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Data from: Hyperbolic discounting underpins response curves of mammalian avoidance behaviour

Cite this dataset

Patten, Michael (2024). Data from: Hyperbolic discounting underpins response curves of mammalian avoidance behaviour [Dataset]. Dryad.


As humans clear natural habitat they are brought into increased conflict with wild animals. Some conflict is direct (e.g., elevated exposure of people to predators), some indirect (e.g., abandoning suitable habitat because of human activity). The magnitude of avoidance is expected to track frequency of human activity, but the type of response is an open question. We postulated that animals do not respond passively to increased disturbance, nor does response follow a power law; instead, their ability to estimate magnitude leads to ‘discounting’ behaviour, as in classic time-to-reward economic models in which individuals discount larger value (or risk) in more distant time. We used a ten-year camera dataset from southern California to characterise response curves of seven mammal species. Bayesian regressions of two non-discounting models (exponential and inverse polynomial) and two discounting models (hyperbolic and harmonic) revealed that the latter better fit response curves. The Arps equation, from petroleum extraction modelling, was used to estimate a discount exponent, a taxon-specific ‘sensitivity’ to humans, yielding a general model across species. Although discounting can mean mammal activity recovers rapidly after disturbance, increased recreational pressure on reserves limits recovery potential, highlighting a need to strike a balance between animal conservation and human use.

README: Hyperbolic discounting underpins response curves of mammalian avoidance behaviour

DATA FILES - hyperbolic discounting

  1. response curves Data used to fit exponential, inverse polynomial, hyberbolic, and harmonic curves. The response variable was the proportion of camera trap records for a given number of humans. As such, the 'disturbance' column is days with 0, 1, 2, 3 . . . hikers, vehicles, cyclists, or equestrians. Data columns are aggregate counts (2007-2016) for mammal species for given disturbance level, both across all mammals ('mammals') and for individual species with good sample size. The 'mammals' column includes a few other species whose incidence was too few to analyse separately.
  2. wilderness access days Camera trap records before (-), during (0), and after (+) a 'wilderness access day', sporadic events during which otherwise strictly protected (i.e., 'off limits') areas of the park. 'Camera'is an abbreviation for the specific camera, but this field was not used in analyses; instead, data were aggregated across the several cameras.
  3. time series Data (2007-2016) used for a time-series analysis. Time steps were quarters, which are coded as numeric month---3 = March, 6 = June, 9 = September, and 12 = December, which accords with the 1st, 2nd, 3rd, and 4th quarter 'steps' through the data from year to year. 'Camera days'is a measure of effort: it is the aggregate number of days cameras (up to 50) were active for a given quarter. 'Disturbance', 'mammals', and individual species are defined as above.


Over fifty camera traps (Cuddeback Expert 3300 or HCO Scoutguard SG-565F) were placed in a complex of urban-adjacent parks with restricted public access in central and coastal Orange County, California [Patten & Burger 2018,Patten et al. 2019]. Cameras were placed inconspicuously (to minimize either spooking animals or drawing unwanted human attention) along trails (62%), at watering troughs (12%), or in vegetation away from either putative ‘concentration point’ (26%). Herein we analyse same-day data collected by 50 cameras June 2007–June 2016. We defined a ‘day’ as human activity < 24 h prior to mammal detection [Patten et al. 2019]. 


California Department of Fish and Wildlife, Award: P1482109