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

Generation intervals and serial intervals are critical quantities for characterizing outbreak dynamics. Generation intervals characterize the time between infection and transmission, while serial intervals characterize the time between the onset of symptoms in a chain of transmission. They are often used interchangeably, leading to misunderstanding of how these intervals link the epidemic growth rate r and the reproduction number R. Generation intervals provide a mechanistic link between r and R but are harder to measure via contact tracing. While serial intervals are easier to measure from contact tracing, recent studies suggest that the two intervals give different estimates of R from r. We present a general framework for characterizing epidemiological delays based on cohorts (i.e., a group of individuals that share the same event time, such as symptom onset) and show that forward-looking serial intervals, which correctly link R with r, are not the same as "intrinsic" serial intervals, but instead change with r. We provide a heuristic method for addressing potential biases that can arise from not accounting for changes in serial intervals across cohorts and apply the method to estimating R for the COVID-19 outbreak in China using serial-interval data --- our analysis shows that using incorrectly defined serial intervals can severely bias estimates. This study demonstrates the importance of early epidemiological investigation through contact tracing and provides a rationale for reassessing generation intervals, serial intervals, and R estimates, for COVID-19.

/pdf/cohort-based-approach-to-understanding-the-roles-of-1acv46c6qs.pdf

Cohort-based approach to understanding the roles of generation and serial intervals in shaping epidemiological dynamics

Goldstein et al.’s (1) article, “Vaccinating the oldest against COVID-19…,” provides a useful and timely analysis of the value of protecting older people from infection. The authors show convincingly that the expected number of life years saved by focusing protection on old people is more than commonly supposed.

Unfortunately, the article is framed, and titled, in a way that seems certain to lead to misunderstanding. The core analysis is about the effects of reducing mortality in different age groups, but is framed in the paper as an analysis of the effects of vaccination. Although superficially similar, these are very different questions, primarily … 

[↵][1]1To whom correspondence may be addressed. Email: dushoff{at}mcmaster.ca.

 [1]: #xref-corresp-1-1

Benjamin M. Bolker

Papers

Cohort-based approach to understanding the roles of generation and serial intervals in shaping epidemiological dynamics

Transmission dynamics are crucial to COVID-19 vaccination policy.

The Impact of the Allee Effect in Dispersal and Patch-Occupancy Age on the Dynamics of Metapopulations

Evolution of dispersal scale and shape in heterogeneous environments: A correlation equation approach

Can existing data on West Nile virus infection in birds and mosquitos explain strain replacement