Permutation tests for random effects in linear mixed models

Inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis. As a result, the asymptotic null distribution of the Wald, score, and likelihood ratio tests will not have the typical χ(2) distribution. Although it has been proved that the correct asymptotic distribution is a mixture of χ(2) distributions, the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect. As alternatives, we present two permutation tests, one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic. Both methods involve weighted residuals, with the weights determined by the among- and within-subject variance components. The null permutation distributions of our statistics are computed by permuting the residuals both within and among subjects and are valid both asymptotically and in small samples. We examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients.     

An exploration of fixed and random effects selection for longitudinal binary outcomes in the presence of nonignorable dropout

We explore a Bayesian approach to selection of variables that represent fixed and random effects in modeling of longitudinal binary outcomes with missing data caused by dropouts. We show via analytic results for a simple example that nonignorable missing data lead to biased parameter estimates. This bias results in selection of wrong effects asymptotically, which we can confirm via simulations for more complex settings. By jointly modeling the longitudinal binary data with the dropout process that possibly leads to nonignorable missing data, we are able to correct the bias in estimation and selection. Mixture priors with a point mass at zero are used to facilitate variable selection. We illustrate the proposed approach using a clinical trial for acute ischemic stroke.     

Diffusion approximations for one-locus multi-allele kin selection,mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics

Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size. In memory of Sam Karlin.     

Schedule discrimination in a mixed schedule: implications for models of the variable-ratio, variable-interval rate difference

In Experiment 1, each of three humans knowledgeable about operant schedules used mouse clicks to respond to a "work key" presented on a monitor. On a random half of the presentations, work-key responses that completed a variable ratio (VR) 12 produced a tone. After five tones, the work key was replaced by two report keys. Pressing the right or left report key, respectively, added or subtracted yen50 from a counter and produced the work key. On the other half of the presentations, a variable interval (VI) associated with the work key was defined so its interreinforcer intervals approximated the time it took to complete the variable ratio. After five tone-producing completions of this schedule, the report keys were presented. Left or right report-key presses, respectively, added or subtracted yen50 from the counter. Subjects achieved high yen totals. In Experiment 2, the procedure was changed by requiring an interresponse time after completion of the variable interval that approximated the duration of the reinforced interresponse time on the variable ratio. Prior to beginning, subjects were shown how a sequence of response bouts and pauses could be used to predict schedule type. Subjects again achieved high levels of accuracy. These results show humans can discriminate ratio from interval schedules even when those schedules provide the same rate of reinforcement and reinforced interresponse times.     

Comment arising from a paper by Wittmer et al.: hypothesis testing for top-down and bottom-up effects in woodland caribou population dynamics

Conservation strategies for populations of woodland caribou Rangifer tarandus caribou frequently emphasize the importance of predator–prey relationships and the availability of lichen-rich late seral forests, yet the importance of summer diet and forage availability to woodland caribou survival is poorly understood. In a recent article, Wittmer et al. (Can J Zool 83:407–418, 2005b) concluded that woodland caribou in British Columbia were declining as a consequence of increased predation that was facilitated by habitat alteration. Their conclusion is consistent with the findings of other authors who have suggested that predation is the most important proximal factor limiting woodland caribou populations (Bergerud and Elliot in Can J Zool 64:1515–1529, 1986; Edmonds in Can J Zool 66:817–826, 1988; Rettie and Messier in Can J Zool 76:251–259, 1998; Hayes et al. in Wildl Monogr 152:1–35, 2003). Wittmer et al. (Can J Zool 83:407–418, 2005b) presented three alternative, contrasting hypotheses for caribou decline that differed in terms of predicted differences in instantaneous rates of increase, pregnancy rates, causes of mortality, and seasonal vulnerability to mortality (Table 1, p 258). These authors rejected the hypotheses that food or an interaction between food and predation was responsible for observed declines in caribou populations; however, the use of pregnancy rate, mortality season and cause of mortality to contrast the alternative hypotheses is problematic. We argue here that the data employed in their study were insufficient to properly evaluate a predation-sensitive foraging hypothesis for caribou decline. Empirical data on seasonal forage availability and quality and plane of nutrition of caribou would be required to test the competing hypotheses. We suggest that methodological limitations in studies of woodland caribou population dynamics prohibit proper evaluation of the mechanism of caribou population declines and fail to elucidate potential interactions between top-down and bottom-up effects on populations. An erratum to this article can be found at     

Non-linear mixed models for repeated data assessment of time and temperature effects on conidia production in the fungus Valdensinia heterodoxa

Valdensinia heterodoxaPeyr. has potential for application as abiological control agent of salal (Gaultheria shallon Pursh) in regeneratingforests in the Pacific Northwest region ofNorth America. Conidia production of twoisolates of Valdensinia heterodoxa wasexamined at four temperature levels during a12-day period. Conidia production was stronglyinfluenced by both temperature (with an optimumbetween 16 and 19 °C) and time (peakedat day 9). Replicate (five) variance was highlyheterogeneous and made a conventional approachto the statistical analyses unsuccessful.However, newly developed generalized nonlinearmodels succeeded in identifying significantdifferences between isolates in theirtemperature specificity. One model was based ona time-dependent Poisson process (logisticmodel) modified by an independent nonlineartemperature function (a scaled gamma function).The other was a nonlinear growth model withfixed (time, isolate) and random (replicate)effects. We believe that nonlinear mixed modelsoffer an attractive framework for analysis oflongitudinal count data common in growth andreproduction studies.     

Exposing the confounding in experimental designs to understand and evaluate them,and formulating linear mixed models for analyzing the data from a designed experiment

Comparative experiments involve the allocation of treatments to units, ideally by randomization. This necessarily confounds treatment information with unit information, which we distinguish from the other forms of information blending, in particular aliasing and marginality. We outline a factor-allocation paradigm for describing experimental designs with the aim of (i) exhibiting the confounding in a design, using analysis-of-variance-like tables, so as to understand and evaluate the design and (ii) formulating a linear mixed model based on the factor allocation that the design involves. The approach exhibits the dispersal of treatments information between units sources, allows designers a choice in the strategy that they adopt for including block-treatment interactions, clarifies differences between experiments, accommodates systematic allocation of factors, and provides a consolidated analysis of nonorthogonal designs. It provides insights into the process of designing experiments and issues that commonly arise with designs. The paradigm has pedagogical advantages and is implemented using the R package dae .     

Robustness of statistical tests for multiplicative terms in the additive main effects and multiplicative interaction model for cultivar trials

The additive main effects multiplicative interaction model is frequently used in the analysis of multilocation trials. In the analysis of such data it is of interest to decide how many of the multiplicative interaction terms are significant. Several tests for this task are available, all of which assume that errors are normally distributed with a common variance. This paper investigates the robustness of several tests (Gollob, F _GH1, F_GH2, F_R)to departures from these assumptions. It is concluded that, because of its better robustness, the F _Rtest is preferable. If the other tests are to be used, preliminary tests for the validity of assumptions should be performed.     

Testing the pluralist approach to sex: the influence of environment on synergistic interactions between mutation load and parasitism in Daphnia magna

Both deleterious mutations and parasites have been acknowledged as potential selective forces responsible for the evolutionary maintenance of sexual reproduction. The pluralist approach to sex proposes that these two factors may have to interact synergistically in order to stabilize sex, and one of the simplest ways this could occur is if parasites are capable of causing synergistic epistasis between mutations in their hosts. However, the effects of both deleterious mutations and parasitism are known to be influenced by a range of environmental factors, so the nature of the interaction may depend upon the organisms' environment. Using chemically mutated Daphnia magna lines, we examined the effects of mutation and parasitism under a range of temperature and food regimes. We found that although parasites were capable of causing synergistic epistasis between mutations in their hosts, these effects were dependent upon an interaction between parasite genotype and temperature.     

GroEL assisted folding of large polypeptide substrates in Escherichia coli: Present scenario and assignments for the future

Escherichia coli chaperonins GroEL and GroES are indispensable for survival and growth of the cell since they provide essential assistance to the folding of many newly translated proteins in the cell. Recent studies indicate that a substantial portion of the proteins involved in the host pathways are completely dependent on GroEL–GroES for their folding and hence providing some explanation for why GroEL is essential for cell growth. Many proteins either small-single domain or large multidomains require assistance from GroEL–ES during their lifetime. Proteins of size up to 70 kDa can fold via the cis mechanism during GroEL–ES assisted pathway, but other proteins (>70 kDa) that cannot be pushed inside the cavity of GroEL–ATP complex upon binding of GroES fold by an evolved mechanism called trans. In recent years, much work has been done on revealing facts about the cis mechanism involving the GroEL assisted folding of small proteins whereas the trans mechanism with larger polypeptide substrates still remains under cover. In order to disentangle the role of chaperonin GroEL–GroES in the folding of large E. coli proteins, this review discusses a number of issues like the range of large polypeptide substrates acted on by GroEL. Do all these substrates need the complete chaperonin system along with ATP for their folding? Does GroEL act as foldase or holdase during the process? We conclude with a discussion of the various queries that need to be resolved in the future for an extensive understanding of the mechanism of GroEL mediated folding of large substrate proteins in E. coli cytosol.     

Preferential codon usage in prokaryotic genes: the optimal codon-anticodon interaction energy and the selective codon usage in efficiently expressed genes

By considering the nucleotide sequence of several highly expressed coding regions in bacteriophage MS2 and mRNAs from Escherichia coli, it is possible to deduce some rules which govern the selection of the most appropriate synonymous codons NNU or NNC read by tRNAs having GNN, QNN or INN as anticodon. The rules fit with the general hypothesis that an efficient in-phase translation is facilitated by proper choice of degenerate codewords promoting a codon-anticodon interaction with intermediate strength (optimal energy) over those with very strong or very weak interaction energy. Moreover, codons corresponding to minor tRNAs are clearly avoided in these efficiently expressed genes. These correlations are clearcut in the normal reading frame but not in the corresponding frameshift sequences +1 and +2. We hypothesize that both the optimization of codon-anticodon interaction energy and the adaptation of the population to codon frequency or vice versa in highly expressed mRNAs of E. coli are part of a strategy that optimizes the efficiency of translation. Conversely, codon usage in weakly expressed genes such as repressor genes follows exactly the opposite rules. It may be concluded that, in addition to the need for coding an amino acid sequence, the energetic consideration for codon-anticodon pairing, as well as the adaptation of codons to the tRNA population, may have been important evolutionary constraints on the selection of the optimal nucleotide sequence.     

Testing a new version of the size-advantage hypothesis for sex change: sperm competition and size-skew effects in the bucktooth parrotfish, Sparisoma radians

A variety of field studies suggest that sex change in animalsmay be more complicated than originally depicted by the size-advantagehypothesis. A modification of the size-advantage hypothesis,the expected reproductive success threshold model, proposesthat sperm competition and size-fecundity skew can stronglyaffect reproductive pay-offs. Size-fecundity skew occurs ifa large female's fecundity is markedly higher than the aggregateof the other members of her social group and, together withpaternity dilution from sperm competition, can produce situationsin which large females benefit by deferring sex change to smallerfemales. Deferral by large females can create sex-size distributionscharacterized by the presence of large females and small sex-changedmales, and it is precisely these distributions that the traditionalsize-advantage model cannot explain. We tested the predictionsof the new model with the bucktooth parrotfish, Sparisoma radians,on coral reefs in St. Croix, U.S. Virgin Islands. Collectionsand spawning observations determined that the local environmentalregime of S. radians is characterized by pervasive sperm competition(accompanying 30% of spawns) and factors that can produce substantialsize-fecundity skew in social groups. Dominant male removalexperiments demonstrate that the largest females in social groupsoften do not change sex when provided an opportunity. Instead,smaller, lower-ranking females change sex when a harem vacancyarises. This pattern of sex change is in contrast to virtuallyall previous studies of social control of sex change in fishes,but provides strong support for the general predictions of theexpected reproductive success threshold model.     

The key role of atom types, reference states, and interaction cutoff radii in the knowledge-based method: new variational approach

We present a variational method to derive knowledge-based potentials. The method is based on an optimization procedure of objective variables: atom types, reference states, and interaction cutoff radii. We suggest and apply new unsymmetrical reference states. The cutoff radii and atom types are optimized to improve docking accuracy of the corresponding potentials. The atom types are varied along an atom type tree, with 6 root and 49 top atom types, and the set of 18 optimal atom types is obtained. We demonstrate strong dependence between the choice of atom types and the docking accuracy of the potentials derived with these atom types. The averaged root-mean square deviations (RMSDs) of the ligand docked positions relative to the experimentally determined positions decrease when the elements C, N, O are split into the optimal types.     

Warming effects in the western Antarctic Peninsula ecosystem: the role of population dynamic models for explaining and predicting penguin trends

The western Antarctica Peninsula and Scotia Sea ecosystems appear to be driven by complex links between climatic variables, primary productivity, krill and Avian predators. There are several studies reporting statistical relationships between climate, krill and Penguin population size. The Adélie (Pygoscelis adeliae), Chinstrap (P. antarctica) and Gentoo (P. papua) penguins appear to be influenced by interannual variability in sea-ice extent and krill biomass. In this paper we developed simple conceptual models to decipher the role of climate and krill fluctuations on the population dynamics of these three Pygoscelis penguin species inhabiting the Antarctic Peninsula region. Our results suggest that the relevant processes underlying the population dynamics of these penguin species at King George Island (South Shetland Islands) are intra-specific competition and the combined effects of krill abundance and sea-ice cover. Our results using population theoretical models appear to support that climate change, specifically regional warming on the western Antarctic Peninsula, represents a major driver. At our study site, penguins showed species-specific responses to climate change. While Chinstrap penguins were only influenced by krill abundance, the contrasting population trends of Adélie and Gentoo penguins appear to be better explained by the “sea-ice hypothesis”. We think that proper population dynamic modeling and theory are essential for deciphering and proposing the ecological mechanisms underlying dynamics of these penguin populations.     

A comparative analysis of the temperature response of leaf elongation in Bromus stamineus and Lolium perenne plants in the field: intrinsic and size-mediated effects

BACKGROUND AND AIMS: Growth of grass species in temperate-humid regions is restricted by low temperatures. This study analyses the origin (intrinsic or size-mediated) and mechanisms (activity of individual meristems vs. number of active meristems) of differences between Bromus stamineus and Lolium perenne in the response of leaf elongation to moderately low temperatures. METHODS: Field experiments were conducted at Balcarce, Argentina over 2 years (2003 and 2004) using four cultivars, two of B. stamineus and two of L. perenne. Leaf elongation rate (LER) per tiller and of each growing leaf, number of growing leaves and total leaf length per tiller were measured on 15-20 tillers per cultivar, for 12 (2003) or 10 weeks (2004) during autumn and winter. KEY RESULTS: LER was faster in B. stamineus than in L. perenne. In part, this was related to size-mediated effects, as total leaf length per tiller correlated with LER and B. stamineus tillers were 71% larger than L. perenne tillers. However, accounting for size effects revealed intrinsic differences between species in their temperature response. These were based on the number of leaf meristems simultaneously active and not on the (maximum) rate at which individual leaves elongated. Species differences were greater at higher temperatures, being barely notable below 5 degrees C (air temperature). CONCLUSIONS: Bromus stamineus can sustain a higher LER per tiller than L. perenne at air temperatures > 6 degrees C. In the field, this effect would be compounded with time as higher elongation rates lead to greater tiller sizes.     

BDNF prevents NMDA‐induced toxicity in models of Huntington's disease: the effects are genotype specific and adenosine A2A receptor is involved

NMDA receptor‐mediated excitotoxicity is thought to play a pivotal role in the pathogenesis of Huntington's disease (HD). The neurotrophin brain‐derived neurotrophic factor (BDNF), which is also highly involved in HD and whose effects are modulated by adenosine A_2ARs, influences the activity and expression of striatal NMDA receptors. In electrophysiology experiments, we investigated the role of BDNF toward NMDA‐induced effects in HD models, and the possible involvement of A_2ARs. In corticostriatal slices from wild‐type mice and age‐matched symptomatic R6/2 mice (a model of HD), NMDA application (75 μM) induced a transient or a permanent (i.e., toxic) reduction of field potential amplitude, respectively. BDNF (10 ng/mL) potentiated NMDA effects in wild‐type, while it protected from NMDA toxicity in R6/2 mice. Both effects of BDNF were prevented by A_2AR blockade. The protective effect of BDNF against NMDA‐induced toxicity was reproduced in a cellular model of HD. These findings may have very important implications for the neuroprotective potential of BDNF and A_2AR ligands in HD.