Regional Trend Model

Objectives

State of Model Development

Currently, the density dependent gompertz models do not mix well and do not converge. The simple_gompertz.R model is probably what to develop from for any density dependent models. It currently assumes constant r and K across sites but allows for environmental (annual) stochasticity. The convergence isn't great, especially for K. So far the model hasn't been able to handle random effects on r or K, given the current data.

The density independent model (model_independent.R) currently includes meteorological covariates, a site-year overdispersion term to produce a random walk when added to the previous year's abundance (environmental stochasticity not captured by deterministic covariates). The model seems to work acceptably well.

Run

1. run_gompertz.R
2. 2_Random walk panel plot.R

Model Structure

Density Dependent

Abundance allows for density-dependent change over time following Gompertz function where r represents the intrinsic population growth rate (lumps survival and recruitment) and K represents the semi-equalibrium abundance (Hostetler and Chandler 2015 Ecology).

Population growth r is modeled as a function of seasonal covariates and a random site effect (intercept). The seasonal effects are currently fixed but we could explore random effects by site or HUC. Ultimately in the future it would be great to add spatial dependence to these.

K is modeled as a random effect by site but I'd like to add drainage area as a covariate.

Density Independent

The density independent effects allow for immigration to rescue populations following local extirpation. They rho are currently modeled as random by site-year, but I'm not sure if this will converge. It represents the average number of immigrants to the population independent of the current population size. It could be a fixed value or random by site and or year rather than site-year. It could also be random at the HUC (8, 10, 12) level, but it gets messy to read too much into it or spend too much time on covariates since it can be a function of so many things related to the surrounding populations and network connectivity.