Carrion ecology modelling for vulture conservation: are vulture restaurants needed to sustain the densest breeding population of the African white‐backed vulture?

As obligate scavengers, vultures are entirely dependent on carrion resources. In this study, we model the carrion ecology of an ecosystem in Swaziland which is home to the densest breeding population of the African white‐backed vulture Gyps africanus. We collected data on life‐history parameters of the avian scavenging guild of the area as well as the potential food available from the ungulate fauna. Using novel Population Dynamics P‐Systems, we show that carrion provided by wild ungulates biomass is currently enough to sustain this vulture species. However, in light of the forecasted population increases, food will become a limiting factor. We discuss the significance of mass closure of supplementary feeding stations in Swaziland which now forces these birds to forage farther afield endangering them to poisoning events. We put these results in the context of biomass management and suggest conservation actions to secure the viability of vulture populations and the important ecosystem services they provide.


Introduction
Carrion ecology examines the link between the organic material provided by animal carcasses and ecosystem functioning (Barton et al., 2013). Carcasses are an ephemeral resource and among members of the scavenger community, avian scavengers are probably the group with the most evident adaptive traits to utilize it (DeVault, Rhodes & Shivik, 2003;Wilson & Wolkovich, 2011). Indeed, the Gyps vultures are entirely dependent on dead animal biomass (Mundy et al., 1992). Given the patchiness of carrion, vultures are under selection pressures to be as energetically conservative as possible in order to exploit such an unpredictable food (Ruxton & Houston, 2002, 2004. In sub-Saharan Africa, alongside poisoning, food reduction and habitat loss are the key threats to the avian scavenging guild . Thus, the practice of providing supplementary resources is a common conserva-tion tool (Piper, Boshoff & Scott, 1999;Piper, 2005). As these 'vulture restaurants' or 'feeding stations' can make carrion more predictable in space and time (Oro et al., 2008), there are implications for the ecosystem services and foraging behaviour of the species affected (Deygout et al., 2010;Margalida et al., 2013;Monsarrat et al., 2013). Although these issues have important management and conservation implications, studies focused on the effects of food shortage on vulture species have not been documented until recent times (Piper, 2005;Camiña & Montelío, 2006;Zuberogoitia et al., 2010).
The African white-backed vulture (AWBV) population of Swaziland is an interesting case study for examining the effect of potential fluctuating food availability given that, at an estimated 300 pairs, it represents the densest nesting population of the birds in the world (Monadjem & Garcelon, 2005). Historical data show that this AWBV population has increased during the latter part of the 20th  . In one conservation area (Mkhaya), the species founded a nesting population in the 1980s which grew to 15 pairs in the late 1990s . Supplementary feeding sites have also been established in the country, but of seven vulture restaurants that were operational in Swaziland at the turn of the century only one is currently operational. These sites would have provided the vultures with a significant proportion (40%) of their annual food requirements (Monadjem, 2003). This represents an apparent paradox because the population of vultures has not declined in the face of this reduction in available food (Monadjem & Garcelon, 2005). Thus, we hypothesized that there are enough carcasses from wild fauna to sustain the AWBV population of Swaziland. Our aim was to determine the energy balance for these birds and use this information to inform conservation measures.
In order to address this question, we needed to determine where the birds forage, how much carrion they require and how much naturally occurring food is available to them. To achieve this, we assessed the potential foraging movements of the AWBV population, estimated food availability for the population in Swaziland and modelled whether current trophic resources are theoretically sufficient to maintain their population.

Study area and species
The Hlane-Mlawula-Mbuluzi reserve network in Swaziland contains the majority (at least 202 nests) of the country's AWBV breeding population (Monadjem & Garcelon, 2005) (Fig. 1). Located in the east of Swaziland, the area is characterized as lowveld savanna (Acocks, 1988) with Acacia providing suitable nesting trees for the vultures present (Monadjem & Garcelon, 2005). The rest of the nesting birds are known from other non-contiguous conservation areas (c. 12 nests at Mkhaya) and protected cattle ranches (19 nests at the Big Bend Conservancy and six at Inyoni nyoni Yami Swaziland Irrigation Scheme) (Monadjem & Garcelon, 2005). AWBVs appear to actively avoid unprotected government ranches in the country, but their reason for doing so is unclear (Monadjem & Garcelon, 2005). In total, Swaziland is home to six avian scavenger species (obligate and facultative) which take a considerable portion of their diet as carrion. The majority of the large ungulates in Swaziland also live in this Hlane-Mlawula-Mbuluzi reserve   (Table 1).

Model parameters for avian scavengers and ungulate carrion
We first determined the potential foraging range of the vultures to see which habitats harbouring natural fauna are available to the birds. We used an extension of the central place forager theory known as the foraging radius concept which was developed by Pennycuick (Sinclair & Norton-Griffiths, 1995). The concept states that every animal is energetically constrained in terms of the spatial range they can cover while foraging (Sinclair & Norton-Griffiths, 1995). Factors such as cost of movement, basal metabolic rate, presence of dependent young, etc., contribute to the overall cost of foraging (Ruxton & Houston, 2002). Many animals must return to a site after they forage every day (as central place foragers). The idea is especially applicable to birds during the breeding season where the origin from which they range is the nest. After foraging, the adults must return to incubate the egg, relieve their mate or feed their young. The following is a model describing the energy budget of the closely related Ruppell's vulture Gyps rueppellii which was used to estimate the foraging radius of that species (Ruxton & Houston, 2002): We employed the same model and applied values from our focal species, the AWBV, where available. Q is the energy density of the carrion (5.2 × 10 −6 J) (Ruxton & Houston, 2002), c is the bird's crop capacity (1.2 kg) (Houston & Cooper, 1975), d is the digestion rate (0.055 kg h −1 ) (Ruxton & Houston, 2002), T is the foraging cycle (48 h) and refers to the fact that the parents take turns to forage with one remaining on the nest each day (Mundy et al., 1992), k is the flight cost (2.0 J m −1 ) (Pennycuick, 1972), V is the flight speed (45 km h −1 ) (Pennycuick, 1972;Tucker, 1988) and r is the foraging radius. If values for the AWBV were not available, we used other Gyps species as a close approximation, in this case for t, the foraging time (8 h) (Xirouchakis, 2007); Ema and Emc are the adult and chick's metabolic rate respectively (24 and 42 W) (Houston, 1976;Sinclair & Norton-Griffiths, 1995). The energy requirements were calculated using hand-reared individuals but Houston (1976) argues the costs between wild and captive birds are similar owing to the low energies that are required for flight. The food requirements of individual AWBV have been described before (Houston, 1976;Mundy et al., 1992). We compiled data on both the adult and nestling energetic requirements for Swaziland using these studies and followed the same approach for the other species in the Swaziland avian scavenging guild. We also collected data on relevant life-history traits such as age at sexual maturity and longevity (see Supporting Information Table S1A-F) (Pennycuick, 1976;Mundy, 1982;Brown, 1991;Mundy et al., 1992;Monadjem et al., 2003Monadjem et al., , 2012. To determine carrion availability, we collected the most recent ungulate population data covering all of Swaziland , life-history values from the PanTHERIA database (Jones et al., 2009) and estimates of adult and infant mortality (Sinclair & Norton-Griffiths, 1995). (More details can be found in the Supporting Information -'Details of Model Assumptions'.)

Population dynamics P system model
Using this information, we developed a population dynamics P system (PDP) model (Colomer, Margalida & Pérez-Jiménez, 2013). This integrated data on food availability, food requirements and population dynamics of the avian scavenging guild and the ungulate populations of Swaziland ( Fig. 1 and Supporting Information) to determine if carcass availability could meet the demands of the AWBV population over a 20-year period [AWBVs have been recorded as living for 20 years (Flower, 1938)]. PDP models are computational methods that are analogous to the machinery of cells (Colomer et al., 2013). The analogy of a PDP system to a real ecosystem has been drawn before (Colomer et al., , 2013 and serves well to illustrate the intuition behind this relatively new method. The cells of the model correspond to the physical space of the environment. Animals (which along with things such as resources, are represented by model 'objects') will feed, reproduce, develop, etc., within an environment which is accounted for by a set of mathematical rules describing these behaviours in the model. Just as animals can move between different areas when circumstances become unfavourable (e.g. food shortages), their simulated counterparts can migrate between the different spatial environments of the model (e.g. between South Africa and Swaziland). The membranes within the cells of an environment separate out specific processes that are applied to the objects in the model (e.g. the different rules associated with different seasons) (see Supporting Information 'PDP Model Components').
The advantage of this approach is that PDP models can integrate a large volume of information and compute the output of a large number of species in parallel and in a relatively short time. In addition, PDP models have been developed and applied to similar ecosystems before (Margalida & Colomer, 2012). There are two environments in our model delimited by the foraging radius of the birds when they are on the nest as defined in our foraging radius calculations. So when the reduced foraging radius of the birds is no longer applicable, the birds are able to forage in the new environment where food is not limiting (Fig. 1). This restricts the birds to game reserves in Swaziland when they have a reduced foraging potential. A bird outside of the breeding season could range hundreds of kilometres on a single foraging trip. A year in the model was divided into four temporal periods: Period 1 = July-August, Period 2 = September-October, Period 3 = November-April and Period 4 = May-June. These periods reflected differences in food availability, foraging ranges and food requirements (this is described in Table S3 in the Supporting Information).

Foraging radius
During the period of nestling dependency, the foraging radius of the breeding vultures is estimated at 45 km (Fig. 2). If we remove the cost of provisioning the chick, it gives a value of approximately 260 km. Thus, the foraging

PDP model
According to our model, most of the biomass available to the scavengers is provided by impala Aepyceros melampus (33%), blue wildebeest Connochaetes taurinus (13%) and zebra Equus burchelli (9%) with the remaining 21 species contributing the remaining carrion (Table 1). Initially, only period 3 (from November-April) has insufficient food for the scavenging guild but eventually as the scavenger populations grow periods 1 (July-August) and 2 (September-October) see a net food deficit at year 5 and 13 respectively. Period 4 (May-June) also develops a decline, although at a shallower rate (see Fig. 3). Period 3, which never sees enough carrion to sustain the scavengers, is a time when the birds can forage outside of Swaziland. In general, the avian scavengers see an increase in their number over the 20-year run of the model (although note that stochastic effects see the single pair of Lappet-faced vultures go extinct in the system) (Fig. 4).

Discussion
The key prediction from our model is that the carrion of Swaziland is sufficient to cover the energetic requirements of the current AWBV population and most of the other scavenging avifauna (Fig. 4), but only for the time being (Fig. 3). The trend of the energy balance makes it clear that, as vulture numbers rise, food will soon become a limiting factor. There is already a predicted net deficit in energy balance for six months of the year, from November to April (Fig. 4). Fortunately, this is a period during which the birds can forage outside of Swaziland. However, this reduction in available food could force the birds to spend more time foraging outside of protected areas, increasing the risk of non-natural mortality factors, such as poisoning, with important consequences on population dynamics if adult survival is affected (Monadjem et al., 2013). The radius we obtained for the vulture foraging movements is consistent with values reported from the literature. For instance, the average movement recorded in the Serengeti was 51 km and in Kruger 34 km (Mundy et al., 1992). A more recent study of immature AWBV showed a mean distance travelled per day of 33.39 km (Phipps et al., 2013). It has been noted that, while nesting without a chick, the birds can fly over 240 km between the nest and a carcass and this is consistent with our value of 260 km (Houston & Cooper, 1975). Kruger National Park is almost 100 km from Hlane, the main site of the nesting birds, and smaller reserves such as Mawewe Cattle/Game Project are all in excess of the radius.
These findings suggest further intervention and modification of existing strategies will be required. Vulture  (Periods 1-4). The italicized text show conditionals for food availability which determine the path the birds can take. If we start at the 'Reproduction' stage, at the upper left hand side, this represents the point at which the birds have their young on the nest. They will undergo 'Natural mortality' during this period and 'Feeding'. If there is enough food during this time, they can progress to period 2; otherwise they perish and so on through the year until they reproduce again.  (Robb et al., 2008), a well-managed vulture restaurant could minimize these issues while maximizing the benefits. For instance, Monsarrat et al. (2013), in their study of Gyps fulvus, showed that 'feeding stations were particularly used when resources were scarce (summer) or when flight conditions were poor (winter), limiting long-ranging movements'. Supplementary feeding can minimize the risk of poisoning (increasing survival) that follows from species foraging outside of protected areas which has been documented in other vulture species (Oro et al., 2008). Although our model suggests that AWBVs in Swaziland will see an increase in their population for a while, the temporal food shortages identified could reduce their breeding output during this period of growth. In Europe, for example, after the outbreak of bovine spongiform encephalopathy in 2001, carcasses were destroyed in authorized plants which reduced the amount of food available to the vultures . A long-term study on bearded vultures Gypaetus barbatus showed this reduction provoked a delay in laying dates, a regressive trend in clutch size, breeding success and survival following this policy change (Margalida, Colomer & Oro, 2014).
Swaziland seems well placed to act as a habitat for a greater number of AWBVs than that of the current population. With the species on the decline globally, it is incumbent on us to secure this valuable population. By ensuring that there is no deficit of carrion at any stage of the year (Fig. 3), we would give the birds the best chance to flourish in this area. Indeed, it could act as a source population for other suitable areas in the region as its population increases.
There is another advantage to creating a long-term vulture restaurant in that it would create the opportunity to capture and tag these birds. High resolution data on the foraging behaviour of this population specifically and AWBVs in general are lacking. We know little of their ageclass structure and whether other vagrant populations visit Swaziland without nesting in the county . Tracking data would improve our knowledge about these issues allowing managers and policymakers to adopt more objective decisions based on the evidence.
The value of theoretical modelling, such as the PDP P systems, is also underscored by the results generated in this study and others like it Margalida & Colomer, 2012). We should note that any model is only as good as the data used to parameterize it. Consequently, basic and up to date biological data are of utmost importance if we are to derive accurate predictions. These methods are another tool for stakeholders to use in identifying threats and solutions to conserving the target species. The conservation implications obtained with this theoretical approach is that the carrying capacity of AWBV in Swaziland is reaching maximum values according to natural food provided by the ecosystem. The dependence of the birds on food resources provided by neighbouring areas shows the importance of international agreements for conservation and the coordination of management actions (Lambertucci et al., 2014). The establishment of wellmanaged vulture restaurants in Swaziland should be seriously considered.

Supporting information
Additional Supporting Information may be found in the online version of this article at the publisher's web-site: Table S1. A, B, C, D, E and F. Parameter values used in the model Table S2. Parameters and definitions used in the model. Table S3. A summary of the changes in ungulate mortality, vulture food requirements and foraging radius throughout the year and according to the periods considered.