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Appendix S1: Do pellet transects mirror changes in moose populations estimated from
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aerial surveys in the study area?
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This figure shows data from stratified random block aerial surveys (red circles), and aerial
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surveys based on a subset (open squares) of the SRB survey. The subset was flown due to
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financial constraints but acted as calf and adult composition surveys. The pellet transect
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abundance value was set to the 2003 population estimate from the aerial surveys, and relative
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change was plotted. It seems the relative change indexed by pellet surveys mirrors the change
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shown by both the complete and subset SRB surveys. Error bars in all cases are 90% CIs. Error
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bars for the SRB surveys include sampling variance and variance from sightability correction
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factors based on Quayle (2001). Additional details are provided in Serrouya et al. (2011).
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Quayle, J.F., MacHutchon, A.G. & Jury, D.N. (2001) Modeling moose sightability in southcentral British Columbia. Alces, 37, 43-54.
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Appendix S2: Linking moose abundance to catch per unit effort data.
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In the treatment area, the correlation between hunter success (CPUE) and census population size
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is 0.91. These data were collected annually in the treatment area from 2003 – 2010. The moose
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population estimate was based on methods outlined in Serrouya et al. 2011, and % hunter
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success was estimated from hunter questionnaires (BC Ministry of Environment data files).
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Appendix S3: R code for the difference equations
rm(list=ls(all=T))
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year <- c(seq(2003,2012,1))
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obs <- c(1650.0,1632.4,1223.0,1122.9,806.0,681.8,448.7,577.0,483.8,466.3)
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N <- 1650 #Initial moose population
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km2 <- 1100 #winter study area size
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#####Parameters
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a <- 0.016160309 # use 0.004098 for a Type I Functional response; Messier (1994) data.
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th <- 0.112271518 # use 0 for a Type I Functional response; Messier 1994 data.
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preg <- 0.897 #proportion pregnant based on captured moose
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AF <- c(0.48,0.48,0.48,0.57,0.48,0.48,0.48,0.48,0.48) #proportion adult females in the
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population
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Ndh <- c(164,250,128.2,46,29,27,48.9,27.1,40.1,18.5) # moose hunting deaths from #Provincial
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surveys
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dc <- 0.02346 # condition/accident death rate from radio collared moose
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Nb <- c()
# No. births
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Ndn <- c()
# Calf deaths
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Ndc <- c() # condition/accident deaths
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Ndp <- c()
# Wolf predation deaths
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c1 <- c()
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c2 <- c() # wolf type II numerical response
# wolf type I numerical response
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table <- data.frame() # empty data frame of annual time steps
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for (i in 1:(length(year)))
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{
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Nb[i]
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Ndn[i] <- Nb[i] * (1- (log(N[i])*(-0.13)+1.245) )# density dependent calf mortality
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Ndc[i]
<- N[i]*preg*AF[i] # No. births
<- N[i]*dc
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c1[i]
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Fuller et al. 2003
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c2[i]
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Messier et al. 1994
<- 3.5+3.3*((6*N[i])/km2)
<- 58.7*(N[i]/km2-0.03)/(0.76+N[i]/km2)
# wolf type I numerical response from
# wolf type II numerical response from
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Ndp[i] <- a*N[i]/(1 +a*N[i]*th)*c2[i] # deaths from predation under a type II numerical
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response and a type II functional response; replace c2 with #c1 if using a type I wolf numerical
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response
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N[i+1] = N[i] + Nb[i] - Ndn[i] - Ndc[i] - Ndh[i] - Ndp[i] # Main equation. Remove #Ndp or Ndh
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to treat these as compensatory, as per Table 2.
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timestep <- data.frame(Year=year[i],Observed = obs[i], Predicted=N[i],Births = Nb[i],
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Calf_deaths = Ndn[i], condition_deaths = Ndc[i],hunt_deaths = Ndh[i] , Pred_deaths = Ndp[i])
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table <- rbind(table,timestep)
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}
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table
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table$Resids <- (table$Predicted-table$Observed)^2 # note that residuals here will not match
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#exactly those from Fig. 4 because Fig. 4 metrics were based on median values from 10,000
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#bootstrap iterations
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table$PR <- table$Pred_deaths/table$Predicted*100 # The predation rate (PR)
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table
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# time lags can easily be incorporated into the above code. Other parameters for a #and th are in
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#Appendix S4.
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plot(table$Predicted,table$Observed)
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Appendix S4. Estimate of the rate of foraging efficiency (a) and handling time (Th) from
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Holling’s disc equation
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The nls package in R was used to estimate two parameters, a and Th, based on Holling’s disc
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equation. For parameter estimation, moose density was multiplied by 1100 to represent the actual
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abundance of moose in the study system, so that a and Th were directly usable in the difference
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equations. The value 1100 was used because the moose winter range covers 1100 km2 in the
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treatment area. a and Th were estimated with and without the “local data” to be used in the
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different model scenarios (see Methods). Using Messier’s data, a = 0.0166 and Th = 0.112.
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Using Messier’s plus the local data: a =0.0176, Th = 0.110. Using only the local data, a = 0.0224
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and Th = 0.114, but a is highly non-significant as would be expected with few data and none near
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the low range. The solid line predicts the Disc equation kill rate for Messier (1994) plus the local
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data collected in the treatment area. For the Type I FR models, Th was set to 0 (by definition),
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thus a was estimated to be 0.0041. Messier presented his winter kill rates as moose killed / wolf /
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100 d, but scaled this to an annual rate by multiplying by 3.65, then by 0.71 based on an
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approximation that summer kill rates are lower. We did the same here, so the a and Th
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parameters are scaled to an annual rate. It is noteworthy that Vucetich et al. (2011) used the same
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0.71 value to calculate annual predation rates, and suggested that it represented a suitable
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approximation for wolves in Banff and Yellowstone National Parks.
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Appendix S5: Density dependent compensatory predation function
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In the main analysis predation was either completely compensatory, or completely additive
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(Table 2). Yet, even though per capita predation rates can take various forms (density dependent
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or independent), animals lost to predation can have a lower impact on the population growth rate
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at higher prey densities, because animals lost to predation may be nutritionally mediated (Mech
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2007). In other words, a proportion of predation may be more compensatory and higher prey
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density, rather than completely compensatory or not. Vucetich et al. (2005) appeared to show
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that wolf predation on elk was completely compensatory, but it is likely that such an effect is
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density dependent. To account for this possibility, we used a monotonic equation (i.e. x / (1–x))
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to model compensation, where compensation would be greater at higher ungulate density. We
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minimized the sums of squares between the observed and predicted moose abundance – the
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predicted relationship was based on the Type II Functional and Type II numerical response –
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because it was shown to have the best predictive ability. Yet, we tried to improve the best
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predicted relationship by including a hypothetical compensatory component, given that there is a
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theoretical underpinning for such a process. This approach may bias the results in favour of
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finding a compensatory component, but as the results show, compensation was not needed to
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explain the dynamic.
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Using least squares minimization between observed and predicted moose abundance, the
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compensation function was estimated to be:
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PC = 1.88*MA / (1 – 1.88 * MA * 19.5)
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where PC is the proportion of mortality that is compensatory, and MA is moose abundance. The
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value 1 was subtracted from PC, and the resultant was multiplied by the number of deaths due to
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predation (Table 2) to obtain the adjusted predation number, which was then considered additive.
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Parameters in the above equation were estimated using the NLS function in R. For the range of
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moose abundance observed in the treatment area from 2003 – 2012, the PC would vary from
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approximately 0.01 at 400 moose, to 0.08 at 1650 moose.
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References
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Mech, L.D. (2007) Femur-marrow fat of white-tailed deer fawns killed by wolves. Journal of
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Wildlife Management, 71, 920-923.
Vucetich, J.A., Smith, D.W. & Stahler, D.R. (2005) Influence of harvest, climate and wolf
predation on Yellowstone elk, 1961-2004. Oikos, 111, 259-270.