SuppMat 2: Comparing different PFIM configurations

One of the challenges with the PFIM is that there are many ways to formalise the mechanistic rules that determine feeding interactions. What is unclear is how the different rule sets may impact/alter the resulting network structure. Here the aim is to identify some of the broader philosophical ‘groups’/approaches to defining the mechanistic rules within the PFIM and comparing the resulting network that they construct.

A note on traits/rules

The rules/traits used here may not reflect the most recent iterations and changes but still represent a general idea of how the different ways we define rules/traits will affect the resulting network structure.

How we specify rules

Maximal Rules

This approach focuses on hyper specific traits for the different species. This allows the user to ‘force’ specific feeding rules and make sure that they are met. For example if looking at the size classes we can see that there are additional traits added to the size classes to ensure that e.g., microcarnivores both consume and are consumed by the correct species

An extremely subdivided-nuanced set of traits and feeding rules. Not arrows represent the direction of ‘energy flow’ i.e., the consumer trait is the one that the arrow is pointing towards.

Minimal Rules

Here we take a minimalist approach to defining the traits of species so that there are no ‘equivalent’ traits that are actually synonyms since they have the same feeding rules as well as ‘forcing’ certain feeding patterns.

Lumping some of the different traits in order to have fewer feeding rules.

Size Rules

Size data

Currently we are defining all species as squares (i.e., \(length \times breadth\)) and it will be good if the Leeds team can modify this to reflect taxonomy/species geometry better…

Instead of using categorical size classes as per Shaw et al. (2024) we could use the estimated sizes of different species. As is the norm (e.g., Petchey et al. 2008) we can define the ‘size rule’ so that consumers must be larger than their resource. In theory moving from categorical to continuous sizes for species would give a more stringent set of size-based feeding rules and we might expect there to be a decrease in the number of links between species.

For this exercise I have used the same feeding rules as the ‘minimal’ example, except that size is now treated as an if statement

How we specify species

Trophic species

Taxonomic Guilds

In a similar fashion to lumping species based on their diets we could also group species as taxonomic guilds - again here guidance from the Leeds team would be beneficial.

Because there are many species that might have the exact same set of traits (and thus the exact same set of feeding links) we can instead ‘collapse’ species to represent trophic species. Theoretically this would remove all ‘redundant’ links in the system BUT it comes at the cost that we lose the species specificity we would have with other networks.

Identifying trophic species

I simply grouped species that had the exact same set of traits as we expect species with the same sets of traits to fulfil the same set of feeding rules.

Including ‘non-trophic’ species

The inclusion of parasites and scavengers represents the inclusion of links that ‘operate’ in a way that is different from the traditional definition of a feeding link. Scavengers are not actively removing individuals from a population but are rather capitalising on ‘dead’ biomass and (generally) for a scavenger the taxonomic identity/ traits of a species i.e., the basis for feeding rules is fundamentally different. Parasites could arguably be viewed the same as herbivores — BUT they are usually highly specialised and complicate our understanding of food webs since they will typically not be predated upon i.e., will have a low degree of vulnerability and will create a lot of short chains in the network e.g., parasites of herbivores would be ‘top predators’ since they would not be predated on by other species

In conclusion although scavengers and parasites are present in communities there are not 100% compatible with the traditional definition of a food web - especially in the way that PFIM specifies feeding rules.

Here we use the same minimum feeding rules but remove all traits (and species) related to scavenging or parasitism

Assumptions on structure

Including a basal node

Shaw et al. (2024) includes a basal node in their networks. Philosophically having a rooted network (basal node) does not make sense in the PFIM space of defining feeding rules. However there is an argument to be had that having a rooted network allows one to ‘protect’ the basal species in the network.

Downsampling

Although PFIM as a network generating tool falls firmly within the metaweb space there is the argument to be had that owing to the coarse granularity of paleo communities (aggregated over large spatial and time scales) means that the resulting networks is ‘over represented’. This begs the question of if we should be downsampling these metawebs to have them represent a slightly more ‘ecologically plausible’ network configuration. Roopnarine (2006) developed a downsampling approach that removes links between species based on the generality of a species.

Results

Networks created

Unless otherwise stated all networks use the minimum feeding rules and are a ‘metaweb’ - i.e., they are not downsampled.

Different structural features

Broadly speaking we observe the same ‘patterns’ over time for the different networks and values are not grossly different (eye test). Often we do see the trophic networks deviating a bit from this generalisation but that makes sense since the communities are more ‘contracted’.

Note that the shapes represent the different time periods.

Overall similarity/clustering

It might also be useful to compare the networks as a ‘whole’ i.e., looking at all traits at the same time. Again we see the trophic networks clustering (to be expected). Interestingly the ‘pre communities’ tend to cluster which I take to mean that the differences between time frames is a stronger signal than the different network construction approaches (broadly).

Bog standard PCA using the different structural features of the networks (excluding motifs because they introduce a lot of NAs and the reason why still remains unclear…). Note that the shapes represent the different time periods.

Redundancy? Structure?

References

Petchey, Owen L., Andrew P. Beckerman, Jens O. Riede, and Philip H. Warren. 2008. “Size, Foraging, and Food Web Structure.” Proceedings of the National Academy of Sciences 105 (11): 4191–96. https://doi.org/10.1073/pnas.0710672105.

Roopnarine, Peter D. 2006. “Extinction Cascades and Catastrophe in Ancient Food Webs.” Paleobiology 32 (1): 1–19. https://www.jstor.org/stable/4096814.

Shaw, Jack O., Alexander M. Dunhill, Andrew P. Beckerman, Jennifer A. Dunne, and Pincelli M. Hull. 2024. “A Framework for Reconstructing Ancient Food Webs Using Functional Trait Data.” bioRxiv. https://doi.org/10.1101/2024.01.30.578036.