INTRODUCTION

Understanding the mechanisms underlying species coexistence and the maintenance of highly diverse communities has been a central issue in ecology for decades (Hutchinson, 1959; Tilman, 2000). Historically much emphasis has been made on the importance of limiting similarity, showing that competing species should differ in their ecological niche—for example, in their resource utilization—to allow stable coexistence (Barabás & Meszéna, 2009; Macarthur & Levins, 1967). However, recent theoretical studies have revealed that competing species can coexist over ecological scales not only by being different but also by being sufficiently similar and thereby escape competitive exclusion. This mechanism leads to distinctive clustering patterns of species distribution along the niche axis with groups of similar species separated by gaps in between (Fort et al., 2010; Sakavara et al., 2018; Scheffer et al., 2018; Scheffer & van Nes, 2006). A growing number of empirical studies report such clustering patterns along trait axes, which can be seen as surrogates of the niche axis (D'Andrea et al., 2020; Segura et al., 2011, 2013; Vergnon et al., 2009, 2012). For instance, clusters have been detected in the distribution of tree height and wood density in tropical forests (D'Andrea et al., 2020), in the size distribution of marine and freshwater phytoplankton (Graco-Roza et al., 2021; Segura et al., 2011, 2013) or aquatic beetles (Scheffer et al., 2015). While various mechanisms have been shown to promote the emergence of niche clustering and its stability over time (D'Andrea et al., 2019; Sakavara et al., 2018; Scheffer & van Nes, 2006), all the mechanisms studied so far still rely on competition among species. Despite the potential generality of niche clustering patterns recently outlined in several theoretical and empirical studies, we still know nothing of how these clusters translate into more complex communities including trophic interactions.

Understanding how trophic interactions affect niche clustering patterns and the related diversity and trait distributions of prey and predators is essential to address the generality of trait clustering patterns in ecological communities. Trophic interactions are fundamentally important for coexistence and diversity, especially regarding their effects on competition among species (Chase et al., 2002; Paine, 1966). Predation can promote coexistence of species in competition by acting as a limiting factor and thereby adding a niche (Levin, 1970), like the case of predators specialized on different prey that compete for a limiting resource (Grover, 1994). Predation can also constrain coexistence by adding apparent competition among prey sharing a generalist predator (Holt, 1977; Holt et al., 1994). In that case, the coexistence outcome depends not only on the species’ relative ability to compete for resources and to resist predation but also on the productivity of the system as apparent competition increases with productivity (Leibold, 1996; Steiner & Leibold, 2004). Chesson and Kuang (2008) highlighted that competition and predation-based coexistence mechanisms are equally capable of promoting or diminishing coexistence and have the potential to enhance or undermine each other. The effects of trophic interactions on niche clustering patterns thus likely depend on predator generalism and productivity as these constrain species coexistence patterns.

Since predation adds a niche axis for prey, the correlation between the traits involved in the competition and predation niche axes might also be key to our understanding of niche clustering patterns in predator–prey communities. In some cases, the same trait might determine both competition and predation, leading to two highly correlated niche axes. For example, body size can determine both resource use and consumption by predators for animals (Brose et al., 2008) and for phytoplankton (Litchman & Klausmeier, 2008). However, in other cases, two different traits of prey might be responsible for competition and predation, leading to uncorrelated competition and predation niche axes. For example, for tropical tree species, the traits involved in resource use and environmental niche are phylogenetically preserved while defensive traits responsible for their interaction with enemies are not (Sun et al., 2022). This suggests the sets of traits involved in competition and predation could be only weakly correlated in that case. D'Andrea et al. (2018) showed that the detection of clustering patterns along a single trait axis might be challenging when multiple and uncorrelated traits determine species niches. While theory on competitive communities still suggests that clustering patterns are overall robust to multidimensional niche space (D'Andrea et al., 2018; Fort et al., 2010), it is unclear how these results translate in the case of niche axes involved in two different interaction types, that is, competition and predation.

We extend existing theory on niche clustering in competitive communities to predator–prey communities using two complementary approaches: first, an analytical approach using the three trophic levels model by Chesson and Kuang (2008), and second, by building from the seminal study of Scheffer and van Nes (2006) with numerical simulations. We show that competition and predation are equally capable of promoting clusters of similar species in prey–predator communities, either with correlated or uncorrelated niche axes for competition and predator interaction. We further reveal that clustering patterns in predator–prey communities are strongly interrelated and depend on prey competition, predator generalism and ecosystem productivity. The analytical approach and numerical simulations consistently highlight that the clustering patterns are shaped by competition among prey at low productivity and by predation at high productivity. Our results also suggest that predation stabilizes the clustering patterns, allowing species to persist in clusters for longer times.

MATHEMATICAL ANALYSIS OF A LOTKA–VOLTERRA MODEL WITH THREE TROPHIC LEVELS

Model description

At first, we analyse the three trophic levels Lotka–Volterra model studied by Chesson and Kuang (2008) and build on their analytical results on species coexistence in the light of species’ traits and niche overlap (Figure 1a, Supplementary). The model is defined by the following set of equations:

$$\frac{d{N}_i}{\mathit{dt}}=N_i\left(\sum _{j=1}^n{w}_{\mathit{ji}}{a}_{\mathit{ji}}{R}_j-\sum _{j=1}^n{c}_{\mathit{ij}}{P}_j-\mu \right)$$(1)

$$\begin{array}{c}\frac{d{R}_m}{\mathit{dt}}=R_m\left(r^R\left(1-{\alpha }^R{R}_m\right)-\sum _{j=1}^n{a}_{\mathit{mj}}{N}_j\right)\end{array}$$(2)

$$\frac{d{P}_k}{\mathit{dt}}=P_k\left(-r^P\left(1+{\alpha }^P{P}_k\right)+\sum _{j=1}^n{e}_{\mathit{jk}}{c}_{\mathit{jk}}{N}_j\right)$$(3)

where N_i, R_m and P_k are the abundances of the intermediate prey species i, the basal resource species m and the top predator species k respectively. The number of intermediate prey species is equal to the number of resource species and to the number of predator species, which is equal to n. The parameters a_ji and c_jk represent the consumption rates of resource j by prey species i and of prey j by predator k, respectively, with w_ji and e_jk the corresponding conversion efficiencies. r^R, r^P and μ are, respectively, the resource intrinsic growth rate and the death rates of predators and intermediate prey. Finally, α^R and α^P are the resource and predator intraspecific competition. All parameters are positive.

Assuming the resources R and the predators P have fast dynamics compared to N, the system can be approximated by a Lotka–Volterra competition model (Supplementary 2):

$$\begin{array}{c}\frac{d{N}_i}{\mathit{dt}}=b_i{N}_i-\sum _{j=1}^n{\beta }_{\mathit{ij}}{N}_i{N}_j\text{with}{\beta }_{\mathit{ij}}=\frac{1}{{\alpha }^R{r}^R}\sum _{k=1}^n{w}_{\mathit{ki}}{a}_{\mathit{ki}}{a}_{\mathit{kj}}\hfill \\ +\frac{1}{{\alpha }^P{r}^P}\sum _{k=1}^n{c}_{\mathit{ik}}{e}_{\mathit{jk}}{c}_{\mathit{jk}}=\frac{1}{{\alpha }^R{r}^R}{\theta }_{\mathit{ij}}+\frac{1}{{\alpha }^P{r}^P}{\gamma }_{\mathit{ij}}\hfill \end{array}$$(4)

θ_ij and γ_ij represent, respectively, the niche overlap for basal resource consumption and consumption by predators between prey species i and j. Following classical assumptions for Lotka–Volterra competition models (Macarthur & Levins, 1967), we hypothesize that the niche overlaps θ_ij and γ_ij are defined by the distance between species i and j on the competition and predation niche axes, respectively, with σ^N the niche width for resource overlap and σ^P the niche width for predator overlap. These assumptions can be met when, for instance, predator consumption rates of prey follow a Gaussian function of the difference between prey trait z and predator trait y, with y = z being the best match between the predator and the prey (Supplementary 2). In such case, the competition between species i and j in the approximated model is mostly a function of σ^N when $\frac{{\alpha }^R{r}^R}{{\alpha }^P{r}^P}\ll 1,$ whereas it is mainly a function of σ^P when $\frac{{\alpha }^R{r}^R}{{\alpha }^P{r}^P}\gg 1$ (Supplementary 2). $\frac{{\alpha }^R{r}^R}{{\alpha }^P{r}^P}$ thus measures the relative importance of predation, as defined by Chesson and Kuang (2008).

NUMERICAL ANALYSIS OF A PREDATOR–PREY LOTKA–VOLTERRA MODEL

Competition and predation coefficients: correlated and uncorrelated niche axes

Competition α_ij depends on the distance among species along the prey niche axis μ^N (niche difference, d^N_ij). It is defined as a stretched exponential function wrapped around the unit circle to mimic an infinite niche axis and avoid edge effects, which otherwise tend to aggregate species at the edges of the axis.

$$d_{\mathit{ij}}^N=\frac{\left({\mu }_i-{\mu }_j\right)2\pi }{L}$$(7)

$${\alpha }_{\mathit{ij}}=\sum _{l=0}^{\infty }{e}^{-{\left|\frac{d_{\mathit{ij}}^N-2\mathit{\pi l}}{\left({\sigma }^{N}2\pi \right)/L}\right|}^Q}$$(8)

μ_i and μ_j are the trait values of the competing species i and j, which we assume is related to their optimal resource exploitation (Figure 2a). L is the total niche range and equals the circumference of the unit circle, and σ^N is the niche width for resource competition among prey. Cluster formation and its stability are known to depend on the shape of the competition kernel, defined by the parameter Q. Since we are interested in the clustering patterns per se, we chose a stretched exponential distribution that fulfilled the criteria for cluster formation by setting Q = 4 (Hernández-García et al., 2009; Pigolotti et al., 2010).

The predation coefficients β_ji are defined using the same approach as for the competition coefficients, which also relates to the trait-matching approach in food-web models (Loeuille & Loreau, 2005):

$$d_{\mathit{ki}}^P=\frac{\left({\mu }_k-v_i\right)2\pi }{L}$$(9)

$${\beta }_{\mathit{ki}}=\sum _{l=0}^{\infty }{e}^{-{\left|\frac{d_{\mathit{ki}}^P-2\mathit{\pi l}}{\left({\sigma }^{P}2\pi \right)/L}\right|}^Q}$$(10)

where μ_k is the trait of predator k along its niche axis μ^P, ν_i is the trait of prey i along the prey niche axis regarding predation ν^N and σ^P is the predator niche width (Figure 2a,c). The consumption rate of predator k is optimum when μ_k = ν_i. σ^P is related to the predator degree of generalism because it determines the relative preference of predators for prey along the niche axis, with lower σ^P corresponding to more specialized predators.

We investigate two alternative cases. First, we assume μ^N = ν^N, meaning there is a single prey niche axis responsible for both competition among prey and interaction between prey and predators (hereafter correlated case, Figure 2a,c). Second, we assume the prey niche axes that determine competition among prey (μ^N) and prey–predator interactions (ν^N) differ (hereafter uncorrelated case, Figure 3a,d). This case applies when different prey traits are responsible for resource competition and interaction with predators.

Comparison with competition only

To further understand how predation affects the prey clustering patterns and their diversity, we compared our results on prey communities to the patterns emerging in communities with competition only (i.e. no predation). The effect of predation on prey clustering patterns is resource dependent and occurs mainly at high productivity for both the correlated and uncorrelated cases (Figure S6a–c), except when considering the number of clusters along the predation niche axis ν^N. However, it should be noted that predation has always a positive or neutral effect on the prey species richness (within cluster diversity and overall diversity, Figure S6a–c). This is because added predation results in more stable clusters meaning that more species coexist within the clusters for longer time (Figure 4). After 5.000 generations, there are on average of 4 species per cluster left in the competing communities. This compares to 20 and 34 species per cluster in prey and predator communities, respectively, in the correlated case, and 12, 20 and 37 species per cluster in prey communities along μ^N and ν^N niche axes and predator communities, respectively, in the uncorrelated case.

DISCUSSION

Our results merge different theories on coexistence and prey–predator interactions and bring new light to the emergent neutrality theory, which has so far only been explored under competition. Analogous to Chesson and Kuang (2008), highlighting that competition and predation can equally determine species coexistence, we show here that the mechanism behind cluster formation, initially highlighted in competition models (Scheffer & van Nes, 2006), can be both competition and predation based as defined by the niche width of prey and predators (σ^N and σ^P). This is a key finding as it shows that coexistence through similarity, by escaping competitive exclusion within clusters of similar species, is just as likely to emerge under predation, which together with competition is one of the most important interaction types in natural systems. We highlight that the predatory interaction is further stabilizing the clusters, as it slows down the extinction of species within clusters. This stabilizing effect by predation was predicted already in the original work by Scheffer and van Nes (2006) in the case of fully specialized predators but is central as it shows that not only competition and predation jointly drive the clustering pattern but that the added predatory interaction maintains the clusters in time. During the timeframe simulated, it is not clear whether the richness per cluster will reach an asymptotic state (Figure 4) or if these predator–prey systems will eventually experience competitive exclusion resulting in only one species per cluster (Macarthur & Levins, 1967). However, since the transient pattern observed here lasts an excessively long time, it emphasizes its significance on an ecological time scale and the possibility that this is a feature that can exist in natural systems. Both the mathematical and numerical analyses demonstrate that productivity is a main driver of the relative effect of competition or predation on niche clustering, which connects with classical theories. We showed that low resource availability promotes the competition-based mechanism meaning that σ^N has a main effect on clustering patterns and that clusters occur only on the competition niche when competition and predation niche axes are uncorrelated. On the contrary, high resource availability promotes the predation-based mechanism with σ^P the main determinant of clustering patterns, and clusters only on the predation niche when niche axes are uncorrelated. These findings extend previous results (Grover & Holt, 1998; Leibold, 1996; Steiner & Leibold, 2004). Indeed, when Grover and Holt (1998) studied resource and apparent competition in a simplified food web, they showed that low resource productivity favoured the superior competitor and that high productivity favoured the less vulnerable competitor. In combination, the coexistence outcome between competing species under predation depends on the productivity of the system as apparent competition increases with productivity (Leibold, 1996; Steiner & Leibold, 2004). Empirical and theoretical work has also shown that the relationship between predation and diversity changes depending on nutrient availability, and that predation promotes higher diversity in the prey community in high-nutrient systems compared to low-nutrient systems (Kondoh, 2001; Proulx & Mazumder, 1998; Worm et al., 2002). We found that predation never causes a decrease in prey diversity in comparison to a community experiencing only competition neither regarding richness per cluster nor overall richness. And in line with previous empirical work, predation promotes higher richess in the prey population when productivity is high, in both the correlated and uncorrelated niche axes cases (Figure S6a–c).

Our results bring new insights for the detection of clustering patterns in the context of empirical studies. First, we show that although clustering patterns are robust to uncorrelated competition and predation niche axes in prey communities, clusters emerge either on the competition or on the predation niche axis in such cases. This means that clusters might be detected on trait axes involved in competition and not on those related to interactions with predators, and vice versa. These results are consistent with previous studies on competition only, showing that clustering patterns were robust to multidimensional niche space but that this likely complicated cluster detection in empirical trait data (D'Andrea et al., 2018; Fort et al., 2010). Thus, it is perhaps not that surprising that most empirical studies of niche clustering so far have been observed in the size distribution of phytoplankton, which expectedly may be related both to resource competition and predator avoidance (Litchman & Klausmeier, 2008). Second, our results reveal that the clustering patterns (i.e. number of clusters and within cluster richness) are often very similar between prey and predator communities and can be strongly interrelated (Figure S3a,b). So far, empirical proofs of clusters with similar species have only been reported from a competition perspective focusing on single communities and only originating from field data (D'Andrea et al., 2020; Graco-Roza et al., 2021; Scheffer & van Nes, 2006; Segura et al., 2011). We lack proof of niche clusters among prey and their predators from both nature and experiments. Thus, whether prey and predator share similar clustering patterns in their trait distributions remains to be tested, although, for example, diversity is known to be influenced by neighbouring trophic levels (Dyer & Letourneau, 2002). While studies on interaction networks between resources and consumers are increasingly incorporating species traits (e.g. plant–frugivore webs, Bender et al., 2018), these studies might offer a good opportunity to test for such parallel clustering trait patterns.

Our results are here limited to Lotka–Volterra models and other key assumptions such as those related to the definition of consumption rates as a function of matching traits of prey and predators. Future studies are needed to assess the generality of our results in the context of other predator–prey models and of stochastic processes, as has been done for competition (D'Andrea et al., 2019). For instance, the classical Rosenzweig–MacArthur model includes a Holling Type II functional response instead of a linear functional response. This model is known to predict cyclic and highly unstable dynamics at high productivity (Rosenzweig, 1971), which might affect the emergence of clustering patterns. Numerical simulations of our model with a Type II functional response, however, suggest clustering patterns can also emerge in such cases (Supplementary 5, Videos S1–S7). Another consequent question is how the niche clustering patterns translate into more complex food webs with multiple trophic levels. Such clustering patterns likely relate to a well-known and central feature of food webs, trophic groups (or guilds). Indeed, trophic groups (guild) is a common notion in ecology, defined as aggregations of species with similar diets (independent of taxonomic identity) (Root, 1967), and thus sharing the same trophic niche and probably traits strongly related to feeding links such as body size (Brose et al., 2019). Several studies suggested that these groups are the main components of clustering patterns in food webs (Fortunato, 2010; Gauzens et al., 2015). Linking the recent theory on niche clustering patterns (Scheffer & van Nes, 2006) to the classical notion of trophic groups in food webs should thus offer promising avenues for research on species coexistence in ecological communities. The structure and topology of a network have important influences on its functionality including its stability (Thébault & Fontaine, 2010), and trophic redundancy in large trophic groups have implications on food web vulnerability to extinctions (Gauzens et al., 2015). Clearly, groups and clusters of similar species have been an important notion in ecology for decades, and understanding the mechanisms behind its structure is a key to preserving food webs and their functions in our rapidly changing world.

AUTHOR CONTRIBUTIONS

MH and ET designed the work. ET performed the analytical analysis, and MH performed the numerical analysis, compiled and analysed the data. MH wrote the first draft of the manuscript and both authors contributed substantially to revisions.

CONFLICT OF INTEREST

The authors declare that they have no known competing financial or personal relationships that could have appeared to influence the work reported in this paper.