*4.4. ISO 14044:2006 Application (from 2009)*

At this stage, the most cited article identified by the search was published by Finnveden et al. [99]. This article repeated that the underlying physical relationships of ISO14044:2006's second hierarchy level should represent physical, chemical, or biological causation (as also specified before in [73]). Consequently, economic, mass, or energy allocations were intended to be used only as the third level option [99].

Following the main path, we found an LCA on a bio-based plastic product derived from a blood meal [100]. Bier et al. highlighted how different approaches for solving allocation issues in LCAs of bio-based materials could widely vary the results. The next two articles of the main research path discussed the choice of allocation approaches to use in LCAs aimed at informing policy-making. Wardenaar et al. [101] pointed out that methodological uncertainty within ISO led to significantly different results due to the influence of the allocation approach, and argued that the policy context could benefit from new guidelines [101]. Concerning the ISO hierarchy, they stated that "several authors have argued that substitution is equivalent to system expansion" referring as an example to [88]. However, "conceptually equivalent does not mean that system expansion and substitution provide the same results" because there are "large differences between these two methods" [101]. As a consequence of this assumed conceptual equivalency, some authors "use this implicit argument to choose for substitution, while still claiming compliance to ISO" [101]. Concerning allocation based on a physical parameter, Wardenaar et al. argued that the physical parameter should be the one reflecting the physical characteristics related to "the purpose or use of the product", i.e., the relevant characteristic for which they are sold [101].

Following the main path, we found a study on the Environmental Footprint guidelines published by the European Commission [65]. The study of 2014 of Pelletier et al. [65] highlighted that in ISO's first level system expansion, the functional unit is expanded to include the other co-functions (enlargement), and the impacts are therefore reported at the system level, i.e., at the level of all co-products [65]. This was claimed to be the "literal interpretation of ISO 14044" [9]. Accordingly, the PEF guide [28] does not consider substitution as a system expansion approach, but only enlargement (similarly the more recent PEFCR guidance [29]). However, the ILCD handbook allows system reduction as an option in CLCA, and for those ALCAs whose aim is to include also the interactions with other systems [27].

The key-route main path analysis allowed us to identify the origins of the "equivalency" substitution-system expansion, i.e., the articles on the side of the bilateral beginning period originated by Tillman et al. [58]. The suggestion of Pelletier et al. [9] that this equivalency originated from the 1994 study of Tillman et al. [58] was therefore confirmed by our analysis. Nevertheless, the article by Tillman et al. [58] was published before any ISO standard and, therefore, did not refer to the system expansion method as intended by ISO.

In the next publication of the main path, Pelletier et al. (2015) observed that, despite the ISO hierarchy, consistent implementation of this hierarchy in the literature was limited, and presented the three schools of thought (consequential, socio-economic ALCA and natural-science ALCA) mentioned at the beginning of Section 3.

The next two articles in the main research path were focused on finding allocation parameters for agricultural systems. The first article proposed an allocation based on plant physiological construction cost for plant compounds, which should represent the underlying physical relationships between co-products, i.e., the physiological mechanism involved in plant growth [102]. Hence, they concluded that, according to ISO, such a method should be preferred to allocation based on common properties of co-products, such as energy or economic content [102]. Subsequently, Mackenzie et al. [69] studied similar biophysical allocation methods and concluded instead that these methods might not represent the causal physical mechanisms of these systems because they overlook the interconnectivity between co-products [69] as instead, an LP would do. Therefore, they concluded that allocation by economics is preferable [69]. Mackenzie et al. also pointed out that many practitioners often choose an allocation based on an arbitrary parameter (e.g., their mass or energy content) also when it does not reflect such a cause-effect mechanism [69].

The last two articles of the main path were focused on how to allocate burdens to by-products which were previously considered wastes [103,104]. These by-products are scarce wastes that can be converted into valuable products. In particular, Pradel et al. constructed a novel allocation method based on relevant causal relationships obtained by mathematical modeling [103]. This model was applied to wastewater treatment plants delivering sludge (by-product) and clean water (main product) and calculated the allocation factor for sludge and water.

#### **5. Discussion and Conclusions**

Despite the existence of a hierarchy for solving multifunctionality in ISO 14044:2006, the complexity of the multifunctionality problem, the lack of sufficient guidance, its difficult interpretation, and the discrepancies in other "ISO-compliant" guides or handbooks have led to a wide variety of allocation procedures in the literature. Such variety is especially present in the system expansion approaches and in the choice of the allocation key.

ISO 14044:2006 does not distinguish between attributional and consequential modeling. For many practitioners, distinguishing between attributional or consequential LCAs is a crucial key to selecting the method to deal with multifunctionality. For other practitioners, some mixed approaches can be considered as advancements in the methodology. We found that only 25% of the LCAs clearly state the approach followed using the terms "attributional" and "consequential". Are practitioners not specifying it because they assume it to be "intrinsically clear" from the goal description, or because they do not agree with such a distinction? Some mixed approaches have also been proposed in the literature.

The first major reason for debate on ISO's multifunctionality hierarchy is the application of substitution as a system expansion method in ALCA (found in 31% of the self-declared attributional studies explored through text mining). Such practice is perceived as inappropriate by many practitioners. However, some practitioners who do not acknowledge substitution as system expansion in ALCA recognize the use of substitution as an allocation method for ALCA. Concerning the use of substitution, another aspect that many practitioners pointed out is that a future ISO standard should emphasize more the criterion of physical/economical significance as a prerequisite to apply substitution to avoid incorrect interpretations of the results.

The second reason for the debate is the meaning and application of the "ISO relationships" criterion for the selection of the allocation method. A first interpretation (found in 28% of the case studies) is that the ISO refers to "causal physical relationships" as relationships mathematically modeled, while "other causal relationships" relate to other relationships (e.g., based on physical or economic parameters) selected based on the best proxy for physical relationships. The second interpretation is that allocation by "physical relationships" refers to an allocation by physical parameters (e.g., mass or energy) while "other relationships" refer to economic relationships.

Most (94%) of the LCAs of multifunctional case studies found in the literature search are linked to bioeconomy (agriculture, biofuels, bioenergy, and biomaterials) and its linked sectors (fossil fuels and petrochemical plastic materials and dairy products). This has generated inconsistencies within each area, but also at the boundaries between these sectors, because of their multiple links. As an example, biogas can be produced from the manure of a farm, which produces dairy products with animals that eat dried distillers' grains with solubles coming from ethanol fermentation. Such ethanol production may have a pre-treatment process shared with lactic acid fermentation. This lactic acid may be used to produce poly-lactide which, in the market, replaces polypropylene. The above biogas can then be used to generate electricity that can be partly consumed on the farm and partially injected in the grid, substituting power from fossil fuels. How much double counting or how many inconsistencies arise when ISO 14044:2006 is interpreted differently in each of these sectors?

The bibliometric review based on the analysis of the main path obtained from tracing the citation network allowed us to (1) reconstruct how the implementation practices of the ISO hierarchy developed in the last 25 years, (2) identify the origin of the different interpretations and their rationales, and (3) understand how the discrepancies found in the critical review were generated. It emerged that, originally, the ISO hierarchy [92] recommended the approach followed by the "socio-economic ALCA school". The socio-economic ALCA school interprets system expansion as enlargement but prefers economic allocation to allocation based on physical parameters representing a proxy for causality. The origin of the "natural-science ALCA school" was traced to ISO 14041:1998 [25], when allocation by physical parameter as well as economic allocation was permitted as an example of ISO "allocation by other relationships". The natural-science ALCA school interprets system expansion as enlargement and applies allocation based on a physical parameter (for a part of the practitioners subscribing to this view, this choice is justified only when a physical parameter representing causality principles is identified). Its role was promoted by the release of the PEF guide and PEFCR guidance [28,29], which expressed a preference for allocation based on physical parameters over economic ones. Another important view is the one of the "CLCA school" interpreting system expansion as substitution and selecting the allocation method based on causality principles. The birth and development of the CLCA school were found in the annex of ISO14041:1998 and in the publications of Ekvall and co-authors [72,88,94]. They were the first ones (in the main path) to acknowledge the suitability of the substitution method to avoid allocation and account for counterfactual effects (originally proposed by Tillman et al. [58]) and the assumption of "conceptual equivalency" of substitution with the system expansion method.

Summarizing, following one or the other school of thought, a different method is often preferred for the same system, goal and decision context. Applying these different methods could lead to different conclusions and, sometimes, opposite conclusions.

To increase the consistency and reliability of LCA, we believe that a future revised ISO should:

1. Clearly state if distinguishing between attributional and consequential LCA is a key principle to implement the hierarchy. If yes, then it should differentiate the hierarchy for the two approaches and clarify if the hierarchy allows substitution as a system expansion method in attributional LCAs. 2. Clarify the meaning of allocation by "physical relationships" and "other relationships", providing more examples and details than the ones reported in ISO 14044:2006 and ISO 14049:2012.

**Author Contributions:** Conceptualization, C.M. and B.C.; methodology, C.M., B.C., A.M. and M.R.; software, C.M.; validation, C.M., B.C., R.E., M.J. and L.S.; formal analysis, C.M., B.C., R.E. and M.R.; investigation, C.M., R.E., A.M.; resources, A.M., M.R. and L.S.; data curation, C.M., B.C., M.J., L.S.; writing—original draft preparation, C.M., B.C., R.E.; writing—review and editing, R.E., M.J., A.M., M.R. and L.S.; visualization, B.C., L.S.; supervision, B.C., M.J., A.M., M.R. and L.S.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**
