The Ecology of Plant Interactions: A Giant with Feet of Clay

Ecologists use the net biotic interactions among plants as a major factor to predict other ecosystem features, such as species diversity, community structure, or plant atmospheric carbon uptake. By adopting this approach, ecologists have built a giant body of theory founded on observational evidence. However, growing evidence points out that this may not be the right approach. The literature addressing the biophysical mechanisms underlying the plant interactions is much scarcer. A rising number of scientists claim the need for a mechanistic understanding of plant interactions due to the limitations that a phenomenological approach raises both in empirical and theoretical studies. Scattered studies have recently taken such a mechanistic approach, but we still lack a general theoretical framework to study mechanistically plant interactions. In this review, we first recapitulate the elementary units of plant interactions, i.e., all the known biophysical processes affected by the presence of an influencing plant and the possible phenotypic responses of plants influenced by those processes. Second, we discuss how a net interaction between two plants emerges from the simultaneous effect of these elementary units. Third, we touch upon the spatial and temporal variability of the net interaction and discuss the links between this variability and the underlying biophysical processes. We conclude by discussing how to integrate these processes into a mechanistic framework for plant interactions that must necessarily focus on the individual scale and explicitly incorporate the spatial structure of the community and environmental factors: the plant interaction models (PIM). A PIM incorporates a pair or few plants interacting with their physical environment so that the biotic interaction is not imposed but emerges from the model. This type of model can provide concise, mechanistic hypotheses to be tested empirically. This review calls for a paradigm shift in the ecology of plant interactions, from the classic species interaction study towards a more mechanistic individual-level approach. It also presents a comprehensive foundation for studying the mechanisms underpinning the net interaction between two plants.

Introduction 5 interaction ecologists. This task will require a conceptual shift in plant community ecology, from a species interaction approach to a purely individualistic one. Most studies that tackle the plant interactions measure the net interaction between individuals and then 130 classify them by species to make conclusions at the species level. While these studies are empirically measuring individuals, they are conceptually focusing on plant populations of different species: By using the species as a main statistical factor, these studies lose track of the interaction mechanisms. Investigating the plant interactions at finer biological scales (Figure 1) in further detail is necessary to cement our understanding of many 135 fundamental ecological principles. In this review, we aim at establishing a framework to study mechanistically plant net interactions, based on the three fundamental features of the interacting plants that shape such interaction: the distance between individual plants, their functional traits, and the 145 environmental conditions in which the interaction takes place (Figure 2). To that end, we first recapitulate the fundamental biophysical processes by which plants can interact with each other. Second, we address plant phenotypical responses to these interaction forces from a game-theoretical perspective. Third, we analyze how interaction forces and plant 6 strategies may integrate into a directional net interaction, i.e., the overall biological effect 150 of one plant on another. Fourth, we tackle the effects of the distance between the pair of interacting plants on the interaction forces and the net interaction. Fifth, we discuss how net interactions may change in space and time and how that relates to the fundamental mechanisms underlying plant interactions. Sixth, we assess the pros and cons of alternative conceptual approaches to plant interactions from the lenses of existing models. 155 Seventh, based on all of the above, we propose developing plant interaction models (PIMs): models based on biophysical and ecophysiological processes in which the net interaction between a pair of individual plants in space emerges from a detailed description of their underlying interaction forces. We hope this review will foster a paradigm shift in the plant interaction ecology, from the currently dominant 160 phenomenological approach towards a more mechanistic approach to plant interactions, necessary to build the theory from the ground up.

Box 1: Glossary
Lexical arbitrariness leads to confusion in the biotic interaction literature. An established definition of the existing terms referring to biotic interaction levels and mechanisms would make literature clearer and more comprehensible (Trinder et al. 2013). A paradigmatic example illustrating this confusion is the word competition, which is used interchangeably to refer to different things. In community-level biotic interaction charts, competition refers to the negative pairwise interaction (-/-), as opposed to, for instance, mutualism (+/+) (e.g., in Godsoe et al. 2017). In some fields, such as plant positive interactions research, it is common to use competition to refer to a negative net interaction instead of facilitation (Filazzola and Lortie 2014). Finally, in an ecophysiology context, competition is the fight among individuals for a specific resource (Grime 1973), regardless of whether the net interactive effect is positive or negative, hence being an interaction force. The Merriam Webster dictionary goes in this same direction and defines competition as the "active demand by two or more organisms or kinds of organisms for some environmental resource in short supply." This problem similarly affects other related terms (West et al. 2007). To avoid confusion within this text, and hopefully to contribute a more precise use of the words across sub-disciplines, we propose the following glossary of biotic interaction terms.

Biophysical process
A local modification of the physical (or chemical) environment that is a direct or indirect result of the presence of a plant.

Primary (biophysical) process
A biophysical process by which a plant directly modifies its direct physical surroundings.

Interaction force
A biophysical process by which a plant affects the environment in a way that impacts the fitness of any neighbor plant.

Competition
(sensu Grime, 1973) Trophic interaction force; plants compete for each quantum of light, molecule of water, or ion nutrient.

Net interaction
The net outcome of all the interaction forces, giving the net biological effect of a plant on the fitness of a neighboring plant.

Pairwise interaction
The complete (bidirectional) biotic interaction between two plants.

Model (PIM)
Family of models that focus on a detailed description of the biophysical processes and plant phenotypic responses letting the net interaction emerge. They must be individual-based, incorporate the spatial structure of the community, and explicitly account for environmental factors.

1-The biophysical processes underpinning plant interactions
To develop a mechanistic understanding of plant net interactions, we first need to know the several, somewhat independent, biophysical processes underneath it. In the context of plant interactions, we can classify biophysical processes as primary processes (the direct 175 effects of the influencing plants in their immediate surrounding), interaction forces (the biophysical changes resulting from the influencing plant that directly affect the influenced plant, i.e., the proximal cause of the interaction), and intermediary processes (any biophysical process mediating between a primary process and an interaction force).
The main primary processes of plant interactions are the effects of a plant canopy casting 180 shade (Fernando Valladares, Laanisto, Niinemets, & Zavala, 2016), baffling wind (Leonard & Croft, 2006), intercepting rainfall (Muzylo et al., 2009), and transpiring water (Flerchinger, Reba, Link, & Marks, 2015); the effects of both plant canopies and root systems producing litter (Xiong & Nilsson, 1999); and the effects of root systems absorbing soil water (Lambers, Chapin III, & Pons, 2008b), exuding plant water (Prieto,185 Armas, & Pugnaire, 2012), absorbing mineral nutrients (Lambers, Chapin III, & Pons, 2008a), altering soil physical structure (Angers & Caron, 1998), and exuding metabolites (Bertin, Yang, & Weston, 2003). These primary processes ultimately affect, sometimes antagonistically, several interaction forces, as it is, for example, the case of shade in hot, semiarid habitats (Figure 3).  A comprehensive literature review on plant interactions allowed us to identify twentyone types of interaction forces potentially relevant to understanding every single net interaction mechanistically (Figure 4). In the supplementary material (SM: A review of 205 plant interaction mechanisms), we provide a full summary of the literature review explaining each of these interaction forces, with references to studies addressing each of them. we now discuss observed plant phenotypical responses.

2-The phenotypic response of plants to interactions
Game theory, originally developed to study the interaction among rational decisionmakers, became a powerful tool to investigate evolutionary questions towards the end of the XX century (Maynard Smith, 1982). More recently, it has become a very successful framework to study plant phenotypical responses to biotic interactions in an evolutionary 220 context (Mcnickle & Dybzinski, 2013). In times of classical optimality (Parker & Maynard Smith, 1990), game theory revolutionized the field of evolutionary ecology because it demonstrated that non-optimal traits might evolve when the net reward of a resource-allocation strategy -that is, the difference between the reproductive benefits of such strategy and the costs of adopting it-are evaluated in the presence of interacting 225 individuals.
Game theory thus broadened the concept of optimality, allowing researchers to define different types of optimal strategies. An individual optimal refers to the strategy maximizing the net reward for an individual growing without neighbors. A collective optimal is the strategy maximizing the overall net reward for a whole population of 230 individuals (hereafter, cooperation). Finally, an evolutionarily stable strategy (ESS) is the strategy that maximizes the net reward for an individual that selfishly interacts with other individuals of the population, and that cannot be invaded by any other better strategy.
While game theory provides methods to solve for collective optimization (e.g., Paretooptimality, see Pulliam et al. 1982), it often assumes that individual responses to biotic To study competition for light from a game-theoretical perspective, we can think of a 240 plant as a photosynthetic crown placed on top of a woody trunk. The crown area determines plants' potential to intercept light and, therefore, its yield. The individual optimal strategy for plants is to invest all their resources into maximizing a flat photosynthetic crown area at the ground level. (Figure 5a). However, in interaction with neighbor plants, competition for light becomes asymmetric because taller individuals get 245 most of it and shaded individuals almost none. Therefore, a plant may benefit from first growing the trunk to be taller than its neighbors and, after that, grow its crown.
Nevertheless, suppose all individuals in the community follow this behavior. In that case, following the ESS, they escalate in the production of increasingly taller trunks and end up engaging in an ecological arms race that makes them invest most of their resources 250 into conflict without getting any significant benefit from it (Dybzinski, Farrior, Wolf, Reich, & Pacala, 2011;Falster & Westoby, 2003) (Figure 5b). Indeed, trees invest about 80% of their biomass in growing robust columns of wood on top of which they place their leaf canopy . Finally, if plants pursue a collective optimal, they would have the same crown area exposed to sunlight but at the ground level (Figure 5c), thereby 255 intercepting the same light at a much lower cost. In that case, all the energy gathered from sunlight could be invested in reproduction.   For a single plant, this increase in uptake is the marginal gain obtained from each consecutive root. Moreover, the form it grows implies that the allocation of new roots 295 reduces the average resource uptake of pre-existing roots (hereafter, new roots "steal" resources from pre-existing roots). For example, if the plant allocates two roots, the uptake per root is (50+25)/2 = 37.5, and the second root has stolen from the first one 37.5-25=12.5 units of the resource. In the hypothetical situation described above, and for an individual optimal, the plant will not grow more than three roots because the marginal 300 benefit of a fourth root is lower than its allocation cost (6.25<8.66) (Figure 5d). However, if a second plant accesses the same patch inhabited by the three-root plant, the new plant's marginal benefit upon allocating its first root -which coincides with the average uptake per root in the soil patch-is (50+25+12.5+6.25)/4=23.43. Notice that the second plant's marginal benefit allocating its first root is much larger than that of the first plant allocating 305 a fourth root, which is 6.25. This difference arises because the new plant steals resources from its neighbor rather than from its own pre-existing roots. Iterating this calculation, one can see that for an ESS, the second plant still benefits from allocating a second and a third root in the same patch, and this whole process repeats if a third individual colonizes the patch, then a fourth, and so on (Figure 5e). The number of roots exploiting the soil 310 patch increases with the number of plants that colonize it, which reduces the average resource uptake per root and ultimately leads to less efficient foraging. This exploitative process continues until the cost of allocating a root equals the average uptake per root, which is at 11 roots in our example. As plants increasingly deplete the resource in the patch, the net gain for the community, i.e., the sum of the net rewards of all coexisting 315 plants, tends to zero. Empirical studies evidencing increased root allocation of plants in response to the presence of neighbors support this theoretical prediction (Maina et al. 2002, O'Brien et al. 2005, but see Semchenko et al. 2007). In our example, the collective optimal, which pursues the maximization of the net gain, is attained with three roots, regardless of how many plants these roots belong to (Figure 5f).

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In their review, Mcnickle and Dybzinski (2013) address cases, beyond competition for light and soil resources, in which plants may inefficiently allocate resources following an ESS, such as the arms races in attracting allies or repelling enemies. As in the examples addressed before, the allocation of resources to plant defenses against enemies must not be seen as an individual optimization. The strategy of the neighbors also must be 325 considered because neighbors can deflect enemies to the focal plant by overinvesting in their own defense. Plants will overinvest resources into defenses to deflect herbivores and parasites to neighbors, but neighbors adopting the same ESS leads to allocating energy into non-effective defense. Similarly, low plant investment in attracting allies can limit their availability if the local environment does not attract them, yet neighbors investing 330 too much in attracting allies can increase competition for them by decreasing the rate at which they visit the focal plant. Individuals whose investment in attracting pollinators or seed-disperser animals is higher than the individual optimal will evolve as an ESS.
However, in a plant community in which all individuals follow that strategy, such investment will not return a net benefit to the plants. While necessary to capture the 335 relevant ecological responses of plants to interaction forces, Mcnickle and Dybzinski (2013) conclude that the game theoretical approach is still not widespread in the plant community ecology literature.

3-Scaling up to the net interaction 340
The different interaction forces and the phenotypical responses of plants scale up, leading to net interactions. However, our understanding of this unifying process is very poor (Filazzola & Lortie, 2014). A first step towards linking net interactions to the underpinning mechanisms is to precisely define what a net interaction is. In general, the net interaction is the net effect a neighbor has on the fitness of the focal plant, i.e., on the 345 success of the focal plant at passing its genes to the next generation (Hamilton, 1964).
While simple to state from a theoretical perspective, evaluating an individual plant's fitness is almost impossible empirically. Hence, researchers need to resort to indicators that can be measured in the field, such as the biomass allocated into reproduction, hereafter fecundity. The fitness-fecundity relation depends on many factors such as 350 differences between pollen or ovules (Primack & Hyesoon Kang, 1989), seed number to seed size ratio (Geritz, Van Der Meijden, & Metz, 1999), or diminishing returns of increased seed sets (Campbell, Brody Proxies such as dry biomass or growth rates tend to correlate well with fecundity in plants and are often used as surrogates (Younginger, Sirová, Cruzan, & Ballhorn, 2017). Indexes to calculate the net interaction based on this type of observations exist (Armas, Ordiales, & Pugnaire, 2004). However, a recent study has shown that the direction of the observed 360 net interaction among plants may depend on the fecundity surrogate (somatic biomass, seed germination, or plant survival). Therefore, empirical observations of net interactions must be interpreted with caution (Lozano, Armas, Hortal, Casanoves, & Pugnaire, 2017).
From a mechanistic perspective, this is a non-surprising finding as biophysical processes may affect these measures differentially: For instance, attracting allies (21) see Figure 1 such 365 as pollinators, will increase the focal plant's seed yield, but it seems unlikely that it would affect its somatic biomass; arms race during the competition for light (1) should increase the allocation into somatic biomass at the expense of reproductive allocation, and similarly; increase soil moisture (10) will enhance plant somatic growth, but it is unclear whether its relation to reproductive yield is linear. All in all, two main questions need to 370 be addressed in order to dive into the mechanisms underpinning plant net interactions.
The first question is, how can we make a connection between biophysical processes and  shrubby plant allows to compare the water stress to which the red plant is exposed through predictions of soil water potentials (s) and atmospheric water potentials (a).

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The second question is, how do plants respond phenotypically to several interaction forces entangled with each other in highly nonlinear ways (Meron, 2015)? Ecologists have long been interested in the study of plant strategies to cope with resource colimitation. For instance, Bloom et al. (1985) developed the optimal foraging hypothesis, stating that plants will adapt their phenotype so that all essential resources are equally modeled biomass allocation to leaves, stem, and roots. They noticed that, although classic-optimality models predict that plants should allocate all their resources into reproduction after reaching a threshold size (Bazzaz, Chiariello, Coley, & Pitelka, 1987), observations from forests show that adult trees invest less than 10% to reproduction 420 (Luyssaert et al., 2007). Calculating the aboveground and belowground ESS regarding biomass allocation into leaves, stems, and roots, they predicted that plants forage inefficiently, over-allocating resources into roots, stems, and leaves, at the expense of their lifetime fecundity. The model, in which allometries emerge naturally from allocation strategies rather than being imposed, successfully predicted the physiognomy of  with the Ripley's K index (Ripley, 1978). Statistical spatial correlations can be used as a proxy to many ecological processes (McIntire & Fajardo, 2009), providing an alternative 440 approach to empirically reporting net interactions from observing fitness differences. For instance, clumped vegetation patterns must be observed when there is facilitation (Haase et al. 1996), but over-dispersed patterns emerge under interference when competition is asymmetric (Stoll & Bergius, 2005). For a comprehensive review of spatial correlation techniques and the ecological importance of patterns and scale, see Dray et al. (2012) and 445 Chave (2013), respectively. Here, we focus on the scarcer literature studying the mechanisms underpinning the change in the net interaction with increasing distance between two plants.
Generally, all interaction forces in Figure 4 must vary in intensity with the distance from an influencing plant. Probably, the first interaction force that was explicitly suggested to 450 vary with the distance between two plants is the effect of a plant attracting enemies (18) to another plant, as stated by the Janzen-Connell hypothesis (Connell, 1971;Janzen, 1970). Like in the Janzen-Connell hypothesis, many other interaction forces will progressively lose strength with increasing distance to the plant center. However, the change in intensity of each interaction force with space is, at least to a certain extent, This novel theory reconciles seemingly opposing previous findings in root foraging literature: root territoriality (Schenk, Callaway, & Mahall, 1999), which intuitively led to 500 assume under-investment into roots, studies that do report this underinvestment (Chen et al., 2015), and the tragedy of the commons (Gersani et al., 2001). It also highlights the importance of incorporating spatial processes in game-theoretical models aiming to investigate plant interactions.

5-A dynamic view of the net interaction
The biophysical processes and the plant phenotypic responses to interaction forces vary with time and space. This variability might be due to changes in the distance between interacting plants, their functional traits, and environmental factors. To mechanistically explain the net interaction between two plants at a given location and moment, researchers 510 need to account for the dynamism of these drivers. In the previous section, we reviewed the case of the distance between plants. Next, we discuss how spatiotemporal changes in environmental conditions and plant functional traits modify net interactions.
Firstly, environmental quality is a major driver of changes in net interactions. Grime (1973) found, for the first time, that competition can become more intense with increasing 515 environmental quality. Later, facilitation among plants started to interest community ecologists (Hunter & Aarssen, 1988), leading to the stress gradient hypothesis (SGH).
The SGH states that positive interaction forces may dominate with increasing environmental stress, allowing the emergence of facilitation (Bertness & Shumway, 1993). It mostly predicts that interference or facilitation dominance is robust to spatial 520 variation in habitat conditions (Maestre, Valladares, & Reynolds, 2005). However, temporal heterogeneity may produce switches in the sign of net interaction at the scale of days (Wright, Schnitzer, & Reich, 2015), seasons (Breshears, Nyhan, Heil, & Wilcox, 1998;Kikvidze, Khetsuriani, Kikodze, & Callaway, 2006) under extreme stress conditions (Holmgren & Scheffer, 2010). This collapse of facilitation has been found in water-limited habitats (Maestre, Bautista, & Cortina, 2003), cold climates (Koyama & Tsuyuzaki, 2013), and along gradients of grazing intensity interactions across stress conditions, very few studies accurately report the biophysical processes responsible for those changes. We have argued that, by modeling the biophysical processes related to a specific resource, we could explain mechanistically the difference in fitness that a plant experiences in the presence of a neighbor (see Figure 6).
However, functional traits are far from being solely restricted to species identity (Cadotte, Carscadden, & Mirotchnick, 2011). Functional traits vary substantially with ontogeny, plant size being a paradigmatic example of that change. For instance, the functional traits of a tree seedling look more like herbaceous plants than to adult individuals of its species 565 (Niklas et al., 2007). Some studies have reported shifts in the net interaction with increasing size of the influencing plants (Miriti, 2006),  (Walter, 1971), or plants with a higher leaf-area index will produce 580 a more intense shade (Jordan, 1969). The treatment of functional traits variation needs to be careful, as discerning the phenotypic plasticity of a plant in response to abiotic environmental change or in response to a biotic interaction is an arduous task.
Predicting major ecologic features is a paramount goal of environmental sciences to fight against the current anthropogenic global crisis. It requires understanding global-scale 585 spatial and temporal vegetation responses to climate change, mediated at least partially by plant interactions (Scheiner et al., 2011). Our current understanding of plant ecophysiology presumably provides tools to start approaching a theoretical treatment of this problem, but its complexity, as depicted through this review, is enormous. Some studies have tackled multi-level effects phenomenologically. For instance, Wright et al.

605
There are several conceptual approaches to study plant interactions, and models incorporating the plant interactions to make predictions of major ecosystem features provide us with a good overview of existing theoretical approaches to plant interactions.
We can classify existing models into three families: population, individual-based, and plant-continuum models, each of them showing different pros and cons ( Table 1). This 610 section reviews these families of models and their main characteristics to get a more indepth insight into the differences between the alternative possible conceptual approaches to plant interactions.
Following a chronological order, the first approach to study populations of interacting agents dates back to the logistic equation for intraspecific competition (Verhulst, 1845).

615
Later work by Lotka, Volterra, and others extended this model to systems with more than one species and other ecological interactions, specially prey-predator (Lotka, 1920(Lotka, , 1924Volterra, 1926). At least two factors explain the great success of this family of demographic models during the last century. First, they provide good fits to empirical observations. Notably remarkable are the data from the Hudson's Bay Company on 620 fluctuations of lynxes and hares in Canada that confirmed predictions of prey-predator models (Hewitt, 1921) and the experiments by Gause et al. (1934) to test intraspecific competition in populations of paramecia. Second, because demographic models focus on the species identity of the interacting agents and are mathematically tractable (Wangersky, 1978), they allowed researchers to identify simple rules that allow 625 coexistence between antagonistic species (Hardin, 1960).  (Lotka, 1924), (Jeltsch, Moloney, Schurr, Köchy, & Schwager, 2008) Individual       (Botkin, Janak, & Wallis, 1972), (Shugart et al., 2018) Continuum  ~    (Lefever & Lejeune, 1997), (Meron et al., 2019)  with increasing computational limits when simulating large populations or spatial scales.

Approach
The first limitation of this population-level approach is that plants are sessile organisms that interact only with their neighbors. The concerns for the low suitability of these models to plant communities was probably first raised by Fagerström (1988) Moreover, most studies on species coexistence are observational, which makes it challenging to control neighbor variability and leads to omitted variable biases in the estimated effects of neighbors on targeted plants (Rinella et al., 2020). All in all, this approach cannot incorporate all the mechanistic complexity underpinning plant 650 interactions (see Figure 1). Two alternative modeling approaches were developed during the last decades of the XX th century: The individual-based approach and the biomassbased continuum approach (Klausmeier, 1999;Lefever & Lejeune, 1997).
Individual-based models (IBM) are, generally, computer simulations of individuals interacting in a spatial environment composed of independent grid cells of the size of the 655 crown of an adult plant. The first vegetation dynamics IBM of this kind is probably jabowa (Botkin et al. 1972), and this approach has received considerable attention since.
Various modeling advances have been developed, such as foret (Shugart, and West 1980), which incorporated dependence between the cells in the grid, and sortie (Pacala et al. 1996), which was the first fully spatially-explicit IBM. Among the hindrances of this type 660 of models, two are the most remarkable. First, the smallest spatial scale is that of the individual. Second, they are mathematically less tractable than models based on ordinary differential equations (Meron et al., 2019), but tools to treat them analytically also exist (Iwasa, 2010;Matsuda, Ogita, Sasaki, & Sato, 1992).
The other alternative to well-mixed demographic-level models is the plant-continuum 665 approach, based on partial differential equations (PDEs) for the evolution in time and space of vegetation biomass density (Holmes, Lewis, Banks, & Veit, 1994 Meron, 2018;Rietkerk et al., 2002). Earlier models in this family were kernel-based models encapsulating every feedback between plants and their environment in the sign of the net interaction among plants (Lefever & Lejeune, 1997). More recent ecohydrological models describe scale-dependent feedbacks between water and vegetation explicitly (Figure 6a) (Klausmeier, 1999;Rietkerk et al., 2002). Albeit more mechanistic, the latter 675 tend to focus on a small set of interactions that are hypothesized to play a critical role in the question under study. This simplification provides an analytically tractable mathematical description of the system that explains large-scale processes that involve many individuals. However, by discarding many other processes, they do not provide good quantitative predictions (Meron et al. 2019

7-A framework to study the mechanisms under net interactions
We propose a new approach to understand plant interactions mechanistically. This approach may help to cement -or, in some cases, challenge-plant ecological theories. interactions among individuals, controlling for -but not focused on-the species identity of the interacting individuals, may also significantly enrich our knowledge of this field.
Only by incorporating the high complexity of mechanisms underpinning net interactions from an individual-level approach will the plant interaction ecology firmly stand on its own two feet.