文件列表:

.assets/
appendix/
code/
data/
figures/
LICENSE.md
Manifest.toml
Project.toml
logo.png
main.jl
metadata.json
references.bib

# Introduction As we try to navigate global biodiversity change, filling in knowledge gaps about biodiversity becomes instrumental to monitoring and mitigating those changes (@Gonzalez2022Monitor, @Abrego2021Accounting). However, cataloging species, populations and, in particular, ecological interactions (e.g., predation, parasitism, and pollination) is a substantial challenge (@Polis1991Complex, @Pascual2006Ecologicala). There are methodological and biological constraints that hinder our ability to observe all ecological interactions, leading to significant uncertainties in our understanding of these interactions. For example, the spatial and temporal uncoupling of species (@Jordano1987PatMut) and the large number of rare and cryptic interactions in a community contribute to these uncertainties (@Jordano2016Samplingb). More generally, a handful of conditions must be satisfied for an interaction to be observed locally. First, both species must have overlapping geographic ranges, i.e. they must co-occur within the region of interest (@Blanchet2020Cooccurrencea). Second, they must have some probability of meeting. Probabilities of interspecific encounters are typically low, especially for rare species with low relative abundances (@Canard2012Emergencea). The probability that species meet each other also depends on their biological characteristics, such as the synchronization of their phenology (@Olesen2010Missing, @Singer2012GeoMos) and their discoverability (e.g., @Broom2005You). Finally, when species do come into contact, an interaction occurs only if their traits are locally compatible (@Poisot2015Speciesa), including but not limited to their body phenotypes (@Bolnick2011WhyInt, @Stouffer2011RolBod, @Gravel2013InfFooa) and behavioral choices (@Pulliam1974Theory, @Choh2012PreRol). Interactions may also be influenced by the presence or prevalence of a third species (e.g., of a more profitable prey species) (@Golubski2011ModMod, @Sanders2012Indirect). Documenting the location and timing of interactions becomes even more difficult when accounting for the spatiotemporal variability of ecological interactions (@Poisot2012Dissimilaritya, @Poisot2015Speciesa). Environmental factors, such as temperature (@Angilletta2004TemGro), drought (@Woodward2012CliCha), climate change (@Gilman2010FraCom, @Woodward2010ChaEco, @Araujo2011Usinga), and habitat modifications (@Tylianakis2007HabMod), contribute to this spatiotemporal variability of interactions by impacting species abundance and traits. Even after satisfying all these conditions, there remains a possibility that the interaction does not occur locally, either due to the intricate nature of the system or simply by chance. If it does occur, it might still go unnoticed, particularly if it happens infrequently. In this context, it is unsurprising that our knowledge of ecological interactions remains limited (@Hortal2015SevSho) despite extensive biodiversity data collection (@Schmeller2015GloTer). Knowing the biological capacity of two species to interact directly (via e.g., trophic interactions) is necessary but not sufficient for inferring their interaction at a specific time and space. The recognition of the intrinsic variability of species interactions has led ecologists to expand their representation of ecological networks (also known as ecological webs) to include a probabilistic view of interactions (@Poisot2016Structure, @Dallas2017Predictinga, @Fu2021Link). This different perspective allows us to fill in the Eltonian shortfall (@Hortal2015SevSho) by modeling the probability of detecting interactions, which can be an important tool for directing efforts and taking action, especially in places where access and resources for research are scarce. Representing interactions probabilistically enables us to capture the spatiotemporal variability of the aforementioned ecological processes and the uncertainties associated with their measurement. As opposed to binary deterministic webs, in which interactions are regarded as either occurring or not, probabilistic webs, within a Bayesian framework, express our degree of belief (or confidence) regarding the occurrence of interactions. Based on the scale at which they are estimated, probabilistic interactions may reflect our level of confidence in whether interactions will be observed, realized, or biologically feasible. As an illustration, we could outline a situation in which there is a 50% certainty that an interaction occurs 50% of the time, or that there is a 50% certainty that it simply occurs. Our level of confidence should be more definitive (approaching either 0 or 1) as we extend our sampling to a broader area and over a longer time period, thereby diminishing the uncertainty of the interactions (but not necessarily the estimation of their variability). In the broadest sense, binary networks are also a type of probabilistic network, in which the numerical value of an interaction is restrained to 0 (non-occurring) or 1 (occurring). Yet, for the sake of clarity, we omit binary networks from our discussion of probabilistic networks in this contribution. In probabilistic webs, only forbidden interactions (i.e., interactions prohibited by biological traits or species absence, @Jordano2003Invarianta, @Olesen2010Missing) have a probability value of zero by default, provided that intraspecific trait variability is considered (@Gonzalez-Varo2016Labilea). By accounting for the uncertainty of interactions, probabilistic webs may provide a more realistic portrait of species interactions and network structure (i.e. community-level properties), which are major drivers of the functioning, dynamics, and resilience of ecosystems worldwide (@Proulx2005Networka, @McCann2007ProBio, @McCann2011FooWeb, @Rooney2012IntFoo). Moreover, the application and development of computational methods in network ecology, often based on a probabilistic representation of interactions, can alleviate (and guide) the sampling efforts required to document species interactions (@Strydom2021Roadmapa). For example, statistical models can be used to estimate the uncertainty of pairwise interactions (@Cirtwill2019QuaFra) and the probability of missing (false negatives) and spurious (false positives) interactions (@Guimera2009MisSpu). Considering the high rate of false negatives in species interaction data due to the difficulty of witnessing rare interactions (@Catchen2023Missinga), these models could inform the identification of priority sampling locations of ecological webs where data collection would yield the most valuable information, thereby reducing errors. Optimization models for sampling locations have mostly found applications in biological systems that are not networks, such as identifying priority sampling sites for disease hotspots (@Andrade-Pacheco2020Finding), but there is substantial promise in applying them to probabilistic ecological interactions. Statistical models can also be used to generate predictions of ecological webs without prior knowledge of pairwise interactions, for instance using body size (@Petchey2008SizFor, @Gravel2013InfFooa), phylogeny (@Elmasri2020HieBay, @Strydom2022Food), or a combination of niche and neutral processes (@Bartomeus2016ComFra, @Pomeranz2019InfPre) for inference. Topological null models, which generate probabilistic networks by preserving chosen characteristics of the binary adjacency matrix while intentionally omitting others (@Bascompte2003NesAss, @Fortuna2006HabLos), serve as other examples of common probabilistic network models. Null models can be used to produce underlying distributions of network measures for null hypothesis significance testing. Many measures have been developed to describe the structure (@Poisot2016Structure) and diversity (@Ohlmann2019Diversity, @Godsoe2022Species) of probabilistic webs. These models and measures support the use of this approach for the study of a wide range of ecological questions, from making better predictions of species distribution (@Cazelles2016Theorya) to forecasting the impact of climate change on ecological webs (@Gilman2010FraCom). The lack of clear guidelines on the use of probabilistic interaction data is worrisome, both for data producers and re-users who generate and manipulate these numbers. This is concerning because sampling strategies and decisions regarding network construction can affect our understanding of network properties (@Brimacombe2023ShoReu). Besides methodological difficulties that may arise when assessing probabilistic interactions, a precise definition of probabilistic interactions appears to be lacking, making the estimation and use of these data more difficult. We aim to take a step back by outlining different ways in which probabilistic interactions are defined and used in network ecology. We distinguish two broad categories of probabilistic webs that necessitate distinct approaches when applied to key ecological questions: local webs describing probabilities of realized interactions, and regional webs (metawebs) describing probabilities of potential interactions. We highlight the distinctions in the ecological meaning of these two representations and show that they yield different statistical outcomes regarding e.g. the spatial and temporal scaling of interactions and the prediction of binary webs across space. Moreover, there is currently no metadata standard that could guide the documentation of all types of probabilistic interactions (although see e.g., @Salim2022Data who discuss data standards for deterministic mutualistic webs). Well-defined metadata for probabilistic webs would support more adequate manipulation and integration of interaction data from different sources and guard against possible misinterpretations arising from ambiguous definitions of probabilistic networks. These metadata should outline the nature (i.e., local or regional) and type (e.g., predatory or pollination) of the interactions, provide information regarding the taxonomic level, identities, and characteristics (e.g., life stages) of the individuals involved in an interaction, present the mathematical formulation of probabilities, including clearly identified conditional variables (e.g., spatial and temporal scales), and describe the methods and contexts (e.g., location, time, environmental conditions) in which interactions were estimated. Inadequately documented probabilistic interaction data should be used with caution when analyzing ecological webs. Our observations and advice can be applied to many types of ecological networks, from food webs to host-virus networks. Indeed, excluding networks of indirect interactions such as competition and facilitation networks (@Kefi2015NetStr, @Kefi2016HowStr), most ecological webs describe probabilities of direct interactions, which are conceptually and mathematically analogous regardless of their biological type (e.g., trophic and parasitic interactions). # Probabilistic representations of interactions One of the first aspects to take into consideration when estimating or interpreting probabilities of interactions is knowing if they describe potential or realized interactions. A potential (regional) interaction is defined as the biological capacity of two taxa to interact (i.e., the probability that they *can* theoretically interact) whereas a realized (local) interaction is the materialization or observation of this interaction in a well-defined space and time (i.e., the probability that they interact locally). Here, we use the terms *metaweb* (@Dunne2006Network) to designate regional webs of potential interactions and *local webs* (@Poisot2012Dissimilaritya) for those of realized interactions. Metawebs are the network analogs of the species pool, where local webs originate from a subset of both species (nodes) and interactions (edges) of the regional metaweb (@Saravia2022Ecological). Without clear documentation, it can be challenging to know if published probabilistic webs describe local or regional interactions (@tbl:prob provides examples of studies employing both types of probabilistic networks), or if so-called probabilities are in reality *interaction scores* (i.e., non-probabilistic quantitative interactions). When probabilistic regional interactions are used and interpreted as local interactions (and conversely), this may generate misleading findings during data analysis. We believe that a better understanding of the differences, similarities, and relationships between these two probabilistic representations of ecological webs would alleviate interpretation errors and facilitate a more adequate utilization of interaction data. ## Pairwise interactions: the building blocks of ecological networks Local and metawebs, like any type of network, are made of nodes and edges that can be represented at different levels of organization and precision. The basic unit of food webs and other ecological networks are individuals that interact with each other (e.g., by predation, @Elton2001Animal), forming individual-based networks (@Melian2011EcoDyn). The aggregation of these individuals into more or less homogeneous groups (e.g., populations, species, families) allows us to represent nodes at broader taxonomic scales, which affects our interpretation of the properties of these systems (@Guimaraes2020Structurea, @Hemprich-Bennett2021AssImp). Edges linking nodes can describe a variety of interaction measures. Ecologists have traditionally represented interactions as binary objects that were considered realized after observing at least one individual from group $i$ interact with at least another individual from group $j$. In a binary adjacency matrix $B$, the presence or absence of an interaction $B_{i \rightarrow j}$ between two taxa can be viewed as the result of a Bernoulli process $B_{i \rightarrow j} \sim {\rm Bernoulli}(P(B_{i \rightarrow j}))$, with $P(B_{i \rightarrow j})$ being the probability of interaction that characterizes our limited knowledge of the system and its intrinsic spatiotemporal variability. In probabilistic networks, $P(B_{i \rightarrow j})$ are edge values, and the only two possible outcomes are the presence ($B_{i \rightarrow j} = 1$) or absence ($B_{i \rightarrow j} = 0$) of an interaction between each pair of nodes. Depending on the type of probabilistic network (local or metaweb), the mathematical formulation and interpretation of stochastic parameters like $P(B_{i \rightarrow j})$ can be linked to environmental and biological factors such as species relative abundance, traits, area, and time (@tbl:prob), for example using logistic regression with a logit link function with continuous explanatory variables. Predicting the number of local webs in which the interaction occurs can be achieved by using a Binomial distribution, assuming a constant probability of interaction and independence between networks (trials). When considering uncertainties around the estimation of $P(B_{i \rightarrow j})$, a Beta distribution can also be used to encompass all possible probability values. In that case, a Beta-Binomial distribution can be used to predict the number of networks in which the interaction occurs. Observing an interaction between two taxa at a given location and time provides important information that can be used to update previous estimates of $P(B_{i \rightarrow j})$, informing us on the biological capacity of both taxa to interact and the environmental conditions that enabled them to interact locally. Even though binary webs constitute a highly valuable source of ecological information (@Pascual2006Ecologicala), they overlook important factors regarding interaction strengths. Represented in a quantitative adjacency matrix $W$ as numbers not confined to the $[0, 1]$ range, interaction strengths better describe the energy flows, demographic impacts or frequencies of interactions between nodes (@Berlow2004Interaction, @Borrett2019Walk), with $W_{i \rightarrow j}$ being a natural $\mathbb{N}$ or real $\mathbb{R}$ number depending on the measure. For example, they may represent local interaction rates between pairs of taxa (e.g., the flower-visiting rates of pollinators in a mutualistic network, @Herrera1989PolAbu). When interaction strengths characterize predation pressure on prey taxa in food webs, they can serve as good estimators of the parameters describing species interactions in a Lotka-Volterra model (e.g., @Emmerson2004Predatora). The extra amount of ecological information in quantitative networks typically comes at a cost of greater sampling effort and data volume in predictive models (@Strydom2021Roadmapa), which can lead to relatively high levels of uncertainties when inferring quantitative webs with limited data. Just like binary networks, the uncertainty and spatiotemporal variability of interaction strengths can be represented probabilistically. However, the need to estimate the probability distribution of all possible values of interaction strengths can make the inference of probabilities more challenging in quantitative webs compared to binary webs, which require only one probability estimate for each interaction. Interaction strengths can follow various probability distributions depending on the measure used. For instance, they can follow a Poisson distribution $W_{i \rightarrow j} \sim {\rm Poisson}(\lambda_{i \rightarrow j})$ when predicting frequencies of interactions between pairs of nodes, with $\lambda_{i \rightarrow j}$ being the expected rate at which individuals of taxa $i$ and $j$ interact (e.g., the average number of prey $j$ consumed by all predators $i$ in a given time period). The Poisson distribution can also be 0-inflated after initially modeling non-interacting taxa (e.g., @Boulangeat2012AccDis employ a 0-inflated model to analyze species abundance following the modeling of species presence and absence), which constitute the majority of taxa pairs in most local webs due to their typically high sparseness (@Jordano2016Samplingb). Because of the methodological difficulties typically encountered when building deterministic quantitative webs (which are only partially mitigated by models such as Ecopath, @Plaganyi2004Criticala), binary webs, which are easier to sample (@Jordano2016Samplingb) and predict (@Strydom2021Roadmapa), have been more frequently studied and modeled. Moreover, most published probabilistic networks and methods describe probabilistic interactions whose outcome is binary (whether interaction probabilities are regarded as constant or variable, e.g. represented by a Beta distribution), which underlines the need for better guidelines regarding the interpretation and manipulation of these types of webs first. For these reasons, our primary focus in this contribution will be on addressing the challenges in interpreting and using interaction probabilities in Bernoulli distributions, in both probabilistic local and metawebs. ## Local webs: communities interacting in space and time Probabilistic local webs describe how likely taxa are to interact at a given location and time period (i.e., interactions are contingent upon the environmental and biological conditions of the community). In local webs, edges commonly represent our degree of belief that two taxa interact in nature, but can also represent the probability of *observing* this interaction (@Catchen2023Missinga). For example, @Gravel2019BriElt used a dataset of binary local European food webs of willow-galling sawflies and their natural enemies, all referenced in space and time and consisting of similar species, to infer the probabilities of locally observing interactions between co-occurring species. This was ... ...

近期下载者：

相关文件：

评论：[我要评论] [举报此文件]

收藏者：