Apportion kriged biomass, abundance, and NASC

Apportion kriged biomass, abundance, and NASC#

Estimate kriged abundance and \(\textit{NASC}\)#

Kriged biomass values can be converted to abundance and subsequently \(\textit{NASC}\) using the mesh_biomass_to_nasc function from the survey.apportionment module. This is a function that can be configured in a variety of ways and has the following arguments:

  • mesh_data: A pandas.DataFrame containing the gridded kriged biomass estimates.

  • biodata: A dictionary of xarray.DataArrays that contain the calculated weight proportions.

  • mesh_biodata_link: A dictionary that maps column names from mesh_data to those in biodata. In this case, we can use it to match the haul-based strata (e.g., stratum_ks) with the latitude-based ones in the gridded data (e.g., geostratum_ks).

  • stratum_weights: An xarray.DataArray that contains the average weights per stratum required for converting biomass to abundance. However, the overall means are used here as opposed to the sex-specific estimates.

  • stratum_sigma_bs: A pandas.DataFrame containing the mean \(\sigma_\text{bs}\) for each stratum.

from echopop.survey import apportionment

apportionment.mesh_biomass_to_nasc(
    mesh_data=unextrapolated_results,
    biodata=dict_ds_weight_proportion,
    group_columns=["sex", "stratum_ks"],
    mesh_biodata_link={"geostratum_ks": "stratum_ks"},
    stratum_weights=da_averaged_weight.sel(sex="all"),
    stratum_sigma_bs=invert_hake.sigma_bs_strata,
)

The mesh_biomass_to_nasc function modifies the DataFrame in-place to add the appropriate columns for sex-apportioned abundance and subsequently \(\textit{NASC}\).

Distributing kriged abundance and biomass over age and length#

Kriged abundance and biomass are both distributed over age (\(\alpha\)) and length (\(\ell\)) distributions using distribute_population_estimates, which has the following arguments:

  • data: pandas.DataFrame containing the population estimates.

  • proportions: Either an xarray.Dataset or dictionary containing the number or weight proportions (depending on whether abundance or biomass is being distributed).

  • variable: Name of the column in data containing the values to distribute (e.g., "abundance", "biomass").

  • group_columns: List of column names that define any biological groups for the distribution (e.g., ["sex", "age_bin", "length_bin"]).

  • data_proportions_link: Dictionary that links column names in data to those in proportions. For instance, the dictionary {"stratum_A": "stratum_B"} links "stratum_A" in data with stratum_B in proportions.

from echopop.survey import apportionment

# Abundance
dict_ds_kriged_abundance_table = apportionment.distribute_population_estimates(
    data = df_kriged_results,
    proportions = dict_ds_number_proportion,
    variable = "abundance",
    group_columns = ["sex", "age_bin", "length_bin", "stratum_ks"],
    data_proportions_link={"geostratum_ks": "stratum_ks"},
)

# Biomass
dict_ds_kriged_biomass_table = apportionment.distribute_population_estimates(
    data=df_kriged_results,
    proportions = dict_da_weight_proportion,
    variable = "biomass",
    group_columns = ["sex", "age_bin", "length_bin", "stratum_ks"],
    data_proportions_link={"geostratum_ks": "stratum_ks"},
)

Redistributing unaged estimates over age#

The next step involves taking the unaged abundance and biomass distributions and redistributing them over age. This is done with distribute_unaged_from_aged, which has the arguments:

  • population_table: Population estimates to be redistributed.

  • reference_table: Reference population table used for the redistribution.

  • stratum_dim: Stratification dimension name to collapse (sum over) during standardization (e.g., ["stratum"]). These dimensions are summed over in the initial step, and the resulting standardized table will not have these dimensions.

  • impute: When True, perform a nearest-neighbor imputation for missing joint \(\alpha\)-\(\ell\) values within each group_columns variable.

  • impute_variable: List of variables used for imputation and required when impute = True. This typically refers to the dimension being imputed (e.g., ["age_bin"]).


# Abundance
dict_ds_kriged_abundance_table["redistributed_unaged"] = apportionment.distribute_unaged_from_aged(
    population_table = dict_ds_kriged_abundance_table["unaged"],
    reference_table = dict_ds_kriged_abundance_table["aged"],
    stratum_dim = "stratum_ks",
    impute = False,
)

# Biomass
dict_ds_kriged_biomass_table["redistributed_unaged"] = apportionment.distribute_unaged_from_aged(
    population_table = dict_ds_kriged_biomass_table["unaged"],
    reference_table = dict_ds_kriged_biomass_table["aged"],
    stratum_dim = "stratum_ks",
    impute=True,
    impute_variable=["age_bin"],
)

With these redistributed values, we can now appropriately sum the aged and unaged distributions since they share the same dimensions: "sex", "age_bin", and "length_bin". This consolidation is done using sum_population_tables function, which has the following arguments:

  • population_tables: The dictionary of xarray.DataArrays containing population estimate tables to be combined. Keys are the table names (e.g., "aged" and "redistributed_unaged").

# Abundance
da_kriged_abundance_table = apportionment.sum_population_tables(
    population_tables={
        "aged": dict_ds_kriged_abundance_table["aged"],
        "unaged": dict_ds_kriged_abundance_table["redistributed_unaged"]
    },
)

# Biomass
da_kriged_biomass_table = apportionment.sum_population_tables(
    population_tables={
        "aged": dict_ds_kriged_biomass_table["aged"],
        "unaged": dict_ds_kriged_biomass_table["redistributed_unaged"]
    },
)

Re-allocating estimates for removed groups#

In some cases, we may exclude certain \(\ell\), \(\alpha\), or other contrasts from earlier in the workflow. An expected example of this would be removing age-1 fish from the entire workflow. Despite these groups being removed from the workflow in general, there is some “leakage” that occurs in the distributions due to how the biological data are processed. This can be accounted by using the reallocate_excluded_estimates function, which has the arguments:

  • population_table: The consolidated population table as an xarray.DataArray with biological groups corresponding coordinates (i.e., "sex", "age_bin", "length_bin").

  • exclusion_filter: Dictionary specifying which table to exclude and redistribute. Keys are column and index names, values are the categories to exclude. For example, exclusion_filter = {"age_bin": [1]} would exclude age-1 fish.

  • group_columns: List of column names that define the grouping variables for redistribution. For example, group_columns = ["sex"] would redistribute the age-1 estimates within each sex.

So if we excluded age-1 fish earlier in the analysis, then we can remove these via:

# Abundance
ds_kriged_abundance_table_noage1 = apportionment.reallocate_excluded_estimates(
    population_table=da_kriged_abundance_table,
    exclusion_filter={"age_bin": [1]},
    group_columns=["sex"],
)

# Biomass
ds_kriged_biomass_table_noage1 = apportionment.reallocate_excluded_estimates(
    population_table=da_kriged_biomass_table,
    exclusion_filter={"age_bin": [1]},
    group_columns=["sex"],
)