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

There are several important topics in the study of infectious diseases that have not been well explored due to technical difficulties. One such topic is pursued by Alizon et al. in “Modelling coinfections to detect within-host interactions from genotype combination prevalences” [1]. Both theory and several important examples have demonstrated that interactions among co-infecting strains can have outsized impacts on disease outcomes, transmission dynamics, and epidemiology. Unfortunately, empirical data on pathogen interactions and their outcomes is often correlational making results difficult to decipher.
The analytical framework developed by Alizon et al. [1] infers the presence and strength of pathogen interactions through their impact on transmission dynamics using a novel application of Approximate Bayesian Computation (ABC)-regression to epidemiological data. Traditional analytic approaches identify pathogen interactions when the observed distribution of pathogens among hosts differ from ‘neutral’ expectations. However, deviations from this expectation are not only a result of inter-strain interactions but can be caused by many ecological interactions, such as heterogeneity in host contact networks. To overcome this difficulty, Alizon et al [1] develop an analytical framework that incorporates explicit epidemiological models to allow inference of interactions among strains of Human Papillomaviruses (HPV) even with other ecological interactions that impact the distribution of strains among hosts. Alizon et al also demonstrate that using more of the available data, including the specific combination of strains present in hosts and knowledge of the connectivity of the hosts (i.e., super-spreaders), leads to more accurate inferences of the strength and direction of within-host interactions among coinfecting strains. This method successfully identified data generated from models with high and moderate inter-strain interaction intensity when the host population was homogeneous and was only slightly less successful when the host population was heterogeneous (super-spreaders present). By comparison, some previously published analytical methods could identify only some inter-strain interactions in datasets generated from models with homogeneous host populations, but host heterogeneity obscured these interactions.
This manuscript makes seamless connections between basic viral biology and its epidemiological consequences by tying them together with realistic models, illustrating the fundamental utility of biological modeling. This analytical framework provides crucial tools for experimentalists, facilitating collaborations with theoreticians to better understand the epidemiological consequences of co-infections. In addition, the method is simple enough to be applied by a broad base of experimentalists to the many pathogens where co-infections are common. Thus, this paper has the potential to impact several research fields and public health practice. Those attempting to apply this method should note the potential limitations noted by the authors. For example, it is not designed to detect the mechanisms of inter-strain interactions (there is no within host component of the models) but to identify the existence of interactions through patterns indicative of these interactions while ruling out other sources that could cause the pattern. This approach is likely to be most accurate when strain identification within hosts is precise and unbiased - which is unlikely in many systems where samples are taken only from symptomatic cases and strain detection is not sufficiently sensitive – and when host contact networks can be reasonably estimated. Importantly, a priori knowledge of the set of possible epidemiological models is needed for accurate parameter estimates, which may be true for several prominent pathogens, but not be so for many other pathogens and symbionts. We look forward to future extensions of this framework where this restriction is relaxed. Alizon et al. [1] have provided a framework that will facilitate theoretical and empirical work on the impact of coinfections on infectious disease and should shape future public health data collection standards.

References

[1] Alizon, S., Murall, C.L., Saulnier, E., & Sofonea, M.T. (2018). Detecting within-host interactions using genotype combination prevalence data. bioRxiv, 256586, ver. 3 peer-reviewed and recommended by PCI Ecology. doi: 10.1101/256586