Retrodiction of forest demography: Backward simulation with reverse matrix models

Abstract

Reconstructing past ecological population dynamics and demographic events is crucial for understanding the dynamics of ecological processes, evaluating the impact of environmental changes and making informed conservation decisions. In forest ecosystems, retrodiction (i.e. the backward projection of ecological populations) plays a pivotal role in understanding historical forest carbon levels and the factors that have influenced their variation over time, because forest demography is a major determinant of the amount of carbon stored in forest ecosystems. The persistent lack of quantitative methods has been a significant obstacle in retrodicting forest demography, especially in applications of a broad geographical scale. While there is a wealth of models for predicting future forest conditions, models that can project these conditions backward in time are scarce. This study presents reverse matrix model (RMM), an innovative retrodiction modelling approach grounded in the principles of transition matrix models. RMM is designed to deduce past demographic characteristics of ecological populations using current data, making it one of the first models capable of projecting the fine‐scale dynamics of forest demography into the past. We assessed the retrodictive performance of RMM by fitting it to a dataset of a disturbed tropical rainforest in French Guiana in 2001–2023, then comparing the retrodictions to observations back to 1983 when the disturbance occurred. We further empirically evaluated the viability of retrodiction over a defined duration by inverting the density‐dependent matrix model by Lin et al. (1996), which predicts the dynamics of northern hardwoods in the United States. The case studies demonstrate significant potential for RMM application in various domains of forestry and conservation, including ecosystem management and conservation planning, global change impact assessment and biodiversity monitoring.