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Wolf Depredations. Sandy Weisberg University of Minnesota School of Statistics March 14 2008. Wolves. “Wolves stir people’s emotions and attract public attention far out of proportion to their numbers.” Naughton-Treves, Groosberg and Treves (2003), Conservation Biology 1500-1511. Wolves.
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Wolf Depredations Sandy Weisberg University of Minnesota School of Statistics March 14 2008
Wolves “Wolves stir people’s emotions and attract public attention far out of proportion to their numbers.” Naughton-Treves, Groosberg and Treves (2003), Conservation Biology 1500-1511
Wolf politics • Pro wolf: Young-to-middle aged, college-educated, affluent, urban, women • Hostile to wolves: Farmers and ranchers who must live with wolves. • Ecologists? Naughton-Treves, Groosberg and Treves (2003), Conservation Biology 1500-1511.
Wolf Management • 1849 to 1965: State managed a bounty program on wolves in Minnesota. • Depredation, or killing of livestock, was one of the reasons cited to justify this program. • During 1960s, about 190 wolves per year were killed, at $35 each. http://www.npwrc.usgs.gov/resource/mammals/minnwolf/history.htm
Wolf Management • 1967: Remaining wolves in lower 48 states mostly in Minnesota. Wolves classified as endangered, but not protected. • 1970: Wolves were protected in the Superior National Forest in Minnesota, and 1974 generally protected; wolves could be killed only if threatening humans. • Wolf control was a Federal responsibility
1978 status changed to threatened, allowed killing of wolves. • Depredation reported by farmer and verified by Minn DNR, or Federal Fish and Wildlife. • Farmer compensated for loss by state. • Trapping by Feds for up to 15 days within 0.8 km of site. Captured adults, and some pups, euthanized. Costs about $1M/year. • Trapping was not always done.
Source: MN DNR Source: MN DNR
Jan 14, 2009: Wolves delisted (again) • States are to be responsible for wolf management in Great Lakes Region. • How should wolf/human, wolf/livestock, and wolf/pet interactions be managed? • MN DNR planning documents modify Fed regulations in detail but not in general. http://www.fws.gov/Midwest/wolf/state-plans/index.htm
How should the State decide what to do about wolf depredations? • Introspection • Casual observation • Biology (plus simulation) • Let the courts decide • Politics • Data assisted decisions
Wisconsin data, October 2001 80 Bear hunters Livestock prod. 40 General pop. Seen Kills hound Kills pet Kills livestock 0 Naughton-Treves, Groosberg and Treves (2003), Conservation Biology 1500-1511
Data-assisted decisions • Experiments? • Quasi-experiments? • Observational studies • Harper, E., Paul, W., Mech, D., and Weisberg, S. (2008). Effectiveness of lethal, directed wolf-depredation control in Minnesota. Journal of Wildlife Management, 72, 778-84.
923 depredations 1440 wolves killed
Top 10 farms had 18% of depredations Poisson (black): 90 farms with zero Negative binomial: 775 farms with zero
Available data • Records of FWS on every reported depredation: Too much data • Not rectangular • Qualitative and quantitative • No obvious ‘treatment’ to study • No data on farms not effected
Available data • Farm characteristics: location, type, size, previous history, local conditions, management characteristics, … • Incident characteristics: Month and year, type of prey, distance to buildings,… • Trapping characteristics: was trapping done? What happened? Counts by sex, maturity, and so on. • What is the response?
Time to next depredation • Seasonal effects and year effectsas covariates • What physical scale? This farm? Within k km? Physical barriers (e.g., a river)? • Time scale: This year? Two years? When does a year start and end?
Comparison groups • No trapping done: why? (about 38 incidents) • Trapping was done, but no wolves were captured (360 incidents) • Trapping was successful; group by number of wolves killed (1 to 16)? (525 incidents)
Kaplan-Meier estimate • No trapping is very different, p < .001 • Similar for other radius, other Censoring time
Influence Analysis • In (at least) 4 cases, redepredation time was so short that trapping could not start. • In each case, trapping started shortly after the second incident. • These four very short redepredation times were classified as “No trapping” • Is this reasonable?
Proportional Hazards Models • Time of year covariates using sin(month/12) and cos(month/12) • Time period (early vs. late, or continuous) • Trapping vs. no trapping • Prey species • If trapping, indicators for breeding males, breeding females, nonbreeding males, nonbreeding females.
coxph in R m0 <- coxph(Surv(days, censored) ~ sin(month/12)+cos(month/12)+Species+ was.trapping+NumKilled)
The results • Modest seasonal adjustment. • Redepredation time varies according to prey species: sheep and turkey farms have higher hazard than cattle farms. • Trapping decreases hazard at 0 km, Dec. 31, but not for 0 km Oct. 31. • Removing breeding males apparently beneficial at 0 km with end = Oct. 31. • No interpretable effects at 8 km scale.
Four groups: p = 0.01 Breeding vs rest p=0.03
What does this mean? • Why is time to redepredation the “right” response? Or is it? • Implications for use of trapping to lessen depredation. • Can trapping be justified for other reasons? (Management, retribution?)
“…[W]e often do not know which is the best of several possible policies and, worse yet, that we may not know if any of them betters what we are now doing.” ---J. Gilbert, R. J. Light and Frederick Mosteller