Threshold harvesting as a conservation or exploitation strategy in population management

Abstract

Threshold harvesting removes the surplus of a population above a set threshold and takes no harvest below the threshold. This harvesting strategy is known to prevent overexploitation while obtaining higher yields than other harvesting strategies. However, the harvest taken can vary over time, including seasons of no harvest at all. While this is undesirable in fisheries or other exploitation activities, it can be an attractive feature of management strategies where removal interventions are costly and desirable only occasionally. In the presence of population fluctuations, the issue of variable harvests and population sizes becomes even more notorious. Here, we investigate the impact of threshold harvesting on the dynamics of both population size and harvests, especially in the presence of population cycles. We take into account semelparous and iteroparous life cycles, Allee effects, observation uncertainty, and demographic as well as environmental stochasticity, using generic mathematical models in discrete time. Our results show that threshold harvesting enhances multiple forms of population stability, namely persistence, constancy, resilience, and dynamic stability. We discuss plausible choices of threshold values, depending on whether the aim is resource exploitation, pest control, or the stabilization of fluctuations.

Heuristics for the sustainable harvest of wildlife in stochastic social-ecological systems

“…Harvest systems including thresholds or proportional harvest were more likely to deliver good outcomes, be perceived as sustainable in more varied contexts, and involved less precipitous risk of population declines compared to constant harvest, particularly when the gains possible from selecting the optimal strategy were the greatest. This supports prior analytical and review comparisons Hilker & Liz, 2020;Lande et al, 1997), and importantly, extends systematic assessment across a diversity of environmental and evaluation contexts more likely to be encountered in applied wildlife harvest management.…”

“…Despite established theory on optimal harvest strategy (e.g. Hilker & Liz, 2020;Lande, Engen, & Saether, 1994, 1995, in practice determining quotas in terrestrial systems is often an inexact, adaptive science at best (Artelle et al, 2018). Due to limited resources and poorly developed institutional frameworks, many wildlife management systems lack all but the most rudimental parameters (van Vliet & Nasi, 2019;Weinbaum et al, 2013), and even in the best cases elements of social-ecological systems remain uncertain or contested Corlatti, Sanz-Aguilar, Tavecchia, Gugiatti, & Pedrotti, 2019;Nilsen, 2017;Pellikka, Kuikka, Lindén, & Varis, 2005;.…”

Optimal control of harvest timing in discrete population models

“…The oscillations are remarkable because we do not know of another harvesting model that is able to destabilize Beverton–Holt population dynamics (except for a harvest control rule inducing a discontinuity in the dynamical system; Lois‐Prados & Hilker, 2021). As cycles have important implications for population management (Barraquand et al, 2017), many empirical and theoretical studies have addressed the impact of harvesting on cycles (Anderson et al, 2008; Beddington & May, 1977; Dattani et al, 2011; Hilker & Liz, 2020; Hilker & Westerhoff, 2006; May et al, 1978; Milner‐Gulland & Mace, 1998; Sah et al, 2013; Shelton & Mangel, 2011). Here, we have demonstrated for the first time that cycles can emerge as the optimal strategy when harvest timing is taken into account.…”

Optimal harvesting strategies for ecological population dynamics

“…Fig. 1 shows the comparison between the mean yield obtained with the constant harvest rate (10) and the statedependent rate (17). Observe how the mean yield is also a concave function of h. Hence, given f , it is possible to find the optimal harvesting rate h * and the corresponding maximum mean yield ⟨y⟩ * in steady state is calculated.…”

“…Some approaches consider harvesting as a perturbative process where the population can be approximated as continuous [9], [10]. A more accurate model should take harvesting as a non-continuous jump where a large amount of resources can be collected [16], [17]. The amount of harvested resource is also subject to random variability since each individual has some probability of not being caught.…”