Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

/pdf/fitting-linear-mixed-effects-models-using-lme4-4zzrpoy9lh.pdf

Fitting Linear Mixed-Effects Models Using lme4

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

The Theory of Island Biogeography

One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. We have implemented the Satterthwaite's method for approximating degrees of freedom for the t and F tests. We have also implemented the construction of Type I - III ANOVA tables. Furthermore, one may also obtain the summary as well as the anova table using the Kenward-Roger approximation for denominator degrees of freedom (based on the KRmodcomp function from the pbkrtest package). Some other convenient mixed model analysis tools such as a step method, that performs backward elimination of nonsignificant effects - both random and fixed, calculation of population means and multiple comparison tests together with plot facilities are provided by the package as well.

/pdf/lmertest-package-tests-in-linear-mixed-effects-models-1x6b86x8v9.pdf

lmerTest Package: Tests in Linear Mixed Effects Models

So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

Model-based, response-surface approaches to quantifying indirect interactions

The loss of animals in tropical forests may alter seed dispersal patterns and reduce seedling recruitment of tree species, but direct experimental evidence is scarce. We manipulated dispersal patterns of Manilkara mabokeensis, a monkey-dispersed tree, to assess the extent to which spatial distributions of seeds drive seedling recruitment. Based on the natural seed shadow, we created seed distributions with seeds deposited under the canopy ("no dispersal"), with declining density from the tree ("natural dispersal"), and at uniform densities ("good dispersal"). These distributions mimicked dispersal patterns that could occur with the extirpation of monkeys, low levels of hunting, and high rates of seed dispersal. We monitored seedling emergence and survival for 18 months and recorded the number of leaves and damage to leaves. "Good dispersal" increased seedling survival by 26%, and "no dispersal" decreased survival by 78%, relative to "natural dispersal." Using a mixed-effects survival model, we decoupled the distance and density components of the seed shadow: seedling survival depended on the seed density, but not on the distance from the tree. Although community seedling diversity tended to decrease with longer dispersal distances, we found no conclusive evidence that patterns of seed dispersal influence the diversity of the seedling community. Local seed dispersal does affect seedling recruitment and survival, with better dispersal resulting in higher seedling recruitment; hence the loss of dispersal services that comes with the reduction or extirpation of seed dispersers will decrease regeneration of some tree species.

Experimental manipulation of seed shadows of an Afrotropical tree determines drivers of recruitment

Historical records reveal the temporal patterns of a sequence of plague epidemics in London, United Kingdom, from the 14th to 17th centuries. Analysis of these records shows that later epidemics spread significantly faster ("accelerated"). Between the Black Death of 1348 and the later epidemics that culminated with the Great Plague of 1665, we estimate that the epidemic growth rate increased fourfold. Currently available data do not provide enough information to infer the mode of plague transmission in any given epidemic; nevertheless, order-of-magnitude estimates of epidemic parameters suggest that the observed slow growth rates in the 14th century are inconsistent with direct (pneumonic) transmission. We discuss the potential roles of demographic and ecological factors, such as climate change or human or rat population density, in driving the observed acceleration.

https://www.pnas.org/content/pnas/117/44/27703.full.pdf

Acceleration of plague outbreaks in the second pandemic.

Inferring the relative strength (i.e. the ratio of reproduction numbers) and relative speed (i.e. the difference between growth rates) of new SARS-CoV-2 variants is critical to predicting and controlling the course of the current pandemic. Analyses of new variants have primarily focused on characterizing changes in the proportion of new variants, implicitly or explicitly assuming that the relative speed remains fixed over the course of an invasion. We use a generation-interval-based framework to challenge this assumption and illustrate how relative strength and speed change over time under two idealized interventions: a constant-strength intervention like idealized vaccination or social distancing, which reduces transmission rates by a constant proportion, and a constant-speed intervention like idealized contact tracing, which isolates infected individuals at a constant rate. In general, constant-strength interventions change the relative speed of a new variant, while constant-speed interventions change its relative strength. Differences in the generation-interval distributions between variants can exaggerate these changes and modify the effectiveness of interventions. Finally, neglecting differences in generation-interval distributions can bias estimates of relative strength.

The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants

Large trees in the tropics are reportedly more vulnerable to droughts than their smaller neighbours. This pattern is of interest due to what it portends for forest structure, timber production, carbon sequestration and multiple other values given that intensified El Nino Southern Oscillation (ENSO) events are expected to increase the frequency and intensity of droughts in the Amazon region. What remains unclear is what characteristics of large trees render them especially vulnerable to drought-induced mortality and how this vulnerability changes with forest degradation. Using a large-scale, long-term silvicultural experiment in a transitional Amazonian forest in Bolivia, we disentangle the effects of stem diameter, tree height, crown exposure and logging-induced degradation on risks of drought-induced mortality during the 2004/2005 ENSO event. Overall, tree mortality increased in response to drought in both logged and unlogged plots. Tree height was a much stronger predictor of mortality than stem diameter. In unlogged plots, tree height but not crown exposure was positively associated with drought-induced mortality, whereas in logged plots, neither tree height nor crown exposure was associated with drought-induced mortality. Our results suggest that, at the scale of a site, hydraulic factors related to tree height, not air humidity, are a cause of elevated drought-induced mortality of large trees in unlogged plots.This article is part of a discussion meeting issue 'The impact of the 2015/2016 El Nino on the terrestrial tropical carbon cycle: patterns, mechanisms and implications'.

https://royalsocietypublishing.org/doi/pdf/10.1098/rstb.2018.0189

Benjamin M. Bolker

Papers

Model-based, response-surface approaches to quantifying indirect interactions

Experimental manipulation of seed shadows of an Afrotropical tree determines drivers of recruitment

Acceleration of plague outbreaks in the second pandemic.

The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants

Interactive effects of tree size, crown exposure and logging on drought-induced mortality.