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14 Dec 2018
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Recommendations to address uncertainties in environmental risk assessment using toxicokinetics-toxicodynamics models

Addressing uncertainty in Environmental Risk Assessment using mechanistic toxicological models coupled with Bayesian inference

Recommended by based on reviews by Andreas Focks and 2 anonymous reviewers

Environmental Risk Assessment (ERA) is a strategic conceptual framework to characterize the nature and magnitude of risks, to humans and biodiversity, of the release of chemical contaminants in the environment. Several measures have been suggested to enhance the science and application of ERA, including the identification and acknowledgment of uncertainties that potentially influence the outcome of risk assessments, and the appropriate consideration of temporal scale and its linkage to assessment endpoints [1].
Baudrot & Charles [2] proposed to approach these questions by coupling toxicokinetics-toxicodynamics models, which describe the time-course of processes leading to the adverse effects of a toxicant, with Bayesian inference. TKTD models separate processes influencing an organismal internal exposure (´toxicokinetics´, i.e., the uptake, bioaccumulation, distribution, biotransformation and elimination of a toxicant) from processes leading to adverse effects and ultimately its death (´toxicodynamics´) [3]. Although species and substance specific, the mechanistic nature of TKTD models facilitates the comparison of different toxicants, species, life stages, environmental conditions and endpoints [4].
Baudrot & Charles [2] investigated the use of a Bayesian framework to assess the uncertainties surrounding the calibration of General Unified Threshold Models of Survival (a category of TKTD) with data from standard toxicity tests, and their propagation to predictions of regulatory toxicity endpoints such as LC(x,t) [the lethal concentration affecting any x% of the population at any given exposure duration of time t] and MF(x,t) [an exposure multiplication factor leading to any x% effect reduction due to the contaminant at any time t].
Once calibrated with empirical data, GUTS models were used to explore individual survival over time, and under untested exposure conditions. Lethal concentrations displayed a strong curvilinear decline with time of exposure. For a given total amount of contaminant, pulses separated by short time intervals yielded higher mortality than pulses separated by long time intervals, as did few pulses of high amplitude when compared to multiple pulses of low amplitude. The response to a pulsed contaminant exposure was strongly influenced by contaminant depuration times. These findings highlight one important contribution of TKTD modelling in ecotoxicology: they represent just a few of the hundreds of exposure scenarios that could be mathematically explored, and that would be unfeasible or even unethical to conduct experimentally.
GUTS models were also used for interpolations or extrapolations of assessment endpoints, and their marginal distributions. A case in point is the incipient lethal concentration. The responses of model organisms to contaminants in standard toxicity tests are typically assessed at fixed times of exposure (e.g. 24h or 48h in the Daphnia magna acute toxicity test). However, because lethal concentrations are strongly time-dependent, it has been suggested that a more meaningful endpoint would be the incipient (i.e. asymptotic) lethal concentration when time of exposure increases to infinity. The authors present a mathematical solution for calculating the marginal distribution of such incipient lethal concentration, thereby providing both more relevant information and a way of comparing experiments, compounds or species tested for different periods of time.
Uncertainties were found to change drastically with time of exposure, being maximal at extreme values of x for both LC(x,t) and MF(x,t). In practice this means that assessment endpoints estimated when the effects of the contaminant are weak (such as LC10, the contaminant concentration resulting in the mortality of 10% of the experimental population), a commonly used assessment value in ERA, are prone to be highly variable.
The authors end with recommendations for improved experimental design, including (i) using assessment endpoints at intermediate values of x (e.g., LC50 instead of LC10) (ii) prolonging exposure and recording mortality over the course of the experiment (iii) experimenting one or few peaks of high amplitude close to each other when assessing pulsed exposure. Whereas these recommendations are not that different from current practices, they are based on a more coherent mechanistic grounding.
Overall, this and other contributions from Charles, Baudrot and their research group contribute to turn TKTD models into a real tool for Environmental Risk Assessment. Further enhancement of ERA´s science and application could be achieved by extending the use of TKTD models to sublethal rather than lethal effects, and to chronic rather than acute exposure, as these are more controversial issues in decision-making regarding contaminated sites.

References

[1] Dale, V. H., Biddinger, G. R., Newman, M. C., Oris, J. T., Suter, G. W., Thompson, T., ... & Chapman, P. M. (2008). Enhancing the ecological risk assessment process. Integrated environmental assessment and management, 4(3), 306-313. doi: 10.1897/IEAM_2007-066.1
[2] Baudrot, V., & Charles, S. (2018). Recommendations to address uncertainties in environmental risk assessment using toxicokinetics-toxicodynamics models. bioRxiv, 356469, ver. 3 peer-reviewed and recommended by PCI Ecol. doi: 10.1101/356469
[3] EFSA Panel on Plant Protection Products and their Residues (PPR), Ockleford, C., Adriaanse, P., Berny, P., Brock, T., Duquesne, S., ... & Kuhl, T. (2018). Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal, 16(8), e05377. doi: 10.2903/j.efsa.2018.5377
[4] Jager, T., Albert, C., Preuss, T. G., & Ashauer, R. (2011). General unified threshold model of survival-a toxicokinetic-toxicodynamic framework for ecotoxicology. Environmental science & technology, 45(7), 2529-2540. doi: 10.1021/es103092a

Recommendations to address uncertainties in environmental risk assessment using toxicokinetics-toxicodynamics modelsVirgile Baudrot and Sandrine Charles<p>Providing reliable environmental quality standards (EQS) is a challenging issue for environmental risk assessment (ERA). These EQS are derived from toxicity endpoints estimated from dose-response models to identify and characterize the environm...Chemical ecology, Ecotoxicology, Experimental ecology, Statistical ecologyLuis Schiesari2018-06-27 21:33:30 View
27 Nov 2023
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Modeling Tick Populations: An Ecological Test Case for Gradient Boosted Trees

Gradient Boosted Trees can deliver more than accurate ecological predictions

Recommended by ORCID_LOGO based on reviews by 2 anonymous reviewers

Tick-borne diseases are an important burden on public health all over the globe, making accurate forecasts of tick population a key ingredient in a successful public health strategy. Over long time scales, tick populations can undergo complex dynamics, as they are sensitive to many non-linear effects due to the complex relationships between ticks and the relevant (numerical) features of their environment.

But luckily, capturing complex non-linear responses is a task that machine learning thrives on. In this contribution, Manley et al. (2023) explore the use of Gradient Boosted Trees to predict the distribution (presence/absence) and abundance of ticks across New York state.

This is an interesting modelling challenge in and of itself, as it looks at the same ecological question as an instance of a classification problem (presence/absence) or of a regression problem (abundance). In using the same family of algorithm for both, Manley et al. (2023) provide an interesting showcase of the versatility of these techniques. But their article goes one step further, by setting up a multi-class categorical model that estimates jointly the presence and abundance of a population. I found this part of the article particularly elegant, as it provides an intermediate modelling strategy, in between having two disconnected models for distribution and abundance, and having nested models where abundance is only predicted for the present class (see e.g. Boulangeat et al., 2012, for a great description of the later).

One thing that Manley et al. (2023) should be commended for is their focus on opening up the black box of machine learning techniques. I have never believed that ML models are more inherently opaque than other families of models, but the focus in this article on explainable machine learning shows how these models might, in fact, bring us closer to a phenomenological understanding of the mechanisms underpinning our observations.

There is also an interesting discussion in this article, on the rate of false negatives in the different models that are being benchmarked. Although model selection often comes down to optimizing the overall quality of the confusion matrix (for distribution models, anyway), depending on the type of information we seek to extract from the model, not all types of errors are created equal. If the purpose of the model is to guide actions to control vectors of human pathogens, a false negative (predicting that the vector is absent at a site where it is actually present) is a potentially more damaging outcome, as it can lead to the vector population (and therefore, potentially, transmission) increasing unchecked.

References

Boulangeat I, Gravel D, Thuiller W. Accounting for dispersal and biotic interactions to disentangle the drivers of species distributions and their abundances: The role of dispersal and biotic interactions in explaining species distributions and abundances. Ecol Lett. 2012;15: 584-593.
https://doi.org/10.1111/j.1461-0248.2012.01772.x

Manley W, Tran T, Prusinski M, Brisson D. (2023) Modeling tick populations: An ecological test case for gradient boosted trees. bioRxiv, 2023.03.13.532443, ver. 3 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2023.03.13.532443

Modeling Tick Populations: An Ecological Test Case for Gradient Boosted TreesWilliam Manley, Tam Tran, Melissa Prusinski, Dustin Brisson<p style="text-align: justify;">General linear models have been the foundational statistical framework used to discover the ecological processes that explain the distribution and abundance of natural populations. Analyses of the rapidly expanding ...Parasitology, Species distributions, Statistical ecologyTimothée PoisotAnonymous, Anonymous2023-03-23 23:41:17 View
12 May 2022
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Riparian forest restoration as sources of biodiversity and ecosystem functions in anthropogenic landscapes

Complex but positive diversity - ecosystem functioning relationships in Riparian tropical forests

Recommended by ORCID_LOGO based on reviews by 2 anonymous reviewers

Many ecological drivers can impact ecosystem functionality and multifunctionality, with the latter describing the joint impact of different functions on ecosystem performance and services. It is now generally accepted that taxonomically richer ecosystems are better able to sustain high aggregate functionality measures, like energy transfer, productivity or carbon storage (Buzhdygan 2020, Naeem et al. 2009), and different ecosystem services (Marselle et al. 2021) than those that are less rich. Antonini et al. (2022) analysed an impressive dataset on animal and plant richness of tropical riparian forests and abundances, together with data on key soil parameters. Their work highlights the importance of biodiversity on functioning, while accounting for a manifold of potentially covarying drivers. Although the key result might not come as a surprise, it is a useful contribution to the diversity - ecosystem functioning topic, because it is underpinned with data from tropical habitats. To date, most analyses have focused on temperate habitats, using data often obtained from controlled experiments. 

The paper also highlights that diversity–functioning relationships are complicated. Drivers of functionality vary from site to site and each measure of functioning, including parameters as demonstrated here, can be influenced by very different sets of predictors, often associated with taxonomic and trait diversity. Single correlative comparisons of certain aspects of diversity and functionality might therefore return very different results. Antonini et al. (2022) show that, in general, using 22 predictors of functional diversity, varying predictor subsets were positively associated with soil functioning. Correlational analyses alone cannot resolve the question of causal link. Future studies should therefore focus on inferring precise mechanisms behind the observed relationships, and the environmental constraints on predictor subset composition and strength.

References

Antonini Y, Beirão MV, Costa FV, Azevedo CS, Wojakowski MM, Kozovits AR, Pires MRS, Sousa HC de, Messias MCTB, Fujaco MA, Leite MGP, Vidigal JP, Monteiro GF, Dirzo R (2022) Riparian forest restoration as sources of biodiversity and ecosystem functions in anthropogenic landscapes. bioRxiv, 2021.09.08.459375, ver. 3 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2021.09.08.459375

Buzhdygan OY, Meyer ST, Weisser WW, Eisenhauer N, Ebeling A, Borrett SR, Buchmann N, Cortois R, De Deyn GB, de Kroon H, Gleixner G, Hertzog LR, Hines J, Lange M, Mommer L, Ravenek J, Scherber C, Scherer-Lorenzen M, Scheu S, Schmid B, Steinauer K, Strecker T, Tietjen B, Vogel A, Weigelt A, Petermann JS (2020) Biodiversity increases multitrophic energy use efficiency, flow and storage in grasslands. Nature Ecology & Evolution, 4, 393–405. https://doi.org/10.1038/s41559-020-1123-8

Marselle MR, Hartig T, Cox DTC, de Bell S, Knapp S, Lindley S, Triguero-Mas M, Böhning-Gaese K, Braubach M, Cook PA, de Vries S, Heintz-Buschart A, Hofmann M, Irvine KN, Kabisch N, Kolek F, Kraemer R, Markevych I, Martens D, Müller R, Nieuwenhuijsen M, Potts JM, Stadler J, Walton S, Warber SL, Bonn A (2021) Pathways linking biodiversity to human health: A conceptual framework. Environment International, 150, 106420. https://doi.org/10.1016/j.envint.2021.106420

Naeem S, Bunker DE, Hector A, Loreau M, Perrings C (Eds.) (2009) Biodiversity, Ecosystem Functioning, and Human Wellbeing: An Ecological and Economic Perspective. Oxford University Press, Oxford. https://doi.org/10.1093/acprof:oso/9780199547951.001.0001

Riparian forest restoration as sources of biodiversity and ecosystem functions in anthropogenic landscapesYasmine Antonini, Marina Vale Beirao, Fernanda Vieira Costa, Cristiano Schetini Azevedo, Maria Wojakowski, Alessandra Kozovits, Maria Rita Silverio Pires, Hildeberto Caldas Sousa, Maria Cristina Teixeira Braga Messias, Maria Augusta Goncalves Fuja...<ol> <li style="text-align: justify;">Restoration of tropical riparian forests is challenging, since these ecosystems are the most diverse, dynamic, and complex physical and biological terrestrial habitats. This study tested whether biodiversity ...Biodiversity, Community ecology, Ecological successions, Ecosystem functioning, Terrestrial ecologyWerner Ulrich2021-09-10 10:51:23 View
05 Jun 2024
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Attracting pollinators vs escaping herbivores: eco-evolutionary dynamics of plants confronted with an ecological trade-off

Plant-herbivore-pollinator ménage-à-trois: tell me how well they match, and I'll tell you if it's made to last

Recommended by ORCID_LOGO based on reviews by Marcos Mendez and Yaroslav Ispolatov

How would a plant trait evolve if it is involved in interacting with both a pollinator and an herbivore species? The answer by Yacine and Loeuille is straightforward: it is not trivial, but it can explain many situations found in natural populations.

Yacine and Loeuille applied the well-known Adaptive Dynamics framework to a system with three interacting protagonists: a herbivore, a pollinator, and a plant. The evolution of a plant trait is followed under the assumption that it regulates the frequency of interaction with the two other species. As one can imagine, that is where problems begin: interacting more with pollinators seems good, but what if at the same time it implies interacting more with herbivores? And that's not a silly idea, as there are many cases where herbivores and pollinators share the same cues to detect plants, such as colors or chemical compounds.

They found that depending on the trade-off between the two types of interactions and their density-dependent effects on plant fitness, the possible joint ecological and evolutionary outcomes are numerous. When herbivory prevails, evolution can make the ménage-à-trois ecologically unstable, as one or even two species can go extinct, leaving the plant alone. Evolution can also make the coexistence of the three species more stable when pollination services prevail, or lead to the appearance of a second plant species through branching diversification of the plant trait when herbivory and pollination are balanced.

Yacine and Loeuille did not only limit themselves to saying "it is possible," but they also did much work evaluating when each evolutionary outcome would occur. They numerically explored in great detail the adaptive landscape of the plant trait for a large range of parameter values. They showed that the global picture is overall robust to parameter variations, strengthening the plausibility that the evolution of a trait involved in antagonistic interactions can explain many of the correlations between plant and animal traits or phylogenies found in nature.

Are we really there yet? Of course not, as some assumptions of the model certainly limit its scope. Are there really cases where plants' traits evolve much faster than herbivores' and pollinators' traits? Certainly not, but the model is so general that it can apply to any analogous system where one species is caught between a mutualistic and a predator species, including potential species that evolve much faster than the two others. And even though this limitation might cast doubt on the generality of the model's predictions, studying a system where a species' trait and a preference trait coevolve is possible, as other models have already been studied (see Fritsch et al. 2021 for a review in the case of evolution in food webs). We can bet this is the next step taken by Yacine and Loeuille in a similar framework with the same fundamental model, promising fascinating results, especially regarding the evolution of complex communities when species can accumulate after evolutionary branchings.

Relaxing another assumption seems more challenging as it would certainly need to change the model itself: interacting species generally do not play fixed roles, as being mutualistic or antagonistic might generally be density-dependent (Holland and DeAngelis 2010). How would the exchange of resources between three interacting species evolve? It is an open question.

References

Fritsch, C., Billiard, S., & Champagnat, N. (2021). Identifying conversion efficiency as a key mechanism underlying food webs adaptive evolution: a step forward, or backward? Oikos, 130(6), 904-930.
https://doi.org/10.1111/oik.07421
 
Holland, J. N., & DeAngelis, D. L. (2010). A consumer-resource approach to the density‐dependent population dynamics of mutualism. Ecology, 91(5), 1286-1295.
https://doi.org/10.1890/09-1163.1

Yacine, Y., & Loeuille, N. (2024) Attracting pollinators vs escaping herbivores: eco-evolutionary dynamics of plants confronted with an ecological trade-off. bioRxiv 2021.12.02.470900; doi: https://doi.org/10.1101/2021.12.02.470900

Attracting pollinators vs escaping herbivores: eco-evolutionary dynamics of plants confronted with an ecological trade-offYoussef Yacine, Nicolas Loeuille<p style="text-align: justify;">Many plant traits are subject to an ecological trade-off between attracting pollinators and escaping herbivores. The interplay of both plant-animal interaction types determines their evolution. As most studies focus...Eco-evolutionary dynamics, Herbivory, Pollination, Theoretical ecologySylvain Billiard2023-03-21 14:23:12 View
12 Sep 2023
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Linking intrinsic scales of ecological processes to characteristic scales of biodiversity and functioning patterns

The impact of process at different scales on diversity and ecosystem functioning: a huge challenge

Recommended by ORCID_LOGO based on reviews by Shai Pilosof, Gian Marco Palamara and 1 anonymous reviewer

Scale is a big topic in ecology [1]. Environmental variation happens at particular scales. The typical scale at which organisms disperse is species-specific, but, as a first approximation, an ensemble of similar species, for instance, trees, could be considered to share a typical dispersal scale. Finally, characteristic spatial scales of species interactions are, in general, different from the typical scales of dispersal and environmental variation. Therefore, conceptually, we can distinguish these three characteristic spatial scales associated with three different processes: species selection for a given environment (E), dispersal (D), and species interactions (I), respectively.  

From the famous species-area relation to the spatial distribution of biomass and species richness, the different macro-ecological patterns we usually study emerge from an interplay between dispersal and local interactions in a physical environment that constrains species establishment and persistence in every location. To make things even more complicated, local environments are often modified by the species that thrive in them, which establishes feedback loops.  It is usually assumed that local interactions are short-range in comparison with species dispersal, and dispersal scales are typically smaller than the scales at which the environment varies (I < D < E, see [2]), but this should not always be the case. 

The authors of this paper [2] relax this typical assumption and develop a theoretical framework to study how diversity and ecosystem functioning are affected by different relations between the typical scales governing interactions, dispersal, and environmental variation. This is a huge challenge. First, diversity and ecosystem functioning across space and time have been empirically characterized through a wide variety of macro-ecological patterns. Second, accommodating local interactions, dispersal and environmental variation and species environmental preferences to model spatiotemporal dynamics of full ecological communities can be done also in a lot of different ways. One can ask if the particular approach suggested by the authors is the best choice in the sense of producing robust results, this is, results that would be predicted by alternative modeling approaches and mathematical analyses [3]. The recommendation here is to read through and judge by yourself.  

The main unusual assumption underlying the model suggested by the authors is non-local species interactions. They introduce interaction kernels to weigh the strength of the ecological interaction with distance, which gives rise to a system of coupled integro-differential equations. This kernel is the key component that allows for control and varies the scale of ecological interactions. Although this is not new in ecology [4], and certainly has a long tradition in physics ---think about the electric or the gravity field, this approach has been widely overlooked in the development of the set of theoretical frameworks we have been using over and over again in community ecology, such as the Lotka-Volterra equations or, more recently, the metacommunity concept [5].

In Physics, classic fields have been revised to account for the fact that information cannot travel faster than light. In an analogous way, a focal individual cannot feel the presence of distant neighbors instantaneously. Therefore, non-local interactions do not exist in ecological communities. As the authors of this paper point out, they emerge in an effective way as a result of non-random movements, for instance, when individuals go regularly back and forth between environments (see [6], for an application to infectious diseases), or even migrate between regions. And, on top of this type of movement, species also tend to disperse and colonize close (or far) environments. Individual mobility and dispersal are then two types of movements, characterized by different spatial-temporal scales in general. Species dispersal, on the one hand, and individual directed movements underlying species interactions, on the other, are themselves diverse across species, but it is clear that they exist and belong to two distinct categories. 

In spite of the long and rich exchange between the authors' team and the reviewers, it was not finally clear (at least, to me and to one of the reviewers) whether the model for the spatio-temporal dynamics of the ecological community (see Eq (1) in [2]) is only presented as a coupled system of integro-differential equations on a continuous landscape for pedagogical reasons, but then modeled on a discrete regular grid for computational convenience. In the latter case, the system represents a regular network of local communities,  becomes a system of coupled ODEs, and can be numerically integrated through the use of standard algorithms. By contrast,  in the former case, the system is meant to truly represent a community that develops on continuous time and space, as in reaction-diffusion systems. In that case, one should keep in mind that numerical instabilities can arise as an artifact when integrating both local and non-local spatio-temporal systems. Spatial patterns could be then transient or simply result from these instabilities. Therefore, when analyzing spatiotemporal integro-differential equations, special attention should be paid to the use of the right numerical algorithms. The authors share all their code at https://zenodo.org/record/5543191, and all this can be checked out. In any case, the whole discussion between the authors and the reviewers has inherent value in itself, because it touches on several limitations and/or strengths of the author's approach,  and I highly recommend checking it out and reading it through.

Beyond these methodological issues, extensive model explorations for the different parameter combinations are presented. Several results are reported, but, in practice, what is then the main conclusion we could highlight here among all of them?  The authors suggest that "it will be difficult to manage landscapes to preserve biodiversity and ecosystem functioning simultaneously, despite their causative relationship", because, first, "increasing dispersal and interaction scales had opposing
effects" on these two patterns, and, second, unexpectedly, "ecosystems attained the highest biomass in scenarios which also led to the lowest levels of biodiversity". If these results come to be fully robust, this is, they pass all checks by other research teams trying to reproduce them using alternative approaches, we will have to accept that we should preserve biodiversity on its own rights and not because it enhances ecosystem functioning or provides particular beneficial services to humans. 

References

[1] Levin, S. A. 1992. The problem of pattern and scale in ecology. Ecology 73:1943–1967. https://doi.org/10.2307/1941447

[2] Yuval R. Zelnik, Matthieu Barbier, David W. Shanafelt, Michel Loreau, Rachel M. Germain. 2023. Linking intrinsic scales of ecological processes to characteristic scales of biodiversity and functioning patterns. bioRxiv, ver. 2 peer-reviewed and recommended by Peer Community in Ecology.  https://doi.org/10.1101/2021.10.11.463913

[3] Baron, J. W. and Galla, T. 2020. Dispersal-induced instability in complex ecosystems. Nature Communications  11, 6032. https://doi.org/10.1038/s41467-020-19824-4

[4] Cushing, J. M. 1977. Integrodifferential equations and delay models in population dynamics 
 Springer-Verlag, Berlin. https://doi.org/10.1007/978-3-642-93073-7

[5] M. A. Leibold, M. Holyoak, N. Mouquet, P. Amarasekare, J. M. Chase, M. F. Hoopes, R. D. Holt, J. B. Shurin, R. Law, D. Tilman, M. Loreau, A. Gonzalez. 2004. The metacommunity concept: a framework for multi-scale community ecology. Ecology Letters, 7(7): 601-613. https://doi.org/10.1111/j.1461-0248.2004.00608.x

[6] M. Pardo-Araujo, D. García-García, D. Alonso, and F. Bartumeus. 2023. Epidemic thresholds and human mobility. Scientific reports 13 (1), 11409. https://doi.org/10.1038/s41598-023-38395-0

Linking intrinsic scales of ecological processes to characteristic scales of biodiversity and functioning patternsYuval R. Zelnik, Matthieu Barbier, David W. Shanafelt, Michel Loreau, Rachel M. Germain<p style="text-align: justify;">Ecology is a science of scale, which guides our description of both ecological processes and patterns, but we lack a systematic understanding of how process scale and pattern scale are connected. Recent calls for a ...Biodiversity, Community ecology, Dispersal & Migration, Ecosystem functioning, Landscape ecology, Theoretical ecologyDavid Alonso2021-10-13 23:24:45 View
10 Aug 2023
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Coexistence of many species under a random competition-colonization trade-off

Assembly in metacommunities driven by a competition-colonization tradeoff: more species in, more species out

Recommended by based on reviews by Canan Karakoç and 1 anonymous reviewer

The output of a community model depends on how you set its parameters. Thus, analyses of specific parameter settings hardwire the results to specific ecological scenarios. Because more general answers are often of interest, one tradition is to give models a statistical treatment: one summarizes how model parameters vary across species, and then predicts how changing the summary, instead of the individual parameters themselves, would change model output. Arguably the best-known example is the work initiated by May, showing that the properties of a community matrix, encoding effects species have on each other near their equilibrium, determine stability (1,2). More recently, this statistical treatment has also been applied to one of community ecology’s more prickly and slippery subjects: community assembly, which deals with the question “Given some regional species pool, which species will be able to persist together at some local ecosystem?”. Summaries of how species grow and interact in this regional pool predict the fraction of survivors and their relative abundances, the kind of dynamics, and various kinds of stability (3,4). One common characteristic of such statistical treatments is the assumption of disorder: if species do not interact in too structured ways, simple and therefore powerful predictions ensue that often stand up to scrutiny in relatively ordered systems. 
 
In their recent preprint, Miller, Clenet, et al. (5) subscribe to this tradition and consider tractable assembly scenarios (6) to study the outcome of assembly in a metacommunity. They recover a result of remarkable simplicity: roughly half of the species pool makes it into the final assemblage. Their vehicle is Tilman’s classic metacommunity model (7), where colonization rates are traded off with competitive ability. More precisely, in this model, one ranks species according to their colonization rate and attributes a greater competitive strength to lower-ranked species, which makes competition strictly hierarchical and thus departs from the disorder usually imposed by statistical approaches. The authors then leverage the simplicity of the species interaction network implied by this recursive setting to analytically probe how many species survive assembly. This turns out to be a fixed fraction that is distributed according to a Binomial with a mean of 0.5. While these results should not be extrapolated beyond the system at hand (4), they are important for two reasons. First, they imply that, within the framework of metacommunities driven by competition-colonization tradeoffs, richer species pools will produce richer communities: there is no upper bound on species richness, other than the one set by the raw material available for assembly. Second, this conclusion does not rely on simulation or equation solving and is, therefore, a hopeful sign of the palatability of the problem, if formalized in the right way. Their paper then shows that varying some of the settings does not change the main conclusion: changing how colonization rates distribute across species, and therefore the nature of the tradeoff, or the order with which species invade seems not to disrupt the big picture. Only when invaders are created “de novo” during assembly, a scenario akin to “de novo” mutation, a smaller fraction of species will survive assembly. 
 
As always, logical extensions of this study involve complicating the model and then looking if the results stay on par. The manuscript cites switching to other kinds of competition-colonization tradeoffs, and the addition of spatial heterogeneity as two potential avenues for further research. While certainly of merit, alternative albeit more bumpy roads would encompass models with radically different behavior. Most notably, one wonders how priority effects would play out. The current analysis shows that different invasion orders always lead to the same final composition, and therefore the same final species richness, confirming earlier results from models with similar structures (6). In models with priority effects, different invasion orders will surely lead to different compositions at the end. However, if one only cares about how many (and not which) species survive, it is unsure how much priority effects will qualitatively affect assembly. Because priority effects are varied in their topological manifestation (8), an important first step will be to evaluate which kinds of priority effects are compliant with formal analysis. 
 
References
 
1. May, R. M. (1972). Will a Large Complex System be Stable? Nature 238, 413–414. https://doi.org/10.1038/238413a0

2. Allesina, S. & Tang, S. (2015). The stability–complexity relationship at age 40: a random matrix perspective. Population Ecology, 57, 63–75. https://doi.org/10.1007/s10144-014-0471-0

3. Bunin, G. (2016). Interaction patterns and diversity in assembled ecological communities. Preprint at http://arxiv.org/abs/1607.04734.

4. Barbier, M., Arnoldi, J.-F., Bunin, G. & Loreau, M. (2018). Generic assembly patterns in complex ecological communities. Proceeding of the National Academy of Sciences, 115, 2156–2161. https://doi.org/10.1073/pnas.1710352115

5. Miller, Z. R., Clenet, M., Libera, K. D., Massol, F. & Allesina, S. (2023). Coexistence of many species under a random competition-colonization trade-off. bioRxiv 2023.03.23.533867, ver 3 peer-reviewed and recommended by PCI Ecology. https://doi.org/10.1101/2023.03.23.533867

6. Serván, C. A. & Allesina, S. (2021). Tractable models of ecological assembly. Ecology Letters, 24, 1029–1037. https://doi.org/10.1111/ele.13702

7. Tilman, D. (1994). Competition and Biodiversity in Spatially Structured Habitats. Ecology, 75, 2–16. https://doi.org/10.2307/1939377

8. Song, C., Fukami, T. & Saavedra, S. (2021). Untangling the complexity of priority effects in multispecies communities. Ecolygy Letters, 24, 2301–2313. https://doi.org/10.1111/ele.13870

Coexistence of many species under a random competition-colonization trade-offZachary R. Miller, Maxime Clenet, Katja Della Libera, François Massol, Stefano Allesina<p>The competition-colonization trade-off is a well-studied coexistence mechanism for metacommunities. In this setting, it is believed that coexistence of all species requires their traits to satisfy restrictive conditions limiting their similarit...Biodiversity, Coexistence, Colonization, Community ecology, Competition, Population ecology, Spatial ecology, Metacommunities & Metapopulations, Theoretical ecologyFrederik De Laender2023-03-30 20:42:48 View