Caribou demographic model

A caribou demographic model with density dependence and interannual variability following Johnson et. al. (2020) with modifications described in Hughes et al. (2025) and Dyson et al. (2022). Default parameter values give the model in Dyson et al. (2022). Set probOption = "matchJohnson2020" to reproduce the model used in Johnson et al. 2020. Set probOption = "continuous", interannualVar = FALSE, and K = FALSE to reproduce the simpler 2-stage demographic model without interannual variability, density dependence, or discrete numbers of animals used by Stewart et al. (2023).

Usage

caribouPopGrowth(
  N0,
  numSteps,
  R_bar,
  S_bar,
  P_0 = 1,
  P_K = 0.6,
  a = 1,
  b = 4,
  K = 10000,
  r_max = 1.3,
  s = 0.5,
  l_R = 0,
  h_R = 0.82,
  l_S = 0.61,
  h_S = 1,
  c = 1,
  interannualVar = list(R_CV = 0.46, S_CV = 0.08696),
  probOption = "binomial",
  progress = interactive()
)

Arguments

N0: Number or vector of numbers. Initial population size for one or more sample populations. If NA then population growth rate is $_t=S_t*(1+cR_t)/s$.
numSteps: Number. Number of years to project.
R_bar: Number or vector of numbers. Expected recruitment rate (calf:cow ratio) for one or more sample populations.
S_bar: Number or vector of numbers. Expected adult female survival for one or more sample populations.
P_0: Number. Maximum recruitment multiplier.
P_K: Number. Recruitment multiplier at carrying capacity.
a: Number. Density dependence shape parameter.
b: Number. Allee effect parameter.
K: Number. Carrying capacity.
r_max: Number. Maximum population growth rate.
s: Number. Sex ratio.
l_R: Number. Minimum recruitment.
h_R: Number. Maximum recruitment.
l_S: Number. Minimum survival.
h_S: Number. Maximum survival.
c: Number. Bias correction term.
interannualVar: list or logical. List containing interannual variability parameters. These can be either coefficients of variation (R_CV, S_CV), beta precision parameters (R_phi, S_phi), or random effects parameters from a logistic glmm (R_annual, S_annual). Set to FALSE to ignore interannual variability.
probOption: Character. Choices are "binomial","continuous" or "matchJohnson2020". See description for details.
progress: Logical. Should progress updates be shown?

Value

A data.frame of population size (N), expected growth rate (lambdaE), true growth rate (lambda), apparent annual reproduction rate (R_t), adjusted reproduction (X_t), survival (S_t), number of recruits (n_recruits), and surviving females (surviving_adFemales) for each sample population projected for numSteps years.

Details

If R_annual and S_annual are provided, interannual variation in survival and recruitment is modelled as in a logistic glmm with random effect of year.

If initial populations size N0 is NA then population growth rate is $_t=S_t*(1+cR_t/s)$. In this case density dependence (P_0,P_K,a,b,K,r_max) and demographic stochasticity (probOption) are ignored.

See vignette("caribouDemography") and Hughes et al. (2025) for additional details and examples.

References

Dyson, M., Endicott, S., Simpkins, C., Turner, J. W., Avery-Gomm, S., Johnson, C. A., Leblond, M., Neilson, E. W., Rempel, R., Wiebe, P. A., Baltzer, J. L., Stewart, F. E. C., & Hughes, J. (2022). Existing caribou habitat and demographic models need improvement for Ring of Fire impact assessment: A roadmap for improving the usefulness, transparency, and availability of models for conservation. https://doi.org/10.1101/2022.06.01.494350

Hughes, J., Endicott, S., Calvert, A.M. and Johnson, C.A., 2025. Integration of national demographic-disturbance relationships and local data can improve caribou population viability projections and inform monitoring decisions. Ecological Informatics, 87, p.103095. https://doi.org/10.1016/j.ecoinf.2025.103095

Johnson, C.A., Sutherland, G.D., Neave, E., Leblond, M., Kirby, P., Superbie, C. and McLoughlin, P.D., 2020. Science to inform policy: linking population dynamics to habitat for a threatened species in Canada. Journal of Applied Ecology, 57(7), pp.1314-1327. https://doi.org/10.1111/1365-2664.13637

Stewart, F.E., Micheletti, T., Cumming, S.G., Barros, C., Chubaty, A.M., Dookie, A.L., Duclos, I., Eddy, I., Haché, S., Hodson, J. and Hughes, J., 2023. Climate‐informed forecasts reveal dramatic local habitat shifts and population uncertainty for northern boreal caribou. Ecological Applications, 33(3), p.e2816. https://doi.org/10.1002/eap.2816

Examples

caribouPopGrowth(100, 2, 0.5, 0.7)
#>    N0    lambda lambdaE  N       R_t       X_t      S_t n_recruits
#> 1 100 0.8485281   0.875 72 0.4214428 0.2107214 0.807669         13
#>   surviving_adFemales
#> 1                  59