Caribou demographic model

A two-stage 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). Demographic rates vary with disturbance as estimated by Johnson et. al. (2020). 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).

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.

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 (lambda), true growth rate (lambdaTrue), 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.

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

See also

Caribou demography functions: caribouBayesianPM(), compositionBiasCorrection(), demographicCoefficients(), demographicProjectionApp(), demographicRates(), getOutputTables(), getPriors(), getScenarioDefaults(), getSimsNational(), plotRes(), popGrowthTableJohnsonECCC, runScnSet(), simulateObservations()

Examples

caribouPopGrowth(100, 2, 0.5, 0.7)
#>    N0 lambdaTrue lambda  N       R_t       X_t     S_t n_recruits
#> 1 100   0.969536  0.875 94 0.5473362 0.2736681 0.71036         21
#>   surviving_adFemales
#> 1                  73