ABSTRACT
We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number [Formula: see text] for time-independent and periodical models and establish the permanence dichotomy: if [Formula: see text], extinction on all patches is imminent, and if [Formula: see text], permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.
ABSTRACT
Small-scale fisheries are critically important for livelihoods around the world, particularly in tropical regions. However, climate variability and anthropogenic climate change may seriously impact small-scale fisheries by altering the abundance and distribution of target species. Social relationships between fishery users, such as fish traders, can determine how each individual responds and is affected by changes in fisheries. These informal cooperative and competitive relationships provide access, support, and incentives for fishing and affect the distribution of benefits. Yet, individuals' actions and impacts on individuals are often the primary focus of the economic analyses informing small-scale fisheries' formal management. This focus dismisses relevant social relationships. We argue that this leads to a disconnect between reality and its model representation used in formal management, which may reduce formal fisheries management's efficiency and efficacy and potentially trigger adverse consequences. Here, we examine this argument by comparing the predictions of a simple bioeconomic fishery model with those of a social-ecological model that incorporates the dynamics of cooperative relationships between fish traders. We illustrate model outcomes using an empirical case study in the Mexican Humboldt squid fishery. We find that (1) the social-ecological model with relationship dynamics substantially improves accuracy in predicting observed fishery variables to the simple bioeconomic model. (2) Income inequality outcomes are associated with changes in cooperative trade relationships. When environmental temperature is included in the model as a driver of species production dynamics, we find that climate-driven temperature variability drives a decline in catch that, in turn, reduce fishers' income. We observe an offset of this loss in income by including cooperative relationships between fish traders (oligopoly) in the model. These relationships break down following species distribution changes and result in an increase in prices fishers receive. Finally, (3) our social-ecological model simulations show that the current fishery development program, which seeks to increase fishers' income through an increase in domestic market demand, is supported by predictions from the simple bioeconomic model, may increase income inequality between fishers and traders. Our findings highlight the real and urgent need to re-think fisheries management models in the context of small-scale fisheries and climate change worldwide to encompass social relationship dynamics. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at (10.1007/s10113-021-01747-5).
