31 Using ecology and history to derive vulnerability multipliers

Vulnerability multipliers are perhaps easiest to understand when it is recognized that they reflect how far an exploited predator is from its carrying capacity (e.g., interpreted as unfished state); vulnerability multipliers should allow consumption rates that enable a species to recover from its Ecopath biomass to its unfished biomass if fishing ceases. EwE can use the ratio between a group’s unfished biomass and its Ecopath base biomass to estimate vulnerability multipliers for exploited groups, see, e.g., the EwE User Guide vulnerability multiplier estimator chapter.

An added corollary is that the unfished state may be associated with high abundance of top predators and low abundance of their prey due to high predation mortality. If such top predator populations are fished down, predator release may cause the prey to increase. For those prey, the vulnerability multipliers should thus be set to a high value, even though the baseline model represents the unfished state.

It can indeed be difficult to specify reasonable vulnerability multipliers for non-exploited species. Here, vulnerability multipliers need to be considered in the context of the foraging arena: the fine-scale spatial structure of the trophic interactions and what proportion of prey may be vulnerable to predation at any moment (Figure 1). The activity, spatial restrictions, and distributions of species provide insight into the likely vulnerability of prey to predation. This in turn provides a starting point from which it is possible to assign vulnerability multipliers. The distribution of predators could be restricted by limited mobility, habitat requirements, or the predation risk they face themselves, whereas prey vulnerability may be influenced by the time they spend in and out of safe behavioral states. This can be related to the availability of shelter, such as macroalgae, or specific ontogenetic life stages (for example juvenile fish may allocate less time to foraging), or be more restricted spatially (and thus unable to access vulnerable pools of prey) than their adult counterparts. Different behaviours, such as dispersal behaviours (e.g., moving to spawning sites), aggressive behaviours, or evolutionary behaviour (e.g., changes in shoaling dynamics) may also influence vulnerability to predation.

Trophic levels have also been used to approximate vulnerability multipliers in situations where time series data were unavailable under the dubious assumption that the vulnerability multipliers are proportional to the trophic level of the predator. This approach assumes that higher trophic levels are further removed from their unfished biomass than lower trophic levels, typically because of historical overfishing. This may seem a reasonable assumption considering how global fisheries have historically targeted and depleted higher trophic level fish stocks^{[1] [2]}, but conflicts with the concept of using a priori knowledge to parameterize vulnerability multipliers based on region specific trends in historical exploitation or ecology.

Finally, an approach to setting vulnerability multipliers was applied by Chagaris et al.^[3] to constrain how much predation mortality by a given predator could increase relative to a prey’s total natural mortality

[latex]k_{ij}=\frac{M2_{cap}\cdot M_i}{M2_{base,ij}}\tag{1}[/latex]

where M2_cap defines the proportion of the natural mortality of a prey that a predator can be responsible for, M_i is the natural mortality of prey i, and M2_base.ij is the base predation mortality by predator j on prey i. There may be ecological reasons, or reasons derived from data, to prevent a single predator from being accountable for large proportions of a prey’s natural mortality. Using these k_ij instead of default or model estimated values, (which are often higher) may also be driven by ambitions for model performance: Chagaris et al.^[4] found that extremely high k_ij estimated by Ecosim led to instability at high fishing mortality rates when evaluating equilibrium yield curves, and  using M2_cap values between 0.75 to 1.0 led to more reasonable estimates for F_MSY (the fishing mortality at maximum sustainable yield) while also constraining theoretical maximum predation mortality rates to values that were compatible with prey natural mortality rates.