Most, if not all, predators consume carrion in some circumstances (Sebastián-Gonzalez et al. 2023). Consequently, significant fluctuations in carrion availability can impact predator-prey dynamics by altering the ratio of carrion to live prey in the predators' diet (Roth 2003). Changes in carrion availability may lead to reduced predation when carrion is more abundant (hypo-predation) and intensified predation if predator populations surge in response to carrion influxes but subsequently face scarcity (hyper-predation), (Moleón et al. 2014, Mellard et al. 2021). However, this relationship between predation and scavenging is often challenging because of the lack of empirical data.
 
In the study conducted by Sidous et al. (2024), they used a large database on the abundance of spotted hyenas and their prey in Zimbabwe and Multivariate Autoregressive State-Space Models to calculate hyena and prey population densities and trends over a 60-year span. The researchers took advantage of abrupt fluctuations in elephant carcass availability that produced alternating periods of high and low carrion availability related to changing management strategies (i.e., elephant culling and water supply).
 
Interestingly, their analyses reveal a coupling of predator and prey densities over time, but they do not detect an effect of carcass availability on predator and prey dynamics. However, the density of prey and hyena was partially driven by the different temporal periods, suggesting some subtle effects of carrion availability on population trends. While it is acknowledged that other variables likely impact the population dynamics of hyenas and their prey, this is the first attempt to understand the influence of carrion pulses on predator-prey interactions across an extensive temporal scale. I hope this helps to establish a new research line on the effect of large carrion pulses, as this is currently largely understudied, even though the occurrence of carrion pulses, such as mass mortality events, is expected to increase over time (Fey et al. 2015).
 
References
 
Courchamp, F. et al. 2000. Rabbits killing birds: modelling the hyperpredation process. J. Anim. Ecol. 69: 154-164.
https://doi.org/10.1046/j.1365-2656.2000.00383.x

Fey, S. B. et al. 2015. Recent shifts in the occurrence, cause, and magnitude of animal mass mortality events. PNAS 112: 1083-1088.
https://doi.org/10.1073/pnas.1414894112
 
Mellard, J. P. et al. 2021. Effect of scavenging on predation in a food web. Ecol. Evol. 11: 6742- 6765.
https://doi.org/10.1002/ece3.7525

Moleón, M. et al. 2014. Inter-specific interactions linking predation and scavenging in terrestrial vertebrate assemblages. Biol. Rev. Camb. Philos. Soc. 89: 1042-1054.
https://doi.org/10.1111/brv.12097
 
Roth, J. 2003. Variability in marine resources affects arctic fox population dynamics. J. Anim. Ecol. 72: 668-676.
https://doi.org/10.1046/j.1365-2656.2003.00739.x
 
Sebastián-González, E. et al. 2023. The underestimated role of carrion in diet studies. Global Ecol. Biogeogr. 32: 1302-1310.
https://doi.org/10.1111/geb.13707
 
Sidous, M. et al. 2024. Insights on the effect of mega-carcass abundance on 1 the population dynamics of a facultative scavenger predator and its prey. bioRxiv, ver. 2 peer-reviewed and recommended by PCI Ecology.
https://doi.org/10.1101/2023.11.08.566247

The late eminent ecologist Gary Polis once stated that “most catalogued food-webs are oversimplified caricatures of actual communities” and are “grossly incomplete representations of communities in terms of both diversity and trophic connections.” Not content with that damning indictment, he went further by railing that “theorists are trying to explain phenomena that do not exist” [1]. The latter critique might have been push back for Robert May´s ground-breaking but ultimately flawed research on the relationship between food-web complexity and stability [2]. Polis was a brilliant ecologist, and his thinking was clearly influenced by his experiences researching desert food webs. Those food webs possess an uncommon combination of properties, such as frequent omnivory, cannibalism, and looping; high linkage density (L/S); and a nearly complete absence of apex consumers, since few species completely lack predators or parasites [3]. During my PhD studies, I was lucky enough to visit Joshua Tree National Park on the way to a conference in New England, and I could immediately see the problems posed by desert ecosystems. At the time, I was ruminating on the “harsh-benign” hypothesis [4], which predicts that the relative importance of abiotic and biotic forces should vary with changes in local environmental conditions (from harsh to benign). Specifically, in more “harsh” environments, abiotic factors should determine community composition whilst weakening the influence of biotic interactions. However, in the harsh desert environment I saw first-hand evidence that species interactions were not diminished; if anything, they were strengthened. Teddy-bear chollas possessed murderously sharp defenses to protect precious water, creosote bushes engaged in belowground “chemical warfare” (allelopathy) to deter potential competitors, and rampant cannibalism amongst scorpions drove temporal and spatial ontogenetic niche partitioning. Life in the desert was hard, but you couldn´t expect your competition to go easy on you.
If that experience colored my thinking about nature’s reaction to a capricious environment, then the seminal work by Robert Paine on the marine rocky shore helped further cement the importance of biotic interactions. The insights provided by Paine [5] brings us closer to the research reported in the preprint “The return of the trophic chain: fundamental vs realized interactions in a simple arthropod food web” [6], given that the authors in that study hold the environment constant and test the interactions between different permutations of a simple community. Paine [5] was able to elegantly demonstrate using the chief protagonist Pisaster ochraceus (a predatory echinoderm also known as the purple sea star) that a keystone consumer could exert strong top-down control that radically reshaped the interactions amongst other community members. What was special about this study was that the presence of Pisaster promoted species diversity by altering competition for space by sedentary species, providing a rare example of an ecological network experiment combining trophic and non-trophic interactions. Whilst there are increasing efforts to describe these interactions (e.g., competition and facilitation) in multiplex networks [7], the authors of “The return of the trophic chain: fundamental vs realized interactions in a simple arthropod food web” [6] have avoided strictly competitive interactions for the sake of simplicity. They do focus on two trophic forms of competition, namely intraguild predation and apparent competition. These two interaction motifs, along with prey switching are relevant to my own research on the influence of cross-ecosystem prey subsidies to receiving food webs [8]. In particular, the apparent competition motif may be particularly important in the context of emergent adult aquatic insects as prey subsidies to terrestrial consumers. This was demonstrated by Henschel et al. [9] where the abundances of emergent adult aquatic midges in riparian fields adjacent to a large river helped stimulate higher abundances of spiders and lower abundances of herbivorous leafhoppers, leading to a trophic cascade. The aquatic insects had a bottom-up effect on spiders and this subsidy facilitated a top-down effect that cascaded from spiders to leafhoppers to plants. The apparent competition motif becomes relevant because the aquatic midges exerted a negative indirect effect on leafhoppers mediated through their common arachnid predators.
In the preprint “The return of the trophic chain: fundamental vs realized interactions in a simple arthropod food web” [6], the authors have described different permutations of a simple mite community present in avocado orchards (Persea americana). This community comprises of two predators (Euseius stipulatus and Neoseiulus californicus), one herbivore as shared prey (Oligonychus perseae), and pollen of Carpobrotus edulis as alternative food resource, with the potential for the intraguild predation and apparent competition interaction motifs to be expressed. The authors determined that these motifs should be realized based off pairwise feeding trials. It is common for food-web researchers to depict potential food webs, which contain all species sampled and all potential trophic links based on laboratory feeding trials (as demonstrated here) or from observational data and literature reviews [10]. In reality, not all these potential feeding links are realized because species may partition space and time, thus driving alternative food-web architectures. In “The return of the trophic chain: fundamental vs realized interactions in a simple arthropod food web” [6], the authors are able to show that placing species in combinations that should yield more complex interaction motifs based off pairwise feeding trials fails to deliver – the predators revert to their preferred prey resulting in modular and simple trophic chains to be expressed. Whilst these realized interaction motifs may be stable, there might also be a tradeoff with function by yielding less top-down control than desirable when considering the potential for ecosystem services such as pest management. These are valuable insights, although it should be noted that here the fundamental niche is described in a strictly Eltonian sense as a trophic role [11]. Adding additional niche dimensions (sensu [12]), such as a thermal gradient could alter the observed interactions, although it might be possible to explain these contingencies through metabolic and optimal foraging theory combined with species traits. Nonetheless, the results of these experiments further demonstrate the need for ecologists to cross-validate theory with empirical approaches to develop more realistic and predictive food-web models, lest they invoke the wrath of Gary Polis´ ghost by “trying to explain phenomena that do not exist”.

References

[1] Polis, G. A. (1991). Complex trophic interactions in deserts: an empirical critique of food-web theory. The American Naturalist, 138(1), 123-155. doi: 10.1086/285208
[2] May, R. M. (1973). Stability and complexity in model ecosystems. Princeton University Press, Princeton, NJ, USA
[3] Dunne, J. A. (2006). The network structure of food webs. In Pascual, M., & Dunne, J. A. (eds) Ecological Networks: Linking Structure to Dynamics in Food Webs. Oxford University Press, New York, USA, 27-86
[4] Menge, B. A., & Sutherland, J. P. (1976). Species diversity gradients: synthesis of the roles of predation, competition, and temporal heterogeneity. The American Naturalist, 110(973), 351-369. doi: 10.1086/283073
[5] Paine, R. T. (1966). Food web complexity and species diversity. The American Naturalist, 100(910), 65-75. doi: 10.1086/282400
[6] Torres-Campos, I., Magalhães, S., Moya-Laraño, J., & Montserrat, M. (2018). The return of the trophic chain: fundamental vs realized interactions in a simple arthropod food web. bioRxiv, 324178, ver. 5 peer-reviewed and recommended by PCI Ecol. doi: 10.1101/324178
[7] Kéfi, S., Berlow, E. L., Wieters, E. A., Joppa, L. N., Wood, S. A., Brose, U., & Navarrete, S. A. (2015). Network structure beyond food webs: mapping non‐trophic and trophic interactions on Chilean rocky shores. Ecology, 96(1), 291-303. doi: 10.1890/13-1424.1
[8] Burdon, F. J., & Harding, J. S. (2008). The linkage between riparian predators and aquatic insects across a stream‐resource spectrum. Freshwater Biology, 53(2), 330-346. doi: 10.1111/j.1365-2427.2007.01897.x
[9] Henschel, J. R., Mahsberg, D., & Stumpf, H. (2001). Allochthonous aquatic insects increase predation and decrease herbivory in river shore food webs. Oikos, 93(3), 429-438. doi: 10.1034/j.1600-0706.2001.930308.x
[10] Brose, U., Pavao-Zuckerman, M., Eklöf, A., Bengtsson, J., Berg, M. P., Cousins, S. H., Mulder, C., Verhoef, H. A., & Wolters, V. (2005). Spatial aspects of food webs. In de Ruiter, P., Wolters, V., Moore, J. C., & Melville-Smith, K. (eds) Dynamic Food Webs. vol 3. Academic Press, Burlington, 463-469
[11] Elton, C. (1927). Animal Ecology. Sidgwick and Jackson, London, UK
[12] Hutchinson, G. E. (1957). Concluding Remarks. Cold Spring Harbor Symposia on Quantitative Biology, 22, 415-427. doi: 10.1101/sqb.1957.022.01.039

Rodents are well known as one of the main animal groups responsible for human-transmitted pathogens. As such, it seems logical to try and survey what kinds of pathogenic microbes might be harboured by wild rodents, in order to establish some baseline surveillance and prevent future zoonotic outbreaks (Bernstein et al., 2022). This is exactly what Abbate et al. (2023) endeavoured and their findings are intimidating. Based on quite a large sampling effort, they collected more than 700 rodents of seven species around two villages in northeastern France. They looked for molecular markers indicative of viral and bacterial infections and proceeded to analyze their pathogen communities using multivariate techniques.

Variation in the prevalence of the different pathogens was found among host species, with e.g. signs of CPXV more prevalent in Cricetidae while some Mycoplasma strains were more prevalent in Muridae. Co-circulation of pathogens was found in all species, with some evidencing signs of up to 12 different pathogen taxa. The diversity of co-circulating pathogens was markedly different between host species and higher in adult hosts, but not affected by sex. The dataset also evinced some slight differences between habitats, with meadows harbouring a little more diversity of rodent pathogens than forests. Less intuitively, some pathogen associations seemed quite repeatable, such as the positive association of Bartonella spp. with CPXV in the montane water vole. The study allowed the authors to test several associations already described in the literature, including associations between different hemotropic Mycoplasma species.

I strongly invite colleagues interested in zoonoses, emerging pandemics and more generally One Health to read the paper of Abbate et al. (2023) and try to replicate them across the world. To prevent the next sanitary crises, monitoring rodents, and more generally vertebrates, population demographics is a necessary and enlightening step (Johnson et al., 2020), but insufficient. Following the lead of colleagues working on rodent ectoparasites (Krasnov et al., 2014), we need more surveys like the one described by Abbate et al. (2023) to understand the importance of the dilution effect in the prevalence and transmission of microbial pathogens (Andreazzi et al., 2023) and the formation of epidemics. We also need other similar studies to assess the potential of different rodent species to carry pathogens more or less capable of infecting other mammalian species (Morand et al., 2015), in other places in the world.

References

Abbate, J. L., Galan, M., Razzauti, M., Sironen, T., Voutilainen, L., Henttonen, H., Gasqui, P., Cosson, J.-F. & Charbonnel, N. (2023) Pathogen community composition and co-infection patterns in a wild community of rodents. BioRxiv, ver.4 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2020.02.09.940494 

Andreazzi, C. S., Martinez-Vaquero, L. A., Winck, G. R., Cardoso, T. S., Teixeira, B. R., Xavier, S. C. C., Gentile, R., Jansen, A. M. & D'Andrea, P. S. (2023) Vegetation cover and biodiversity reduce parasite infection in wild hosts across ecological levels and scales. Ecography, 2023, e06579.
https://doi.org/10.1111/ecog.06579
 
Bernstein, A. S., Ando, A. W., Loch-Temzelides, T., Vale, M. M., Li, B. V., Li, H., Busch, J., Chapman, C. A., Kinnaird, M., Nowak, K., Castro, M. C., Zambrana-Torrelio, C., Ahumada, J. A., Xiao, L., Roehrdanz, P., Kaufman, L., Hannah, L., Daszak, P., Pimm, S. L. & Dobson, A. P. (2022) The costs and benefits of primary prevention of zoonotic pandemics. Science Advances, 8, eabl4183.
https://doi.org/10.1126/sciadv.abl4183
 
Johnson, C. K., Hitchens, P. L., Pandit, P. S., Rushmore, J., Evans, T. S., Young, C. C. W. & Doyle, M. M. (2020) Global shifts in mammalian population trends reveal key predictors of virus spillover risk. Proceedings of the Royal Society B: Biological Sciences, 287, 20192736.
https://doi.org/10.1098/rspb.2019.2736
 
Krasnov, B. R., Pilosof, S., Stanko, M., Morand, S., Korallo-Vinarskaya, N. P., Vinarski, M. V. & Poulin, R. (2014) Co-occurrence and phylogenetic distance in communities of mammalian ectoparasites: limiting similarity versus environmental filtering. Oikos, 123, 63-70.
https://doi.org/10.1111/j.1600-0706.2013.00646.x
 
Morand, S., Bordes, F., Chen, H.-W., Claude, J., Cosson, J.-F., Galan, M., Czirjak, G. Á., Greenwood, A. D., Latinne, A., Michaux, J. & Ribas, A. (2015) Global parasite and Rattus rodent invasions: The consequences for rodent-borne diseases. Integrative Zoology, 10, 409-423.
https://doi.org/10.1111/1749-4877.12143

Functional traits are “morpho-physio-phenological traits which impact fitness indirectly via their effects on growth, reproduction and survival” [1]. Most functional traits are defined at organ level, e.g. for leaves, roots and stems, and reflect key aspects of resource acquisition and resource use by organisms for their development and reproduction [2]. More rarely, some functional traits can be related to spatial development, such as vegetative height and lateral spread in plants.
Organ-level traits are especially popular because they can be measured in a standard way and easily compared over many plants. But these traits can broadly vary during the life of an organism. For instance, Roggy et al. [3] found that Leaf Mass Area can vary from 30 to 140 g.m^(-2) between seedling and adult stages for the canopy tree Dicorynia guianensis in French Guiana. Fortunel et al. [4] have also showed that developmental stages much contribute to functional trait variation within several Micropholis tree species in lowland Amazonia.
The way plants grow and invest resources into organs is variable during life and allows defining specific developmental sequences and architectural models [5,6]. There is clear ontogenic variation in leaf number, leaf properties and ramification patterns. Ontogenic variations reflect changing adaptation of an individual over its life, depending on the changing environmental conditions.
In this regard, measuring a single functional trait at organ level in adult trees should miss the variation of resource acquisition and use strategies over time. Thus we should built a more integrative approach of ecological development, also called “eco-devo” approach [7].
Although the ecological significance of ontogeny and developmental strategies is now well known, the extent to which it contributes to explain species survival and coexistence in communities is still broadly ignored in functional ecology. Levionnois et al. [8] investigated intraspecific variation of functional traits and growth trajectories in a typical, early-successional tree species in French Guiana, Amazonia. This species, Cecropia obtusa, is generalist regarding soil type and can be found on both white sand and ferralitic soil. The study examines whether there in intraspecific variation in functional traits and growth trajectories of C. obtusa in response to the contrasted soil types.
The tree communities observed on the two types of soils include species with distinctive functional trait values, that is, there are changes in species composition related to different species strategies along the classical wood and leaf economic spectra. The populations of C. obtusa found on the two soils showed some difference in functional traits, but it did not concern traits related to the main economic spectra. Conversely, the populations showed different growth strategies, in terms of spatial and temporal development.
The major lessons we can learn from the study are:
(i) Functional traits measured at organ level cannot reflect well how long-lived plants collect and invest resources during their life. The results show the potential of considering architectural and developmental traits together with organ-level functional traits, to better acknowledge the variation in ecological strategies over plant life, and thus to better understand community assembly processes.
(ii) What makes functional changes between communities differs when considering interspecific and intraspecific variation. Species turnover should encompass different corteges of soil specialists. These specialists are sorted along economic spectra, as shown in tropical rainforests and globally [2]. Conversely, a generalist species such as C. obtusa does occur on contrasted soil, which entails that it can accommodate the contrasted ecological conditions. However, the phenotypic adjustment is not related to how leaves and wood ensure photosynthesis, water and nutrient acquisition, but regards the way the resources are allocated to growth and reproduction over time.
The results of the study stress the need to better integrate growth strategies and ontogeny in the research agenda of functional ecology. We can anticipate that organ-level functional traits and growth trajectories will be more often considered together in ecological studies. The integration should help better understand the temporal niche of organisms, and how organisms can coexist in space and time with other organisms during their life. Recently, Klimešová et al. [9] have proposed standardized protocols for collecting plant modularity traits. Such effort to propose easy-to-measure traits representing plant development and ontogeny, with clear functional roles, should foster the awaited development of an “eco-devo” approach.

References

[1] Violle, C., Navas, M. L., Vile, D., Kazakou, E., Fortunel, C., Hummel, I., & Garnier, E. (2007). Let the concept of trait be functional!. Oikos, 116(5), 882-892. doi: 10.1111/j.0030-1299.2007.15559.x
[2] Díaz, S. et al. (2016). The global spectrum of plant form and function. Nature, 529(7585), 167-171. doi: 10.1038/nature16489
[3] Roggy, J. C., Nicolini, E., Imbert, P., Caraglio, Y., Bosc, A., & Heuret, P. (2005). Links between tree structure and functional leaf traits in the tropical forest tree Dicorynia guianensis Amshoff (Caesalpiniaceae). Annals of forest science, 62(6), 553-564. doi: 10.1051/forest:2005048
[4] Fortunel, C., Stahl, C., Heuret, P., Nicolini, E. & Baraloto, C. (2020). Disentangling the effects of environment and ontogeny on tree functional dimensions for congeneric species in tropical forests. New Phytologist. doi: 10.1111/nph.16393
[5] Barthélémy, D., & Caraglio, Y. (2007). Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny. Annals of botany, 99(3), 375-407. doi: 10.1093/aob/mcl260
[6] Hallé, F., & Oldeman, R. A. (1975). An essay on the architecture and dynamics of growth of tropical trees. Kuala Lumpur: Penerbit Universiti Malaya.
[7] Sultan, S. E. (2007). Development in context: the timely emergence of eco-devo. Trends in Ecology & Evolution, 22(11), 575-582. doi: 10.1016/j.tree.2007.06.014
[8] Levionnois, S., Tysklind, N., Nicolini, E., Ferry, B., Troispoux, V., Le Moguedec, G., Morel, H., Stahl, C., Coste, S., Caron, H. & Heuret, P. (2020). Soil variation response is mediated by growth trajectories rather than functional traits in a widespread pioneer Neotropical tree. bioRxiv, 351197, ver. 4 peer-reviewed and recommended by PCI Ecology. doi: 10.1101/351197
[9] Klimešová, J. et al. (2019). Handbook of standardized protocols for collecting plant modularity traits. Perspectives in Plant Ecology, Evolution and Systematics, 40, 125485. doi: 10.1016/j.ppees.2019.125485

A network includes a set of vertices or nodes (e.g., species in an interaction network), and a set of edges or links (e.g., interactions between species). Whether and how networks vary in space and/or time are questions often addressed in ecological research. 

Two ecological networks can differ in several extents: in that species are different in the two networks and establish new interactions (species turnover), or in that species that are present in both networks establish different interactions in the two networks (rewiring). The ecological meaning of changes in network structure is quite different according to whether species turnover or interaction rewiring plays a greater role. Therefore, much attention has been devoted in recent years on quantifying and interpreting the relative changes in network structure due to species turnover and/or rewiring.

Poisot et al. (2012) proposed to partition the global variation in structure between networks, \( \beta_{WN} \) (WN = Whole Network) into two terms: \( \beta_{OS} \) (OS = Only Shared species) and \( \beta_{ST} \) (ST = Species Turnover), such as \( \beta_{WN} = \beta_{OS} + \beta_{ST} \).

The calculation lays on enumerating the interactions between species that are common or not to two networks, as illustrated on Figure 1 for a simple case. Specifically, Poisot et al. (2012) proposed to use a Sorensen type measure of network dissimilarity, i.e., \( \beta_{WN} = \frac{a+b+c}{(2a+b+c)/2} -1=\frac{b+c}{2a+b+c} \) , where \( a \) is the number of interactions shared between the networks, while \( b \) and \( c \) are interaction numbers unique to one and the other network, respectively. \( \beta_{OS} \) is calculated based on the same formula, but only for the subnetworks including the species common to the two networks, in the form \( \beta_{OS} = \frac{b_{OS}+c_{OS}}{2a_{OS}+b_{OS}+c_{OS}} \) (e.g., Fig. 1). \( \beta_{ST} \) is deduced by subtracting \( \beta_{OS} \) from \( \beta_{WN} \) and represents in essence a "dissimilarity in interaction structure introduced by dissimilarity in species composition" (Poisot et al. 2012).

Figure 1. Ecological networks exemplified in Fründ (2021) and discussed in Poisot (2022). a is the number of shared links (continuous lines in right figures), while b+c is the number of edges unique to one or the other network (dashed lines in right figures).

Alternatively, Fründ (2021) proposed to define \( \beta_{OS} = \frac{b_{OS}+c_{OS}}{2a+b+c} \) and \( \beta_{ST} = \frac{b_{ST}+c_{ST}}{2a+b+c} \), where \( b_{ST}=b-b_{OS} \)  and \( c_{ST}=c-c_{OS} \) , so that the components \( \beta_{OS} \) and \( \beta_{ST} \) have the same denominator. In this way, Fründ (2021) partitioned the count of unique \( b+c=b_{OS}+b_{ST}+c_{ST} \) interactions, so that \( \beta_{OS} \) and \( \beta_{ST} \) sums to \( \frac{b_{OS}+c_{OS}+b_{ST}+c_{ST}}{2a+b+c} = \frac{b+c}{2a+b+c} = \beta_{WN} \). Fründ (2021) advocated that this partition allows a more sensible comparison of \( \beta_{OS} \) and \( \beta_{ST} \), in terms of the number of links that contribute to each component.

For instance, let us consider the networks 1 and 2 in Figure 1 (left panel) such as \( a_{OS}=2 \) (continuous lines in right panel), \( b_{ST} + c_{ST} = 1 \) and \( b_{OS} + c_{OS} = 1 \) (dashed lines in right panel), and thereby \( a = 2 \), \( b+c=2 \), \( \beta_{WN} = 1/3 \). Fründ (2021) measured \( \beta_{OS}=\beta_{ST}=1/6 \) and argued that it is appropriate insofar as it reflects that the number of unique links in the OS and ST components contributing to network dissimilarity (dashed lines) are actually equal. Conversely, the formula of Poisot et al. (2012) yields \( \beta_{OS}=1/5 \), hence \( \beta_{ST} = \frac{1}{3}-\frac{1}{5}=\frac{2}{15}<\beta_{OS} \). Fründ (2021) thus argued that the method of Poisot tends to underestimate the contribution of species turnover.

To clarify and avoid misinterpretation of the calculation of \( \beta_{OS} \) and \( \beta_{ST} \) in Poisot et al. (2012), Poisot (2022) provides a new, in-depth mathematical analysis of the decomposition of \( \beta_{WN} \). Poisot et al. (2012) quantify in \( \beta_{OS} \) the actual contribution of rewiring in network structure for the subweb of common species. Poisot (2022) thus argues that \( \beta_{OS} \) relates only to the probability of rewiring in the subweb, while the definition of \( \beta_{OS} \) by Fründ (2021) is relative to the count of interactions in the global network (considered in denominator), and is thereby dependent on both rewiring probability and species turnover. Poisot (2022) further clarifies the interpretation of \( \beta_{ST} \). \( \beta_{ST} \) is obtained by subtracting \( \beta_{OS} \) from \( \beta_{WN} \) and thus represents the influence of species turnover in terms of the relative architectures of the global networks and of the subwebs of shared species. Coming back to the example of Fig.1., the Poisot et al. (2012) formula posits that \( \frac{\beta_{ST}}{\beta_{WN}}=\frac{2/15}{1/3}=2/5 \), meaning that species turnover contributes two-fifths of change in network structure, while rewiring in the subweb of common species contributed three fifths.  Conversely, the approach of Fründ (2021) does not compare the architectures of global networks and of the subwebs of shared species, but considers the relative contribution of unique links to network dissimilarity in terms of species turnover and rewiring. 

Poisot (2022) concludes that the partition proposed in Fründ (2021) does not allow unambiguous ecological interpretation of rewiring. He provides guidelines for proper interpretation of the decomposition proposed in Poisot et al. (2012).

References

Fründ J (2021) Dissimilarity of species interaction networks: how to partition rewiring and species turnover components. Ecosphere, 12, e03653. https://doi.org/10.1002/ecs2.3653

Poisot T, Canard E, Mouillot D, Mouquet N, Gravel D (2012) The dissimilarity of species interaction networks. Ecology Letters, 15, 1353–1361. https://doi.org/10.1111/ele.12002

Poisot T (2022) Dissimilarity of species interaction networks: quantifying the effect of turnover and rewiring. EcoEvoRxiv Preprints, ver. 4 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.32942/osf.io/gxhu2