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.

种群内的个体生长情况存在差异，这种差异源于年龄、遗传、环境、疾病以及过往环境遗留效应等可见与隐藏因素。由于体型关联个体适合度，生长轨迹会进一步影响种群动态。然而，针对存在观测缺失与观测误差的野生种群数据，估算个体生长情况往往颇具挑战。既往研究表明，当重复测量数据缺失比例超过25%时，线性混合模型（Linear Mixed Models, LMMs）会低估隐藏的个体异质性。本研究提出了一种灵活且稳健的生长轨迹建模方案：我们证实，当针对存在重复测量缺失与观测误差的模拟数据集进行拟合时，使用R包growmod拟合的状态空间模型（State-Space Models, SSMs）的估计偏差远低于线性混合模型。该方法的运算速度远高于马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）方法，可在更短时间内测试更多模型。在我们模拟的研究场景中，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。我们将该方法应用于索艾羊（Soay sheep）的生长量量化研究，基于长期标记重捕研究的数据，证实个体生长会随年龄增加、种群密度上升、天气条件变化以及个体处于繁殖状态而下降。该方法提升了我们量化个体生长如何随自身属性与所处环境变化而产生个体差异的能力，对野生种群研究具有重要参考价值。