PALEO INDEX

To assess the scientific value and vulnerability of fossil sites the methodology proposed by Faggi et al. (2023) is followed. Three categories of parameters are considered: probability of discovery, the site's interest, and its vulnerability.

These parameters enable the calculation of four distinct indices:

• Probability of discovery index (Pr),

• Interest of the site (In),

• Scientific value index (S*),

• Vulnerability index (V).

In general, sites that contain direct fossil evidence of organisms—such as the Pietraroja deposit—are categorized differently from those where organismal presence is inferred indirectly, as with fossil trace sites like the Ciampate del diavolo. As a result, each type of site is described using distinct criteria, and the indicators used to evaluate them rely on different variables that are not interchangeable between site types. For instance, locations preserving skeletal remains involve different probabilities of discovery and levels of scientific interest compared to those that preserve only fossilized traces.

Discovery probability index (Pr)

The discovery probability index serves as a methodological tool for estimating the likelihood of uncovering fossil remains within a delineated area, thereby providing strategic support to governmental bodies and local institutions in the planning and implementation of construction activities. Moreover, this index enables the systematic comparison and classification of fossiliferous sites based on their paleontological relevance. For instance, low index values may reflect a limited abundance of fossil material or a reduced potential for preservation.

The parameters that make up the discovery probability (Pr) are the numerical consistency of fossils recovered (P1) and the site extension (P2) as follows:

𝑃𝑟 = 𝑃1 + 𝑃2

For localities with ichnofossils, the parameter P1 is replaced by the numerical consistency of the recovered traces (Pt1) modifying the Pr equation as:

𝑃𝑟 = 𝑃𝑡1 + 𝑃2

As the name implies, numerical consistency of fossils/traces recovered (P1/Pt1) is simply defined as the number of single fossil elements or traces recovered from a site. Unidentifiable bone fragments and unidentifiable plant matter are not included in the calculation.

The site extension parameter (P2) defines the areal extension of the fossiliferous locality. Due to the difficulty of quantifying an area, sites can be classified as punctual sites (very spatially limited fossiliferous areas), medium areal site (including fossiliferous sites located on small quarry fronts, medium-sized outcrops, cave complexes, mines), and areal site (large quarries and extensive outcrops).

Site interest index (In)

The site interest index (in) evaluates the scientific significance of a site based on several parameters.

For sites containing fossil remains, the index considers the following criteria: total taxa diversity (I1), relative taxa diversity (I2), citation frequency (I3), knowledge level (I4), taxa rarity (I5), presence of valid and / or historical type specimens (i.e., the site is a type locality) (I6), and potential for tourism and educational activities (I7).

For sites that preserve trace fossils (such as footprints or burrows), some parameters are adapted to better reflect their characteristics. The index in these cases includes: variety of ichnogroups and/or ichnotypes (It1), number of trackways (It2), citation frequency (I3), knowledge level (I4), length of trackways (It5), presence of valid and/or historically important types (I6), and potential for tourism and education (I7).

The total taxa diversity (I1) simply defines the number of different taxa identified in a site. Unidentifiable bone fragments or plant matter are not included in this count. Similarly, the variety of ichnogroups and/or ichnotypes (It1) defines the number of ichnotaxa recognized.

Relative taxa diversity (I2) is assessed based on the presence and relative abundance of three major fossil groups: invertebrates, vertebrates, and plants. Higher I2 values indicate fossil sites where more than one of these groups is represented. Locations with a broader range of fossil types, such as Pietraroja, provide a more complete ecological overview. This allows for a more accurate reconstruction of the paleoenvironment, increasing the site's overall scientific importance.

The citation frequency (I3) was used to quantify scientific interest in a given site and how it has changed over time. This can be calculated using online academic databases (e.g., Google Scholar, Web of Science, Scopus) by identifying the first and/or most representative publication on each site and dividing its total citations by the number of years since publication. This citation rate reflects the temporal trend of scholarly attention. Using a ratio rather than total citations helps to reduce the bias favoring older or more famous fossil sites. In cases where the original publication is too old to be accurately cited in modern databases, the most cited or representative paper can be used instead.

The knowledge level parameter (I4) assesses the influence of a site and its fossils on both the scientific community and the general public.

Taxa rarity (I5) records the presence of rare or very rare taxa, reflecting the scientific and cultural importance of the site. Taxa are classified as common if widespread across many sites, uncommon if abundant at a single site or rare elsewhere.

The presence of valid and/or historic types (I6) highlights sites that have yielded valid or historically significant type specimens, underlining their scientific relevance.

Tourist and educational potential (I7) measures a site's value for public outreach (touristic, academic, etc.), based on accessibility, on-site fossils, proximity to infrastructure, availability of guided tours, and overall public interest.

For sites preserving trace fossils, relative taxa diversity (I2) and taxa rarity (I5) are replaced by the number of trackways (It2) and length of trackways (It5). This substitution follows established ichnological literature, as a greater number and diversity of trackways allow for more robust comparative analyses and scientific conclusions (Falkingham et al., 2016; Mampel et al., 2009), enhancing the site's scientific and cultural significance. The length of trackways (It5) is calculated differently depending on the trackmaker: for vertebrates, it is based on the number of preserved steps; for invertebrates, on the physical length of the track.

The sum of these seven parameters produces the site interest index:

𝐼𝑛 = 𝐼1 + 𝐼2 + 𝐼3 + 𝐼4 + 𝐼5 + 𝐼6 + 𝐼7

In case of localities with fossil tracks, the equation is modified as follows:

𝐼𝑛 = 𝐼𝑡1 + 𝐼𝑡2 + 𝐼3 + 𝐼4 + 𝐼t5 + 𝐼6 + 𝐼7

Scientific value index (S*)

The combination of the discovery probability index and the site interest index defines the scientific value index (S*). This is a more exhaustive parameter to evaluate the significance of a site. The maximum value obtainable with the current methodology is 156, but it is usually expressed as a percentage:

S* = (𝑃𝑟 x 𝐼𝑛 x 100)/156

Vulnerability index (V)

The vulnerability index uses the same parameters for sites with body fossils and those with fossil traces: productivity (p), active/inactive (a), site use (U), and natural erosion (E).

Productivity (p) and active/inactive (a) are discriminants as they can only have values of 0 or 1. They help identify sites that are no longer productive or accessible. For example, a fully excavated site with no fossils left in place, but historical significance, has a vulnerability of zero and does not require protection. Likewise, sites that are inaccessible due to human or natural causes (e.g., collapsed mines, buried outcrops, urban development) also do not need protection. Site use (U) measures current land use and its impact on fossil preservation, ranging from 0 for fully protected musealized sites to 5 for highly disturbed areas like quarries or urban zones. Intermediate values represent varying human influence levels. Natural erosion (E) is used to describe the intensity of erosion to which the site is subject. Land erosion is often influenced by many different contributing factors, such as lithology, land cover, soil susceptivity, topography, etc., often resulting in peculiar local effects. The erosion can be expressed qualitatively, assigning values of E from 0 (fully protected site) to 3 (severely affected by natural erosion). In the absence of site-specific data, following Mampel et al. (2009), a minimum default value of 0.5 can be used. To refine the natural erosion parameter, a comparison can be used between the qualitative evaluation of the degree of potential erosion and data from local institutions and geological services that report erosive potential at local or regional scales.

The vulnerability index (V) can be calculated using the following formula:

𝑉 = (S*×𝑎×𝑝×(𝑈+𝐸))/100

The vulnerability scale ranges from 0, representing protected or museum-preserved sites, to 5, indicating sites of highest vulnerability. Although the vulnerability index equation may yield values slightly exceeding 5, these are normalized to the upper limit of the scale, as any value above 4 denotes a high-risk condition requiring urgent intervention.