caribouPopGrowth: National caribou demographic model
In LandSciTech/caribouMetrics: Models and Metrics of Boreal Caribou Demography and Habitat Selection

caribouPopGrowth

R Documentation

National caribou demographic model

Description

A two-stage demographic model with density dependence and interannual variability following Johnson et. al. (2020) with modifications described in 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). See vignette("caribouDemography") for additional details and examples.

Usage

caribouPopGrowth(
  N0,
  numSteps,
  R_bar,
  S_bar,
  P_0 = 1,
  P_K = 0.6,
  a = 1,
  b = 4,
  K = 100,
  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",
  adjustR = FALSE,
  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 multiplier.
`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) or beta precision parameters (R_phi, S_phi). Set to `FALSE` to ignore interannual variability.
`probOption`	Character. Choices are "binomial","continuous" or "matchJohnson2020". See description for details.
`adjustR`	Logical. Adjust R to account for delayed age at first reproduction (DeCesare et al. 2012; Eacker et al. 2019).
`progress`	Logical. Should progress updates be shown?

Details

Given a population of post-juvenile females at the beginning of year t, \dot{N}_t, the number of post-juvenile females that survive from year t to the census \dot{W}_t is binomially distributed with survival probability \dot{S}_t: \dot{W}_{t} \sim \text{Binomial}(\dot{N}_t,\dot{S}_t). Maximum potential recruitment rate is adjusted for sex ratio, misidentification biases, and (optionally) delayed age at first reproduction

\dot{X}_t=\frac{\dot{c}\dot{R}_t/2}{1+\dot{c}\dot{R}_t/2}.

Realized recruitment rate varies with population density, and the number of juveniles recruiting to the post-juvenile class at the census is a binomially distributed function of the number of surviving post-juvenile females and the adjusted recruitment rate:

\dot{J}_{t} \sim \text{Binomial}(\dot{W}_t,\dot{X}_t[p_0-(p_0-p_k)(\frac{\dot{W}_t}{N_0k})^b]\frac{\dot{W}_t}{\dot{W}_t+a}).

Given default parameters, recruitment rate is lowest (0.5\dot{X}_t) when \dot{N}_t=1, approaches a maximum of \dot{X}_t at intermediate population sizes, and declines to 0.6\dot{X}_t as the population reaches carrying capacity of k=100 times the initial population size. The post-juvenile female population in the next year includes both survivors and new recruits: \dot{N}_{t+1}=\text{min}(\dot{W}_t+\dot{J}_t,r_{max}\dot{N}_t).

Interannual variation in survival and recruitment is modelled using truncated beta distributions: \dot{R}_t \sim \text{TruncatedBeta}(\bar{R}_t,\nu_R,l_R,h_R); \dot{S}_t \sim \text{TruncatedBeta}(\bar{S}_t,\nu_S,l_S,h_S). (\nu_R,\nu_S) are coefficients of variation among years and l_R,h_R,l_S,h_S are maximum/minimum values for recruitment and survival.

Value

A data.frame of population size (N), average 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.

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

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