Evaluating the consequences: Impact of sex-selective harvesting on fish population and identifying tipping points via life-history parameters

TL;DR

A novel early warning tool based on the concept of basin stability to pinpoint tipping points before they occur and it is shown that density-dependent female stocking upon receiving an EWT signal significantly shifts the tipping point, allowing safe harvesting even at MSY levels, thus can act as a potential intervention strategy.

Abstract

Fish harvesting often targets larger individuals, which can be sex-specific due to size dimorphism or differences in behaviors like migration and spawning. Sex-selective harvesting can have dire consequences in the long run, potentially pushing fish populations towards collapse much earlier due to skewed sex ratios and reduced reproduction. To investigate this pressing issue, we used a single-species sex-structured mathematical model with a weak Allee effect on the fish population. Additionally, we incorporate a realistic harvesting mechanism resembling the Michaelis-Menten function. Our analysis illuminates the intricate interplay between life history traits, harvesting intensity, and population stability. The results demonstrate that fish life history traits, such as a higher reproductive rate, early maturation of juveniles, and increased longevity, confer advantages under intensive harvesting. To anticipate potential population collapse, we employ a novel early warning tool (EWT) based on the concept of basin stability to pinpoint tipping points before they occur. Harvesting yield at our proposed early indicator can act as a potential pathway to achieve optimal yield while keeping the population safely away from the brink of collapse, rather than relying solely on the established maximum sustainable yield (MSY), where the population dangerously approaches the point of no return. Furthermore, we show that density-dependent female stocking upon receiving an EWT signal significantly shifts the tipping point, allowing safe harvesting even at MSY levels, thus can act as a potential intervention strategy.

Figures (14)

• Figure 1: $(a)$ The existence of two positive real roots of $\psi=0$ for $h<h_{sn}=1.35$. $(b)$ The existence of a double positive root of $\psi=0$ at $h=h_{sn}$. $(c)$ For $h>h_{sn}$ and other parameter values as in Table $1$, $\psi=0$ possesses no positive real root.
• Figure 2: $(a)$ A one-parameter bifurcation diagram of the system \ref{['eq:1']} with $h$ as a bifurcation parameter, other parameter values as given in Table $1$. The inset represents a measure of the sensitivity of the population to the changes in $h$ close to $h_{sn}$. The separatrix surfaces demarcating the basins of extinction and recovery for $(b)$$h=0$ and $(c)$$h=1.2$. $(d)$ The percent probability of reaching $E_0$ or $E^*_1$ for $h=0$ and $h=1.2$.
• Figure 3: A one-parameter bifurcation diagrams of the system \ref{['eq:1']} with $(a)$$r$, $(b)$$\beta$, and $(c)$$m_1$ as bifurcation parameters, other parameter values as given in Table $1$.
• Figure 4: $(a)$ The probability of reaching the steady states of the system \ref{['eq:1']} with the changes in $h$. $(a)$ A stochastic model used to simulate the biomass data that reflects a transition to extinction equilibrium. $(c-d)$ The sudden transition is preceded by an increase in the fluctuation about its mean value. $(e)$ Lag-1 autocorrelation computed with the changes in $h$. The gray bands identify the transition phases. The parameter thresholds for saddle-node bifurcations and early warning are indicated in green inverted triangles and red circles respectively.
• Figure 5: For $\alpha=0.7$ the changes in the $(a)$ harvesting yield and $(b)$ the fish population density with the changes in harvesting effort. For $\alpha=0.9$ the changes in the $(c)$ harvesting yield and $(d)$ the fish population density with the changes in harvesting effort.