1. Indirect interactions are widespread among prey species that share a common predator, but the underlying mechanisms driving these interactions are often unclear, and our ability to predict their outcome is limited.
2. Changes in behavioural traits that impact predator space use could be a key proximal mechanism mediating indirect interactions, but there is little empirical evidence of the causes and consequences of such behavioural-numerical response in multi-species systems. 
3. Here, we investigate the complex ecological relationships between seven prey species sharing a common predator. We used a path analysis approach on a comprehensive 9-year dataset simultaneously tracking predator space use, prey densities, and prey mortality rate on key species of a simplified Arctic food-web. 
4. We show that high availability of a clumped and spatially predictable prey (goose eggs) leads to a two-fold reduction in predator (arctic fox) home range size, which increases local predator density and strongly decreases nest survival of an incidental prey (American golden plover). On the other hand, a scattered cyclic prey with potentially lower spatial predictability (lemming) had a weaker effect on fox space use and an overall positive impact on the survival of incidental prey.
5. These contrasting effects underline the importance of studying behavioural responses of predators in multi-prey systems and to explicitly integrate behavioural-numerical responses in multi-species predator-prey models.

The data set contains two sheets of data collected from 2008 to 2016 in the southwest plain of Bylot Island (72°530N, 79°540W), in Sirmilik National Park, Nunavut, Canada. 

Fox home range data. The first data sheet contains home range size of individual foxes estimated from Argos relocation data, the sex and breeding status of the fox, and the availability of lemmings and goose eggs. Raw Argos relocation data are available on Movebank (doi: 10.5441/001/1.3gg33bd4).

To quantify fox’s annual home range (95% isopleth), we used autocorrelated kernel density estimation implemented in the ctmm R package. This approach accounts for location accuracy and provides a reliable measure of the estimation error associated to each home range contour. We estimated fox annual home ranges using locations collected between 01 May and 30 October, to maximise data between the onset of goose laying and the end of the ice-free season. We used filtered Argos locations as available in the Movebank data repository (doi: 10.5441/001/1.3gg33bd4), and only kept the most precise positions with location classes LC3 and LC2, which correspond to positioning errors having a 68% probability of being < 250 m and < 500 m. We then made scatter plots of the relocation data and calculated empirical variograms to identify and remove obvious extraterritorial trips and to ensure that all foxes included in the analyses showed range residency. An appropriate home range model was selected for each individual using Akaike information criterion (AIC_c) to compare different movement processes (independent identically distributed, Ornstein-Uhlenbeck, integrated Ornstein-Uhlenbeck, Ornstein-Uhlenbeck Foraging). We estimated the area of the 95% home range contour for each individual-year based on the selected models and extracted the variance of each home range area to account for estimate uncertainty in subsequent analyses.

Home ranges were then classified based on the availability of goose eggs and lemming. Using the goose colony contour traced with a GPS receiver aboard a helicopter, we classified each fox home range into one of three classes of goose availability: 1) centroid of home range inside the goose colony – full access, 2) centroid outside of the colony but home range overlaps the colony – partial access, 3) centroid outside of the goose colony and no overlap – no access. Based on mark-recapture estimates of annual lemming density, we classified each annual fox home range into one of two classes of lemming density, that is low (<14.2 lemming/km²) or high (>235.2 lemmings/km²).

Incidental prey nest survival data. The second data sheet contains nest survival of fox incidental prey species (American golden plovers, sandpipers, and Lapland longspurs) monitored within fox home ranges, the id of the fox home range, and the number of days nests were monitored. Nest monitoring was conducted as follows:

Shorebird and passerine nests were monitored each year from mid-June to mid-July. Nests were found opportunistically or through line transect surveys conducted within fox home ranges across the study area, both inside and outside of the goose colony. Lay date and expected hatch date were calculated for nests found during laying, or estimated using the flotation method for nests found during incubation. Nest status was assessed every 2–6 days, increasing monitoring efforts when nearing the expected hatch date. A nest was considered successful if at least one egg hatched, or if one of the following criteria was met: 1) small fragments of residual egg shells were found in the nest material close to the expected hatch date, 2) the nest was hatching (starred or pipped) on the last visit and was empty on the following visit, 3) the nest was empty on the last visit and the banded adult was resighted with chicks.