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.
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()
)Number or vector of numbers. Initial population size for one or more sample populations.
Number. Number of years to project.
Number or vector of numbers. Expected recruitment rate (calf:cow ratio) for one or more sample populations.
Number or vector of numbers. Expected adult female survival for one or more sample populations.
Number. Maximum recruitment multiplier.
Number. Recruitment multiplier at carrying capacity.
Number. Density dependence shape parameter.
Number. Allee effect parameter.
Number. Carrying capacity.
Number. Maximum population growth rate.
Number. Sex ratio.
Number. Minimum recruitment.
Number. Maximum recruitment.
Number. Minimum survival.
Number. Maximum survival.
Number. Bias correction term.
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.
Character. Choices are "binomial","continuous" or "matchJohnson2020". See description for details.
Logical. Should progress updates be shown?
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.
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 and misidentification biases $$\dot{X}_t=\dot{c}\dot{R}_t/2.$$ 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 \(K=10000\). The post-juvenile female population in the next year includes both survivors and new recruits: \(\dot{N}_{t+1}=\text{min}(\dot{W}_t+\dot{J}_t,r_{max}\dot{N}_t)\).
If coefficients of variation are provided, 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.
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.
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
Caribou demography functions:
caribouBayesianPM(),
compositionBiasCorrection(),
demographicCoefficients(),
demographicProjectionApp(),
demographicRates(),
getOutputTables(),
getPriors(),
getScenarioDefaults(),
getSimsNational(),
plotRes(),
popGrowthTableJohnsonECCC,
runScnSet(),
simulateObservations()
caribouPopGrowth(100, 2, 0.5, 0.7)
#> N0 lambdaTrue lambda N R_t X_t S_t n_recruits
#> 1 100 0.7745967 0.875 60 0.3089671 0.1544836 0.7090493 8
#> surviving_adFemales
#> 1 52