Wolves contribute to disease control in a multi-host system

We combine model results with field data for a system of wolves (Canis lupus) that prey on wild boar (Sus scrofa), a wildlife reservoir of tuberculosis, to examine how predation may contribute to disease control in multi-host systems. Results show that predation can lead to a marked reduction in the prevalence of infection without leading to a reduction in host population density since mortality due to predation can be compensated by a reduction in disease induced mortality. A key finding therefore is that a population that harbours a virulent infection can be regulated at a similar density by disease at high prevalence or by predation at low prevalence. Predators may therefore provide a key ecosystem service which should be recognised when considering human-carnivore conflicts and the conservation and re-establishment of carnivore populations.

This parameter limits the total population to the carrying capacity K in the populated disease-free steady state, and is derived from steady-state analysis of the model without infection. Units: density −1 .
The rate that piglets mature to yearlings and yearlings mature to adults. These rates assume that it takes on average 1 year to enter the next age class. Units: year −1 .
The natural death rate of all classes which implies an average life expectancy of 7 years. Units: year −1 . c = 0.3 The continuous culling rate effective on all yearlings and adults, set to achieve a total hunting bag of approximately 20% of the wild boar population in Asturias. Units: year −1 .
β DA = 1.06 The rate that adults are infected by direct contact frequency dependent transmission fitted to give prevalence levels observed in the wild boar TB system in Asturias. Units: year −1 .
β DP = β DY = c β β DA The direct contact frequency dependent infection rate for piglets and yearlings. We assume that c β = 3 and so disease transmission to piglets and yearlings is three times that of the adult rate. Units: year −1 .
β FA = 20 K The rate that adults are infected by contact through environmental infection fitted to give prevalence levels observed in the wild boar TB system in Asturias. Units: density −1 × year −1 β FP = β FY = c β β FA The environmental infection rate for piglets and yearlings. We assume that c β = 3 and so disease transmission to piglets and yearlings is three times that of the adult rate. Units: density −1 × year −1 . ω = 0.1 (Asturias); 1 (high prevalence regions) This parameter scales the level of environmental transmission. Environmental transmission typically occurs at shared water holes and it therefore high when water resources are scarce. In Asturias ω = 0.1 to reflect plentiful resources. In high prevalence regions (such as central and southern Spain) resources are scarce and ω = 1. Units: scalar.
This is the rate that infectious adults become generalised. This assumes that it takes on average 18 months for an infected adult to progress to the generalised class. Units: year −1 .
The rate that infected piglets and yearlings become generalised. In the Asturias model these are set to the same value as that for adults (c ε = 1). For high prevalence regions c ε = 3 assuming that it takes on average 6 months for an infected piglet or yearling to progress to the generalised class. This value is 3 times that of adults, and recognises the fact that in high prevalence regions that typically have scarce resources the body condition of wild boar is generally poor and co-infections are common. It is acknowledged that the stress of co-infections can shorten the length of time to progress to generalised 3 . Units: year −1 .
α = 1 This is the additional disease induced death rate of the generalised class and assumes that on average individuals spend 1 year in the generalised class before death. Units: year −1 .
The rate of shedding of infectious particles by generalised classes. We normalise this value to 1. This is valid as we have explored a range of values for β P , β Y and β A which scale with the size of λ and the density of free-particles, F.
Units: year −1 . µ = 6 This is the decay rate for free-living particles, indicating that they have an average life expectancy of 2 months. Units: year −1 .
a P = a PG = a Y G = a AG = 0.00099 The successful predation rates for wolves on susceptible and infected piglets, generalised piglets, generalised yearlings and generalised adults respectively following Nores et al.

Asturias: prey selection
Figures S3 and S4 represent the same scenario as in main paper Figure 2 for the period 2000-2014 except for changes to the classes of wild boar that wolves prey on. In both these cases wolf predation, measured as the number of wild boar taken per year per wolf, is adjusted to be similar over the first 10 years to that of main paper Figure 2. This results in using the same predation rate when only piglet predation occurs, and a halved predation rate for indiscriminate predation. Figure S3 shows that when wolves prey indiscriminately, infected prevalence is reduced but not as quickly as in main paper Figure 2 for the period 2000-2014. However, as now there is also predation on adult and yearling wild boar, there is less reproduction and therefore a reduction in the overall population density and the number of susceptibles available for infection. This results in a 40% decrease in the level of the pathogen in the environment, and also reduced wild boar density. Figure S4 shows that when wolves only prey on piglets, infection is not reduced as quickly as for predation on piglets and generalised individuals (main paper Figure 2) such that the number of generalised wild boar in the population and hence the level of free living pathogen is not significantly reduced. The wild boar density rises, but the disease prevalence is not reduced significantly.