title: Harvest timing and its population dynamic consequences in a discrete single-species model.
abstract: The timing of harvesting is a key instrument in managing and exploiting biological populations and renewable resources. Yet, there is little theory on harvest timing, and even less is known about the impact of different harvest times on the stability of population dynamics, even though this may drive population variability and risk of extinction. Here, we employ the framework proposed by Seno to study how harvesting at specific moments in the reproductive season affects not only population size but also stability. For populations with overcompensation, intermediate harvest times tend to be stabilizing (by simplifying dynamics in the case of unimodal maps and by preventing bubbling in the case of bimodal maps). For populations with a strong Allee effect, however, intermediate harvest times can have a twofold effect. On the one hand, they facilitate population persistence (if harvesting effort is low). On the other hand, they provoke population extinction (if harvesting effort is high). Early harvesting, currently considered common sense to take advantage of compensatory effects, may cut into the breeding stock when the population has not yet surpassed the critical Allee threshold. The results in this paper highlight, for the first time, the crucial interplay between harvest timing and Allee effects. Moreover, they demonstrate that harvesting with the same effort but at different moments in time can dramatically alter the impact on the population.
authors.affiliation: Departamento de Matemática Aplicada II, Universidade de Vigo, 36310 Vigo, Spain. Electronic address: bego@dma.uvigo.es.
authors.forename: Begoña
authors.initials: B
authors.lastname: Cid
authors.affiliation: Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Electronic address: f.hilker@bath.ac.uk.
authors.forename: Frank M
authors.initials: FM
authors.lastname: Hilker
authors.affiliation: Departamento de Matemática Aplicada II, Universidade de Vigo, 36310 Vigo, Spain. Electronic address: eliz@dma.uvigo.es.
authors.forename: Eduardo
authors.initials: E
authors.lastname: Liz
mesh_terms: D000818:Animals; D001947:Breeding; D003247:Conservation of Natural Resources / Q000379:methods* / Q000706:statistics & numerical data; D017753:Ecosystem; D005260:Female; D005398:Fisheries; D008297:Male; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D012098:Reproduction; D012621:Seasons; D013997:Time Factors
keywords: Allee effect; Bubbling; Constant effort harvesting; Discrete population model; Ricker map; Stability