Population Forecasting

Functions to set demographic and cost parameter, to perform forecasting, and to inspect the results.

wildlift_settings(pen.type = c("mat.pen",  "pred.excl",
    "moose.red", "wolf.red", "cons.breed"), herd = NULL, ...)

wildlift_forecast(settings, tmax = 20, pop.start = 100,
    fpen.prop, fpen.inds)

wildlift_breakeven(forecast, lambda=1,
    type=c("prop", "inds"), max=10^4, tol=0.01)

# S3 method for wildlift_settings
print(x, ...)
# S3 method for wildlift_forecast
print(x, ...)
# S3 method for wildlift_forecast
plot(x, plot = TRUE, ...)
# S3 method for wildlift_forecast
lines(x, pen = TRUE, plot = TRUE, ...)
# S3 method for wildlift_forecast
summary(object, ...)
# S3 method for summary.wildlift_forecast
print(x, ...)

Arguments

pen.type	character: maternity penning, predator exclusion, moose reduction, wolf reduction, or conservation breeding. It can also be a settings object.
herd	NULL (default, East Side Athabasca) or character. The following herds are available: "EastSideAthabasca" (Boreal ecotype) "ColumbiaNorth", "ColumbiaSouth", "FrisbyQueest", "WellsGreySouth", "Groundhog", "Parsnip", "KennedySiding", "KlinsezaMoberly", "Quintette" (Southern Mountain ecotype). Note: only "KennedySiding", "KlinsezaMoberly", or "Quintette" can be selected when pen.type = "wolf.red", beside a generic herd setting when herd is NULL that is specific to the 'wolf removal' treatment type (wild, i.e. 'no wolf removal' settings for these herds are available under the default pen.type = "mat.pen" treatment but no separate generic herd settings are provided for the 'no wolf removal' treatment).
settings	a settings object returned by wildlift_settings.
tmax	positive integer, number of years to forecast after initial year 0.
pop.start	positive integer, initial population size in year 0.
fpen.prop, fpen.inds	fpen.prop is a single numeric value between 0 and 1 for the proportion of females penned; fpen.inds is a non-negative integer for the number of females penned, can be a vector giving number of females penned in each year to be accumulated. Only one of fpen.prop or fpen.inds can be provided at a time. Any of the two arguments can be NULL or missing, but not both at the same time.
forecast	a forecast object returned by wildlift_forecast.
lambda	numeric, annual intrinsic growth rate, must be >0.
type	what to provide as output: proportion ("prop") or numbers ("inds") of females penned at breakeven point.
max	numeric (>0), maximum value for breakeven optimization when type = "inds".
tol	numeric, tolerance limit, i.e. the maximum acceptable deviation from lambda when solving for 'breakeven' proportion of females penned.
x, object	an object to print, summarize, plot, etc.
plot	logical, whether a plot is to be produced.
pen	logical, whether to display the pen or no-pen (baseline) results.
...	additional arguments to functions. For wildlift_settings see Details.

Details

The following cost parameters can be set by wildlift_settings:

pen.cap: how many adult females can live in a single maternity pen.

pen.cost.setup: initial cost in thousands to set up pen.

pen.cost.proj: annual costs in thousands for project manager.

pen.cost.maint: annual cost in thousands for patrolling and repairing fence.

pen.cost.capt: annual cost in thousands to capture cows, monitor, survey, calf collar.

pen.cost.pred: annual cost in thousands for removing predators.

The following demographic parameters can be set by wildlift_settings:

c.surv.wild: calf survival rate in the wild, annual.

c.surv.capt: calf survival rate when captive, annual.

f.surv.wild: adult female survival when wild, annual.

f.surv.capt: adult female survival when captive, annual.

f.preg.wild: pregnancy rate when wild.

f.preg.capt: pregnancy rate when captive.

Value

wildlift_settings returns a settings object.

wildlift_forecast returns a forecast object.

wildlift_breakeven returns a numeric value representing the 'breakeven' proportion of females penned where lambda is within tolerance. It returns NA when proportion satisfying the lambda criterion cannot be found, alongside a warning.

The print method returns the input object x invisibly.

The summary method returns population and cost summaries for the forecast object (cost is in million dollars).

The plot and lines methods return the plotted data invisibly (years, pen and no-pen population size for plot; years, pen or no-pen population size for lines). Both methods produce plots as a side effect.

See also

wildlift_matrix, wildlift_breeding

Examples

## Predefined settings
(s1 <- wildlift_settings("mat.pen"))
#> Caribou settings - pen type: mat.pen 
#> 
#>  - c.surv.wild   :0.163
#>  - c.surv.capt   :0.598
#>  - f.surv.wild   :0.853
#>  - f.surv.capt   :0.903
#>  - f.preg.wild   :0.92
#>  - f.preg.capt   :0.92
#>  - pen.cap       :35
#>  - pen.cost.setup:500
#>  - pen.cost.proj :80
#>  - pen.cost.maint:300
#>  - pen.cost.capt :250
#>  - pen.cost.pred :0
(s2 <- wildlift_settings("pred.excl"))
#> Caribou settings - pen type: pred.excl 
#> 
#>  - c.surv.wild   :0.163
#>  - c.surv.capt   :0.72
#>  - f.surv.wild   :0.853
#>  - f.surv.capt   :0.95
#>  - f.preg.wild   :0.92
#>  - f.preg.capt   :0.92
#>  - pen.cap       :35
#>  - pen.cost.setup:1868
#>  - pen.cost.proj :80
#>  - pen.cost.maint:600
#>  - pen.cost.capt :200
#>  - pen.cost.pred :80

## Modifying predefined settings
wildlift_settings("mat.pen", c.surv.capt=0.65, pen.cap=30)
#> Caribou settings - pen type: mat.pen 
#> 
#>  - c.surv.wild   :0.163
#>  - c.surv.capt   :0.65
#>  - f.surv.wild   :0.853
#>  - f.surv.capt   :0.903
#>  - f.preg.wild   :0.92
#>  - f.preg.capt   :0.92
#>  - pen.cap       :30
#>  - pen.cost.setup:500
#>  - pen.cost.proj :80
#>  - pen.cost.maint:300
#>  - pen.cost.capt :250
#>  - pen.cost.pred :0
wildlift_settings(s1, c.surv.capt=0.65, pen.cap=30)
#> Caribou settings - pen type: mat.pen 
#> 
#>  - c.surv.wild   :0.163
#>  - c.surv.capt   :0.65
#>  - f.surv.wild   :0.853
#>  - f.surv.capt   :0.903
#>  - f.preg.wild   :0.92
#>  - f.preg.capt   :0.92
#>  - pen.cap       :30
#>  - pen.cost.setup:500
#>  - pen.cost.proj :80
#>  - pen.cost.maint:300
#>  - pen.cost.capt :250
#>  - pen.cost.pred :0

## Forecast based on settings for 75% females penned
(f1 <- wildlift_forecast(s1, fpen.prop = 0.75))
#> Caribou forecast - pen type: mat.pen 
#> 
#>  - tmax     :20
#>  - pop.start:100
#>  - fpen.prop:0.75
(f2 <- wildlift_forecast(s2, fpen.prop = 0.75))
#> Caribou forecast - pen type: pred.excl 
#> 
#>  - tmax     :20
#>  - pop.start:100
#>  - fpen.prop:0.75

## Get population and cost summaries
summary(f1)
#> Caribou forecast - pen type: mat.pen 
#> 
#>  - tmax     :20
#>  - pop.start:100
#>  - fpen.prop:0.75
#> 
#>  - npens      :3
#>  - lam.pen    :1.03
#>  - lam.nopen  :0.914
#>  - Nend.nopen :17
#>  - Nend.pen   :195
#>  - Nend.diff  :178
#>  - Cost.total :30.5
#>  - Cost.percap:0.171
summary(f2)
#> Caribou forecast - pen type: pred.excl 
#> 
#>  - tmax     :20
#>  - pop.start:100
#>  - fpen.prop:0.75
#> 
#>  - npens      :7
#>  - lam.pen    :1.09
#>  - lam.nopen  :0.914
#>  - Nend.nopen :17
#>  - Nend.pen   :556
#>  - Nend.diff  :539
#>  - Cost.total :87
#>  - Cost.percap:0.161

## Plot the results
plot(f2)
lines(f1, col = 2)
legend("topleft", col = c(1,1,2), lty = c(2,1,1),
    legend = c("No pen", "Mat pen", "Pred excl"))

## Find 'breakeven' proportion of females penned where lambda=1
(b1 <- wildlift_breakeven(f1, lambda = 1))
#> [1] 0.5171369
(b2 <- wildlift_breakeven(f2, lambda = 1))
#> [1] 0.3441178
f3 <- wildlift_forecast(s1, fpen.prop = b1)
f4 <- wildlift_forecast(s2, fpen.prop = b2)
## See that lines are truly flat
op <- par(mfrow = c(1, 2))
plot(f3, main = "Mat pen")
plot(f4, main = "Pred excl")
par(op)