Conserving large carnivores amidst human-wildlife conflict: The scope of ecological theory to guide conservation practice

Accepted Manuscript Conserving large carnivores amidst human-wildlife conflict: The scope of ecological theory to guide conservation practice

Sumanta Bagchi PII: DOI: Article Number: Reference:

S2352-2496(18)30035-1 https://doi.org/10.1016/j.fooweb.2018.e00108 e00108 FOOWEB 108

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Please cite this article as: Sumanta Bagchi , Conserving large carnivores amidst humanwildlife conflict: The scope of ecological theory to guide conservation practice. Fooweb (2018), https://doi.org/10.1016/j.fooweb.2018.e00108

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ACCEPTED MANUSCRIPT [Revision of FOOWEB_2018_35] Conserving large carnivores amidst human-wildlife conflict: the scope of ecological theory to guide conservation practice

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Sumanta Bagchi*

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Centre for Ecological Sciences, Indian Institute of Science, Bangalore 560012, India

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Running title: Ecological theory and conservation practice

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EMail: [email protected], Fax: +91 80 23601428, Telephone: +91 80 22933528

*Correspondence: Sumanta Bagchi, Centre for Ecological Sciences, Indian Institute of Science,

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Bangalore 560012, India. Tel: +91 80 22933528; Fax: +91 80 23601428; E-mail:

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[email protected]

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ACCEPTED MANUSCRIPT Conserving large carnivores amidst human-wildlife conflict: the scope of ecological theory to guide conservation practice

ABSTRACT

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Predator-prey interactions where livestock are killed by carnivores, are a serious global

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challenge. Conservation interventions to address this conflict are inadequately guided by

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ecological theory, and instead rely on pragmatic experiential decisions. I review four families of theoretical models that can accommodate essential features of this human-wildlife conflict,

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namely – prey-refuge, specialist/generalist predation, social-ecological, and metapopulation

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models. I evaluate their relevance for conservation and arrange each model’s predictions along two conceptual dimensions: coexistence and stability. These models are described with examples

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of pastoralists and snow leopards in the Himalayas, but they can have broader relevance to other

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regions. All models suggest that livestock-loss can be better controlled in highly productive habitats, than under low productivity. But, they differed in the ease with which their predictions

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may be translated into real-world conservation interventions. These constraints can be

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circumvented through animal movement between patches which is represented only in metapopulation models. But, metapopulation models do not offer much clarity on size of the

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predator population. Instead, they can prescribe rotational-grazing policies for livestock – another pragmatic management concern. This comparison of models identifies lacunae where ecological theory could be better integrated within conservation practice. One option is better integration with emerging knowledge of animal movement. Comparative analyses of models helps identify future directions where outcomes of alternative management interventions can be predicted and evaluated.

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ACCEPTED MANUSCRIPT Keywords: Prey-predator; carnivore conservation; endangered species; grazing management;

1. Introduction Large carnivores face grim conservation challenges. They range over large expansive habitats,

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occupy apex positions in food-webs, and depend on prey species that are often in-turn also wide-

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ranging (Gittleman et al., 2001). A suite of other life-history traits make them inherently prone to

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extinction in a human-dominated world (Ripple et al., 2014). Most terrestrial large carnivores currently face real extinction risks and have experienced severe population declines in the last

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century (Ripple et al., 2014), particularly among Felidae, Canidae and Ursidae (Fig. 1).

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Carnivore extinctions can trigger far-reaching trophic cascades that impact herbivores, vegetation and soil, disease epidemiology, hydrology, and biogeochemical cycles (Estes et al.,

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2011; Peterson et al., 2014). Their interface with humans, through livestock losses, as well as

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occasional mortality and morbidity for humans, is of particular concern. In addition to habitat loss, fragmentation, degradation, prey depletion, and other threats, carnivores also face

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retaliatory persecution from ranchers and pastoralists. There are historical precedents to resolve

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such conflict by eradicating carnivores altogether (Paddle, 2002), and/or other controversial measures such as restricting them within small fenced reserves (Creel et al., 2013; Packer et al.,

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2013; Woodroffe et al., 2014). For millennia, across different human societies, the tiger (Panthera tigris), lion (Panthera leo), wolf (Canis lupus), jaguar (Panthera onca), bear (Ursus spp.), and other big fierce animals have been revered as cultural icons, have featured in our mythology and fairy-tales. Yet, their future now depends on whether we can mitigate their damage to our livestock. Repercussions of losses to livestock and livelihoods are most severely felt in under-developed economies, and this strains societal tolerance of large carnivores (Aryal

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ACCEPTED MANUSCRIPT et al., 2014; Harihar et al., 2015; Pooley et al., 2017; Redpath et al., 2013, 2017; Singh and Bagchi, 2013; Treves and Bruskotter, 2014). Despite numerous studies on human-carnivore conflict, it remains uncertain whether conservation efforts actually reduce livestock losses, or not (Eklund et al., 2017). Large

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carnivores enter into other types of conflict as well. For example, beyond ranchers and

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pastoralists, they often antagonize other stakeholders such as recreational hunters (Schwartz et

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al., 2003). Many forms of such conflicts have roots in the ecological realm, but extend deep into the human dimension (Pooley et al., 2017; Redpath et al., 2017). But, reducing the impact of

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large carnivores on livestock is a pressing need; one that can be a first step toward effective

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conservation planning (Eklund et al., 2017).

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2. Conservation practice and ecological theory

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Response to human-carnivore conflict revolves around seeking a pragmatic solution to the problem of coexistence between the predator, its natural prey, and livestock. There is a long

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history of discussion on this challenge, spanning a variety of dimensions including legislature,

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economics, peoples’ perceptions, cultural attributes of tolerance, external incentives, etc. (Harihar et al., 2015; Mishra et al., 2003; Redpath et al., 2013; Treves and Karanth, 2003). Often

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it is advocated that inter-disciplinary approaches may help address conflicts better (Pooley et al., 2017; Redpath et al., 2017), but it remains unclear how disparate disciplines can be mobilized simultaneously into effective action (Thébaud et al., 2017). The role of ecological theory and models rarely features in this discussion. This is surprising because ecology is supposedly awash with theories and models (Marquet et al., 2014; Scheiner, 2013); many of which are thought pertinent to conservation practice (Doak and Mills, 1994; Ryall and Fahrig, 2006; Simberloff,

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ACCEPTED MANUSCRIPT 1988). Yet, empirical researchers and conservation practitioners often ignore theoretical work altogether (Driscoll and Lindenmayer, 2012; Ryall and Fahrig, 2006). Are empirical researchers and conservation practitioners unaware of existing theoretical predictions? Are models irrelevant in the real world (Colyvan et al., 2009; van Grunsven and Liefting, 2015)? Or, are theoretical

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guidelines poorly communicated (Jacobson, 2009)? A large and sophisticated body of work by

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theoretical ecologists, therefore, remains under-utilized.

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At the same time, it is also often lamented that conservation policies remain uninformed by ecological theory and are heavily dependent on expert opinions and experiential decisions

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(Doak and Mills, 1994; Driscoll and Lindenmayer, 2012; Ryall and Fahrig, 2006). For example,

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a well-meaning decision to connect fragmented habitats through corridors can hasten extinction due to destabilizing effects of dispersal (Earn et al., 2000), and progress stalls under the strain of

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such conflicting results. Admittedly, managers are frequently required to take decisions under

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data-deficient conditions as the focal species are imperiled and preclude detailed study. From a pedagogical viewpoint, it may also be worrisome that the next generation of conservation

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scientists is receiving inadequate training in theory, and may be under-appreciative of any role

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theory can potentially play (Bagchi, 2017; Jordan et al., 2009; Kendall, 2015; Knapp and D’Avanzo, 2010; Marquet et al., 2014; Ryall and Fahrig, 2006). Interestingly, at the same time,

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the roots of many familiar ecological models lie in the search for solutions to practical problems. For example, the history of classical prey-predator models (Volterra, 1926), can be traced to a need for fisheries management (Kingsland, 1995).

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ACCEPTED MANUSCRIPT 3. Models as simplifications of the real-world 3.1. Identifying relevant theoretical models From literature, I identified theoretical models that are relevant to human-wildlife conflict, based on key characteristics. I included models that attempt to explain dynamics and coexistence of at

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least three interacting species, and be broadly applicable to different ecosystems rather than a

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specific study area, or particular taxa. Insights can be obtained from these models with linear

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algebra and calculus, and no advanced techniques are needed. These model are sufficiently simple to have tractable analytical solutions. The mathematical interpretation of 3-species

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coexistence is already fairly complex. More complex formulations that require numerical

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analyses are excluded from this review. Often, researchers use dimensionless variants to aid mathematical analysis. But, since this offers coefficients that may be difficult to interpret in the

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real world (e.g., ratio of growth rate and carrying capacity, Ranjan and Bagchi, 2016), I review

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the models in their full form. However, a necessary drawback is that simplified models do not incorporate many potentially interesting features of real-world interactions (see section 4,

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below). For e.g., individual-level variation in predator behavior may be a feature in real

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ecosystems. Such features are excluded from further analysis via simplifying assumptions, but this does not preclude broad insights (see section 3.2 below).

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From the literature (Case, 1999; Gotelli, 1995; Hastings and Gross, 2012; Murdoch et al., 2003; Turchin, 2003; Yodzis, 1989), four families of models were judged suitable for review and analysis (Table 1). Of these, three models are fairly well-studied, as they were proposed 3-4 decades ago, and one is more recent. I review and compare their predictions in the context of controlling livestock losses to carnivores (Table 1), and also evaluate the extent to which they can accommodate real-world conflict scenarios. I use illustrative examples linked with loss of

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ACCEPTED MANUSCRIPT livestock to snow leopards (Panthera uncia) in the Himalayas, but these models can have broad and general relevance for other systems as well. Specifically, I consider model parameters that can be influenced through conservation interventions, and discuss their implications against the predicted outcomes. I arrange model interpretations over two conceptual dimensions: the

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conditions for coexistence, and conditions for stability. This exercise can afford some clarity on

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how to design interventions, distinguish the options which are likely to succeed from the ones

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that are difficult to implement, and add value to current discussion on the multi-dimensional nature of human-carnivore interactions (Pooley et al., 2017; Redpath et al., 2017), and why

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conservation interventions do not seem to work (Eklund et al., 2017). It also provides clear

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testable predictions that can be the basis for empirical studies, and for design of conservation interventions. The goal is to compare predictions from different models, and assess their real-

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world implications, particularly the nature of their stabilizing features. And, identify anticipated

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outcomes that can be potentially implemented through management interventions, at least qualitatively. These steps can offer predictions, which can become relevant to ask under what

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conditions conservation interventions should work (Eklund et al., 2017; Ferraro and Pattanayak,

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2006).

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3.2. Relevance of theoretical models to the real-world For decades, researchers have pondered whether or not theory and models have any direct realworld applicability, and if so, how much (Colyvan et al., 2009; Marquet et al., 2014; Scheiner, 2013). Part of the confusion stems from simplifying assumptions that are made when questions across diverse disciplines are formulated mathematically. Often, these assumptions create a distance between equations and reality. In thermodynamics, molecular collisions are assumed to

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ACCEPTED MANUSCRIPT be elastic. In astrophysics, black bodies are assumed to exist. Famously, model assumptions have even led to amusing propositions (e.g., spherical chicken; Stellman, 1973). So, it is justified to question whether simplifying assumptions render their carrier models useless in the real world. Another related aspect is the time-lag (years, decades, even a century) between the availability of

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model predictions and their empirical falsification/acceptance as well as their utilization toward

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pressing problems (e.g., Adler et al., 2018; Wainright et al., 2017) – it is seldom that models

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become useful right away.

Mathematical models are caricatures of the natural world, rather than replicas. Models

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remove clutter, and create idealized conditions within which mathematical formalism can take

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hold. They exclude many familiar characteristics of the real world in order to do so. The four families of models I evaluate below contain their own sets of assumptions; they can only

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partially accommodate the complexities seen in real-world conditions. But, these models can

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help our understanding of how a complex natural system might work (i.e., description), or it ought to work (i.e., prediction). Importantly, they yield falsifiable predictions which can be

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targets of thought-experiments, and actual empirical data. In other words, models can tell us

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something useful about chicken that are spherical; from this we can learn about the ones which

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are more familiar in shape.

4. Prey-refuge model (Sih, 1987; Vance, 1978) 4.1. Model structure Prey-predator interactions reflecting human-carnivore conflict can be captured by models that consider refuges for prey (Sih, 1987; Vance, 1978). Here, two alternative prey differ in their degree of susceptibility to a predator; this makes them a suitable template for understanding

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ACCEPTED MANUSCRIPT systems with livestock, wild prey and carnivores. The basic model for density of wild-prey (W), livestock (L), and predator (P) is of the following form: dW r r    W  r  W  L  c f (W ) P  dt K K  

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dL r r    L r  βW  L  (c  ε ) P  dt K K  

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dP  Pbcf (W )W  b(c  ε) L  D dt

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The three equations, for dynamics in W, L, and P are inter-linked such that each influences the others. Here, r is the maximum per-capita growth rate of wild-prey and K is the carrying capacity

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for the habitat. Per-capita growth is considered equal for W and L. Capture rate of prey by predator is c; β is competitive advantage of one prey over another; ε is predator avoidance

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advantage of L through husbandry; b is conversion efficiency of predator and D its density

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independent mortality through metabolic demands of the predator. Predation on wild prey follows a functional response depending on availability of refuges (R) as:

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(W-R ) /W, W  R . In this way, the number of wild prey captured is influenced by their f(W) 0, W R 

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abundance relative to the availability of refuges.

4.2. Model characteristics and assumptions In this model, prey can grow at the rate r in absence of a competitor or predators. But,  W growth is influenced by density dependence (i.e., logistic growth), through r 1   for wild K 

L  prey, and r 1   for livestock when they are alone, respectively. This assumes bottom-up  K

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ACCEPTED MANUSCRIPT regulation in absence of predators. The wild prey and livestock are sufficiently similar in their life history traits (e.g., body size, fecundity, resource consumption rates, etc.) so that their r and K are not modeled separately, but by common terms (see section 5 when there are separate terms, below). Search rate of the predator is c, and it can capture wild prey at the rate cf(W)W. The

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predator’s functional response f(W) describes how capture rate varies with prey density. If all

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wild prey are protected, and hidden in refuges (R), then f(W) = 0. Any surplus wild prey which

W R . This is a reasonable approximation for many W

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only a fraction of the wild prey population

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are not protected in refuges, W-R, are susceptible to predation. Effectively, the predator can catch

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natural systems. For example, in the Himalayas; ibex (Capra sibirica) stay in proximity of steep cliffs in order to avoid attacks by snow leopards; they are more vulnerable when foraging away

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from cliffs (Fox et al., 1992). Similarly, the predator searches the habitat and captures livestock

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at the rate (c-ε)L instead of cL, as ε represents the predator avoidance among livestock, since some encounters (ε) get thwarted by vigilant herders and guard dogs, etc. The two prey compete

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with each other; the net competitive effect of one prey over the other is β. The predator converts

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prey (food) into offspring with a conversion efficiency b. Net foraging return on wild prey can be bcf(W)W = bc(W-R), and on livestock it is b(c-ε)L. In absence of any prey, the predator

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population declines due to starvation at the rate -DP.

4.3. Model interpretation Intuitively, this model has two stabilizing elements: the habitat’s carrying capacity K, which keeps the prey becoming too abundant, and refuges R, which prevent prey from becoming too rare. One should expect stable coexistence of all three species (Vance, 1978). But, the important question is whether 3-species coexistence can occur without livestock losses.

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ACCEPTED MANUSCRIPT Conservation interventions would aim to establish conditions where L is immune to attacks, or, c=ε. This is often attempted via increased vigilance while herding, strengthening of corrals, and guard dogs (Gehring et al., 2010). If successful, then at the nontrivial equilibrium (where the * symbol denotes equilibrial density) we get

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D   W *   R  bc   *   *  L    K  βW  . At this equilibrium, all three species can have positive densities.  P*   rc( β  1) W * 2     DK 

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Interestingly, predator density is seen to depend on W, and not on L; and this is consistent with empirical observations on snow leopards in the Himalayas (Suryawanshi et al., 2017). High

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livestock populations can be maintained when competitive interactions (β) are weak. But, high

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predator density exists when competition is weak. So, meaningful densities of all species can exist only within a narrow range of competitive interactions that satisfy these opposing demands: 𝑊∗

≫ 𝛽 and 𝛽 > 1, and this is more likely to be met in high-productivity ecosystems.

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𝐾

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Now, the next important question is whether this equilibrium is stable, or not.

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Conservation efforts that result in increased predator populations can intensify conflicts (Rigg et al., 2011). Local stability of such mathematical models can be judged using well-known

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principles of linear algebra (e.g., Routh-Hurwitz criteria, Brassil, 2012; May, 1973). Models are judged stable when a small perturbation at equilibria dissipates over time; they are unstable if the disturbance grows. It is known (Vance, 1978), that these solutions are stable only when

D D  K  β  R   and R  . The key insight from model solutions is that three-species stable bc  bc  coexistence depends on the size of refuges, R. High predator and wild-prey density can be achieved only under plentiful refuges; which necessarily also lead to low density of livestock

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ACCEPTED MANUSCRIPT (because carrying capacity is split between the two types). Consistent with the coexistence conditions, these stability conditions are also likely to be met in high-productive habitats.

4.4. Conservation implications

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In this model, humans can intervene to alter prey-predator encounters. But, for simplicity,

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livestock and wild prey are considered to be sufficiently similar in their life-history traits (e.g.,

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sheep/bharal in Himalayas, or zebu cattle/wildebeest in Africa, etc.). It contains a number of parameters that are ecologically meaningful. But, these parameters, or traits (R, D, b and c), may

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be difficult to manipulate in free-ranging animals in order to meet the coexistence and/or stability

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criteria. Perhaps, forage competition (β) can be manipulated, and competitive effects of livestock on wild prey can be reduced via measures such as stall-feeding. But, this can inflate their

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populations, and have indirect effects on carrying capacity (K, see section 6 below for further

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discussion). Protecting livestock alone can enable coexistence; the model also prescribes reducing livestock density which will likely compromise human livelihoods, thus undermining

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the constituency for conservation (Harihar et al., 2015; Redpath et al., 2013). In summary,

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conflict-free scenarios are possible in the prey-refuge model. But, the common practice of protecting livestock in conflict situations may actually be detrimental for predator’s survival,

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unless the carrying capacity of the habitat is high enough to accommodate refuges for the wild prey. This approach to reducing conflict may lead to favorable outcomes in productive habitats (high K). It is less likely to succeed in less productive ones (low K), because it is difficult to manipulate the parameter space determined by β, R, D, b and c. When a habitat is naturally very productive, it may be possible to prevent all attacks on livestock, and have sufficient refuges for

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ACCEPTED MANUSCRIPT wild prey, and have meaningful density of the predator. However, this model offers strong justification to strive for at least some areas that are inviolate of human use as parks and reserves.

5. Generalist/Specialist predators (Holt, 1984)

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5.1. Model structure

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Key features of human-carnivore conflict can also be captured by models for generalist versus

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specialist predators (Holt, 1984). These models revolve around alternative prey that share a common predator, and are distributed across distinct patches in space. A generalist predator will

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include both prey in its diet. But, a specialist predator includes only the most profitable prey,

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depending on model parameters. The predator (P) encounters two non-overlapping patches, with

system is:

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dW  Wf W (W )  aW PWW dt

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dPW  PW (aW bWW  DW )  IW  EW dt

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wild-prey (W) and livestock (L) where its densities are PW and PL respectively, and the model

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dPL  PL (aLbL L  DL )  I L  EL dt

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dL  Lf L ( L)  aL PL L dt

As before, the equations for L, W and P, are inter-linked, as each influences the others. Here, fW(W) and fL(L) are per-capita growth rates of wild-prey and livestock, respectively. aW and aL are rates at which predator’s searches for prey in the two patches. bi is predator’s conversion efficiency for food to new predators. DW and DL are predator’s metabolic expenditure in these

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ACCEPTED MANUSCRIPT patches. Ii and Ei are the rates of predator immigration and emigration for patch type i, respectively.

5.2. Model characteristics and assumptions

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In this model, the wild prey can grow at the rate fW(W) in absence of predation, and

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similarly fL(L) for livestock. The predator searches the habitat and encounters wild prey at the

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rate aWPW and livestock at the rate aLPL. More complex foraging patterns, e.g., Holling type-II functional responses can be considered, but are not necessary to understand the broad and

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general behavior of this system (see below). The predator converts prey (food) into new

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predators with an efficiency of bW and bL, so that its net foraging returns on wild prey is aWbWPW, and returns on livestock is aLbLPL. The predator’s movement into a W-type patch is given by IW

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and its movement away from it is given by EW; similarly it is IL and EL for the L-type patch. For

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5.3. Model interpretation

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simplicity, this model assumes that the predator does not starve while moving between patches.

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The solutions to this model can be examined under conditions of specialist versus generalist predation. All predators should be found in the patch with greater net foraging returns;

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if the net foraging returns are equal between patches, then the predators will follow an ideal-free distribution (Fretwell, 1972; Holt, 1984). It is known, that if the predator is initially specialized on wild prey in patch type W, it should expand its diet to kill livestock in patch type L, only if KL 

aW bW * W ; where W* is the equilibrial density of wild prey, and KL is the carrying capacity aL bL

of L determined by fL(L) (Holt, 1984). This prediction requires optimal decision-making behavior

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ACCEPTED MANUSCRIPT on behalf of the predator. This inequality has straightforward conservation implications: livestock losses can be reduced if this condition remains unfulfilled.

5.4. Conservation implications

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Can conservation interventions strive to make livestock perpetually unprofitable for the

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predator? In this way, predators remain specialized on wild prey and do not become generalists

aW bW * W , this is possible only if one lowers livestock densities. However, as seen aLbL

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KL 

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and include livestock in their diet. From the left hand side of the inequality condition,

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previously, such measures would compromise human livelihoods. The right hand side of the inequality contains parameters related to search rate and conversion efficiency, which cannot be

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easily manipulated by conservation interventions. Once again, as seen before, predictions from

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this model may also lead to a path of antagonizing people (Redpath et al., 2013), unless the habitat is already very productive. In summary, although the predictions from

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generalist/specialist predator models are more encouraging, they may be practically difficult to

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implement in real-world scenarios. As in the prey-refuge model, this model also prescribes a reduction in livestock abundance. The perceptive reader will notice that implementing a

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nonlinear functional responses does not fundamentally alter this broad interpretation. Although equilibrial densities will change, but the model’s solution would continue to remain difficult for real-world action. This is because the parameters for search rate and metabolic conversion efficiency are difficult to manipulate for free-ranging mammals. So, while this model is biologically informative, there is limited scope to mobilize it toward conservation action.

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ACCEPTED MANUSCRIPT 6. Social-ecological models (Wilman and Wilman, 2016) 6.1. Model structure Social-ecological models include conditions where the livestock population (L) is determined by economics, while wild prey (W) and predator (P) populations are determined by species

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interactions (competition and predation). In such a scenario, the dynamics of the 3-species can be

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dW  W  L   rW 1    aWP dt K  

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represented as (adapted from Wilman and Wilman, 2016):

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dP  caWP  caLP  mP  ePL dt

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dL   p  fP  gLL dt

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As before, the these equations are coupled with one another. Here, r is the intrinsic growth rate, β

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is the effect of competition between L and W, a is rate of prey capture, c is the conversion efficiency of predators, m is metabolic requirements of predators, and e is retaliatory persecution

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by humans, p is capital value of livestock, f is resources spent on protecting livestock from

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predators and g is their maintenance costs (Wilman and Wilman, 2016).

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6.2. Model characteristics and assumptions In this model the wild prey can grow at a maximum rate or r in absence of competing livestock and the predator, but this is influenced by density dependence (i.e., logistic growth) as  W r 1  K 

  . The effect of livestock competition (β) on wild prey is captured through 

 W  L  r 1   . A predator searches the habitat at the rate a, and encounters wild prey at the rate K  

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ACCEPTED MANUSCRIPT aW and livestock at the rate aL. The predator converts prey (food) into new predators with an efficiency c, so that net return on W is caW and on L is caL. In absence of any prey, the predator population declines due to starvation at the rate –mP, and a second source of mortality in predators is persecution by people at a rate proportional to their densities, -ePL. The livestock

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population can grow at the rate p (their capital value), but this growth is reduced by two factors.

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One is the expenditure costs of pastoralists in upkeep of their herds, -gL. This may include

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aspects such as veterinary care, supplemental feeding, corral space, and other limitations due to manpower. Another cost is the additional expenditure for pastoralists to protect their herds from

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predators, -fP. This includes investment in vigilance, guarding and protection, and similar limits

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to manpower. The size of the livestock population is set by balancing these economic considerations (Wilman and Wilman, 2016). These constraints may be more severe for

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individual pastoralists who raise a few head of livestock, than for ranchers who operate with

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large herds (Schiess-Meier et al., 2007). Interaction between livestock and wild prey is

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 W  L  represented by β as a numerator-term   . This captures scenarios of land-sharing or  K 

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forage competition, e.g., pastoralism in the Himalayas. Competition term in the denominator would represent land-sparing, or interference competition, where livestock have exclusive access

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 W  to a fraction of the habitat   , e.g., ranching in the Pampas. Readers may notice that both  K  L  scenarios are qualitatively similar (they are approximately interchangeable via a Taylor series expansion).

6.3. Model interpretation For a model showcasing the conflict scenario, the nontrivial equilibrium densities are

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ACCEPTED MANUSCRIPT  (e  ac)(aKp  fkr)  m( fr  agK )    a 2 cgK  acfr  efr  acf r W *     *    acgKr  gmr  acpr  epr  ac pr  . Here the predator kills livestock, and people P     a 2 cgK  acfr  efr  acf r * L      a 2 cKp  acfKr  fmr     a 2 cgK  acfr  efr  acf r

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retaliate by killing the predator. At this equilibrium, all three species can attain positive densities.

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But, the important question is whether this equilibrium is stable, or not. Stability of this 3-species

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equilibrium depends on a series of exceedingly stringent conditions (i.e., a large number of terms

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in Routh-Hurwitz criteria obtained from the Jacobian matrix). Thus, even if there is coexistence, it is unlikely to be stable across large regions of the parameter space. Now, conservation

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interventions can ameliorate the conflict by protecting livestock (caLP=0; fP=0) and simultaneously preventing retaliatory persecution (ePL=0). Such attempts often involve a mix of

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different interventions such as improved herding, and insurance for livestock (Gehring et al.,

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2010; Mishra et al., 2003). When successful, livestock would be protected, and people would not

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persecute predators. Under these conditions, the new nontrivial equilibrium densities are

p g



m . This condition is less stringent than those mentioned above. ac

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K

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 m ac W *    r (acgK  gm  acp)   * P   . Now, meaningful and stable equilibrium can be achieved if   a 2 cgK *   L     p g 

6.4. Conservation implications In this model, conflict-free 3-species coexistence can be achieved only if carrying capacity of the habitat is greater than a threshold level. Readers will notice that this result is qualitatively similar to the previous two models. A solution may exist in habitats that are

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ACCEPTED MANUSCRIPT sufficiently high in productivity (high K). The left hand side of the inequality concerns overall habitat quality. Since K is often determined by biophysical constraints, it may not always be possible to design interventions at sufficiently large spatial scales that can increase a habitat’s carrying capacity. Also, increasing K (e.g., fertilization) may be destabilizing (i.e., paradox of

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enrichment, Holyoak, 2000; Rip and McCann, 2011; Rosenzweig, 1971), and ultimately

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counterproductive. However, preventing declines in habitat quality due to negative impacts of

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livestock on ecosystem function is an option (Bagchi et al., 2012; Bagchi and Ritchie, 2010; Mishra et al., 2010). Otherwise, one has to evaluate the implications of the right-hand side of the

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above condition. But, many parameters here are related to life-history traits of the participant

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species (e.g., m, a, and c), and therefore, cannot be effectively altered through conservation interventions. It is hard to imagine that metabolic rate, search rate and conversion efficiency to

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be affected by management action. To design interventions over the economic parameters (p and

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g) requires lowering the capital value of livestock, and/or increasing their maintenance costs, both of which would likely undermine human livelihoods. The only remaining option is

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designing interventions around β, in order to reduce competition between livestock and wild

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prey. How does one alter the per-capita competitive effects of one species on another? One option is lease of designated livestock-free patches which are for exclusive use by wild prey

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(Mishra et al. 2003), and would require considerable investment to offset loss of grazing rights for people. Or, previous work suggests that when two species are matched in their body-sizes, they may compete less strongly than when they differ widely in their body-size (Bagchi and Ritchie, 2012; Ranjan and Bagchi, 2016). But, with greater difference in body-size, the two prey populations also begin to differ in their sensitivity to predation, and this could make stable coexistence more difficult (Holt, 1984). One can explore options where the composition of

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ACCEPTED MANUSCRIPT livestock is such that they are similar in body-size to the wild prey, rather than being much smaller/larger than the wild prey. However, the scope to implement any changes in livestock herd composition may be very limited in real-world scenarios (e.g., one cannot expect to substitute sheep with cattle, or vice-versa). In summary, while the predictions of this model are

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encouraging, similar to the previous two cases (section 4 and 5), implementing the predicted

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outcome from socio-ecological models, and translating them into effective policy interventions,

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may be practically challenging. Perceptive readers will notice that, as before, more complex models which implement nonlinear functional responses would likely change the equilibrial

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densities and also introduce new terms in the stability conditions. This additional complexity

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makes the model analytically intractable. But the difficulty in converting the model’s prediction into practical management interventions would continue to persist, without fundamentally

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altering the broad inference.

7.1. Model structure

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7. Metapopulation models (Hanski, 1997; Nee et al., 1997)

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Key aspects of human-carnivore conflict can also be captured by metapopulation models. These concern occupancy of patches by a single species, or by communities of interacting

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species. These models allow inclusion of spatial structure into ecological dynamics, and date back to Levins (1969), although the underlying philosophy appeared earlier in epidemiology (Kermack and McKendrick, 1927). The basic model for single species accounts for the fraction of occupied sites (P) and number of empty sites (1-P), using local colonization (c) and extinction (e) parameters (Hanski, 1997) as:

dP  cP(1  P)  eP . At equilibrium, the fraction of occupied dt

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ACCEPTED MANUSCRIPT e e sites are P*  1  , and the metapopulation persists regionally as long as  1. This basic model c c can be extended to include prey-predator interactions (Bascompte and Sole, 1998; Nee et al., 1997; Swihart et al., 2001), and we explore this scenario for wild prey, livestock and predators.

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First, in pristine conditions with wild prey and predators, and without livestock, let the fraction

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of empty patches be o; fraction occupied by wild prey alone be w, and the fraction occupied by

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both wild prey and predator be p. Dynamics of this system are given by:

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do  ew w  e p p  cwow dt

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dw  cwow  c p wp  ew p dt

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dp  c p wp  e p p dt

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Here, ew is wild prey extinction rate in absence of predators, ep is extinction rate of both wild prey and the predator. Likewise, cw is colonization rate of wild prey, and cp is colonization rate

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by both wild prey and predator.

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7.2. Model characteristics and assumptions

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In this model, empty patches increase when wild prey go extinct at the rate eww, as well as when wild prey and predator simultaneously go extinct at the rate epp. Colonization of a previously empty patch occurs at the rate cwow by wild prey, and the model assumes that predators do not colonize previously empty patches since there are no prey in these. Patches occupied by wild prey can decrease at the rate cpwp due to effect of predator, and at the rate ewp even without the predator. Patches used by predator increase when it colonizes a patch featuring wild prey at the rate cpwp, and is reduced due to extinctions at the rate epp.

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ACCEPTED MANUSCRIPT 7.3. Model interpretation This system reaches the following nontrivial equilibrium, which is known to be stable

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    * *   * 1  w  p o    ep  *   . At this equilibrium, there are some empty (Nee et al. 1997):  w     c p  p*       cw   e p ew    c  c 1   c  c    w   w p  p 

patches, some that are occupied by wild prey, and others that are occupied by both wild prey and

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e e  the predator. The predator and wild prey can persist, if  p  w   1 , which can be compared c   p cw 

with the previous result for single species (i.e.,

ei

c

 1 ).

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i

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Into this pristine condition, one can now introduce livestock and investigate their effects (Fig. 2). In absence of any human-wildlife conflict, livestock would occupy a fraction of the total

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patches, l, such that [1-l] patches now remain available for the wild prey and the predator. Conservation action would attempt to keep these patch-types distinct in order to prevent conflict.

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In other words, reduce the interface between the predator and livestock, similar to the prey-

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refuge model which now has spatial structure as a metapopulation. Previously, we saw (o+w+p=1), and after introduction of livestock, the available habitat for wild prey and the predator shrinks to (o+w+p)=1-l (Fig. 2). Substituting this into the previous equations, we get

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ACCEPTED MANUSCRIPT

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    * *   * (1  l )  w  p o    ep    . Under these restrictions new equilibrium densities as:  w*      cp  p*       e p ew     cw     c  c  (1  l )   c  c   p  w   p  w 

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imposed by habitat lost to accommodate the livestock, the wild prey and the predator can coexist

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e e  if  p  w   1  l . There exists a threshold level of livestock patches, up to which it is possible c   p cw 

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e e  to achieve conflict-free coexistence of wildlife and humans; given by lˆ  1   p  w  . The c   p cw 

model predicts a threshold fraction on patches that can be used to raise livestock, while the

7.4. Conservation implications

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predator subsists on wild prey in the remaining ones.

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This approach to prey-predator metapopulation effectively considers that a fraction of the

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habitat becomes unavailable to wild prey and predators, much like habitat degradation/loss (Bascompte and Sole, 1998; Nee et al., 1997; Swihart et al., 2001). More elaborate models can

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consider colonization-extinction of all the 3-species across all possible patch-types (Dos Santos and Costa, 2010; Holt, 1997), but they reach a similar qualitative conclusion. In a scenario where predators kill livestock, the conflict can be ameliorated by maintaining a prescribed fraction of the habitat available to wild prey, and allocating the rest for livestock. This effect may be most pronounced in situations where livestock outnumber wild prey by orders of magnitude (Mishra et al., 2010, 2003). However, this model does not directly provide information on size of the predator population, which is often of high relevance to managers (but see section 8, below). In

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ACCEPTED MANUSCRIPT fact, predator populations may respond positively to conservation efforts, and this may intensify the nature and severity of conflicts (Rigg et al., 2011). Importantly, this model may not preclude humans from raising meaningful densities of livestock within their designated patches (Fig. 2). In a livestock-patch, or across a collection of

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designated patches, people can strive for sustainable livestock densities, determined by the

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habitat’s carrying capacity. It can be challenging to ascertain livestock stocking rates accurately,

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as overstocking may cause habitat degradation and loss of ecosystem functions (Bagchi et al., 2012; Bagchi and Ritchie, 2010). But conservation interventions can strive to implement

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rotational grazing practices that foster ecosystem stewardship (Briske et al., 2011). In fact,

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management concerns about rotational grazing may also be effectively addressed by metapopulation models that involve population asynchrony across patches brought about through

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animal movement between habitat patches (Abrams and Ruokolainen, 2011; Wang et al., 2015).

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Dynamics of local livestock populations can be determined by resource-dependent vegetation growth and movement between patches (Abrams and Ruokolainen, 2011; Wang et al., 2015). In

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the simplest form, one can consider a 2-patch habitat used for livestock grazing (Abrams and

i are given by:

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Ruokolainen, 2011), where the population dynamics of vegetation (Vi) and livestock (Li) in patch

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dVi  Vi r  kV   f (Vi , Li ) dt

dLi  Li  f (Vi , Li )c  d   mLi g (Wij )  mL j g (W ji ) , dt i, j = 1, 2, where Wij  (Wi  W j ) from Wi  f (Vi , Li )c  d Here, r is the maximum growth rate of vegetation, and k is density dependent reduction in r, such that vegetation reaches a carrying capacity r/k in absence of livestock. For simplicity, the two

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ACCEPTED MANUSCRIPT patches are considered sufficiently similar to not warrant separate analyses of their r and k, but this restriction can be removed in more elaborate assessments (Ruokolainen et al., 2011). Forage consumption by livestock is given by the functional response f(Vi, Li). Vegetation biomass is maintained below carrying capacity in presence of herbivory by an amount governed by f(Vi, Li).

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Livestock convert vegetation (food) into new livestock with an efficiency c. Due to metabolic

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expenditure, the livestock population declines at the rate d in absence of forage. Movement

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between patches is given by m, and net movement depends on the difference in foraging returns between the two patches given by a function g(ΔWij). Here, foraging return is the net gain given

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by f(Vi, Li)c-d.

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Several interesting interpretations emerge when one considers a density-dependent saturating functional response for livestock along a gradient of vegetation biomass (i.e., Holling

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type-II). First, livestock and vegetation enter limit cycles in any patch (Abrams and Ruokolainen,

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2011). With time it becomes unsuitable to continue foraging there and seek the alternative patch. This is simply because animals can potentially consume plants are a rate faster than the rate at

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which plants can grow. One can readily notice that the same reasoning also applies to the

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predator; when it travels between patches it encounters livestock and can be persecuted in retaliation – this is the origin of the conflict (Abrams et al., 2012). Indeed, many pastoral systems

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show periodic movement of livestock between patches (Kuiper et al., 2015), and this affords further discussion on a rotational grazing policy (Briske et al., 2011). Second, with movement between patches, out-of-phase cycles in either patch reduces the variability in total livestock population size (Abrams and Ruokolainen, 2011), which aligns favorably with sustaining human livelihoods. Similar conclusions are reached even when the patches differ and have non-identical r and k (Ruokolainen et al., 2011). This branch of theory on metapopulation regulation through

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ACCEPTED MANUSCRIPT local movement is still developing (Wang et al., 2015); this can afford management options to avoid the destabilizing elements, and encourage livestock husbandry to stay within the boundaries of the parameter space that offers stable livestock populations (Abrams and Ruokolainen, 2011; Wang et al., 2015). In summary, predictions from metapopulation models

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may allow the goals of human livelihoods to remain broadly aligned with those of wildlife

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conservation. They also offer opportunities to implement accurate grazing practices (Abrams and

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Ruokolainen, 2011; Briske et al., 2011; Wang et al., 2015), as there are clear parallels between adaptive movement between habitat patches and livestock husbandry. This demonstrates that

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pragmatic management concerns about human-wildlife conflict and rotational grazing, may both

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be addressed using theoretical models (Fig. 2).

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8. Meaningful densities in metapopulations

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Coexistence without livestock-loss, of the predator, livestock and wild prey in their respective patches (above), is a necessary condition for conservation. But this alone is not sufficient. The

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problem of whether or not these patches can hold meaningful densities of the predator, still

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remains. For this, I evaluate food-web models with adaptive dispersal between patches (Cressman and Křivan, 2013). This helps address the necessary and sufficient conditions for

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conservation, through the connection between well-known models of population dynamics with dispersal (Gadgil, 1971; Hamilton and May, 1977; McPeek and Holt, 1992) and models of metapopulation dynamics between patches (seen above). The basic model for population dynamics under dispersal considers the following coupled equation for one species with population sizes xi and xj in two patches i and j (Cressman and Křivan, 2013):

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ACCEPTED MANUSCRIPT dxi  xi fi ( xi )   (dij xi  d ji x j ), for i=1 and j=2; dt where fi is per-capita growth rate in the patch i; δ denotes dispersal speed between patches, and dij is the probability of dispersing from patch i to patch j. The internal equilibrium of this model

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is known to be stable (Cressman and Křivan, 2013), and it can be extended into food-web models

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with a prey and its predator. One we include a predator (yi, i = 1, 2) into this model, the

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predator’s fitness gi (i = 1, 2) is determined the patch’s prey density (xi), as follows:

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dxi  xi fi ( xi , yi )  Dx ( x, y)[ fi ( xi , yi )  f j ( x j , y j )], dt

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dyi  yi gi ( xi )  Dy ( x, y)[ gi ( xi )  g j ( x j )], for i=1 and j=2; dt

where xi and yi are wild prey and predator density in patch i, respectively. Their dispersal rates

xi x j xi  x j

and Dy ( x, y )   y

yi y j

yi  y j

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Dx ( x, y )   x

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are Dx(x, y) and Dy(x, y). These depend on their respective dispersal speeds and population sizes, . The dynamics of this model are known to

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provide a meaningful, non-trivial, internal equilibrium xi* , x*j , yi* , y *j  , which is independent of

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dispersal rates (Cressman and Křivan, 2013). The important implication from this is that differences between dispersal rates of the prey and the predator do not lead to instability in such

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two-patch models. Hence, meaningful densities of the predator and wild prey can exist in both patches, once they are identified by the metapopulation approach (as seen above). For simplicity, we can consider linear functional response for the predator (Cressman and Křivan, 2013), f i ( xi , yi )  ai (1 

densities are xi* 

xi )  i yi , and gi ( xi )  ci i xi  mi . Now, the equilibrium Ki

mi a (c  K  mi ) , and yi*  i i i 2 i , for i = 1, 2. One can readily infer that for a ci i ci i K i

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ACCEPTED MANUSCRIPT conservation objective of meaningful predator densities, it is necessary that K i 

mi . Or, habitat ci i

quality (i.e., carrying capacity) for each patch should be above a minimal threshold level, and the patches cannot be too degraded. This inference matches the conditions we have seen previously

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in the other models (above). A solution may exist for habitats that are already very productive

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(high K). Otherwise, this re-iterates that habitat management, reversal and/or prevention of

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degradation, rotational grazing, and other interventions must be an integral part of conservation efforts. This basic interpretation of two-patch dispersal models remains unchanged even if we

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consider non-linear saturating functional response for the predator (Cressman and Křivan, 2013).

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In summary, metapopulation models prescribe the necessary conditions for livestock, wild prey and predator to coexist. Next, dispersal between a subset of patches available for wild

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prey and the predator can potentially provide the sufficient condition for conflict-free

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coexistence. Likewise, rotational grazing in the livestock-patches also allows for raising them at meaningful densities. Management of habitat quality and controlling degradation appear as key

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conservation targets under this framework. These insights are consistent with other recent

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theoretical results (Dannemann et al., 2018) which describe how predator movement allows coexistence through a balance between patch exploitation and regeneration over a wide range of

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demographic parameter values of the prey. Emerging knowledge of movement ecology promises to be applicable across diverse settings (Bagchi et al., 2017; Nathan et al., 2008), perhaps it can also inform the linkages between prey-predator theory and conservation of carnivores.

9. Ecological theory and conservation practice The results of four families of models about prey-predator interactions show the implications of ecological theory for guiding conservation practice. The four families of models were evaluated

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ACCEPTED MANUSCRIPT against equilibrium densities, and the stability of the equilibrium. This two-step approach is necessary because knowledge of population densities is insufficient to evaluate conservation success. For example, increase in wild prey abundance can coincide with strengthening of conflict with predators (Stahl et al., 2002; Suryawanshi et al., 2017). So, it is important to know

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whether the equilibrial solutions from each model are stable, or not. The insights from each

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model could be arranged along two conceptual axes, one for species coexistence, and another for

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stability. Encouragingly, all four models show that conservation targets can be achieved via their respective stabilizing elements. The models also show that reducing livestock-loss is more likely

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in habitats that are already highly productive, compared to unproductive ones. Solutions to the

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conflict by protecting livestock alone (i.e., prey-refuge), or through generalist/specialist predation, or socio-ecological models are theoretically plausible, but are difficult to translate into

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management actions. Conditions for coexistence and stability are more likely to be

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simultaneously satisfied in productive habitats. Metapopulation models appear to be better equipped of the four families of models, at least qualitatively, to circumvent the constraints

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attached with habitat productivity. But, they need to be coupled with knowledge of movement

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and dispersal (Cressman and Křivan, 2013; Dannemann et al., 2018; Wang et al., 2015). This enables the meta-population approach to circumvent the constraints imposed by habitat

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productivity, and become more broadly applicable than the other three approaches reviewed here. They can be applied towards two pragmatic concerns: human-wildlife conflict and grazingmanagement. Better integration of knowledge about animal movement into the meta-population approach can offer insights into the necessary as well as sufficient conditions for conflict-free coexistence between livestock, wild prey, and predators. Further, metapopulation models concern parameters that most land managers are already likely familiar with – habitat patchiness,

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ACCEPTED MANUSCRIPT carrying capacity, animal movement, etc. (Fig. 2), This familiarity may be advantageous for communicating theoretical principles to managers, and visualizing concepts and predictions (Jacobson, 2009). One can see that impacts of large carnivores on livestock can be managed in the realm of

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calculus and algebra. But, how realistic are these scenarios for a practitioner? The final, and

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crucial, step is to assess whether real-world efforts can implement strategies that are informed by

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these models – without this, the existing gap between theory and practice is not bridged. Quantitative tests of these model predictions will be difficult to achieve, but one can use

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qualitative guidelines. I am not aware of any existing real-world conservation efforts that can,

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sensu stricto, serve as case studies or field-tests of these models (reviewed by Eklund et al., 2017). However, one attempt to reduce livestock damage by snow leopards in the Himalayas

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(Bagchi and Mishra, 2006; Mishra et al., 2010, 2003), does seem to capture many essential

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features of the metapopulation model. Here, livestock outnumber wild prey and the snow leopard is heavily dependent on livestock. From the late 1990s and early 2000s, conservation

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interventions created livestock-free patches (strategically identified valleys, and watersheds in

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the mountainous landscape) which were expected to help recovery of the wild prey, and reduce impact of snow leopard on livestock (basic mathematical analyses provided in Mishra et al.,

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2010). This essentially creates designated patches for the wild prey and livestock – a key feature of the metapopulation models. Over the next decade, population-level changes do seem to qualitatively match the expected outcomes and general reduction of livestock losses (Mishra et al., 2016), without causing declines in the predator population (Sharma et al., 2015). Better integration of theory with conservation practice (Doak and Mills, 1994; Driscoll and Lindenmayer, 2012) can help refine management options and anticipate their outcomes.

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ACCEPTED MANUSCRIPT Acknowledgements This work was supported by grants from MHRD-India, DST, MoEFCC, and DBT-IISc. Discussions with Mark E. Ritchie, Lasse Ruokolainen, and Navinder J. Singh helped in preparing the manuscript. Onam Bisht helped in preparing Fig. 1, and many colleagues helped in

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preparing Fig. 2. I am grateful to the editors, and the referees.

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References

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Abrams, P.A., Ruokolainen, L., 2011. How does adaptive consumer movement affect population dynamics in consumer-resource metacommunities with homogeneous patches? J. Theor. Biol. 277, 99–110. Abrams, P.A., Ruokolainen, L., Schuter, B.J., McCann, K.S., 2012. Harvesting creates ecological traps: consequences of invisible mortality riskes in predator-prey metacommunities. Ecology 93, 281– 293. Adler, P.B., Smull, D., Beard, K.H., Choi, R.T., Furniss, T., Kulmatiski, A., Meiners, J.M., Tredennick, A.T., Veblen, K.E., 2018. Competition and coexistence in plant communities: intraspecific competition is stronger than interspecific competition. Ecol. Lett. 21, 1319–1329. https://doi.org/10.1111/ele.13098 Aryal, A., Brunton, D., Ji, W., Barraclough, R.K., Raubenheimer, D., 2014. Human–carnivore conflict: ecological and economical sustainability of predation on livestock by snow leopard and other carnivores in the Himalaya. Sustain. Sci. 9, 321–329. https://doi.org/10.1007/s11625-014-02468 Bagchi, S., 2017. Research opportunities for undergraduates. Curr. Sci. 112, 1797. Bagchi, S., Bhatnagar, Y.V., Ritchie, M.E., 2012. Comparing the effects of livestock and native herbivores on plant production and vegetation composition in the Trans-Himalayas. Pastor. Res. Policy Pract. 2, 21. Bagchi, S., Mishra, C., 2006. Living with large carnivores: predation on livestock by the snow leopard (Uncia uncia). J. Zool. 268, 217–224. Bagchi, S., Ritchie, M.E., 2012. Body size and species coexistence in consumer-resource interactions: A comparison of two alternative theoretical frameworks. Theor. Ecol. 5, 141–151. Bagchi, S., Ritchie, M.E., 2010. Introduced grazers can restrict potential soil carbon sequestration through impacts on plant community composition. Ecol. Lett. 13, 959–968. https://doi.org/10.1111/j.1461-0248.2010.01486.x Bagchi, S., Singh, N.J., Briske, D.D., Bestelmeyer, B.T., McClaran, M.P., Murthy, K., 2017. Quantifying long-term plant community dynamics with movement models: implications for ecological resilience. Ecol. Appl. 27, 1514–1528. https://doi.org/10.1002/eap.1544 Bascompte, J., Sole, R.V., 1998. Effect of habitat destruction in a prey-predator metapopulation model. J. Theor. Biol. 195, 383–393. Brassil, C.E., 2012. Stability Analysis, in: Hastings, A., Gross, L. (Eds.), Encyclopedia of Theoretical Ecology. University of California Press, Berkeley and Los Angeles, pp. 680–685.

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ACCEPTED MANUSCRIPT Table 1. Description of four families of ecological models, their characteristics, and the conservation implications of their predictions.

Conservation interventions can strive to avoid the threshold condition where it becomes profitable for the predator to become a generalist. But, this will not support high density of predators and of livestock, simultaneously. These models Retaliatory Conservation consider coupled persecution interventions can human-and-natural of predators create conditions ecosystems. Here, by herders, where the predator economic factors in response can subsist on wild influence the size of to attacks on prey, without livestock population. livestock causing conflict. Species interactions offer Further, it possible determine the size of opportunities to support the wild-prey and to evaluate meaningful predator. this model. densities of all Conservation three species. But

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Conservation implication Vigilant Protecting herders livestock from and/or guard predators is not a dogs can very suitable thwart solution to the predator conflict. This will attacks, and not support high create density of conditions to predators and of evaluate this livestock, model. simultaneously.

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Model characteristics These models depict dynamics of one predator and two alternative prey (wild-prey and livestock). Conservation implications revolve around strategies that protect livestock from predators, i.e., immunity or refugia. These models also consider one predator and two alternative prey. An otherwise specialist predator that hunts only wild-prey will include livestock in its diet, based on relative abundance of the two prey types.

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Difference in profitability between wild prey and livestock, can create conditions to evaluate this model.

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These models concern patch dynamics for one predator and two prey types. Conservation scenarios relate to situations where predators can be sustained on patches occupied by wildprey alone, without visiting livestock patches.

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Hanski (1997), Nee et al. (1997)

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Metapopulations

the scope for designing interventions on the target parameters may be fairly limited in real-world scenarios. When wild Predicts a fraction prey and of patches can be livestock occupied by occur in livestock. Predator spatially and wild prey exist segregated in the remaining patches, then patches. It is it creates possible to support conditions to meaningful evaluate this densities of all model. three species. Stocking densities in the livestock patches can be calculated using a rotational grazing policy.

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scenarios concern three-species coexistence without any livestock loss.

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ACCEPTED MANUSCRIPT Fig. 1. Summary of conservation status of terrestrial species in order Carnivora (data from IUCN Redlist, www.iucnredlist.org, accessed 1st Jan 2016). Conservation status across families of terrestrial carnivores in (a), and population trends in (b). Conservation status across body size (at 20-kg intervals) in (c), and population trends in (d). Abbreviations: CR, critically endangered,

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DD; data deficient; EN, endangered; EX, extinct; LC, least concern; NT, near threatened; VU,

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vulnerable. Carnivore families: AIL, Ailuridae (red panda); CAN, Canidae (dogs); EUP,

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Eupleridae (fossas); FEL, Felidae (cats); HER, Herpestidae (mongooses); HYA, Hyaenidae (hyenas); MEP, Mephitidae (skunks); MUS, Mustelidae (weasels); NAN, Nandiniidae (African

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ACCEPTED MANUSCRIPT Fig. 2. Schematic representation of the metapopulation model with occupied and empty patches for livestock (ovals), and wild prey and predator (squares). The model prescribes the maximum number of patches that can be allocated for livestock, which are kept distinct from the other patches (dashed line). Occupancy of wild prey and the predator of their respective patches

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(dotted arrows) is governed by inherent extinction-colonization dynamics (ei and ci). But,

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ACCEPTED MANUSCRIPT CONFLICT OF INTEREST: I declare no conflict of interest. -Sumanta Bagchi

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ORCID ID 0000-0002-4841-6748

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