Data from: Estimation of individual growth trajectories when repeated measures are missing

Individuals in a population vary in their growth due to hidden and observed factors such as age, genetics, environment, disease, and carryover effects from past environments. Because size affects fitness, growth trajectories scale up to affect population dynamics. However, it can be difficult to estimate growth in data from wild populations with missing observations and observation error. Previous work has shown that linear mixed models (LMMs) underestimate hidden individual heterogeneity when over 25% of repeated measures are missing. Here we demonstrate a flexible and robust way to model growth trajectories. We show that state-space models (SSMs), fit using R package growmod, are far less biased than LMMs when fit to simulated datasets with missing repeated measures and observation error. This method is much faster than MCMC methods, allowing more models to be tested in a shorter time. For the scenarios we simulated, SSMs gave estimates with little bias when up to 87.5 % of repeated measures were missing. We use this method to quantify growth of Soay sheep, using data from a long-term mark-recapture study, and demonstrate that growth decreased with age, population density, weather conditions, and when individuals are reproductive. The method improves our ability to quantify how growth varies among individuals in response to their attributes and the environments they experience, with particular relevance for wild populations.

种群中的个体生长速率存在差异，这类差异由潜在与可观测的因素共同导致，包括年龄、遗传、环境、疾病，以及过往环境遗留的累积效应。由于个体体型影响其适合度，生长轨迹会进一步作用于种群动态。然而，针对存在观测缺失与观测误差的野生种群数据，精准估计个体生长速率颇具挑战。过往研究表明，当超过25%的重复测量数据缺失时，线性混合模型（linear mixed models, LMMs）会低估个体的潜在异质性。本文提出一种灵活且稳健的生长轨迹建模方法。研究表明，借助R包growmod拟合的状态空间模型（state-space models, SSMs），在处理存在重复测量缺失与观测误差的模拟数据集时，其估计偏差远低于线性混合模型（LMMs）。该方法的运算速度远快于马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）方法，能够在更短时间内完成更多模型的测试。在我们构建的模拟场景中，当重复测量数据缺失比例高达87.5%时，状态空间模型的估计结果仍几乎无偏。我们借助该方法，基于长期标记重捕研究获取的数据，量化了索艾羊（Soay sheep）的生长情况，并证实其生长速率会随年龄、种群密度、天气条件以及个体处于繁殖期时出现下降。该方法提升了我们量化个体生长速率如何随自身属性与所处环境发生变化的能力，尤其适用于野生种群相关研究。