Data from: Definition and estimation of vital rates from repeated censuses: choices, comparisons and bias corrections focusing on trees

1.Mortality and recruitment rates are fundamental measures of population dynamics. Ecologists and others have defined and estimated these vital rates in various ways. We review these alternatives focusing on tree population census data in fixed area plots, though many aspects have wider application when similar data characteristics and assumptions apply: our goal is to guide choices and facilitate comparisons.

2.We divide our estimates into ‘instantaneous’ and ‘annual’ rates, corresponding to continuous- or discrete-time dynamics respectively. In each case, vital rate estimates can be further divided into those based on population density (‘per-capita’ rates) and those based on census area (‘per-area’ rates). We also examine how all such rate estimates relate to each other and can thus be interconverted and compared.

3.In a heterogeneous population (e.g., trees in forest stand) comprising subpopulations (e.g., species, locations, exposure classes), estimates of vital rates that assume homogeneity (equal likelihood of mortality and equal likelihood of recruitment for all individuals) are biased towards lower vital rates in stable mixed populations (due to survivorship bias) and towards lower absolute values of population change rate (due to changing-frequency bias).

4.We describe and illustrate an individual-based Bayesian procedure for estimating vital rates that reduces biases by accounting for demographic heterogeneity and sampling errors among and within subpopulations.

1. 死亡率与补充率（Mortality and recruitment rates）是种群动态（population dynamics）的核心度量指标。生态学家及相关领域研究者已通过多种路径对这类生命率（vital rates）开展定义与估算工作。本文综述各类备选估算方法，重点聚焦固定面积样地（fixed area plots）内的林木种群普查数据——尽管当数据特征与假设前提一致时，诸多方法具备更广泛的适用场景；本文的核心目标是为研究者提供方法选择指导，并促进不同研究间的结果对比。
2. 我们将估算方法划分为"瞬时率（instantaneous rates）"与"年率（annual rates）"两类，分别对应连续时间动态（continuous-time dynamics）与离散时间动态（discrete-time dynamics）场景。两类场景下，生命率估算均可进一步划分为基于种群密度的"每个体率（per-capita rates）"，以及基于普查样地面积的"每单位面积率（per-area rates）"。此外，本文还探讨各类速率估算方法间的内在关联，明确其相互转换与结果对比的可行路径。
3. 在包含亚种群（subpopulations，如物种、生境位置、暴露等级类群）的异质种群（heterogeneous population，例如林分中的林木）中，若假设种群同质（即所有个体的死亡概率与补充概率均等），则得到的生命率估算结果存在偏差：在稳定混合种群中，估算值会因存活偏差（survivorship bias）偏低；而种群变化率的绝对值则会因频率变化偏差（changing-frequency bias）偏低。
4. 本文将介绍并演示一种基于个体的贝叶斯估算方法（individual-based Bayesian procedure），该方法通过考虑亚种群间及亚种群内部的种群统计异质性（demographic heterogeneity）与抽样误差（sampling errors），有效降低估算偏差。