The experiment is done in two aquariums, with one aquarium exposed to light while the other is kept in the dark.
Building the network model
The first step is to build the network model structure. This is done in exactly the same way as in the previous vignettes: we have to specify the network topology, some initial values, and potentially some covariates.
Let’s start with the topology:
mod <- new_networkModel() %>%
set_topo("NH4 -> algae -> daphnia -> NH4")
## Using default distribution family for proportions ("gamma_cv").
## (eta is the coefficient of variation of gamma distributions.)
## Using default distribution family for sizes ("normal_cv").
## (zeta is the coefficient of variation of normal distributions.)
We prepare a table of initial values which could be used in the real-life experiment we want to prepare:
inits <- tibble::tribble(
~comps, ~sizes, ~props, ~treatment,
"NH4", 0.2, 0.8, "light",
"algae", 1, 0.004, "light",
"daphnia", 2, 0.004, "light",
"NH4", 0.5, 0.8, "dark",
"algae", 1.2, 0.004, "dark",
"daphnia", 1.3, 0.004, "dark")
We had the initial values to the model, and we indicate that we want to group initial values by "treatment":
mod <- set_init(mod, inits, comp = "comps", size = "sizes",
prop = "props", group_by = "treatment")
mod
## # A tibble: 2 × 5
## topology initial observations parameters group
## <list> <list> <list> <list> <list>
## 1 <topology [3 × 3]> <tibble [3 × 3]> <NULL> <tibble [8 × 2]> <chr [1]>
## 2 <topology [3 × 3]> <tibble [3 × 3]> <NULL> <tibble [8 × 2]> <chr [1]>
Setting parameter values
We have the basic model ready to be given some “true” parameter values. What are the parameters we have to specify?
## # A tibble: 8 × 2
## in_model value
## <chr> <dbl>
## 1 eta NA
## 2 lambda_algae NA
## 3 lambda_daphnia NA
## 4 lambda_NH4 NA
## 5 upsilon_algae_to_daphnia NA
## 6 upsilon_daphnia_to_NH4 NA
## 7 upsilon_NH4_to_algae NA
## 8 zeta NA
Let’s say that we want to simulate an effect of "treatment" (light/dark) on the uptake of NH4 by the algae:
mod <- add_covariates(mod, upsilon_NH4_to_algae ~ treatment)
Now we have more parameters to specify:
## # A tibble: 9 × 2
## in_model value
## <chr> <dbl>
## 1 eta NA
## 2 lambda_algae NA
## 3 lambda_daphnia NA
## 4 lambda_NH4 NA
## 5 upsilon_algae_to_daphnia NA
## 6 upsilon_daphnia_to_NH4 NA
## 7 upsilon_NH4_to_algae|dark NA
## 8 upsilon_NH4_to_algae|light NA
## 9 zeta NA
We can set the parameter values with the set_params() function:
mod <- mod %>%
set_params(c("eta" = 0.2, "lambda_algae" = 0, "lambda_daphnia" = 0,
"lambda_NH4" = 0, "upsilon_NH4_to_algae|light" = 0.3,
"upsilon_NH4_to_algae|dark" = 0.1,
"upsilon_algae_to_daphnia" = 0.13,
"upsilon_daphnia_to_NH4" = 0.045, "zeta" = 0.1))
Once the parameter values are stored in the network model, they are visible in the parameters column:
## [[1]]
## # A tibble: 8 × 3
## in_replicate in_model value
## <chr> <chr> <dbl>
## 1 eta eta 0.2
## 2 lambda_algae lambda_algae 0
## 3 lambda_daphnia lambda_daphnia 0
## 4 lambda_NH4 lambda_NH4 0
## 5 upsilon_algae_to_daphnia upsilon_algae_to_daphnia 0.13
## 6 upsilon_daphnia_to_NH4 upsilon_daphnia_to_NH4 0.045
## 7 upsilon_NH4_to_algae upsilon_NH4_to_algae|light 0.3
## 8 zeta zeta 0.1
##
## [[2]]
## # A tibble: 8 × 3
## in_replicate in_model value
## <chr> <chr> <dbl>
## 1 eta eta 0.2
## 2 lambda_algae lambda_algae 0
## 3 lambda_daphnia lambda_daphnia 0
## 4 lambda_NH4 lambda_NH4 0
## 5 upsilon_algae_to_daphnia upsilon_algae_to_daphnia 0.13
## 6 upsilon_daphnia_to_NH4 upsilon_daphnia_to_NH4 0.045
## 7 upsilon_NH4_to_algae upsilon_NH4_to_algae|dark 0.1
## 8 zeta zeta 0.1
The model is now complete and can be used to generate data!
