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Expand Up @@ -123,8 +123,6 @@ Perhaps not as intuitive when thinking about the processes that determine feedin

The suite of different network representations [@sec-representation] that we have at our disposal allow us to isolate and operate within one (or a few) of the constraints discussed in @sec-process, and have an influence on the way we construct networks, specifically in terms of the development of different models. The act of constructing a 'real world' network through the empirical collection of interaction data is both costly and challenging to execute [@jordanoChasingEcologicalInteractions2016; @jordanoSamplingNetworksEcological2016], thus we often turn to models to either predict networks (be that the interaction between two species, or network structure [@strydomRoadmapPredictingSpecies2021]), identify missing interactions (gap fill) within an existing empirical dataset [*e.g.,* @bitonInductiveLinkPrediction2024; @stockPairwiseLearningPredicting2021; @dallasPredictingCrypticLinks2017]. In the context of this discussion food web models are also a valuable to that will allow us to better understand the different constraints determining interactions [@stoufferAllEcologicalModels2019; @songRigorousValidationEcological2024], allowing us to interrogate, generate, and reflect upon different ecological theories.

Here we will present the broader bodies of theory that have underpinned the development of different food web models, specifically in terms of understanding what drives the presence of interactions between species. Broadly we can think of interactions being 'stochastic', determined by the feasibility of traits (*sensu* @sec-process-feasibility), and more broadly the behaviour and dynamics of biological systems (*sensu* @sec-process-realisation). Each of these categories have their own set of accompanying theories and modelling approaches that have been developed within them and mapping these out is beneficial for two reasons 1) it is critical that the 'correct' network (and thus underlying models and assumptions) are used if we truly want to understand how different processes determine interactions [@estayEditorialPatternsProcesses2023; @moulatletScalingTrophicSpecialization2024; @saberskiImpactDataResolution2024; @saraviaEcologicalNetworkAssembly2022] and constructively move the field forward, and 2) provide guidance as to the identifying the appropriate networks for different research questions [@petcheyFitEfficiencyBiology2011, see also @sec-progress and Box 1].

::: {#box-hypothetical .callout-note}
# Box 1 - Why we need to aggregate networks at different scales: A hypothetical case study {.unnumbered}

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## Feasibility networks (metawebs)

Metawebs (depending on the aggregation) can help us develop our understanding of the intersection of species interactions and their co-occurrence [*sensu* a fusion of the the Eltonian (interactions) and Grinnellian (environmental) niches, @soberonGrinnellianEltonianNiches2007; @gravelBringingEltonGrinnell2019]. Whereby a *global metaweb* presents an approximation of the fundamental Eltonian niche of a species (*i.e.,* its relation to its food source), whereas as *regional metawebs* represent an intersection of Elton and Grinnell. As discussed in @sec-process-feasibility the feasibility of an interaction is typically assessed on a pairwise basis, and is often assessed based on the idea that interactions are governed by a set of 'feeding rules' [@morales-castillaInferringBioticInteractions2015], and are broadly elucidated in two different ways; *mechanistic models*, [*e.g.,* @shawFrameworkReconstructingAncient2024; @dunneCompilationNetworkAnalyses2008; @roopnarineEcologicalModellingPaleocommunity2017] and *pattern finding models* [*e.g.,* @strydomGraphEmbeddingTransfer2023; @pichlerMachineLearningAlgorithms2020; @strydomFoodWebReconstruction2022; @caronAddressingEltonianShortfall2022; @llewelynPredictingPredatorPrey2023; @desjardins-proulxEcologicalInteractionsNetflix2017; @eklofSecondaryExtinctionsFood2013; @cirtwillQuantitativeFrameworkInvestigating2019]. The fundamental difference between these two model groups is that *mechanistic models* rely on expert knowledge and make explicit assumptions on trait-feeding relationships, whereas the *pattern finding models* are dependent on existing interaction datasets from feeding rules can be elucidated. It perhaps also bears repeating that these models are often only presenting a list of feasible interactions and that the rresulting netowrk is 'unstructured', as it is uconstrained by any processes or conditions that generate structure. While these networks can be imprinted with external definitions of trophic position and guild identity to deliver hypothetical structure, this structure is not an emergent property of the links and species pairs [@caronTraitmatchingModelsPredict2024].
Metawebs (depending on the aggregation) can help us develop our understanding of the intersection of species interactions and their co-occurrence[@soberonGrinnellianEltonianNiches2007; @gravelBringingEltonGrinnell2019]. Whereby a *global metaweb* presents an approximation of the fundamental Eltonian niche of a species (*i.e.,* its relation to its food source), whereas as *regional metawebs* represent an intersection of Elton and Grinnell. As discussed in @sec-process-feasibility the feasibility of an interaction is typically assessed on a pairwise basis, and is often assessed based on the idea that interactions are governed by a set of 'feeding rules' [@morales-castillaInferringBioticInteractions2015], and are broadly elucidated in two different ways; *mechanistic models*, [*e.g.,* @shawFrameworkReconstructingAncient2024; @dunneCompilationNetworkAnalyses2008; @roopnarineEcologicalModellingPaleocommunity2017] and *pattern finding models* [*e.g.,* @strydomGraphEmbeddingTransfer2023; @pichlerMachineLearningAlgorithms2020; @strydomFoodWebReconstruction2022; @caronAddressingEltonianShortfall2022; @llewelynPredictingPredatorPrey2023; @desjardins-proulxEcologicalInteractionsNetflix2017; @eklofSecondaryExtinctionsFood2013; @cirtwillQuantitativeFrameworkInvestigating2019]. The fundamental difference between these two model groups is that *mechanistic models* rely on expert knowledge and make explicit assumptions on trait-feeding relationships, whereas the *pattern finding models* are dependent on existing interaction datasets from feeding rules can be elucidated. It perhaps also bears repeating that these models are often only presenting a list of feasible interactions and that the rresulting netowrk is 'unstructured', as it is uconstrained by any processes or conditions that generate structure. While these networks can be imprinted with external definitions of trophic position and guild identity to deliver hypothetical structure, this structure is not an emergent property of the links and species pairs [@caronTraitmatchingModelsPredict2024].

Feasibility networks are useful for determining all feasible interactions for a specific community, and the models that have been developed in this context have the potential to allow us to construct first draft networks for communities for which we have no interaction data [@strydomFoodWebReconstruction2022], and are valuable not only in data poor regions but also for predicting interactions for 'unobservable' communities *e.g.,* prehistoric networks [@yeakelCollapseEcologicalNetwork2014; @frickeCollapseTerrestrialMammal2022; @dunhillExtinctionCascadesCommunity2024] or future, novel community assemblages. Conceptually this is particularly valuable if we want to understand interactions between novel communitites, as well as the rewiring capacity of species. Additionally, an understanding of the role of interactions between species has allowed us to better determine the distribution of a species by accounting not only for the role of the environment but also the role of species interactions [@higinoMismatchIUCNRange2023; @pollockUnderstandingCooccurrenceModelling2014].

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# Making Progress with Networks {#sec-progress}

It should be clear that there is a high degree of interrelatedness and overlap between the way in which a network is constructed and the process(es) that it captures [@fig-process], these are encoded (embedded) within the network representation and ultimately influences how the network can and should be used [@petcheyFitEfficiencyBiology2011; @berlowGoldilocksFactorFood2008], with different network representations (and models) yielding different interpretations of processes [@keyesSynthesisingRelationshipsFood2024].

It is probably both this nuance as well as a lack of clear boundaries and guidelines as to the links between network form and function [although see @delmasAnalysingEcologicalNetworks2019] that has stifled the 'productive use' of networks beyond the inventorying the interactions between species. Although progress with using networks as a means to address questions within larger bodies of ecological theory *e.g.,* invasion biology [@huiHowInvadeEcological2019] and co-existence theory [@garcia-callejasNonrandomInteractionsGuilds2023] has been made we still lack explicit guidelines as to what the appropriate network representation for the task at hand would be, and as highlighted in Box 1, underscores the need to evaluate exactly what process a specific network representation captures as well as its suitability for the question of interest. Below we present a mapping of what we believe are some of the key questions for which interaction networks can be used to the different networks representations that are most suitable, as well as highlight some of the methodological challenges that still need to be improved upon.

## Making use of the different network representations
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