Mimicry between species has long attracted the attention of scientists. Over a century ago, Bates first proposed that palatable species should gain a benefit by resembling unpalatable species (Bates 1862). Not long after, Müller suggested that there could also be a mutual advantage for two unpalatable species to mimic one another to reduce predator error (Müller 1879). These forms of mimicry, Batesian and Müllerian, are now widely studied, providing broad insights into behaviour, ecology and evolution.

Numerous taxa, including both invertebrates and vertebrates, show examples of Batesian or Müllerian mimicry. Bees and wasps provide a particularly interesting case due to the differences in defence between females and males of the same species. While both males and females may display warning colours, only females can sting and inject venom to cause pain and allow escape from predators. Therefore, males are palatable mimics and can resemble females of their own species or females of another species (dual sex-limited mimicry). This asymmetry in defence could have impacts on both population structure and community assembly, yet research into mimicry largely focuses on systems without sex differences.

Here, Boutin and colleagues (2023) use a differential equations model to explore the effect of mimicry on population structure and community assembly for sex-limited defended species. Specifically, they address three questions, 1) how do female noxiousness and sex-ratio influence the extinction risk of a single species?; 2) what is the effect of mimicry on species co-existence? and 3) how does dual sex-limited mimicry influence species co-existence? Their results reveal contexts in which populations with undefended males can persist, the benefit of Müllerian mimicry for species coexistence and that dual sex-limited mimicry can have a destabilising impact on species coexistence.

The results not only contribute to our understanding of how mimicry is maintained in natural systems but also demonstrate how changes in relative abundance or population structure of one species could impact another species. Further insight into the population and community dynamics of insects is particularly important given the current population declines (Goulson 2019; Seibold et al 2019).

References

Bates, H. W. 1862. Contributions to the insect fauna of the Amazon Valley, Lepidoptera: Heliconidae. Trans. Linn. Soc. Lond. 23:495- 566. https://doi.org/10.1111/j.1096-3642.1860.tb00146.x

Boutin, M., Costa, M., Fontaine, C., Perrard, A., Llaurens, V. 2022 Influence of sex-limited mimicry on extinction risk in Aculeata: a theoretical approach. bioRxiv, ver. 2 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.1101/2022.10.21.513153

Goulson, D. 2019. The insect apocalypse, and why it matters. Curr. Biol. 29: R967-R971. https://doi.org/10.1016/j.cub.2019.06.069

Müller, F. 1879. Ituna and Thyridia; a remarkable case of mimicry in butterflies. Trans. Roy. Entom. Roc. 1879:20-29.

Seibold, S., Gossner, M. M., Simons, N. K., Blüthgen, N., Müller, J., Ambarlı, D., ... & Weisser, W. W. 2019. Arthropod decline in grasslands and forests is associated with landscape-level drivers. Nature, 574: 671-674. https://doi.org/10.1038/s41586-019-1684-3

Humans are exploiting biological resources since thousands of years. Exploitation of biological resources has become particularly intense since the beginning of the 20th century and the steep increase in the worldwide human population size. Marine and freshwater fishes are not exception to that rule, and they have been (and continue to be) strongly harvested as a source of proteins for humans. For some species, fishery has been so intense that natural stocks have virtually collapsed in only a few decades. The worst example begin that of the Northwest Atlantic cod that has declined by more than 95% of its historical biomasses in only 20-30 years of intensive exploitation (Frank et al. 2005). These rapid and steep changes in biomasses have huge impacts on the entire ecosystems since species targeted by fisheries are often at the top of trophic chains (Frank et al. 2005). 

Beyond demographic impacts, fisheries also have evolutionary impacts on populations, which can also indirectly alter ecosystems (Uusi-Heikkilä et al. 2015; Palkovacs et al. 2018). Fishermen generally focus on the largest specimens, and hence exert a strong selective pressure against these largest fish (which is called “harvest selection”). There is now ample evidence that harvest selection can lead to rapid evolutionary changes in natural populations toward small individuals (Kuparinen & Festa-Bianchet 2017). These evolutionary changes are of course undesirable from a human perspective, and have attracted many scientific questions. Nonetheless, the consequence of harvest selection is not always observable in natural populations, and there are cases in which no phenotypic change (or on the contrary an increase in mean body size) has been observed after intense harvest pressures. In a conceptual Essay, Edeline and Loeuille (Edeline & Loeuille 2020) propose novel ideas to explain why the evolutionary consequences of harvest selection can be so diverse, and how a cross talk between ecological and evolutionary dynamics can explain patterns observed in natural stocks.

 The general and novel concept proposed by Edeline and Loeuille is actually as old as Darwin’s book; The Origin of Species (Darwin 1859). It is based on the simple idea that natural selection acting on harvested populations can actually be strong, and counter-balance (or on the contrary reinforce) the evolutionary consequence of harvest selection. Although simple, the idea that natural and harvest selection are jointly shaping contemporary evolution of exploited populations lead to various and sometimes complex scenarios that can (i) explain unresolved empirical patterns and (ii) refine predictions regarding the long-term viability of exploited populations. 

The Edeline and Loeuille’s crafty inspiration is that natural selection acting on exploited populations is itself an indirect consequence of harvest (Edeline & Loeuille 2020). They suggest that, by modifying the size structure of populations (a key parameter for ecological interactions), harvest indirectly alters interactions between populations and their biotic environment through competition and predation, which changes the ecological theatre and hence the selective pressures acting back to populations. They named this process “size-dependent eco-evolutionary feedback loops” and develop several scenarios in which these feedback loops ultimately deviate the evolutionary outcome of harvest selection from expectation. The scenarios they explore are based on strong theoretical knowledge, and range from simple ones in which a single species (the harvest species) is evolving to more complex (and realistic) ones in which multiple (e.g. the harvest species and its prey) species are co-evolving.

I will not come into the details of each scenario here, and I will let the readers (re-)discovering the complex beauty of biological life and natural selection. Nonetheless, I will emphasize the importance of considering these eco-evolutionary processes altogether to fully grasp the response of exploited populations. Edeline and Loeuille convincingly demonstrate that reduced body size due to harvest selection is obviously not the only response of exploited fish populations when natural selection is jointly considered (Edeline & Loeuille 2020). On the contrary, they show that –under some realistic ecological circumstances relaxing exploitative competition due to reduced population densities- natural selection can act antagonistically, and hence favour stable body size in exploited populations. Although this seems further desirable from a human perspective than a downsizing of exploited populations, it is actually mere window dressing as Edeline and Loeuille further showed that this response is accompanied by an erosion of the evolvability –and hence a lowest probability of long-term persistence- of these exploited populations.

Humans, by exploiting biological resources, are breaking the relative equilibrium of complex entities, and the response of populations to this disturbance is itself often complex and heterogeneous. In this Essay, Edeline and Loeuille provide –under simple terms- the theoretical and conceptual bases required to improve predictions regarding the evolutionary responses of natural populations to exploitation by humans (Edeline & Loeuille 2020). An important next step will be to generate data and methods allowing confronting the empirical reality to these novel concepts (e.g. (Monk et al. 2021), so as to identify the most likely evolutionary scenarios sustaining biological responses of exploited populations, and hence to set the best management plans for the long-term sustainability of these populations.

References

Darwin, C. (1859). On the Origin of Species by Means of Natural Selection. John Murray, London.

Edeline, E. & Loeuille, N. (2021) Size-dependent eco-evolutionary feedbacks in fisheries. bioRxiv, 2020.04.03.022905, ver. 4 peer-reviewed and recommended by PCI Ecology. doi: https://doi.org/10.1101/2020.04.03.022905

Frank, K.T., Petrie, B., Choi, J. S. & Leggett, W.C. (2005). Trophic Cascades in a Formerly Cod-Dominated Ecosystem. Science, 308, 1621–1623. doi: https://doi.org/10.1126/science.1113075

Kuparinen, A. & Festa-Bianchet, M. (2017). Harvest-induced evolution: insights from aquatic and terrestrial systems. Philos. Trans. R. Soc. B Biol. Sci., 372, 20160036. doi: https://doi.org/10.1098/rstb.2016.0036

Monk, C.T., Bekkevold, D., Klefoth, T., Pagel, T., Palmer, M. & Arlinghaus, R. (2021). The battle between harvest and natural selection creates small and shy fish. Proc. Natl. Acad. Sci., 118, e2009451118. doi: https://doi.org/10.1073/pnas.2009451118 

Palkovacs, E.P., Moritsch, M.M., Contolini, G.M. & Pelletier, F. (2018). Ecology of harvest-driven trait changes and implications for ecosystem management. Front. Ecol. Environ., 16, 20–28. doi: https://doi.org/10.1002/fee.1743

Uusi-Heikkilä, S., Whiteley, A.R., Kuparinen, A., Matsumura, S., Venturelli, P.A., Wolter, C., et al. (2015). The evolutionary legacy of size-selective harvesting extends from genes to populations. Evol. Appl., 8, 597–620. doi: https://doi.org/10.1111/eva.12268

Eyespots—round or oval spots, usually accompanied by one or more concentric rings, that together imitate vertebrate eyes—are found in insects of at least three orders and in some tropical fishes (Stevens 2005). They are particularly frequent in Lepidoptera, where they occur on wings of adults in many species (Monteiro et al. 2006), and in caterpillars of many others (Janzen et al. 2010). The resemblance of eyespots to vertebrate eyes often extends to details, such as fake « pupils » (round or slit-like) and « eye sparkle » (Blut et al. 2012). Larvae of one hawkmoth species even have fake eyes that appear to blink (Hossie et al. 2013). Eyespots have interested evolutionary biologists for well over a century. While they appear to play a role in mate choice in some adult Lepidoptera, their adaptive significance in adult Lepidoptera, as in caterpillars, is mainly as an anti-predator defense (Monteiro 2015). However, there are two competing hypotheses about the mechanism by which eyespots confer defense against predators. The « intimidation » hypothesis postulates that eyespots intimidate potential predators, startling them and reducing the probability of attack. The « deflection » hypothesis holds that eyespots deflect attacks to parts of the body where attack has relatively little effect on the animal’s functioning and survival. In caterpillars, there is little scope for the deflection hypothesis, because attack on any part of a caterpillar’s body is likely to be lethal. Much observational and some experimental evidence supports the intimidation hypothesis in caterpillars (Hossie & Sherratt 2012). In adult Lepidoptera, however, both mechanisms are plausible, and both have found support (Stevens 2005). The most spectacular examples of intimidation are in butterflies in which eyespots located centrally in hindwings and hidden in the natural resting position are suddenly exposed, startling the potential predator (e.g., Vallin et al. 2005). The most spectacular examples of deflection are seen in butterflies in which eyespots near the hindwing margin combined with other traits give the appearance of a false head (e.g., Chotard et al. 2022; Kodandaramaiah 2011). 

Most studies have attempted to test for only one or the other of these mechanisms—usually the one that seems a priori more likely for the butterfly species being studied. But for many species, particularly those that have neither spectacular startle displays nor spectacular false heads, evidence for or against the two hypotheses is contradictory.  

Iserhard et al. (2024) attempted to simultaneously test both hypotheses, using the neotropical nymphalid butterfly Caligo martia. This species has a large ventral hindwing eyespot, exposed in the insect’s natural resting position, while the rest of the ventral hindwing surface is cryptically coloured. In a previous study of this species, De Bona et al. (2015) presented models with intact and disfigured eyespots on a computer monitor to a European bird species, the great tit (Parus major). The results favoured the intimidation hypothesis. Iserhard et al. (2024) devised experiments presenting more natural conditions, using fairly realistic dummy butterflies, with eyespots manipulated or unmanipulated, exposed to a diverse assemblage of insectivorous birds in nature, in a tropical forest. Using color-printed paper facsimiles of wings, with eyespots present, UV-enhanced, or absent, they compared the frequency of beakmarks on modeling clay applied to wing margins (frequent attacks would support the deflection hypothesis) and (in one of two experiments) on dummies with a modeling-clay body (eyespots should lead to reduced frequency of attack, to wings and body, if birds are intimidated). Their experiments also included dummies without eyespots whose wings were either cryptically coloured (as in unmanipulated butterflies) or not. Their results, although complex, indicate support for the deflection hypothesis: dummies with eyespots were mostly attacked on these less vital parts. Dummies lacking eyespots were less frequently attacked, especially when they were camouflaged. Camouflaged dummies without eyespots were in fact the least frequently attacked of all the models. However, when dummies lacking eyespots were attacked, attacks were usually directed to vital body parts. These results show some of the complexity of estimating costs and benefits of protective conspicuous signals vs. camouflage (Stevens et al. 2008).

Two complementary experiments were conducted. The first used facsimiles with « wings » in a natural resting position (folded, ventral surfaces exposed), but without a modeling-clay « body ». In the second experiment, facsimiles had a modeling-clay « body », placed between the two unfolded wings to make it as accessible to birds as the wings. However, these dummies displayed the ventral surfaces of unfolded wings, an unnatural resting position. The study was thus not able to compare bird attacks to the body vs. wings in a natural resting position. One can understand the reason for this methodological choice, but it is a limitation of the study.

The naturalness of the conditions under which these field experiments were conducted is a strong argument for the biological significance of their results. However, the uncontrolled conditions naturally result in many questions being left open. The butterfly dummies were exposed to at least nine insectivorous bird species. Do bird species differ in their behavioral response to eyespots? Do responses depend on the distance at which a bird first detects the butterfly? Do eyespots and camouflage markings present on the same animal both function, but at different distances (Tullberg et al. 2005)? Do bird responses vary depending on the particular light environment in the places and at the times when they encounter the butterfly (Kodandaramaiah 2011)? Answering these questions under natural, uncontrolled conditions will be challenging, requiring onerous methods, (e.g., video recording in multiple locations over time). The study indicates the interest of pursuing these questions.

References

Blut, C., Wilbrandt, J., Fels, D., Girgel, E.I., & Lunau, K. (2012). The ‘sparkle’ in fake eyes–the protective effect of mimic eyespots in Lepidoptera. Entomologia Experimentalis et Applicata, 143, 231-244. https://doi.org/10.1111/j.1570-7458.2012.01260.x

Chotard, A., Ledamoisel, J., Decamps, T., Herrel, A., Chaine, A.S., Llaurens, V., & Debat, V. (2022). Evidence of attack deflection suggests adaptive evolution of wing tails in butterflies. Proceedings of the Royal Society B, 289, 20220562. https://doi.org/10.1098/rspb.2022.0562

De Bona, S., Valkonen, J.K., López-Sepulcre, A., & Mappes, J. (2015). Predator mimicry, not conspicuousness, explains the efficacy of butterfly eyespots. Proceedings of the Royal Society B, 282, 1806. https://doi.org/10.1098/RSPB.2015.0202

Hossie, T.J., & Sherratt, T.N. (2012). Eyespots interact with body colour to protect caterpillar-like prey from avian predators. Animal Behaviour, 84, 167-173. https://doi.org/10.1016/j.anbehav.2012.04.027

Hossie, T.J., Sherratt, T.N., Janzen, D.H., & Hallwachs, W. (2013). An eyespot that “blinks”: an open and shut case of eye mimicry in Eumorpha caterpillars (Lepidoptera: Sphingidae). Journal of Natural History, 47, 2915-2926. https://doi.org/10.1080/00222933.2013.791935

Iserhard, C.A., Malta, S.T., Penz, C.M., Brenda Barbon Fraga; Camila Abel da Costa; Taiane Schwantz; & Kauane Maiara Bordin (2024). The large and central Caligo martia eyespot may reduce fatal attacks by birds : a case study supports the deflection hypothesis in nature. Zenodo, ver. 1 peer-reviewed and recommended by Peer Community in Ecology. https://doi.org/10.5281/zenodo.10980357

Janzen, D.H., Hallwachs, W., & Burns, J.M. (2010). A tropical horde of counterfeit predator eyes. Proceedings of the National Academy of Sciences, USA, 107, 11659-11665. https://doi.org/10.1073/pnas.0912122107

Kodandaramaiah, U. (2011). The evolutionary significance of butterfly eyespots. Behavioral Ecology, 22, 1264-1271. https://doi.org/10.1093/beheco/arr123

Monteiro, A. (2015). Origin, development, and evolution of butterfly eyespots. Annual Review of Entomology, 60, 253-271. https://doi.org/10.1146/annurev-ento-010814-020942

Monteiro, A., Glaser, G., Stockslager, S., Glansdorp, N., & Ramos, D. (2006). Comparative insights into questions of lepidopteran wing pattern homology. BMC Developmental Biology, 6, 1-13. https://doi.org/10.1186/1471-213X-6-52

Stevens, M. (2005). The role of eyespots as anti-predator mechanisms, principally demonstrated in the Lepidoptera. Biological Reviews, 80, 573–588. https://doi.org/10.1017/S1464793105006810

Stevens, M., Stubbins, C.L., & Hardman C.J. (2008). The anti-predator function of ‘eyespots’ on camouflaged and conspicuous prey. Behavioral Ecology and Sociobiology, 62, 1787-1793. https://doi.org/10.1007/s00265-008-0607-3

Tullberg, B.S., Merilaita, S., & Wiklund, C. (2005). Aposematism and crypsis combined as a result of distance dependence: functional versatility of the colour pattern in the swallowtail butterfly larva. Proceedings of the Royal Society B, 272, 1315-1321. https://doi.org/10.1098/rspb.2005.3079

Vallin, A., Jakobsson, S., Lind, J., & Wiklund, C. (2005). Prey survival by predator intimidation: an experimental study of peacock butterfly defence against blue tits. Proceedings of the Royal Society B, 272, 1203-1207. https://doi.org/10.1098/rspb.2004.3034

Conservation biology is strongly rooted in the theory of island biogeography (TIB). In island systems where the ocean constitutes the inhospitable matrix, TIB predicts that species richness increases with island size as extinction rates decrease with island area (the species-area relationship, SAR), and species richness increases with connectivity as colonisation rates decrease with island isolation (the species-isolation relationship, SIR)[1]. In conservation biology, patches of habitat (habitat islands) are often regarded as analogous to islands within an unsuitable matrix [2], and SAR and SIR concepts have received much attention as habitat loss and habitat fragmentation are increasingly threatening biodiversity [3,4].
The existence of SAR in patch-matrix systems has been confirmed in several studies, while the relative importance of SIR remains debated [2,5] and empirical evidence is mixed. For example, Thiele et al. [6] showed that connectivity effects are trait specific and more important to explain species richness of short-distant dispersers and of specialist species for which the matrix is less permeable. Some authors have also cautioned that the relative support for or against the existence of SIR may depend on methodological decisions related to connectivity metrics, patch classification, scaling decisions and sample size [7].
In this preprint, Laroche and colleagues [8] argue that methodological limits should be fully understood before questioning the validity of SIR in patch-matrix systems. In consequence, they used a virtual ecologist approach [9] to qualify different methodological aspects and derive good practice guidelines related to patch delineation, patch connectivity indices, and scaling of indices with species dispersal distance.
Laroche et al. [8] simulated spatially-explicit neutral meta-communities with up to 100 species in artificial fractal (patch-matrix) landscapes. Each habitat cell could hold up to 100 individuals. In each time step, some individuals died and were replaced by an individual from the regional species pool depending on relative local and regional abundance as well as dispersal distance to the nearest source habitat cell. Different scenarios were run with varying degrees of spatial autocorrelation in the fractal landscape (determining the clumpiness of habitat cells), the proportion of suitable habitat, and the species dispersal distances (with all species showing the same dispersal distance). Laroche and colleagues then sampled species richness in the simulated meta-communities, computed different local connectivity indices for the simulated landscapes (Buffer index with different radii, dIICflux index and dF index, and, finally, related species richness to connectivity.
The complex simulations allowed Laroche and colleagues [8] to test how methodological choices and landscape features may affect SIR. Overall, they found that patch delineation is crucial and should be fine enough to exclude potential within-patch dispersal limitations, and the scaling of the connectivity indices (in simplified words, the window of analyses) should be tailored to the dispersal distance of the species group. Of course, tuning the scaling parameters will be more complicated when dispersal distances vary across species but overall these results corroborate empirical findings that SIR effects are trait specific [6]. Additionally, the results by Laroche and colleagues [8] indicated that indices based on Euclidian rather than topological distance are more performant and that evidence of SIR is more likely if Buffer indices are highly variable between sampled patches.
Although the study is very technical due to the complex simulation approach and the different methods tested, I hope it will not only help guiding methodological choices but also inspire ecologists to further test or even revisit SIR (and SAR) hypotheses for different systems. Also, Laroche and colleagues propose many interesting avenues that could still be explored in this context, for example determining the optimal grid resolution for the patch delineation in empirical studies.

References

[1] MacArthur, R.H. and Wilson, E.O. (1967) The theory of island biogeography. Princeton University Press, Princeton.
[2] Fahrig, L. (2013) Rethinking patch size and isolation effects: the habitat amount hypothesis. Journal of Biogeography, 40(9), 1649-1663. doi: 10.1111/jbi.12130
[3] Hanski, I., Zurita, G.A., Bellocq, M.I. and Rybicki J (2013) Species–fragmented area relationship. Proceedings of the National Academy of Sciences U.S.A., 110(31), 12715-12720. doi: 10.1073/pnas.1311491110
[4] Giladi, I., May, F., Ristow, M., Jeltsch, F. and Ziv, Y. (2014) Scale‐dependent species–area and species–isolation relationships: a review and a test study from a fragmented semi‐arid agro‐ecosystem. Journal of Biogeography, 41(6), 1055-1069. doi: 10.1111/jbi.12299
[5] Hodgson, J.A., Moilanen, A., Wintle, B.A. and Thomas, C.D. (2011) Habitat area, quality and connectivity: striking the balance for efficient conservation. Journal of Applied Ecology, 48(1), 148-152. doi: 10.1111/j.1365-2664.2010.01919.x
[6] Thiele, J., Kellner, S., Buchholz, S., and Schirmel, J. (2018) Connectivity or area: what drives plant species richness in habitat corridors? Landscape Ecology, 33, 173-181. doi: 10.1007/s10980-017-0606-8
[7] Vieira, M.V., Almeida-Gomes, M., Delciellos, A.C., Cerqueira, R. and Crouzeilles, R. (2018) Fair tests of the habitat amount hypothesis require appropriate metrics of patch isolation: An example with small mammals in the Brazilian Atlantic Forest. Biological Conservation, 226, 264-270. doi: 10.1016/j.biocon.2018.08.008
[8] Laroche, F., Balbi, M., Grébert, T., Jabot, F. and Archaux, F. (2020) Three points of consideration before testing the effect of patch connectivity on local species richness: patch delineation, scaling and variability of metrics. bioRxiv, 640995, ver. 5 peer-reviewed and recommended by PCI Ecology. doi: 10.1101/640995
[9] Zurell, D., Berger, U., Cabral, J.S., Jeltsch, F., Meynard, C.N., Münkemüller, T., Nehrbass, N., Pagel, J., Reineking, B., Schröder, B. and Grimm, V. (2010) The virtual ecologist approach: simulating data and observers. Oikos, 119(4), 622-635. doi: 10.1111/j.1600-0706.2009.18284.x

Understanding the factors that govern the relationship between structure, stability and functioning of food webs has been a central problem in ecology for many decades. Historically, apart from microbial and soil food webs, the role of nutrient cycling has largely been ignored in theoretical and empirical food web studies. A prime example of this is the widespread use of Lotka-Volterra type models in theoretical studies; these models per se are not designed to capture the effect of nutrients being released back into the system by interacting populations. Thus overall, we still lack a general understanding of how nutrient cycling affects food web dynamics.
A new study by Quévreux, Barot and Thébault [1] tackles this problem by building a new food web model. This model features some important biological details: trophic interactions and vital rates constrained by species' body masses (using Ecological Metabolic Theory), adaptive foraging, and stoichiometric rules to ensure meaningful conversion between carbon and nutrient flows. The authors analyze the model through detailed simulations combined with thorough sensitivity analyses of model assumptions and parametrizations (including of allometric scaling relationships). I am happy to recommend this preprint because of the novelty of the work and it's technical quality.
The study yields interesting and novel findings. Overall, nutrient cycling does have a strong effect on community dynamics. Nutrient recycling is driven mostly by consumers at low mineral nutrient inputs, and by primary producers at high inputs. The extra nutrients made available through recycling increases species' persistence at low nutrient input levels, but decreases persistence at higher input levels by increasing population oscillations (a new, nuanced perspective on the classical "paradox of enrichment"). Also, for the same level of nutrient input, food webs with nutrient recycling show more fluctuations in primary producer biomass (and less at higher trophic levels) than those without recycling, with this effect weakening in more complex food webs.
Overall, these results provide new insights, suggesting that nutrient cycling may enhance the positive effects of species richness on ecosystem stability, and point at interesting new directions for future theoretical and empirical studies.

References

[1] Quévreux, P., Barot, S. and E. Thébault (2020) Interplay between the paradox of enrichment and nutrient cycling in food webs. bioRxiv, 276592, ver. 7 peer-reviewed and recommended by PCI Ecology. doi: 10.1101/276592