biomass production. It suggests that net ecosystem carbon uptake increases with increasing GEP. The ecosystem was a net sink of CO₂ during 5–6 months and total seasonal uptakes were ?1128 ± 130 and ?1796 ± 217 g CO₂ m^?2 in 2011 and 2012, respectively. In conclusion, our findings suggest that the annual carbon status of a switchgrass ecosystem can be a small sink to small source in this region if carbon loss from biomass harvesting is considered. However, year‐round measurements over several years are required to assess a long‐term source‐sink status of the ecosystem.     

Bivariate line-fitting methods for allometry

Fitting a line to a bivariate dataset can be a deceptively complex problem, and there has been much debate on this issue in the literature. In this review, we describe for the practitioner the essential features of line-fitting methods for estimating the relationship between two variables: what methods are commonly used, which method should be used when, and how to make inferences from these lines to answer common research questions. A particularly important point for line-fitting in allometry is that usually, two sources of error are present (which we call measurement and equation error), and these have quite different implications for choice of line-fitting method. As a consequence, the approach in this review and the methods presented have subtle but important differences from previous reviews in the biology literature. Linear regression, major axis and standardised major axis are alternative methods that can be appropriate when there is no measurement error. When there is measurement error, this often needs to be estimated and used to adjust the variance terms in formulae for line-fitting. We also review line-fitting methods for phylogenetic analyses. Methods of inference are described for the line-fitting techniques discussed in this paper. The types of inference considered here are testing if the slope or elevation equals a given value, constructing confidence intervals for the slope or elevation, comparing several slopes or elevations, and testing for shift along the axis amongst several groups. In some cases several methods have been proposed in the literature. These are discussed and compared. In other cases there is little or no previous guidance available in the literature. Simulations were conducted to check whether the methods of inference proposed have the intended coverage probability or Type I error. We identified the methods of inference that perform well and recommend the techniques that should be adopted in future work.     

Predicting evolutionary responses to selection on polyandry in the wild: additive genetic covariances with female extra-pair reproduction

The evolutionary forces that underlie polyandry, including extra-pair reproduction (EPR) by socially monogamous females, remain unclear. Selection on EPR and resulting evolution have rarely been explicitly estimated or predicted in wild populations, and evolutionary predictions are vulnerable to bias due to environmental covariances and correlated selection through unmeasured traits. However, evolutionary responses to (correlated) selection on any trait can be directly predicted as additive genetic covariances (cov_A) with appropriate components of relative fitness. I used comprehensive life-history, paternity and pedigree data from song sparrows (Melospiza melodia) to estimate cov_A between a female''s liability to produce extra-pair offspring and two specific fitness components: relative annual reproductive success (ARS) and survival to recruitment. All three traits showed non-zero additive genetic variance. Estimates of cov_A were positive, predicting evolution towards increased EPR, but 95% credible intervals overlapped zero. There was therefore no conclusive prediction of evolutionary change in EPR due to (correlated) selection through female ARS or recruitment. Negative environmental covariance between EPR and ARS would have impeded evolutionary prediction from phenotypic selection differentials. These analyses demonstrate an explicit quantitative genetic approach to predicting evolutionary responses to components of (correlated) selection on EPR that should be unbiased by environmental covariances and unmeasured traits.