Allelopathy as an evolutionarily stable strategy

In plants, most competition is resource competition, where one plant simply pre-empts the resources away from its neighbours. Interference competition, as the name implies, is a form of direct interference to prevent resource access. Interference competition is common among animals who can physically fight, but in plants, one of the main mechanisms of interference competition is Allelopathy. allelopathic plants release of cytotoxic chemicals into the environment which can increase their ability to compete with surrounding organisms for limited resources. The circumstances and conditions favoring the development and maintenance of allelochemicals, however, is not well understood. Particularly, it seems strange that, despite the obvious benefits of allelopathy, it seems to have only rarely evolved. To gain insight into the cost and benefit of allelopathy, we have developed a 2 × 2 matrix game to model the interaction between plants that produce allelochemicals and plants that do not. Production of an allelochemical introduces novel cost associated with synthesis and detoxifying a toxic chemical but may also convey a competitive advantage. A plant that does not produce an allelochemical will suffer the cost of encountering one. Our model predicts three cases in which the evolutionarily stable strategies are different. In the first, the non-allelopathic plant is a stronger competitor, and not producing allelochemicals is the evolutionarily stable strategy. In the second, the allelopathic plant is the better competitor and production of allelochemicals is the more beneficial strategy. In the last case, neither is the evolutionarily stable strategy. Instead, there are alternating stable states, depending on whether the allelopathic or non-allelopathic plant arrived first. The generated model reveals circumstances leading to the evolution of allelochemicals and sheds light on utilizing allelochemicals as part of weed management strategies. In particular, the wide region of alternative stable states in most parameterizations, combined with the fact that the absence of allelopathy is likely the ancestral state, provides an elegant answer to the question of why allelopathy rarely evolves despite its obvious benefits. Allelopathic plants can indeed outcompete non-allelopathic plants, but this benefit is simply not great enough to allow them to go to fixation and spread through the population. Thus, most populations would remain purely non-allelopathic.


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Competition is ubiquitous in the natural world, as there are finite resources available in a

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Allelopathy is the production of chemicals, called allelochemicals, that are released into 65 the environment and negatively affect the growth and development of competing individuals 9 .

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Although the term was first used in 1937, the effect has been recognized for thousands of years 9 . Australia, affecting up to 30 Mha, whose invasion success is partially attributed to production of 80 the allelochemical shikonin and its derivatives 16 . Indeed, one commonly invoked mechanism for 81 invasion by non-native species is the novel weapons hypothesis, which suggests invasive species 82 are successful through use of competitive strategies for which native species have not co-evolved 83 counter strategies 17,18 . This mechanism has been linked to the invasion success of allelopathic

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Policeman's helmet (Impatiens glandulifera) 19 , which releases a compound structurally similar to 85 shikonin called 2-methoxy-1,4-naphthoquinone (2-MNQ) that elicits negative effects on herb 86 germination and mycelium growth and is otherwise absent in soils without I. glandulifera, thus 87 suggesting 2-MNQ may function as a "novel weapon" [19][20][21] . From these studies, it may be possible 88 that allelochemicals may have significant potential for genetically modified cropping systems to 89 enhance the competitive ability of crop species over weeds.

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Despite the potential advantages of allelochemicals as an evolved tool for interference 92 competition, they seem to have only rarely evolved. Here, we report an evolutionary game 93 theoretic model to probe the benefits and circumstances that might favor the evolution of 94 allelochemicals to better understand why they might not be more common in plants. Specifically,

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we ask: 1) What circumstances favor the production of allelochemicals? 2) How does the cost of 5 producing an allelochemical affect fitness of the plant producing the allelochemical and plants 97 competing with that plant? 3) When will allelopathic plants be stable in a population? Beyond the 98 implications for evolutionary ecology, understanding the evolution of allelopathy has the potential 99 to inform the design of applications for agriculture, from the integration of allelopathic crops into 100 farming systems to the use of synthetic biology to create a crop that produces its own 101 allelochemical-based weed control. We developed a 2 × 2 matrix game of interactions among a plant player with (+A) and 107 without (-A) allelopathy. We assumed that competition creates benefits of available resources 108 ( ), that the cost ( ) to the player of producing allelochemicals is the sum of the costs of 109 production of the allelochemical and detoxification to prevent autotoxicity, and that allelochemicals 110 impose some different cost to the opponent in the form of toxicity and/or detoxification ( ). We 111 further assumed that benefits were shared unequally, encompassed by a parameter, , that Combining these parameters, we can derive the payoff, , , across several competitive 123 contexts where is the focal plant strategy (+ or − ), and is the neighboring plant strategy 124 (+ or − ). Finally, we also assume that there are two plants competing in something like a pot 125 experiment, because we imagine this is the most likely way to empirically test our model in the 126 future (e.g. 10,11 ). However, the equations below can be extended to any number of competing 127 plants by simply replacing 2 with , where is the number of competing plants.

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First, when both plants produce allelochemicals, we argue that they will, on average, share 130 the total benefit of the soil volume equally, , but will also pay the cost of producing and detoxifying  Equations 7a can be rearranged to find: The isoclines in equations 5-7 create two parallel lines, each with slope , but that either 193 intercept the y-axis at 0 or at . Thus, depending on the values of and , we can plot the 194 entire solution space graphically in positive and phase space ( Figure 2). For + to be the 9 ESS, the parameters need to be above both isoclines. For − to be the ESS, the parameters 196 need to be below both isoclines. Between the two lines, which will never cross as they have the 197 same slope, there is a region of alternative stable states, also sometimes called a priority effect.

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In the region of alternative stable states, either strategy might occur, but the answer depends on 199 the history of the system. That is, whichever strategy was there first becomes the ESS> product. Thus, non-target-site resistance is referred to as "metabolism-based resistance" 42 .

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Metabolism-based resistance to herbicides is primarily achieved via four gene families: thaliana was shown to be sufficient to confer resistance to multiple herbicides 46 . Moreover,

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Arabidopsis seedlings grown in vitro in the presence of GSH in juglone-containing media were 273 found to display root growth phenotypes indistinguishable from wild type (Meyer et al 2020).

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Beyond conjugation with GSH, glycosylation appears to be a major mechanism of detoxification 275 of specialized metabolites 47 . Indeed, much of the juglone found in black walnut is glycosylated 48 ,

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suggesting that one of the mechanisms black walnut uses to tolerate producing and storing an

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According to the matrix game presented here, the fitness pay-off to both cotton and purple 325 nutsedge (the -A species) would be expected to decrease as the toxicity, , of allelochemicals 326 produced by sorghum, soybean, or sesame (the +A species) increased. Indeed, seed cotton yield 327 was found to decrease between 8-23% in all intercropping systems, compared to unmanaged 328 cotton alone. Similarly, the presence of allelopathic species led to 70-96% reduced purple 329 nutsedge density 55 . That control of purple nutsedge was found to be more effective in the second

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year of the study compared to the first year, which was suggested to be the result of residual 331 allelochemicals leftover in the soil in year two 55 . This is consistent with purple nutsedge paying an 332 increased penalty, , to detoxify higher levels of allelochemicals. Our model predicts three ESS cases, differing in the benefit and cost to the allelopathic plant. In 369 the first, the non-allelopathic plant is a stronger competitor due to high metabolic costs to the 370 allelopathic plant, and not producing allelochemicals is the evolutionarily stable strategy. In the 371 second, the allelopathic plant is the better competitor and production of allelochemicals is the more beneficial strategy. In the last case, the allelopathic and non-allelopathic plants are equal 373 competitors, but pay different costs resulting in alternative stable states depending on the history 374 of the system. We find that despite the obvious benefits of allelopathy, there are relatively few 375 conditions that lead to + as a pure ESS, and that ifis the ancestral state the large regions 376 dominated by priority effects would mean + mutants cannot successfully spread in a population.

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We argue that these results potentially help explain the relative rarity of allelopathy in nature.

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Additionally, the four parameters give insight into molecular mechanisms that future biochemical   Therefore, +A can never be the ESS in this simpler three parameter version of the game because 583 is by definition greater than zero, so the first condition in equations 9b cannot be met.

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Conversely, for -A to be a pure ESS, (i) -A needs to be able to invade a population of +A and (ii) 586 needs to resist invasion from +A. According to the ESS definition, this occurs when:

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Interestingly, a model that only includes a fitness benefit to the focal plant that emerges from 629 alleopathy could be a useful model of allopathy. It lacks the priority effects predicted by the 630 four parameter model in the main text (Fig 2), which presents a testable hypothesis. However, given that the main biological feature of alleopathy is the toxicity that they cause to neighbours,

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we opted to include in the model described in the main text, even though this model shows 633 that this toxicity is not strictly necessary.