“…For some prey species, any degree of predator reduction may have some benefit (i.e., linear relationships), while for some vulnerable prey species there may be no response unless predator densities are reduced to very low levels. The empirical evidence for most secondary prey species supports the latter (Figure 2)-positive responses generally occur below threshold predator densities, but note that some prey populations show little or no response even at low predator densities (see Figure 2 in Binny et al, 2020;Figure 5 in Carpenter et al, 2021; Figure 2 to Figure 5 in Norbury et al, 2022;Figure 3 in Spencer et al, 2017). There are many explanations for this (see Doherty & Ritchie, 2017), including compensatory effects of other pest predators (e.g., Courchamp et al, 1999a;Norbury et al, 2013), or persistence of factors that are more limiting than predation, such as inadequate food supply or shelter (e.g., Fischer et al, 2020;Lavers et al, 2010).…”