How optimal foragers should respond to habitat changes? On the consequences of habitat conversion.
Vincent Calcagno, Frederic Hamelin, Ludovic Mailleret, Frederic Grognard
10.1101/273557
Optimal foraging in a changing world: old questions, new perspectives
Recommended by Francois-Xavier Dechaume-Moncharmont based on reviews by Frederick Adler, Andrew Higginson and 1 anonymous reviewer
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
| How optimal foragers should respond to habitat changes? On the consequences of habitat conversion. | Vincent Calcagno, Frederic Hamelin, Ludovic Mailleret, Frederic Grognard | The Marginal Value Theorem (MVT) provides a framework to predict how habitat modifications related to the distribution of resources over patches should impact the realized fitness of individuals and their optimal rate of movement (or patch residen... |  | Behaviour & Ethology, Dispersal & Migration, Foraging, Landscape ecology, Spatial ecology, Metacommunities & Metapopulations, Theoretical ecology | Francois-Xavier Dechaume-Moncharmont | | 2018-03-05 10:42:11 | View |
When higher carrying capacities lead to faster propagation
Marjorie Haond, Thibaut Morel-Journel, Eric Lombaert, Elodie Vercken, Ludovic Mailleret & Lionel Roques
https://doi.org/10.1101/307322
When the dispersal of the many outruns the dispersal of the few
Recommended by Matthieu Barbier based on reviews by Yuval Zelnik and 1 anonymous reviewer
Are biological invasions driven by a few pioneers, running ahead of their conspecifics? Or are these pioneers constantly being caught up by, and folded into, the larger flux of propagules from the established populations behind them?
In ecology and beyond, these two scenarios are known as "pulled" and "pushed" fronts, and they come with different expectations. In a pushed front, invasion speed is not just a matter of how good individuals are at dispersing and settling new locations. It becomes a collective, density-dependent property of population fluxes. And in particular, it can depend on the equilibrium abundance of the established populations inside the range, i.e. the species’ carrying capacity K, factoring in its abiotic environment and biotic interactions.
This realization is especially important because it can flip around our expectations about which species expand fast, and how to manage them. We tend to think of initial colonization and long-term abundance as two independent axes of variation among species or indeed as two ends of a spectrum, in the classic competition-colonization tradeoff [1]. When both play into invasion speed, good dispersers might not outrun good competitors. This is useful knowledge, whether we want to contain an invasion or secure a reintroduction.
In their study "When higher carrying capacities lead to faster propagation", Haond et al [2] combine mathematical analysis, Individual-Based simulations and experiments to show that various mechanisms can cause pushed fronts, whose speed increases with the carrying capacity K of the species. Rather than focus on one particular angle, the authors endeavor to demonstrate that this qualitative effect appears again and again in a variety of settings.
It is perhaps surprising that this notable and general connection between K and invasion speed has managed to garner so little fame in ecology. A large fraction of the literature employs the venerable Fisher-KPP reaction-diffusion model, which combines local logistic growth with linear diffusion in space. This model has prompted both considerable mathematical developments [3] and many applications to modelling real invasions [4]. But it only allows pulled fronts, driven by the small populations at the edge of a species range, with a speed that depends only on their initial growth rate r.
This classic setup is, however, singular in many ways. Haond et al [2] use it as a null model, and introduce three mechanisms or factors that each ensure a role of K in invasion speed, while giving less importance to the pioneers at the border.
Two factors, the Allee effect and demographic stochasticity, make small edge populations slower to grow or less likely to survive. These two factors are studied theoretically, and to make their claims stronger, the authors stack the deck against K. When generalizing equations or simulations beyond the null case, it is easy to obtain functional forms where the parameter K does not only play the role of equilibrium carrying capacity, but also affects dynamical properties such as the maximum or mean growth rate. In that case, it can trivially change the propagation speed, without it meaning anything about the role of established populations behind the front. Haond et al [2] avoid this pitfall by disentangling these effects, at the cost of slightly more peculiar expressions, and show that varying essentially nothing but the carrying capacity can still impact the speed of the invasion front.
The third factor, density-dependent dispersal, makes small populations less prone to disperse. It is well established empirically and theoretically that various biological mechanisms, from collective organization to behavioral switches, can prompt organisms in denser populations to disperse more, e.g. in such a way as to escape competition [5]. The authors demonstrate how this effect induces a link between carrying capacity and invasion speed, both theoretically and in a dispersal experiment on the parasitoid wasp, Trichogramma chilonis.
Overall, this study carries a simple and clear message, supported by valuable contributions from different angles. Although some sections are clearly written for the theoretical ecology crowd, this article has something for everyone, from the stray physicist to the open-minded manager. The collaboration between theoreticians and experimentalists, while not central, is worthy of note. Because the narrative of this study is the variety of mechanisms that can lead to the same qualitative effect, the inclusion of various approaches is not a gimmick, but helps drive home its main message. The work is fairly self-contained, although one could always wish for further developments, especially in the direction of more quantitative testing of these mechanisms.
In conclusion, Haond et al [2] effectively convey the widely relevant message that, for some species, invading is not just about the destination, it is about the many offspring one makes along the way.
References
[1] Levins, R., & Culver, D. (1971). Regional Coexistence of Species and Competition between Rare Species. Proceedings of the National Academy of Sciences, 68(6), 1246–1248. doi: 10.1073/pnas.68.6.1246
[2] Haond, M., Morel-Journel, T., Lombaert, E., Vercken, E., Mailleret, L., & Roques, L. (2018). When higher carrying capacities lead to faster propagation. BioRxiv, 307322. doi: 10.1101/307322
[3] Crooks, E. C. M., Dancer, E. N., Hilhorst, D., Mimura, M., & Ninomiya, H. (2004). Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions. Nonlinear Analysis: Real World Applications, 5(4), 645–665. doi: 10.1016/j.nonrwa.2004.01.004
[4] Shigesada, N., & Kawasaki, K. (1997). Biological Invasions: Theory and Practice. Oxford University Press, UK.
[5] Matthysen, E. (2005). Density-dependent dispersal in birds and mammals. Ecography, 28(3), 403–416. doi: 10.1111/j.0906-7590.2005.04073.x
| When higher carrying capacities lead to faster propagation | Marjorie Haond, Thibaut Morel-Journel, Eric Lombaert, Elodie Vercken, Ludovic Mailleret & Lionel Roques | <p>This preprint has been reviewed and recommended by Peer Community In Ecology (https://dx.doi.org/10.24072/pci.ecology.100004). Finding general patterns in the expansion of natural populations is a major challenge in ecology and invasion biology... |  | Biological invasions, Colonization, Dispersal & Migration, Experimental ecology, Population ecology, Spatial ecology, Metacommunities & Metapopulations, Theoretical ecology | Matthieu Barbier | Yuval Zelnik | 2018-04-25 10:18:48 | View |
Does elevated parasite richness in the environment affect daily path length of animals or is it the converse? An answer bringing some new elements of discussion
Recommended by Cédric Sueur based on reviews by 2 anonymous reviewers
In 2015, Brockmeyer et al. [1] suggested that mandrills (Mandrillus sphinx) may accept additional ranging costs to avoid heavily parasitized areas. Following this paper, Bicca-Marques and Calegaro-Marques [2] questioned this interpretation and presented other hypotheses. To summarize, whilst Brockmeyer et al. [1] proposed that elevated daily path length may be a consequence of elevated parasite richness, Bicca-Marques and Calegaro-Marques [2] viewed it as a cause. In this current paper, Charpentier and Kappeler [3] respond to some of the criticisms by Bicca-Marques and Calegaro-Marques and discuss the putative parsimony of the two competing scenarios. The manuscript is interesting and focuses on an important question concerning the discussion about the social organization and home range use in wild mandrills. This answer helps to move this debate forward and should stimulate more empirical studies of the role of environmentally-transmitted parasites in shaping ranging and movement patterns of wild vertebrates. Given the elements this paper brings to the topics, it should have been published in American Journal of Primatology, the journal that published the two previous articles.
References
[1] Brockmeyer, T., Kappeler, P. M., Willaume, E., Benoit, L., Mboumba, S., & Charpentier, M. J. E. (2015). Social organization and space use of a wild mandrill (Mandrillus sphinx) group. American Journal of Primatology, 77(10), 1036–1048. doi: 10.1002/ajp.22439
[2] Bicca-Marques, J. C., & Calegaro-Marques, C. (2016). Ranging behavior drives parasite richness: A more parsimonious hypothesis. American Journal of Primatology, 78(9), 923–927. doi: 10.1002/ajp.22561
[3] Charpentier, M. J., & Kappeler, P. M. (2018). A reply to “Ranging Behavior Drives Parasite Richness: A More Parsimonious Hypothesis.” ArXiv:1805.08151v2 [q-Bio]. Retrieved from http://arxiv.org/abs/1805.08151
| A reply to “Ranging Behavior Drives Parasite Richness: A More Parsimonious Hypothesis” | Charpentier MJE, Kappeler PM | <p>In a recent article, Bicca-Marques and Calegaro-Marques [2016] discussed the putative assumptions related to an interpretation we provided regarding an observed positive relationship between weekly averaged parasite richness of a group of mandr... |  | Behaviour & Ethology, Evolutionary ecology, Foraging, Host-parasite interactions, Spatial ecology, Metacommunities & Metapopulations, Zoology | Cédric Sueur | | 2018-05-22 10:59:33 | View |
Data-based, synthesis-driven: setting the agenda for computational ecology
Timothée Poisot, Richard Labrie, Erin Larson, Anastasia Rahlin
https://doi.org/10.1101/150128
Some thoughts on computational ecology from people who I’m sure use different passwords for each of their accounts
Recommended by Phillip P.A. Staniczenko based on reviews by Matthieu Barbier and 1 anonymous reviewer
Are you an ecologist who uses a computer or know someone that does?
Even if your research doesn’t rely heavily on advanced computational techniques, it likely hasn’t escaped your attention that computers are increasingly being used to analyse field data and make predictions about the consequences of environmental change. So before artificial intelligence and robots take over from scientists, now is great time to read about how experts think computers could make your life easier and lead to innovations in ecological research.
In “Data-based, synthesis-driven: setting the agenda for computational ecology”, Poisot and colleagues [1] provide a brief history of computational ecology and offer their thoughts on how computational thinking can help to bridge different types of ecological knowledge.
In this wide-ranging article, the authors share practical strategies for realising three main goals: (i) tighter integration of data and models to make predictions that motivate action by practitioners and policy-makers; (ii) closer interaction between data-collectors and data-users; and (iii) enthusiasm and aptitude for computational techniques in future generations of ecologists.
The key, Poisot and colleagues argue, is for ecologists to “engage in meaningful dialogue across disciplines, and recognize the currencies of their collaborations.”
Yes, this is easier said than done. However, the journey is much easier with a guide and when everyone involved serves to benefit not only from the eventual outcome, but also the process.
References
[1] Poisot, T., Labrie, R., Larson, E., & Rahlin, A. (2018). Data-based, synthesis-driven: setting the agenda for computational ecology. BioRxiv, 150128, ver. 4 recommended and peer-reviewed by PCI Ecology. doi: 10.1101/150128
| Data-based, synthesis-driven: setting the agenda for computational ecology | Timothée Poisot, Richard Labrie, Erin Larson, Anastasia Rahlin | <p>Computational ecology, defined as the application of computational thinking to ecological problems, has the potential to transform the way ecologists think about the integration of data and models. As the practice is gaining prominence as a way... |  | Meta-analyses, Statistical ecology, Theoretical ecology | Phillip P.A. Staniczenko | | 2018-02-05 20:51:41 | View |
