For decades, the effect of population density on individual performance has been studied by ecologists using both theoretical, observational, and experimental approaches. The generally accepted definition of the Allee effect is a positive correlation between population density and average individual fitness that occurs at low population densities, while individual fitness is typically decreased through intraspecific competition for resources at high population densities.  Allee effects are very relevant in conservation biology because species at low population densities would then be subjected to much higher extinction risks. 

However, due to all kinds of stochasticity, low population numbers are always more vulnerable to extinction than larger population sizes. This effect by itself cannot be necessarily ascribed to lower individual performance at low densities, i.e, Allee effects. Vercken and colleagues (2021) address this challenging question and measure the extent to which average individual fitness is affected by population density analyzing 30 experimental populations. As a model system, they use populations of parasitoid wasps of the genus Trichogramma. They report Allee effect in 8 out 30 experimental populations. Vercken and colleagues's work has several strengths. 

First of all, it is nice to see that they put theory at work. This is a very productive way of using theory in ecology. As a starting point, they look at what simple theoretical population models say about Allee effects (Lewis and Kareiva 1993; Amarasekare 1998; Boukal and Berec 2002). These models invariably predict a one-humped relation between population-density and per-capita growth rate. It is important to remark that pure logistic growth, the paradigm of density-dependence, would never predict such qualitative behavior. It is only when there is a depression of per-capita growth rates at low densities that true Allee effects arise. Second, these authors manage to not only experimentally test this main prediction but also report additional demographic traits that are consistently affected by population density. 

In these wasps, individual performance can be measured in terms of the average number of individuals every adult is able to put into the next generation ---the lambda parameter in their analysis. The first panel in figure 3 shows that the per-capita growth rates are lower in populations presenting Allee effects, the ones showing a one-humped behavior in the relation between per-capita growth rates and population densities (see figure 2). Also other population traits, such maximum population size and exitinction probability, change in a correlated and consistent manner. 

In sum, Vercken and colleagues's results are experimentally solid and based on theory expectations. However, they are very intriguing. They find the signature of Allee effects in only 8 out 30 populations, all from the same genus Trichogramma, and some populations belonging to the same species (from different sampling sites) do not show consistently Allee effects. Where does this population variability comes from? What are the reasons underlying this within- and between-species variability? What are the individual mechanisms driving Allee effects in these populations? Good enough, this piece of work generates more intriguing questions than the question is able to clearly answer. Science is not a collection of final answers but instead good questions are the ones that make science progress. 

References

Amarasekare P (1998) Allee Effects in Metapopulation Dynamics. The American Naturalist, 152, 298–302. https://doi.org/10.1086/286169

Boukal DS, Berec L (2002) Single-species Models of the Allee Effect: Extinction Boundaries, Sex Ratios and Mate Encounters. Journal of Theoretical Biology, 218, 375–394. https://doi.org/10.1006/jtbi.2002.3084

Lewis MA, Kareiva P (1993) Allee Dynamics and the Spread of Invading Organisms. Theoretical Population Biology, 43, 141–158. https://doi.org/10.1006/tpbi.1993.1007

Vercken E, Groussier G, Lamy L, Mailleret L (2021) The hidden side of the Allee effect: correlated demographic traits and extinction risk in experimental populations. HAL, hal-02570868, ver. 4 peer-reviewed and recommended by Peer community in Ecology. https://hal.archives-ouvertes.fr/hal-02570868

Marginal value theorem (MVT) is an archetypal model discussed in every behavioural ecology textbook. Its popularity is largely explained but the fact that it is possible to solve it graphically (at least in its simplest form) with the minimal amount of equations, which is a sensible strategy for an introductory course in behavioural ecology [1]. Apart from this heuristic value, one may be tempted to disregard it as a naive toy model. After a burst of interest in the 70's and the 80's, the once vivid literature about optimal foraging theory (OFT) has lost its momentum [2]. Yet, OFT and MVT have remained an active field of research in the parasitoidologists community, mostly because the sampling strategy of a parasitoid in patches of hosts and its resulting fitness gain are straightforward to evaluate, which eases both experimental and theoretical investigations [3].
This preprint [4] is in line with the long-established literature on OFT. It follows two theoretical articles [5,6] in which Vincent Calcagno and co-authors assessed the effect of changes in the environmental conditions on optimal foraging strategy. This time, they did not modify the shape of the gain function (describing the diminishing return of the cumulative intake as a function of the residency time in a patch) but the relative frequencies of good and bad patches. At first sight, that sounds like a minor modification of their earlier models. Actually, even the authors initially were fooled by the similarities before spotting the pitfalls. Here, they genuinely point out the erroneous verbal prediction in their previous paper in which some non-trivial effects of the change in patch frequencies have been overlooked. The present study indeed provides a striking example of ecological fallacy, and more specifically of Simpson's paradox which occurs when the aggregation of subgroups modifies the apparent pattern at the scale of the entire population [7,8]. In the case of MVT under constraints of habitat conversion, the increase of the residency times in both bad and good patches can result in a decrease of the average residency time at the level of the population. This apparently counter-intuitive property can be observed, for instance, when the proportion of bad quality patches strongly increases, which increases the probability that the individual forages on theses quickly exploited patches, and thus decreases its average residency time on the long run.
The authors thus put the model on the drawing board again. Proper assessment of the effect of change in the frequency of patch quality is more mathematically challenging than when one considers only changes in the shape of the gain function. The expected gain must be evaluated at the scale of the entire habitat instead of single patch. Overall, this study, which is based on a rigorous formalism, stands out as a warning against too rapid interpretations of theoretical outputs. It is not straightforward to generalize the predictions of previous models without careful evaluating their underlying hypotheses. The devil is in the details: some slight, seemingly minor, adjustments of the assumptions may have some major consequences.
The authors discussed the general conditions leading to changes in residency times or movement rates. Yet, it is worth pointing out again that it would be a mistake to blindly consider these theoretical results as forecasts for the foragers' behaviour in natura. OFT models has for a long time been criticized for sweeping under the carpet the key questions of the evolutionary dynamics and the maintenance of the optimal strategy in a population [9,10]. The distribution of available options is susceptible to change rapidly due to modifications of the environmental conditions or, even more simply, the presence of competitors which continuously remove the best options from the pool of available options [11]. The key point here is that the constant monitoring of available options implies cognitive (neural tissue is one of the most metabolically expensive tissues) and ecological costs: assessment and adjustment to the environmental conditions requires time, energy, and occasional mistakes (cost of naiveté, [12]). While rarely considered in optimal analyses, these costs should severely constraint the evolution of the subtle decision rules. Under rapidly fluctuating conditions, it could be more profitable to maintain a sub-optimal strategy (but performing reasonably well on the long run) than paying the far from negligible costs implied by the pursuit of optimal strategies [13,14]. For instance, in the analysis presented in this preprint, it is striking how close the fitness gains of the plastic and the non-plastic forager are, particularly if one remembers that the last-mentioned cognitive and ecological costs have been neglected in these calculations.
Yet, even if one can arguably question its descriptive value, such models are worth more than a cursory glance. They still have normative value insofar that they provide upper bounds for the response to modifications of the environmental conditions. Such insights are precious to design future experiments on the question. Being able to compare experimentally measured behaviours with the extremes of the null model (stubborn non-plastic forager) and the optimal strategy (only achievable by an omniscient daemon) informs about the cognitive bias or ecological costs experienced by real life foragers. I thus consider that this model, and more generally most OFT models, are still a valuable framework which deserves further examination.

References

[1] Fawcett, T. W. & Higginson, A. D. 2012 Heavy use of equations impedes communication among biologists. Proc. Natl. Acad. Sci. 109, 11735–11739. doi: 10.1073/pnas.1205259109
[2] Owens, I. P. F. 2006 Where is behavioural ecology going? Trends Ecol. Evol. 21, 356–361. doi: 10.1016/j.tree.2006.03.014
[3] Louâpre, P., Fauvergue, X., van Baaren, J. & Martel, V. 2015 The male mate search: an optimal foraging issue? Curr. Opin. Insect Sci. 9, 91–95. doi: 10.1016/j.cois.2015.02.012
[4] Calcagno, V., Hamelin, F., Mailleret, L., & Grognard, F. (2018). How optimal foragers should respond to habitat changes? On the consequences of habitat conversion. bioRxiv, 273557, ver. 4 peer-reviewed and recommended by PCI Ecol. doi: 10.1101/273557
[5] Calcagno, V., Grognard, F., Hamelin, F. M., Wajnberg, É. & Mailleret, L. 2014 The functional response predicts the effect of resource distribution on the optimal movement rate of consumers. Ecol. Lett. 17, 1570–1579. doi: 10.1111/ele.12379
[6] Calcagno, V., Mailleret, L., Wajnberg, É. & Grognard, F. 2013 How optimal foragers should respond to habitat changes: a reanalysis of the Marginal Value Theorem. J. Math. Biol. 69, 1237–1265. doi: 10.1007/s00285-013-0734-y
[7] Galipaud, M., Bollache, L., Wattier, R., Dechaume-Moncharmont, F.-X. & Lagrue, C. 2015 Overestimation of the strength of size-assortative pairing in taxa with cryptic diversity: a case of Simpson's paradox. Anim. Behav. 102, 217–221. doi: 10.1016/j.anbehav.2015.01.032
[8] Kievit, R. A., Frankenhuis, W. E., Waldorp, L. J. & Borsboom, D. 2013 Simpson's paradox in psychological science: a practical guide. Front. Psychol. 4, 513. doi: 10.3389/fpsyg.2013.00513
[9] Bolduc, J.-S. & Cézilly, F. 2012 Optimality modelling in the real world. Biol. Philos. 27, 851–869. doi: 10.1007/s10539-012-9333-3
[10] Pierce, G. J. & Ollason, J. G. 1987 Eight reasons why optimal foraging theory is a complete waste of time. Oikos 49, 111–118. doi: 10.2307/3565560
[11] Dechaume-Moncharmont, F.-X., Brom, T. & Cézilly, F. 2016 Opportunity costs resulting from scramble competition within the choosy sex severely impair mate choosiness. Anim. Behav. 114, 249–260. doi: 10.1016/j.anbehav.2016.02.019
[12] Snell-Rood, E. C. 2013 An overview of the evolutionary causes and consequences of behavioural plasticity. Anim. Behav. 85, 1004–1011. doi: 10.1016/j.anbehav.2012.12.031
[13] Fawcett, T. W., Fallenstein, B., Higginson, A. D., Houston, A. I., Mallpress, D. E. W., Trimmer, P. C. & McNamara, J. M. 2014 The evolution of decision rules in complex environments. Trends Cogn. Sci. 18, 153–161. doi: 10.1016/j.tics.2013.12.012
[14] Marshall, J. A. R., Trimmer, P. C., Houston, A. I. & McNamara, J. M. 2013 On evolutionary explanations of cognitive biases. Trends Ecol. Evol. 28, 469-473. doi: 10.1016/j.tree.2013.05.013

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.

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

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

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