This vignette covers several common forest inventory use cases that can be covered by allometric

Making Predictions of Volume for Multiple Species with Models of the Same Form

This vignette demonstrates a simple forest inventory example using allometric using plot data obtained from the Forest Inventory and Analysis (FIA) program. An example dataset is included in the package and can be loaded using data(fia_trees). Our objective is to calculate a plot-level volumes for every plot in this dataset.

Allometric predictions can be made in any manner of ways according to the user’s preference. We will use the suite of tidyverse packages to manipulate our data, but this is merely the author’s preference. allometric is capable of producing predictions using base R if preferred. For this example, we will use a set of models that all have the same functional form. That is, the required covariates are identitcal across models, and are in the same order. For a more advanced case, refer to the following section.

Preparing the Data

In reading ?fia_trees the user will notice that all tree species are encoded using the FIA SPCD numbering system. The first task is to prepare a data frame that will translate these codes into taxonomic groupings.


target_species <- tibble(
  SPCD = c(202, 263, 15, 122),
  genus = c('Pseudotsuga', 'Tsuga', 'Abies', 'Pinus'),
  species = c('menziesii', 'heterophylla', 'concolor', 'ponderosa')

The target_species dataframe serves two purposes. First, it allows us to link genus and species information to fia_trees. Second, it allows us to easily filter out allometric models that are not related to these types of trees.

Finding Appropriate Models

The user will note that fia_trees is composed entirely of trees from the state of Oregon in the United States. Using dplyr and purrr we can efficiently filter out unnecessary models from the allometric_models table. Refer to the ?allometric_models help page for more information.

For this example, we need stem volume models for our species of interest that, preferably, were fit using data in the state of Oregon.


allometric_models <- load_models()

stemvol_mods <- allometric_models %>%
    model_type == "stem volume"


We can see that stemvol_mods contains a huge amount of stem volume models. That is because allometric is global in scope. Most of these models are not relavent for our needs. Next, we will drill down and select models that were developed with data from US-OR (the state of Oregon, United States).

stemvol_or_mods <- stemvol_mods %>%
  filter(map_lgl(region, ~ 'US-OR' %in% .))


Here we see all stem volume models available fit using data from the state of Oregon. Still, the amount of models is very high. Next, we will select only our target species. First, we use the unnest_taxa() function, that will append family, genus, and species columns, which will facilitate merging the target species later.

stemvol_or_unnested <- stemvol_or_mods %>%
stemvol_or_spc_mods <- stemvol_or_unnested %>%
  inner_join(target_species, by=c('genus', 'species'))


Finally, something a bit more digestible. Even still, we have multiple models per species. The last step is to ensure that each of these remaining models are compatible with our available data. fia_trees only contains DIA, the diameter at breast height, and HT the total height of the tree. In allometric these covariates are standardized as dsob and hst respectively. See the Variable Naming System for more information. Using some clever filtering, we can find which models are compatible with this set of covariates.

stemvol_or_spc_dia_ht_mods <- stemvol_or_spc_mods %>%
  filter(map_lgl(covt_name, ~ length(.) == 2 & all(c('dsob', 'hst') %in% .)))

The call to map_lgl answers the question, “which models contain only two covariates that are named dsob and hst”? Only a handful of models remain.


At this stage, we only need to determine a single model for Pseudotsuga menziesii. We will decide to select only those models from poudel_2019, a recent study that contains the volume models for the species we need.

final_set <- stemvol_or_spc_dia_ht_mods %>% filter(pub_id == "poudel_2019") %>%
  select(SPCD, model)

At last we have all four species attached to one allometric model, and we can proceed with prediction. If the above steps seem cumbersome, fear not, the “Storing an Internal Set of Equations for Routine Use” section resolves these issues.

Making Volume Predictions

To make a volume prediction correctly, we must know the order of the arguments to the allometric function. Inspecting the first model in our set reveals this order.

final_set %>% mutate(call = map_chr(model, ~model_call(.)))

The model_call function shows that vsa = f(dsob, hst) is the allometric function call for each model we have specified, which means that the diameter of the stem outside bark at breast height (dsob) is the first argument and the total height of the stem (hst) is the second argument.

Using final_set, we can easily merge the models to our tree-list and make predictions. Predictions made in this manner are done using the predict_allo function.

tree_vols <- final_set %>%
  left_join(fia_trees, by = "SPCD") %>%
  mutate(vol_m3 = predict_allo(model, DIA * 2.54, HT * 0.3048)) %>%
  mutate(vol_cuft = units::set_units(vol_m3, "ft^3"))


predict_allo takes each model in the model column and applies it to the covariates, DIA and HT assigned in the function call. Aggregating to the plot-level we obtain

tree_vols %>%
  group_by(PLOT) %>%
  summarise(vol_ac = sum(vol_cuft * TPA_UNADJ))

Note that all models in final_set take centimeters for diameter and meters for height. This can be checked by printing the model summary


It is always important to check the model summary before implementing a model in an analysis. Indeed, users should carefully read the publication source as well to be absolutely sure the model is implemented appropriately.

Making Predictions of Volume for Multiple Species with Models of Different Forms

In many cases, allometric model inputs will differ in the required covariates and, potentially, their order. This complicates the use of predict_allo, which assumes that the covariates are identical and of the same order for each model used in the analysis.

For this example we will use a different set of models from the same publication, Poudel et al. (2019) to calculate tree biomass (bt) for the same set of trees.

Finding Appropriate Models

In this case we have a publication in mind, and can filter allometric_models directly to obtain the models we want. We want a set of tree-level biomass models from poudel_2019 that use dsob or hst as covariates. We obtain

biomass_models <- allometric_models %>%
    pub_id == "poudel_2019",
    model_type == "tree biomass",
    map_lgl(covt_name, ~(any(c("dsob", "hst") %in% .) & length(.) <= 2))
  ) %>%
  mutate(call = map_chr(model, ~model_call(.))) %>%
  unnest_taxa() %>%
  right_join(target_species, by = c("genus", "species"))

We can see that the model for Abies concolor takes only a dsob argument but the remaining models take dsob and hst arguments. This renders the direct use of predict_allo on biomass_models infeasible.

Instead we must engage in some clever programming and break our dataframe of models into call groups, use predict_allo for each group, and stitch the prediction frame back together for our final result.

Making Biomass Predictions with Different Model Forms

First, we need to make a function that will take each call group and its covariate key. This allows us to implement different prediction logic for each call group using a tree of if statements. We obtain:

call_group_predict <- function(data, covt_key) {
  if(identical(covt_key[[1]][[1]], c("dsob"))) {
    data$agb_kg <- predict_allo(data$model, data$DIA * 2.54)
  } else if (identical(covt_key[[1]][[1]], c("dsob", "hst"))) {
    data$agb_kg <- predict_allo(data$model, data$DIA * 2.54, data$HT * 0.3048)


Then, we simply merge the models to the tree list, group by the covt_name column, and utilize dplyr::group_map() to apply our call_group_predict function to each group of trees.

tree_agbs <- biomass_models %>%
  left_join(fia_trees, by = "SPCD") %>%
  group_by(covt_name) %>%
  group_map(call_group_predict) %>%


Finally, we can aggregate the tree_agbs to the plot-level as before.

agb_plot <- tree_agbs %>%
  group_by(PLOT) %>%
  summarise(agb_ac = sum(agb_kg * TPA_UNADJ))


Storing an Internal Set of Equations for Routine Use

It is unlikely that most organizations need all models stored in allometric_models for routine use. For example, the Forest Inventory and Analysis (FIA) program has specified sets of allometric models over the years that are used to produce cubic volumes and biomasses for the national FIA database. Subsets of the allometric_models table can be prepared by analysts and stored locally as RDS files, which can then be used in routine analysis or even as components of other software packages.

For example, we can save the model table we created in the last section

saveRDS(final_set, './my_directory/final_set.RDS')

It can be reloaded and used readily in other software


If you will be using other allometric functionality in your software, (e.g., predict_allo) it will be necessary to run library(allometric) to gain access to those functions.