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

Predicting the combined effects of predators on shared prey has long been a focus of community ecology, yet quantitative predictions often fail. Failure to account for nonlinearity is one reason for this. Moreover, prey depletion in multiple predator effects (MPE) studies generates biased predictions in applications of common experimental and quantitative frameworks. Here, we explore additional sources of bias stemming from nonlinearities in prey predation risk. We show that in order to avoid bias, predictions about the combined effects of independent predators must account for nonlinear size-dependent risk for prey as well as changes in prey risk driven by nonlinear predator functional responses and depletion. Historical failure to account for biases introduced by well-known nonlinear processes that affect predation risk suggest that we may need to reevaluate the general conclusions that have been drawn about the ubiquity of emergent MPEs over the past three decades.

Incorporating nonlinearity with generalized functional responses to simulate multiple predator effects

29 and 2929=67 are both prime. We explore that curiosity and find connections to deep questions on the distribution of the primes: the prime number theorem, Dickson’s conjecture, and Zhang’s bounde...

A Curious Possible Prime Pattern

The Cox proportional hazards model is commonly used in evaluating risk factors in cancer survival data. The model assumes an additive, linear relationship between the risk factors and the log hazard. However, this assumption may be too simplistic. Further, failure to take time-varying covariates into account, if present, may lower prediction accuracy. In this retrospective, population-based, prognostic study of data from patients diagnosed with cancer from 2008 to 2015 in Ontario, Canada, we applied machine learning-based time-to-event prediction methods and compared their predictive performance in two sets of analyses: (1) yearly-cohort-based time-invariant and (2) fully time-varying covariates analysis. Machine learning-based methods-gradient boosting model (gbm), random survival forest (rsf), elastic net (enet), lasso and ridge-were compared to the traditional Cox proportional hazards (coxph) model and the prior study which used the yearly-cohort-based time-invariant analysis. Using Harrell's C index as our primary measure, we found that using both machine learning techniques and incorporating time-dependent covariates can improve predictive performance. Gradient boosting machine showed the best performance on test data in both time-invariant and time-varying covariates analysis. 

/pdf/comparing-machine-learning-approaches-to-incorporate-time-ui5mdw59.pdf

Comparing machine learning approaches to incorporate time-varying covariates in predicting cancer survival time

Peer Review #1 of "Should I use fixed effects or random effects when I have fewer than five levels of a grouping factor in a mixed-effects model? (v0.1)"

View Large Image | Download PowerPoint SlideRuss Lande, Steinar Engen and Bernt-Erik Saether have been using stochastic models to understand ecological communities for a combined total of nearly 60 years, individually and in collaboration. Their new book, Stochastic Population Dynamics in Ecology and Conservation, presents a broad sampling of these efforts, and is a smorgasbord that will be palatable to mathematically proficient readers, or to those willing to take some of the results on faith.The book covers a wide range of topics that are relevant to both basic and applied ecology: linear and nonlinear population growth, extinction dynamics, population viability analysis, sustainable harvesting, biodiversity metrics, and neutral theories in community ecology, among others. The authors prefer simple models, aiming for general conclusions rather than mathematical rigor. They rightly criticize overdependence on simulations, but use them where appropriate to extend the conclusions of analytical models. Lande et al. follow in the tradition of ecological modelers such as Nisbet and Gurney [1xNisbet, R.M and Gurney, W.S.C. See all References[1], emphasizing the power and applicability of linear approximations rather than the complexities of strongly nonlinear models. They also sensibly eschew discrete models, such as branching processes, which achieve realism by following the fates of discrete individuals but pay a high price in flexibility and tractability. The authors show that the continuous-population alternative, stochastic partial differential equations, are a powerful framework for answering a broad spectrum of ecological questions (they wisely sweep the difficult mathematical assumptions that underlie these models under the rug).The drawback of the tremendous breadth of the book is that it prevents it from being a solid introduction to any particular topic. I was hoping to find an introductory text on stochastic dynamics (complementary to Denny and Gaines' excellent Chance [2xDenny, M and Gaines, S. See all References[2]), but this book doesn't fill that niche. The authors do introduce the basics of stochastic dynamics in the first chapter, and generally present modeling frameworks, such as diffusion approximations, early and return them in later chapters. However, the style assumes a high mathematical comfort level, and the book sometimes glosses over the deeper context of the methods: the assurance of the Introduction that readers need only a working knowledge of elementary calculus and statistics is technically correct, but optimistic. For this reason, Stochastic Population Dynamics will work best as a sampler of applications for mathematically inclined ecologists who can then go back to the primary literature for more detail.The authors challenge their theories with empirical data, weighing in on a variety of current topics. For example, they point out that temporal autocorrelation in population dynamics, often taken as a proxy for density dependence, can also arise from lags implicit in the life history of an organism. They present a straightforward method, based on simulating population dynamics with bootstrapped parameters, to address recent concerns [3xWhen is it meaningful to estimate an extinction probability?. Fieberg, J and Ellner, S.P. Ecology. 2000; 81: 2040–2047CrossrefSee all References[3] that population viability analysis fails to incorporate uncertainty in parameters. (Although I like their approach, I was disappointed by their rote dismissal of Bayesian approaches. I also disagree with their recommendation to present only the upper confidence limit of the extinction probability, which leads to the conclusion that any poorly understood species is endangered. Isn't it more honest to say that the confidence limits on extinction probability are 1–99% than to say only that there is a chance that extinction rate could be as high as 99%?) The authors also showcase their recent work on the roles of dispersal and environmental variation in driving spatial synchrony in population fluctuations. Finally, they use a new approach to partitioning metrics of biodiversity, which I initially took to be of theoretical interest only, as a platform to test (and reject) Hubbell's neutral theory of community assembly [4xHubbell, S.P. See all References[4] for a community of tropical butterflies.Stochastic Population Dynamics provides a snapshot of research into stochastic population dynamics by some of the best workers in the field. It gives the flavor of the authors' accomplished and well balanced approach to stochastic dynamic modeling, but it is definitely a sampler rather than a practical introduction to the methods. It will appeal to ecologists who are up for a mathematical challenge and who want to see the variety of theoretical and applied questions that one can answer by clever application of stochastic models to ecological systems.

https://www.cell.com/trends/ecology-evolution/pdf/S0169-5347(03)00289-1.pdf

A smorgasbord of stochastic dynamics: Stochastic Population Dynamics in Ecology and Conservation by Russ Lande, Steinar Engen and Bernt-Erik Saether. Oxford University Press, 2003. £60.00/£27.50 hbk/pbk (222 pages) ISBN 0 19 852524 9/0 19 852525 7

Benjamin M. Bolker

Papers

Incorporating nonlinearity with generalized functional responses to simulate multiple predator effects

A Curious Possible Prime Pattern

Comparing machine learning approaches to incorporate time-varying covariates in predicting cancer survival time

Peer Review #1 of "Should I use fixed effects or random effects when I have fewer than five levels of a grouping factor in a mixed-effects model? (v0.1)"

A smorgasbord of stochastic dynamics: Stochastic Population Dynamics in Ecology and Conservation by Russ Lande, Steinar Engen and Bernt-Erik Saether. Oxford University Press, 2003. £60.00/£27.50 hbk/pbk (222 pages) ISBN 0 19 852524 9/0 19 852525 7