Quantifying individual variation in reaction norms: how study design affects the accuracy, precision and power of random regression models

1.Quantifying individual heterogeneity in plasticity is becoming common in studies of evolutionary ecology, climate change ecology and animal personality. Individual variation in reaction norms is typically quantified using random effects in a mixed modelling framework. However, little is known about what sampling effort and design provide sufficient accuracy, precision and power. 2.I developed 'odprism', an easy-to-use software package for the statistical language R, which can be used to investigate the accuracy, precision and power of random regression models for various types of data structures. Moreover, I conducted simulations to derive rules-of-thumb for four design decisions that biologists often face. 3.First, I investigated the trade-off between sampling many individuals a few times versus sampling few individuals often. Generally, at least 40 individuals should be sampled with a total sample size of at least 1000 to obtain accurate and precise estimates of individual variation in elevation and slopes of linear reaction norms and their correlation. Contrasting a previous recommendation, it is worthwhile to bias the ratio of number of individuals over replicates towards sampling more individuals. 4.Second, I considered how the range of environmental conditions over which individuals are sampled affects the optimal sampling strategy. I show that when all individuals experience the same conditions during a sampling event, sampling each individual only twice should be strictly avoided. 5.Third, I examined the case where the number of replicates per individual is constrained by their lifespan, as is common when sampling annual traits in the wild. I show that for a given sampling effort, it is much easier to detect individual variation in reaction norms for long-lived than for short-lived species. 6.Fourth, I investigated the performance of random regression models when studying traits under selection. Reassuringly, directional viability selection barely caused any bias in estimates of variance components. 7.Random regression models are inherently data hungry, and reviewing the literature shows that particularly behavioural studies have low sampling effort. Therefore, the software and rules-of-thumbs I identified for designing reaction-norm studies should help researchers make more informed choices, which likely improve the reliability and interpretation of plasticity studies

Cross-lags and the unbiased estimation of life-history and demographic parameters

Biological processes exhibit complex temporal dependencies due to the sequential nature of allocation decisions in organisms' life cycles, feedback loops and two-way causality. Consequently, longitudinal data often contain cross-lags: the predictor variable depends on the response variable of the previous time step. Although statisticians have warned that regression models that ignore such covariate endogeneity in time series are likely to be inappropriate, this has received relatively little attention in biology. Furthermore, the resulting degree of estimation bias remains largely unexplored. We use a graphical model and numerical simulations to understand why and how regression models that ignore cross-lags can be biased, and how this bias depends on the length and number of time series. Ecological and evolutionary examples are provided to illustrate that cross-lags may be more common than is typically appreciated and that they occur in functionally different ways. We show that routinely used regression models that ignore cross-lags are asymptotically unbiased. However, this offers little relief, as for most realistically feasible lengths of time-series conventional methods are biased. Furthermore, collecting time series on multiple subjects—such as populations, groups or individuals—does not help to overcome this bias when the analysis focusses on within-subject patterns (often the pattern of interest). Simulations, a literature search and a real-world empirical example together suggest that approaches that ignore cross-lags are likely biased in the direction opposite to the sign of the cross-lag (e.g. towards detecting density dependence of vital rates and against detecting life-history trade-offs and benefits of group living). Next, we show that multivariate (e.g. structural equation) models can dynamically account for cross-lags, and simultaneously address additional bias induced by measurement error, but only if the analysis considers multiple time series. We provide guidance on how to identify a cross-lag and subsequently specify it in a multivariate model, which can be far from trivial. Our tutorials with data and R code of the worked examples provide step-by-step instructions on how to perform such analyses. Our study offers insights into situations in which cross-lags can bias analysis of ecological and evolutionary time series and suggests that adopting dynamical models can be important, as this directly affects our understanding of population regulation, the evolution of life histories and cooperation, and possibly many other topics. Determining how strong estimation bias due to ignoring covariate endogeneity has been in the ecological literature requires further study, also because it may interact with other sources of bias

Climwin: Climate Window Analysis

Contains functions to detect and visualise periods of climate sensitivity (climate windows) for a given biological response. Please see van de Pol et al. (2016) and Bailey and van de Pol (2016) for details. Climwin is designed for those interested in understanding the impacts of climate, particularly focussed on biological systems. When seeking to understand the effects of climate it is necessary to select a sampling period over which climate is recorded, a climate window. Often this choice is made arbitrarily, with many studies using seasonal values (e.g. spring temperature, winter precipitation). However, these climate windows may not be the most relevant for the biological system in question. If we fail to find a relationship between climate and the biological response it can be difficult to determine whether this is due to climate insensitivity in the biological response or if the choice of climate window is flawed. Rather than being required to make a single arbitrary choice of climate window, climwin allows users to test the effectiveness of a wide range of possible climate windows with the aim of identifying the most appropriate climate window for further use. climwin gives users the ability to visualise the results of their climate window analysis, using ggplot2, as a means to best interpret and understand the climate window results

Habitat geometry does not affect levels of extrapair paternity in an extremely unfaithful fairy-wren

Density of potential mates has often been proposed to explain the enormous variation in extrapair paternity. However, density is often confounded by other ecological factors that might affect extrapair paternity in their own way. Furthermore, extrapair mating shows strong phylogenetic inertia, making both meaningful intra- and interspecific comparisons difficult. An extreme way to change density is through habitat fragmentation that reduces connectivity between territories. Recently, habitat connectivity was hypothesized to explain the surprising discovery of a virtually monogamous species among the world's most unfaithful bird genus. The monogamous Malurus coronatus lives in narrow riparian strips that limit contact with neighbors to both extreme ends of territories, whereas Malurus species with high levels of extragroup paternity typically live in high-connected habitat in which they are surrounded by neighbors. Here, we test the habitat geometry hypothesis by comparing levels of extragroup paternity of Malurus elegans living in fragmented low-connected habitat and in high-connected habitat. We found that M. elegans does not have lower levels of extragroup paternity in low-connected habitat (68%) than in high-connected habitat (56% of offspring), indicating that connectivity does not limit opportunities for extragroup paternity. Furthermore, there was no evidence that females in low-connected habitat gained extragroup paternity further away or from less sires or that they were more likely to be closely related to their social mate. We conclude that behavioral plasticity in response to density-dependent cost and benefits of mating behavior does not explain intrageneric variation in extragroup paternity in Malurus

R package HIPHOP: parentage assignment using bi-allelic genetic markers

R package hiphop is a method for parentage assignment using bi-allelic genetic markers like SNPs (Single Nucleotide Polymorphism). It has widespread application (paternity and maternity assignment in a variety of mating systems) and outperforms conventional methods where closely related individuals occur in the pool of possible parents. The method compares the genotypes of offspring with any combination of potentials parents and scores the number of mismatches of these individuals at bi-allelic genetic markers (e.g. Single Nucleotide Polymorphisms). It elaborates on a prior exclusion method based on the Homozygous Opposite Test (HOT; Huisman 2017 ) by introducing the additional exclusion criterion HIPHOP (Homozygous Identical Parents, Heterozygous Offspring are Precluded; Cockburn et al., 2021). Potential parents are excluded if they have more mismatches than can be expected due to genotyping error and mutation, and thereby one can identify the true genetic parents and detect situations where one (or both) of the true parents is not sampled. Package 'hiphop' can deal with (a) the case where there is contextual information about parentage of the mother (i.e. a female has been seen to be involved in reproductive tasks such as nest building), but paternity is unknown (e.g. due to promiscuity), (b) where both parents need to be assigned, because there is no contextual information on which female laid eggs and which male fertilized them (e.g. polygynandrous mating system where multiple females and males deposit young in a common nest, or organisms with external fertilisation that breed in aggregations). For details: Cockburn, Andrew, Peñalba, Joshua V., Jaccoud, Damian, Kilian, Andrzej, Brouwer, Lyanne, Double, Michael C., Margraf, Nicolas, Osmond, Helen L., Kruuk, Loeske E.B., and van de Pol, Martijn (2021) Hiphop: improved paternity assignment among close relatives using a simple exclusion method for biallelic markers. Molecular Ecology Resources, 21 (6). pp. 1850-1865. https://doi.org/10.1111/1755-0998.1338

The demographic causes of population change vary across four decades in a long-lived shorebird

Understanding which factors cause populations to decline begins with identifying which parts of the life cycle, and which vital rates, have changed over time. However, in a world where humans are altering the environment both rapidly and in different ways, the demographic causes of decline likely vary over time. Identifying temporal variation in demographic causes of decline is crucial to assure that conservation actions target current and not past threats. However, this has rarely been studied as it requires long time series. Here we investigate how the demography of a long-lived shorebird (the Eurasian Oystercatcher Haematopus ostralegus) has changed in the past four decades, resulting in a shift from stable dynamics to strong declines (−9% per year), and recently back to a modest decline. Since individuals of this species are likely to respond differently to environmental change, we captured individual heterogeneity through three state variables: age, breeding status, and lay date (using integral projection models). Timing of egg-laying explained significant levels of variation in reproduction, with a parabolic relationship of maximal productivity near the average lay date. Reproduction explained most variation in population growth rates, largely due to poor nest success and hatchling survival. However, the demographic causes of decline have also been in flux over the last three decades: hatchling survival was low in the 2000s but improved in the 2010s, while adult survival declined in the 2000s and remains low today. Overall, the joint action of several key demographic variables explain the decline of the oystercatcher, and improvements in a single vital rate cannot halt the decline. Conservations actions will thus need to address threats occurring at different stages of the oystercatcher's life cycle. The dynamic nature of the threat landscape is further supported by the finding that the average individual no longer has the highest performance in the population, and emphasizes how individual heterogeneity in vital rates can play an important role in modulating population growth rates. Our results indicate that understanding population decline in the current era requires disentangling demographic mechanisms, individual variability, and their changes over time