Towards a mechanistic understanding of the synergistic effects of harvesting timber and non‐timber forest products

Abstract

Summary Classic theories of resource harvest assume logistic growth and incorporate harvest through an additional loss term. This methodology has been applied successfully in forest products harvesting such as timber logging. However, modelling harvest through a loss term is not appropriate for non‐timber forest products (NTFP) since harvesting in this case does not always require the complete removal of individual plants. Empirical evidence suggest that NTFP harvest affects plant population growth rates. Additionally, timber and NTFP harvest can have synergistic effects on population dynamics. We develop and analyse a simple model that incorporates non‐lethal harvest implicitly through the population growth rate of plants and lethal harvest explicitly through permanent removal of whole plants, with additional synergistic effects on population growth rate. To capture transient dynamics, we model the growth rate of plants explicitly as a dynamic variable affected by harvesting. Transient dynamics results indicate that populations have delayed response to discrete harvesting. We demonstrate exactly how the sustainability of lethal harvest, non‐lethal harvest or both types of harvests depends on the demographic effect of each type of harvest on the population growth rate. Finally, we identify a threshold parameter scriptR, such that combined lethal and non‐lethal harvest results in plant population sustainability when R>1 and extinction when R≤1.

A mathematical model to study the dynamics of carbon capture in forest plantations

“…In this work, we studied the local stability of a mathematical model that analyzes the dynamics of carbon stored in fast-growing exotic species and provide new insights into the modeling of carbon capture dynamics in forest plantations. We start from a mathematical model proposed in [14], in which the authors demonstrate how the sustainability of the lethal and non-lethal harvest depends on the demographic effect of each type of harvest on growth. Furthermore, in [20] by applying the optimal control theory and assuming the mathematical model presented in [14], the authors showed that slow-growing species have optimal collection rates and lower profits than fast-growing species.…”

“…We start from a mathematical model proposed in [14], in which the authors demonstrate how the sustainability of the lethal and non-lethal harvest depends on the demographic effect of each type of harvest on growth. Furthermore, in [20] by applying the optimal control theory and assuming the mathematical model presented in [14], the authors showed that slow-growing species have optimal collection rates and lower profits than fast-growing species. In [13] they studied the dynamics of maintaining biomass at a certain level and maximizing oil production and carbon absorption at longer harvest ages.…”

“…However, they do not include the probability of natural or anthropogenic disasters, such a foresty fires. We extended the model presented in [14] and included the burned area as a new variable.…”

“…In this model h 1 is the environmental humidity parameter and µ 1 is the rate at which the biomass decreases due to the effects of fire. In the case of intrinsic growth r(t), it was originally proposed in [14], where r 0 represents the maximum rate of individual growth under ideal conditions and ρ is the effect of the natural mortality rate for individual growth.…”

“…However, despite that there are mathematical models originally presented in [13,14], which incorporates the dynamics of living biomass and the intrinsic growth of biomass and consider the felling rate as a control variable, they do not analyze variables such as the burned area and the ambient humidity in joint form. In this context, the novelty of this research will be to jointly analyze the dynamics of living biomass, the intrinsic growth of biomass, and the burned area, under different environmental humidity conditions.…”