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

van de Pol, Martijn, and Brouwer, Lyanne (2021) Cross-lags and the unbiased estimation of life-history and demographic parameters. Journal of Animal Ecology, 90 (10). pp. 2234-2253.

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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.

Item ID: 69611
Item Type: Article (Research - C1)
ISSN: 1365-2656
Copyright Information: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. Journal of Animal Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society.
Date Deposited: 12 Oct 2021 05:00
FoR Codes: 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490502 Biostatistics @ 50%
31 BIOLOGICAL SCIENCES > 3103 Ecology > 310301 Behavioural ecology @ 25%
31 BIOLOGICAL SCIENCES > 3103 Ecology > 310307 Population ecology @ 25%
SEO Codes: 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280102 Expanding knowledge in the biological sciences @ 75%
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences @ 25%
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