Summary

The use of both linear and generalized linear mixed-effects models (LMMs and GLMMs) has become popular not only in social and medical sciences, but also in biological sciences, especially in the field of ecology and evolution. Information criteria, such as Akaike Information Criterion (AIC), are usually presented as model comparison tools for mixed-effects models.


The presentation of ‘variance explained’ (R2) as a relevant summarizing statistic of mixed-effects models, however, is rare, even though R2 is routinely reported for linear models (LMs) and also generalized linear models (GLMs). R2 has the extremely useful property of providing an absolute value for the goodness-of-fit of a model, which cannot be given by the information criteria. As a summary statistic that describes the amount of variance explained, R2 can also be a quantity of biological interest.


One reason for the under-appreciation of R2 for mixed-effects models lies in the fact that R2 can be defined in a number of ways. Furthermore, most definitions of R2 for mixed-effects have theoretical problems (e.g. decreased or negative R2 values in larger models) and/or their use is hindered by practical difficulties (e.g. implementation).


Here, we make a case for the importance of reporting R2 for mixed-effects models. We first provide the common definitions of R2 for LMs and GLMs and discuss the key problems associated with calculating R2 for mixed-effects models. We then recommend a general and simple method for calculating two types of R2 (marginal and conditional R2) for both LMMs and GLMMs, which are less susceptible to common problems.


This method is illustrated by examples and can be widely employed by researchers in any fields of research, regardless of software packages used for fitting mixed-effects models. The proposed method has the potential to facilitate the presentation of R2 for a wide range of circumstances.

https://besjournals.onlinelibrary.wiley.com/doi/epdf/10.1111/j.2041-210x.2012.00261.x

A general and simple method for obtaining R2 from generalized linear mixed-effects models

http://talklab.psy.gla.ac.uk/KeepItMaximalR2.pdf

Random effects structure for confirmatory hypothesis testing: Keep it maximal

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Count data can be analyzed using generalized linear mixed models when observations are correlated in ways that require random effects However, count data are often zero-inflated, containing more zeros than would be expected from the typical error distributions We present a new package, glmmTMB, and compare it to other R packages that fit zero-inflated mixed models The glmmTMB package fits many types of GLMMs and extensions, including models with continuously distributed responses, but here we focus on count responses glmmTMB is faster than glmmADMB, MCMCglmm, and brms, and more flexible than INLA and mgcv for zero-inflated modeling One unique feature of glmmTMB (among packages that fit zero-inflated mixed models) is its ability to estimate the Conway-Maxwell-Poisson distribution parameterized by the mean Overall, its most appealing features for new users may be the combination of speed, flexibility, and its interface’s similarity to lme4

/pdf/glmmtmb-balances-speed-and-flexibility-among-packages-for-efr2bq6jaw.pdf

glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling

Repeatability (more precisely the common measure of repeatability, the intra-class correlation coefficient, ICC) is an important index for quantifying the accuracy of measurements and the constancy of phenotypes. It is the proportion of phenotypic variation that can be attributed to between-subject (or between-group) variation. As a consequence, the non-repeatable fraction of phenotypic variation is the sum of measurement error and phenotypic flexibility. There are several ways to estimate repeatability for Gaussian data, but there are no formal agreements on how repeatability should be calculated for non-Gaussian data (e.g. binary, proportion and count data). In addition to point estimates, appropriate uncertainty estimates (standard errors and confidence intervals) and statistical significance for repeatability estimates are required regardless of the types of data. We review the methods for calculating repeatability and the associated statistics for Gaussian and non-Gaussian data. For Gaussian data, we present three common approaches for estimating repeatability: correlation-based, analysis of variance (ANOVA)-based and linear mixed-effects model (LMM)-based methods, while for non-Gaussian data, we focus on generalised linear mixed-effects models (GLMM) that allow the estimation of repeatability on the original and on the underlying latent scale. We also address a number of methods for calculating standard errors, confidence intervals and statistical significance; the most accurate and recommended methods are parametric bootstrapping, randomisation tests and Bayesian approaches. We advocate the use of LMM- and GLMM-based approaches mainly because of the ease with which confounding variables can be controlled for. Furthermore, we compare two types of repeatability (ordinary repeatability and extrapolated repeatability) in relation to narrow-sense heritability. This review serves as a collection of guidelines and recommendations for biologists to calculate repeatability and heritability from both Gaussian and non-Gaussian data.

Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists.

How should ecologists and evolutionary biologists analyze nonnormal data that involve random effects? Nonnormal data such as counts or proportions often defy classical statistical procedures. Generalized linear mixed models (GLMMs) provide a more flexible approach for analyzing nonnormal data when random effects are present. The explosion of research on GLMMs in the last decade has generated considerable uncertainty for practitioners in ecology and evolution. Despite the availability of accurate techniques for estimating GLMM parameters in simple cases, complex GLMMs are challenging to fit and statistical inference such as hypothesis testing remains difficult. We review the use (and misuse) of GLMMs in ecology and evolution, discuss estimation and inference and summarize 'best-practice' data analysis procedures for scientists facing this challenge.

/pdf/generalized-linear-mixed-models-a-practical-guide-for-3gh61pkir0.pdf

Generalized linear mixed models: a practical guide for ecology and evolution

We examine the relative importance of processes that underlie plant population abundance and distribution. Two opposing views dominate the field. One posits that the ability to establish at a site is determined by the availability of suitable microsites (establishment limitation), while the second asserts that recruitment is limited by the availability of seeds (seed limitation). An underlying problem is that establishment and seed limitation are typically viewed as mutually exclusive. We conducted a meta-analysis of seed addition experiments to assess the relative strength of establishment and seed limitation to seedling recruitment. We asked (1) To what degree are populations seed and establishment limited? (2) Under what conditions (e.g., habitats and life-history traits) are species more or less limited by each? (3) How can seed addition studies be better designed to enhance our understanding of plant recruitment? We found that, in keeping with previous studies, most species are seed limited. However, the effects of seed addition are typically small, and most added seeds fail to recruit to the seedling stage. As a result, establishment limitation is stronger than seed limitation. Seed limitation was greater for large-seeded species, species in disturbed microsites, and species with relatively short-lived seed banks. Most seed addition experiments cannot assess the relationship between number of seeds added and number of subsequent recruits. This shortcoming can be overcome by increasing the number and range of seed addition treatments.

https://www.jstor.org/stable/10.1086/518565

Are Plant Populations Seed Limited? A Critique and Meta‐Analysis of Seed Addition Experiments

Within the last decade the study of phenology has taken on new importance because of its contribution to climate-change research. However, phenology data sets spanning many years are rare in the tropics, making it difficult to evaluate possible responses of tropical communities to climate change. Here we use two data sets (1970-1983 and 1990-2002) to describe the fruiting patterns of the tropical tree community in Kibale National Park, Uganda. To address variation in spatial patterns, we describe fruiting over 2-3 y among four sites each separated by 12-15 km. Presently, the Kibale region is receiving c. 300 mm more rain than it did at the start of the century, droughts are less frequent, the onset of the rainy season is earlier, and the average maximum monthly temperature is 3.5 ◦ C hotter than it was 25 y ago. The 1990-2002 phenology data illustrated high temporal variability in the proportion of the populations fruiting. Interannual variation in community-wide fruit availability was also high; however, the proportion of trees that fruited has increased over the past 12+ y. At the species level a variety of patterns were exhibited; however, a number of the most common species currently rarely fruit, and when they do, typically < 4% of the individuals take part in fruiting events. Combining the data set from 1990 to 2002 with that from 1970 to 1983 for specific species again reveals an increase in the proportion of trees fruiting between 1990 and 2002; however, the proportion of the populations fruiting decreased during the earlier period. When one examines particular species over this whole period a variety of patterns are evident. For example, Pouteria altissima exhibited a relatively regular pattern of fruiting during the 1970s; however, it rarely fruited in the 1990s. Contrasting phenological patterns at four sites revealed that at the community level the fruiting patterns of only one of the six pair-wise site combinations were correlated. Relationships between rainfall and fruiting were variable among sites. Contrasting changes in fruiting patterns over the 30 y with differences among the four sites varying in rainfall, suggests that the changes observed in fruiting may be due to climate change. Responses to this climate change are likely complex and will vary among species. However, for some species, current conditions appear unsuitable for fruiting.

A long-term evaluation of fruiting phenology: importance of climate change

Although spatial patterns of seed distribution are thought to vary greatly among plant species dispersed by different vectors, few studies have directly examined this assumption. We compared patterns of seed rain of nine species of trees disseminated by large birds, monkeys, and wind in a closed canopy forest in Cameroon. We used maximum-likelihood methods to fit seed rain data to four dispersal functions: inverse power, negative exponential, Gaussian, and Student t. We then tested for differences in dispersal characteristics (1) among individuals within species, and (2) among species dispersed by the same vector. In general, an inverse power function best described animal-dispersed species and the Gaussian and Student t functions best described wind-dispersed species. Animal-dispersed species had longer mean dispersal distances than wind-dispersed species, but lower fecundities. In addition to these distinct differences in average dispersal distance and functional form of the seed shadow between animal- and wind-dispersed species, seed shadows varied markedly within species and vector, with conspecifics and species within vector varying in their dispersal scale, fecundity, and clumping parameters. Dispersal vectors determine a significant amount of variation in seed distribution, but much variation remains to be explained. Finally, we demonstrate that most seeds, regardless of vector, fall directly under the parent canopy. Long-distance dispersal events (>60 m) account for a small proportion of the seed crop but may still be important in terms of the absolute numbers of dispersed seeds and effects on population and community dynamics.

https://www.jstor.org/stable/pdfplus/3450695.pdf

Comparative seed shadows of bird-, monkey-, and wind-dispersed trees

Unsustainable hunting of wildlife for food empties tropical forests of many species critical to forest maintenance and livelihoods of forest people. Extractive industries, including logging, can accelerate exploitation of wildlife by opening forests to hunters and creating markets for bushmeat. We monitored human demographics, bushmeat supply in markets, and household bushmeat consumption in five logging towns in the northern Republic of Congo. Over 6 years we recorded 29,570 animals in town markets and collected 48,920 household meal records. Development of industrial logging operations led to a 69% increase in the population of logging towns and a 64% increase in bushmeat supply. The immigration of workers, jobseekers, and their families altered hunting patterns and was associated with increased use of wire snares and increased diversity in the species hunted and consumed. Immigrants hunted 72% of all bushmeat, which suggests the short-term benefits of hunting accrue disproportionately to "outsiders" to the detriment of indigenous peoples who have prior, legitimate claims to wildlife resources. Our results suggest that the greatest threat of logging to biodiversity may be the permanent urbanization of frontier forests. Although enforcement of hunting laws and promotion of alternative sources of protein may help curb the pressure on wildlife, the best strategy for biodiversity conservation may be to keep saw mills and the towns that develop around them out of forests.

Connie J. Clark

Papers

Generalized linear mixed models: a practical guide for ecology and evolution

Are Plant Populations Seed Limited? A Critique and Meta‐Analysis of Seed Addition Experiments

A long-term evaluation of fruiting phenology: importance of climate change

Comparative seed shadows of bird-, monkey-, and wind-dispersed trees

Bushmeat supply and consumption in a tropical logging concession in northern Congo.