Total response models as a conceptual management framework for conserving vulnerable secondary prey

Many of the world's native fauna suffer unsustainable losses from invasive mammalian predators. Conservation managers control predators on the premise that if large numbers are removed, prey will respond. This is sometimes true, but not always. Empirical relationships between predator densities and responses of vulnerable prey in Oceania often show little or no response across a broad range of predator reductions, with positive responses only at low threshold predator densities. Even then, some prey populations fail to respond. More research is required to identify predator thresholds across a range of prey taxa. This uncertainty of outcomes, coupled with the considerable cost of mammalian pest control, risks little or no return from limited conservation funds. A unifying theory is required to help understand why conservation outcomes from predator control are so variable despite the best efforts of conservation managers, and to expedite the right kind of management for a given prey species. We argue that a modern synthesis of numerical and functional response theory, in the form of total response models, provides such a theory. Stochastic consumer-resource models are recommended for dynamic systems, but they are difficult to parameterize. Total response models, on the other hand, present a simple conceptual framework that managers can use as a heuristic to understand predator – prey systems, help explain some of the variability in predator control outcomes and stimulate thinking about other management options that can be integrated with predator control to improve conservation outcomes. Five rules of thumb are suggested to assist conservation managers.


| INTRODUCTION
Many of the world's native fauna suffer unsustainable losses from invasive mammalian predators (Blackburn et al., 2004;Doherty et al., 2016). Many native prey species, particularly those on the continents and islands scattered throughout the Pacific Ocean (hereafter Oceania), are highly vulnerable because of their behavioral naivety to invasive predators (Banks & Dickman, 2007) and low rates of fecundity. Low fecundity is an inherent feature of many Oceanic island species (e.g., Covas, 2012;Cree, 1994) or occurs episodically during periods of environmental stress, such as drought (e.g., Mac Nally et al. 2009). Also, in Australia, New Zealand, Hawaii and many other Pacific islands, populations of invasive generalist predators, such as feral cats (Felis catus), foxes (Vulpes vulpes), mustelids (Mustela spp.), and to some extent herpestids (Urva spp.), are often boosted by the abundance of invasive primary prey, such as rabbits (Oryctolagus cuniculus) and rodents (Rattus spp. and Mus musculus) (Cooke, 2012;Cruz et al., 2013;King, 1983;Mostello & Conant, 2018), and by lack of predators, competitors, and diseases from their native range. Consequently, endangered native fauna that are depredated by these subsidized predators become secondary prey as a food source.. Given these impacts, conservation managers undertake predator control programmes (and sometimes measure outcomes for native biodiversity) with the expectation that if large numbers of predators are removed, secondary prey populations will respond. This is sometimes true, but not always. Control of generalist predator populations leads to highly variable outcomes (e.g., Duncan et al., 2020;Smith et al., 2010). Prey responses can be strong (e.g., O'Donnell et al., 2017;Raine et al., 2020), moderate (e.g., Clark & Hebblewhite, 2021;Comer et al., 2020), or weak to nonexistent (e.g., Fischer et al., 2020;Walsh et al., 2012). Further evidence for this variability is apparent from relationships between predator densities and impacts on numerous sensitive prey taxa (termed effort-outcome relationships, sensu Hone et al., 2017; or predator density-impact functions or DIFs, sensu Norbury et al., 2015). The shapes of these relationships are important for cost-effective predator management. In theory, shapes can take various linear or nonlinear forms ( Figure 1). Nonlinear forms are especially interesting as they indicate threshold predator densities at which impacts change rapidly, indicating a tangible management target. 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). But even when these effects are absent and predation is known to be a key limiting factor, prey can still fail to respond. This uncertainty of outcomes, coupled with the considerable cost of mammalian pest control (see , risks little or no return from limited conservation funds. A unifying theory is required to help understand why conservation outcomes from predator control are so variable despite the best efforts of conservation managers. Such a theory would help expedite the right kind of management at the right time for a given vulnerable prey species, rather than the current expectation that predator removal will always confer some benefit. We argue that such a theory can be found in a modern synthesis of numerical and functional responses, in the form of total response models (Fryxell et al., 2014;Pech et al., 1995). These models provide a simple conceptual framework that managers can use to understand predator-prey systems, help explain some of the variability in predator control outcomes and stimulate thinking about other management options that can be integrated with predator control to improve conservation outcomes. This is consistent with Caughley's (1994) call for more theory to underpin population declines.

| A PRECIS OF NUMERICAL AND FUNCTIONAL RESPONSES, AND PREY RECRUITMENT THEORY
A predator's numerical response can be expressed as the relationship between the density of the predator and the density of the prey, while the functional response is the relationship F I G U R E 1 Four simple theoretical relationships between predator density and positive secondary prey response variables (e.g., fecundity, survival, abundance, rate of population increase). The x-axes span the full range of predator densities. Threshold levels of predator density (a, b and c) are evident for the three curvilinear relationships. Modified from Norbury et al. (2015).
between the numbers of prey individuals consumed per predator versus the density of prey (Solomon, 1949). These responses can be multiplied to give the total response; that is, the total number of prey consumed versus the density of prey, with consumption expressed as a proportion of the prey population (i.e., percentage mortality due to predation, or predation rate) (Holling, 1959) (and see recent expanded variants in Dick et al., 2017;Latombe et al., 2022). As explained earlier, because generalist invasive predators in Oceania are often boosted by invasive primary prey, the predator numerical response will usually be invariant to the abundance of native secondary prey because predators do not rely on them for their survival. This means that predators' total response to these secondary prey will be determined largely by the functional response.
In this paper, we use three basic forms of the functional response as simple heuristics for conservation managers: linear (called a Type I), asymptotic or saturating (Type II), and sigmoidal (Type III) where a predator's food intake increases slowly at first and then asymptotes (see Figure 2.1 in DeLong, 2021). The ecology of functional responses is far more complex than these simple depictions given the influence of factors other than the density of the focal prey, such as the density of alternative prey, food caching, surplus killing, diet switching and predator interference (e.g., Abrams, 2022;DeLong, 2021;Gobin et al., 2022;Krebs, 2022). These complexities are not considered here.
The other key relationship is between per capita recruitment rate of prey and prey density, measured in areas where predators are scarce or, ideally, absent. Per capita recruitment is assumed to be constant with prey density (i.e., the number of recruits is assumed to increase as the population increases) until resources become limiting and negative feedbacks reduce net recruitment as prey numbers approach carrying capacity (e.g., for song sparrows, Melospiza melodia, Arcese and Smith 1988). House mice (Mus musculus), for example, display various forms of spacing behavior that appear to regulate their populations through density-dependent F I G U R E 2 Examples of empirically derived predator density-impact functions for vulnerable secondary prey species, showing relationships between: percentage trap catch of brushtail possums (Trichosurus vulpecula) and percentage of pairs of North Island k okako (Callaeas cinerea) fledging young (a) (modified from Innes et al., 1999); mouse printing rates of tracking tunnels and numbers of southern grass skinks (Oligosoma polychroma) (b) and ground w et a (Hemiandrus spp.) (c) in pitfall traps (modified from Norbury et al., 2022); ship rat (Rattus rattus) tracking index and number of kerer u in 5 min bird counts (d) (reproduced from Carpenter et al., 2021); and residual ship rat tracking index (RTI) and predicted rat control effect size on recovery rates of deeply endemic New Zealand bird species for each endemicity level 7 years after the onset of control (e) (solid lines, predicted mean effect size; marker sizes depict relative weight each study contributed to overall effect size; shading, 95% confidence band; dotted lines, 95% prediction interval upper and lower bounds) (reproduced from Binny et al., 2020, with permission from Wiley). Approximate predator thresholds are apparent where prey recruitment or population size rapidly increase where predator density indices are less than about 10%. Points inside dashed circles are populations that showed little or no response despite very low predator densities. mechanisms (Fitzgerald et al., 1981;Lidicker, 1976). When the total response function is superimposed on the net recruitment function (Figure 3), it can either sit above the recruitment function across all prey densities (i.e., predation rate is always greater than prey recruitment), in which case prey will decline, or they can intersect, with hypothetical cross-over points where prey numbers increase or decline depending on the density of prey and the shape of the functions.
Various hypothetical total response and prey recruitment models are illustrated in Messier (1994), Pech et al. (1995), Sinclair et al. (1998) and Fryxell et al. (2014). Evidence for these models is apparent from density-dependent rates of predation by wolves (Canis lupus) on moose (Alces alces) in North America (Boutin, 1992;Messier, 1991;Messier, 1994;Serrouya et al., 2015), by feral cats and ferrets (Mustela furo) on skinks (Oligosoma maccanni, O. polychroma) in New Zealand (Norbury, 2001), and from rates of predation and population change of vulnerable secondary prey species in Australia (Sinclair et al., 1998). These studies are based mostly on Type II and Type III functional responses. Recent evidence suggests that Type I responses may be more common in nature than previously thought (e.g., Beardsell et al., 2022;Chan et al., 2017), which may be the case for vulnerable secondary prey species whose densities have been depleted below the intake saturation levels of predators.

| HYPOTHETICAL TOTAL RESPONSE MODELS FOR VULNERABLE SECONDARY PREY
The mechanisms or processes that threaten secondary prey are not always immediately obvious. We suggest that the hypothetical model in Figure 3a (analogous to Figure 2b in Sinclair et al.1998) applies to many secondary prey species in Oceania that are highly vulnerable to F I G U R E 3 Hypothetical total response models (solid lines = predation rates, or proportion of the secondary prey population consumed versus density of secondary prey) superimposed on prey recruitment functions (dashed lines = net per capita recruitment rates of prey in the absence of predation versus prey density). The left, middle and right panels reflect Type II, Type I, and Type III functional responses, respectively. The predator numerical response to secondary prey abundance is not considered here because generalist predators in Oceania are often decoupled from the dynamics of native prey because they usually do not rely on them as a primary food source for their survival. High predation rates without predator control are depicted in the top panels, with arrows showing prey densities declining to extinction or to low density "a," because predation rates mostly exceed net recruitment rates (due to behavioral naivety, low or episodic recruitment, or hyper-predation from abundant primary prey). Figure 2d-f show two moderate intensities of predator control, with no change in outcomes for prey (explaining the lack of prey responses across a broad range of reductions in predator densities). The lower panels show two intensive levels of predator control that lower the predation curve (mostly) below the net recruitment curve, allowing most prey densities to increase to the stable points "c" or "c*." However, note "b" and "b*" are unstable thresholds below which the prey goes to extinction (in the case of panel g) or collapses to low density domain "a" (in the case of panel i) (explaining the low prey populations within the hatched circles in Figure 2). Note that for most systems, these states will infrequently be stable given seasonal fluctuations and stochastic events that temporarily shift the predation and recruitment curves up or down depending on the nature of the event and the biology of the predators and prey.
predation and subject to decline or extinction without predator control. There are two features to note: (1) the gap between predation and recruitment rates is very large across all prey densities, and (2) predation rates accelerate at low prey densities. This means that at all prey density levels there is decline leading to extinctions. The large gap between recruitment and predation mortality can result from several compounding factors. As mentioned, high predation can result from predator populations that are boosted by primary prey (leading to "hyperpredation"; Courchamp et al., 2000;Smith & Quin, 1996), or from over-exposure of secondary prey to predation due to behavioral naivety or lack of habitat refuge (Forrester & Steele, 2004), making it easier for predators to find and attack them (i.e., a Type II predator functional response, sensu Holling, 1959). Inherent or episodically low prey recruitment rates also contribute to the large gap.
Accelerated predation rates at low prey densities result from the fact that generalist predators are often decoupled from the dynamics of native prey because they usually do not rely on them as a primary food source for their survival, but rather take them incidentally as secondary prey. This means predators can remain abundant even when secondary prey are scarce or even absent, enabling them to consume increasingly large proportions of secondary prey populations as they approach critically low levels. Pech et al. (1995) and Fryxell et al. (2014) refer to these accelerated predation rates as "depensatory" or "inversely density-dependent." All these factors widen the gap between predation and recruitment of the secondary prey, leading to prey population declines and, eventually, extinction. This is a process known as predator-mediated apparent competition, where increase in one prey results in increased predation on a second prey which then declines, thus appearing to show competition between the prey (DeCesare et al., 2010;Holt, 1977), but the mechanisms or threatening processes are not always immediately obvious.
The model in Figure 3a represents the worse-case scenario for secondary prey. The model in Figure 3b is a slightly less pessimistic variant based on a Type I functional response. Again, the gap between recruitment and predation is wide across all prey densities, leading to extinction but because predation rates are flat and density-independent, they do not accelerate at low prey densities.
The model in Figure 3c is more optimistic, representing secondary prey species that are in decline but have refuge at low density (analogous to Figure 1 "Predation Model" in Messier, 1994;and Figure 3b in Sinclair et al. 1998). Again, the gap between recruitment and predation is wide across most prey densities, with prey mostly in decline, but at low prey densities predation rates decline rather than accelerate (i.e., predation is directly "density-dependent," sensu Fryxell et al., 2014;Pech et al., 1995). In this situation, predators can no longer maintain high intake rates at low prey densities if, for example, the habitat provides prey with sufficient refuge (discussed further below), or if prey are especially cryptic or become so rare they are reduced in predators' search image when hunting (Gendron & Staddon, 1983). These factors result in a Type III predator functional response, with the total response predation curve now intersecting the prey recruitment curve at low prey density "a" (Figure 3c). While most prey populations still decline, they stabilize at the predator-regulated point "a," resulting in a theoretical low-density domain. This might explain why some vulnerable secondary prey species persist at low density in the presence of predators in relatively stable systems. Prey in such low-density domains, however, are vulnerable to inbreeding depression (e.g., Saccheri et al., 1998) or harmful stochastic perturbations (see below), which can potentially push density "a" even lower, or to extinction (Purvis et al., 2000).

| TOTAL RESPONSE MODELS PREDICT PREDATOR DENSITY-IMPACT FUNCTIONS FOR VULNERABLE SECONDARY PREY
The wide disparity between recruitment and predation rates in Figure 3a-c implies that predator control must be sufficiently intense (i.e., greater than the relatively moderate control intensities depicted in Figure 3d-f) to lower the predation curve below the recruitment curve, as shown in Figure 3g-i. In these cases, prey can potentially increase to density "c" or "c*" but note that densities below "b" or "b*" can still decline to extinction (in the case of Figure 3g) or to a low-density domain "a" (in the case of Figure 3i). These predictions are evident in the empirical predator density-impact functions for birds, lizards, and invertebrates in Figure 2-positive prey outcomes occur only when predator densities are reduced below a low critical level, but below this level some prey populations still fail to respond (as shown in Binny et al., 2020;Carpenter et al., 2021;Norbury et al., 2022;Spencer et al., 2017). While there are many potential mechanisms for this type of response (outlined earlier), the models in Figure 3 offer an alternative explanation based on total response predation theory. It is important to note that the shape of the total response models in Figure 3, and the thresholds indicated, are illustrative only. They will vary according to the forms of the functional response for the system of interest.

| STOCHASTICITY AND REPRODUCTIVE PLASTICITY
Note that total response functions are "densitydependent" models; that is, they relate predation and recruitment rates to prey density alone, condensing very complex interactions into simple relationships. Choquenot and Parkes (2001) and Krebs (2002) called for greater understanding of how environmental factors, such as variable food supply, disease outbreaks or weather conditions affect population growth rates, and advocated the use of stochastic consumer-resource models that include these extrinsic influences to predict outcomes (e.g., Choquenot, 2006). This is especially relevant for highly variable systems such as arid environments with episodic rainfall events (Pavey & Nano, 2013), or for forest or grassland systems that undergo periodic mast seeding events (Kelly et al., 2013). Also, temperate systems have variable peaks in spring productivity (Richardson et al., 2010). Severe droughts or storms can temporarily lower prey recruitment, or seedmasting events can boost invasive predator numbers and temporarily elevate the predation curve (King & Powell, 2011). Seed masting explains the stepwise declines to extinction of some vulnerable prey species (Elliott, 1996;O'Donnell, 1996). Vulnerability to stochastic events may also depend on the reproductive plasticity of prey. Species such as k ak ariki (New Zealand parakeet, Cyanoramphus spp.), for example, may be temporarily boosted by a food surfeit during seed-masting events, but this is usually swamped by elevated predation resulting from ensuing rodent irruptions; rodents are both predators and primary prey for top-order predators, such as mustelids . In comparison, prey species with only modest reproductive plasticity, such as lizard taxa (James & Whitford, 1994;Jordan & Snell, 2002), may not respond reproductively to masting events, yet still suffer increased predation from predator irruptions. Depending on the nature of the stochastic event, the states depicted in Figure 3 are therefore unlikely to be stable for most systems.
Unfortunately, models that incorporate stochastic consumer-resource dynamics are complex and datahungry, and so are infrequently used by practitioners to guide predator management and species conservation. This could be due to lack of awareness of predator-prey theory, difficulty in understanding models, or model parameters (e.g., food availability effects on the dynamics of predators and prey) requiring long-term data that are difficult and expensive to obtain. Pech et al. (1995) argued that total response models, on the other hand, predict what will happen on average and are therefore better suited to more stable ecological systems rather than fluctuating boom/bust systems (although note Krebs', 2022 concerns about "average" functional responses). The utility of total response models lies not so much in their ability (or lack thereof) to predict predator-prey dynamics, but as simple heuristics for understanding general principles behind predator-prey relationships and generating rules of thumb for actively managing the recovery of secondary prey. Even a basic understanding allows conservation managers to think about how their system might be working and how the potential effects of stochastic changes in predation and/or recruitment rates, in general terms, may affect the overall response of vulnerable secondary prey, rather than applying the common assumption that any reduction in predator density will have a proportional benefit for threatened prey species (Figure 1a). This conceptual thinking is potentially very valuable because it prompts managers to consider a suite of other threatening processes and highlights the risk of failed management efforts where predator suppression is applied naively. McGregor et al. (2016) suggested that high levels of predation by feral cats caused by loss of cover and habitat complexity is a fundamental driver of native mammal decline across northern Australia. The models in Figure 4 illustrate the potential benefits of improving the quality and structure of habitat for secondary prey. Extra food, shelter and breeding sites in high-quality habitat can elevate the recruitment curve for species that are limited by these factors (e.g., Reay & Norton, 1999). Combining habitat improvement with a moderate intensity of predator control (as depicted in Figure 4b) is thus an alternative way of narrowing the gap between recruitment and predation for some species, rather than relying solely on intensive predator control. Also, if improved habitat structure provides enough refuge for prey to avoid predators, it may reduce predators' intake rate of prey, changing their functional response from Type II (in this case) to Type III (Sinclair et al., 1998). This has the dramatic effect of changing the shape of the total response function (Figure 4c), with the slope reversing from negative to positive at low prey density, thereby removing an extinction density and creating a low-density domain.

| HABITAT EFFECTS ON PREDATION OF SECONDARY PREY
Positive effects of habitat refuge on prey population size and demographics have been demonstrated for many terrestrial prey species (e.g., Finke & Denno, 2002;Laidlaw et al., 2017;McGregor et al., 2015), including effects on prey behavior, particularly increased foraging opportunities afforded by reduced predation risk (e.g., Druce et al., 2006;Jones et al., 2001;Stokes et al., 2004). In a similar vein, Holt (1984) explored the effects of increased habitat heterogeneity on the coexistence of prey species with a shared predator. Habitat restoration is therefore often recommended as a means of reducing unwanted predation (e.g., Doherty et al., 2015;McDonald et al., 2016;Sinclair et al., 1998).
An untested question is whether prey species that are behaviorally naïve to invasive predators can exploit refuge sufficiently to escape most predation attempts. For example, prey species such as lizards and invertebrates, which are vulnerable to predation by small invasive mammals, such as invasive house mice (e.g., St Clair 2011), must access refugia that mice cannot. In New Zealand, where native fauna co-evolved with only avian predators, native prey may have evolved antipredator behaviors that hide them from avian predators that hunt using visual cues, but not necessarily from small, recently invaded mammalian predators that hunt using olfactory cues. A nuanced understanding of antipredator behavior and species' refuge requirements (e.g., Croak et al., 2008), particularly in Oceanic systems, is desperately needed to guide the use of habitat management for reducing predation.
Increasing habitat structure might have the added benefit of displacing predator species, such as feral cats, that prefer to hunt in more open areas (McGregor et al., 2014;Stobo-Wilson, Stokeld, et al., 2020) (although see Alterio et al., 1998) or reducing the abundance of their primary prey. For example, European rabbits, the primary prey species for predators in many ecosystems, prefer open grasslands and are less abundant where vegetation is thick and complex (Moreno & Villafuerte, 1995;Petrovan et al., 2011). A potential disadvantage of increased habitat structure is it can attract invasive rodents, who prefer thick, vegetated understories (e.g., Knox et al., 2012;Norbury et al., 2013). Whilst invasive rodents do not depredate rabbits, they do consume a range of other prey species (St Clair 2011) and are the primary prey for other generalist invasive predators. In this case, a combination of rodent control and habitat restoration may be required. If rodents are the primary target predator, increasing habitat complexity alone may not be an appropriate strategy, but this requires further research. Caughley's (1994) review of conservation biology highlighted an urgent need for more theory to underpin population declines. Total response models offer a conceptual framework for understanding the general principles of predator-prey relationships and for generating the following rules of thumb to protect and restore vulnerable secondary prey species.

| Reduce predator densities to threshold levels
A critical issue for managers is the intensity and frequency of predator control required to achieve recovery of prey. Control must be sufficient to lower the predation curve below the recruitment curve. Return for effort will tend to be nonlinear for prey species with a total response function that sits well above the recruitment function (i.e., species in Figure 3a-c that are behaviorally naïve, have low or episodic recruitment, poor refuge, or are subjected to hyper-predation from abundant primary prey).
F I G U R E 4 Hypothetical benefits of improving the quality and structure of habitat for secondary prey. Extra food, shelter, and breeding sites can elevate the recruitment curve for species that are limited by these factors. Elevated recruitment, combined with moderate amounts of predator control, that is, moving from panel (a) to (b), may be a better way of narrowing the gap between recruitment and predation than by predator control alone (note, densities below "b" can still decline to extinction). Panel (c) illustrates the effect of providing extra refuge for prey by improving habitat structure, potentially changing predators' prey intake rate from a Type II to a Type III functional response and reversing the slope of the predation curve at low prey density from negative to positive. This replaces the extinction density at "b" in panel (b) with a low-density domain at "a." As explained earlier, this means that predator control may achieve little or no result unless control is sufficiently intense. It is important to note, however, that predator density thresholds are likely to shift in response to stochastic events, and they may be time-bound depending on whether predation is year-round or confined to critical periods of prey vulnerability, such as nesting in birds. This presents a complex challenge for conservation managers, as both the degree of predator suppression and its periodicity will need to be determined. Unfortunately, there is a general lack of empirical data to identify these predator density thresholds. An adaptive management approach (sensu Holling, 1978) that combines known levels of predator densities with outcome monitoring is valuable. In most cases, investment in research will be required to address these knowledge gaps, unless operating in familiar ecosystems with well-understood predator-prey relationships.

| Intensive predator control does not guarantee favorable outcomes
Even if predator control lowers the predation curve below the recruitment curve, some prey populations that are subject to Type II predator functional responses (due to behavioral naivety or poor refuge) can fail to respond due to accelerated predation rates at low prey densities. Recognizing this removes the false expectation that predator control ensures positive prey responses, and highlights the importance of measuring outcomes for prey (see . Indeed, for some critically endangered prey species (e.g., New Zealand saddleback, Philesturnus carunculatus, Hooson & Jamieson, 2003), total predator removal or exclusion may be the only viable option for in situ recovery, especially if one or very few individual "rogue" predators cause disproportionate damage. Lack of prey responses opens options for managers to consider alternative threatening processes.

| Reduce primary prey
For generalist predators that rely on invasive prey species as their primary food source, reducing the abundance of these prey can be an indirect means of reducing predator abundance and increasing survival and recruitment of secondary prey (e.g., Pedler et al., 2016). Indeed, rabbit and rodent control are often proposed as viable indirect methods to control the impacts of generalist predators (e.g., Courchamp et al., 1999b;Lavery et al., 2020;McGregor et al., 2020;Norbury, 2001;Rendall et al., 2022;Stobo-Wilson, Brandle, et al., 2020). Or moving further down the food chain, manipulating habitat that drives the abundance of primary prey. Habitat modification and landscape supplementation of invasive species (Dunning et al., 1992) (e.g., livestock grazing and fertilization of pastures that boost rabbit populations, Norbury et al., 2013), or timber harvesting that boosts the primary prey of predators (e.g., moose Alces alces or white-tailed deer Odocoileus virginianus, Wittmer 2007), are regarded as major threats to the persistence of some native species (Bogich et al., 2012;Didham et al., 2012). Government processes that consent land developments need to consider not only its direct effects on native biodiversity, but also the potential indirect effects via increased predation rates on native secondary prey.

| Increase prey refuge
Increasing the structural complexity of habitat by restoring degraded vegetation (Doherty & Ritchie, 2017), managing fire appropriately (Hradsky et al., 2017;Leahy et al., 2016), or providing artificial refuge (Cowan et al., 2021;Stokes et al., 2004) is an additional approach for mitigating predation, by changing the shape of the predation curve or displacing predators that prefer not to hunt in thick habitat. This may be a better option where landscape-scale predator control is too difficult or expensive (Doherty et al., 2015). Restoring vegetation by controlling unwanted herbivores, for example, may in some circumstances be an easier option than controlling predators. However, the extent to which habitat improvement mitigates predation will depend on the way predators hunt and how prey detect or avoid predators (see Kotler et al., 1992). Habitat manipulation must therefore be tailored to the predator and prey species of interest. More experiments are required to test the effects of habitatfocused predator management, especially for prey species that are behaviorally naive to mammalian predators.

| Boost prey recruitment
Improving the quality of habitat in a way that increases food supply, shelter, and breeding sites for prey species with reproductive plasticity can potentially elevate recruitment rates above predation rates. Other more direct options for increasing prey recruitment include supplementary feeding (Castro et al., 2003;Ewen et al., 2015), adding genetic diversity (Bell et al., 2019), increasing the proportion of breeding females with supplemental releases (Armstrong & Ewen, 2001), providing artificial nest or denning sites (Cowan et al., 2021), and manipulating the social structure of populations where there is social inhibition of recruitment (Christian, 1970).

| FUTURE RESEARCH
The above rules of thumb are predictions from total response theory. Whilst they are generally supported from empirical studies, testing the extent to which they hold true for a manager's particular system of interest is essential as it adds to our general understanding of predator-prey relationships in different ecological contexts. We also recommend taking guidance from Caughley and Gunn's (1996) hypothesis-driven experimental approach to tease apart the efficacy of these various management options. The many tens of millions of dollars spent on predator management are arguably high risk because we tend not to invest in such experiments or indeed in describing relationships between densitydependent predation and recruitment rates of prey. Deriving these relationships is not a trivial undertaking as it requires good field and analytical skills, robust experimental design (Kalinkat et al., 2023), stable funding, and an opportunity to measure prey recruitment in the absence of predators. Measuring the variation in these rates is a step further, as putative prey density crossover points would become more realistic "domains of recovery" or "domains of decline" rather than single points. An alternative approach taken by Sinclair et al. (1998) is to infer the difference between predation and recruitment rates of prey from the rates of change in prey populations measured at different densities.

| WHAT CAN CONSERVATION MANAGERS DO WITH TOTAL RESPONSE MODELS?
We believe the greatest utility of total response models is as a conceptual framework for understanding the general principles of predator-prey relationships to achieve locallyappropriate management approaches for secondary prey in an ecosystem context. As efforts to control invasive pests for biodiversity conservation grow, it is important that these principles become foundational knowledge for both professionals and the wider conservation community, especially when dealing with threatened species that do not respond readily to simple management interventions. The principles discussed here suggest management options that, either individually or in combination, could improve the conservation status of vulnerable secondary prey species.
Historically, the dominant management approach in Oceania has been suppression of invasive predator populations. This is understandable given that predation by invasive predators is a key limiting factor for native secondary prey in this region, and many established lethal methods are available (e.g., Eason et al., 2017;Johnston et al., 2020). But this should not preclude consideration of alternative management options to integrate with lethal control, including more bottom-up approaches such as primary prey manipulations and habitat management. Like predator density-impact functions (DIFs), it may be possible to construct bottom-up "resource-impact functions" (or RIFs) that help managers identify resources that drive predatorprey interactions, such as habitat structure, nesting holes, primary prey, and rainfall.
If a manager's primary interest is to predict specific outcomes of predator management regimes, especially in dynamic systems, total response models may not be appropriate. Instead, stochastic consumer-resource models are recommended, notwithstanding the fact that parameterizing these models is an even greater challenge. While total response models may have limited ability to predict detailed predator-prey dynamics, they offer a "systems thinking" approach (Meadows, 2008) for understanding principles of predator-prey relationships and for generating rules of thumb for the recovery of vulnerable secondary prey. They also help bridge the gap between theoretical models and conservation practice and create an awareness and understanding of the theory behind why some interventions either work or they do not. Simple models also generate ideas, which is arguably as valid as complex models that generate numbers (Nurse, 2021).
AUTHOR CONTRIBUTIONS Grant L. Norbury wrote the first draft and James T. Reardon contributed significantly to further iterations.

CONFLICT OF INTEREST STATEMENT
The authors have no conflict of interest.
ACKNOWLEDGMENT Open access publishing facilitated by Landcare Research New Zealand, as part of the Wiley -Landcare Research New Zealand agreement via the Council of Australian University Librarians.

DATA AVAILABILITY STATEMENT
Data sharing is not applicable to this article as no new data were created or analyzed in this study.