Modelling species interactions in macroevolution and macroecology
Xu, Liang
DOI:
10.33612/diss.125954510
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Publication date: 2020
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Xu, L. (2020). Modelling species interactions in macroevolution and macroecology. University of Groningen. https://doi.org/10.33612/diss.125954510
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Synthesis
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B
iotic and abiotic interactions have created an incredibly diverse world but also buried a lot more in history. This lost information, on such large time scales of evolutionary history, is a huge obstacle to uncover these underlying mechanisms. The fossil record provides some evidence of what happened in the past, but is lim-ited due to low preservation rates and temporal, taxonomic and geographic bias. In recent years, molecular data e.g. DNA se uences and mathematical models have supplied researchers with a powerful tool to use to reconstruct phylogenetic relationships among species Mauro and Agorreta121 . These relationships show to what extent a species is similar to other species and allow biologists to test hypotheses of evolutionary processes. They inform us about the divergence time of two daughter species from their common parent species. Thereby, testing hy-pothesis on the mode of evolution and conducting comparative studies on species characters has become possible.In this thesis, I first explored whether diversity-dependence can be detected with a global inference model, even in scenarios where diversity-dependent diver-sification is, more realistically, local Chapter 2 . I found that the power to detect local diversity-dependence signal is related to the dispersal ability of species and the local extinction rate. Then, I studied in Chapter 3 how environmental stabiliz-ing selection and competition drive morphological trait evolution along a phylogeny. Our study implies that the trait distribution pattern is informative for the strength of the stabilizing selection and competition under certain conditions. Furthermore, species abundances can help distinguish among distinct mechanism models when similar trait patterns are generated under those models. Lastly, in Chapter 4, I investigated a spatial phylogenetic Janzen-Connell effect on an individual-based simulation community with a setup similar to a neutral model. e show that the phylogenetic relatedness effect reduces the power of J-C effects to explain hyperdi-versity. e further conclude that the spatially explicit phylogenetic Janzen-Connell model has the power to explain a wide range of ecological and phylogenetic pat-terns.
Diversity-dependence on local and regional scales
Species diversification is envisaged as a response to a changing environment. However, not all species can persist up to the present. Many species are losers in the evolutionary race, going extinct as a conse uence of abiotic interactions such as climate change, geological changes, and asteroid impacts and biotic interac-tions such as competition, parasitism and predation Lawton and May1 , Raup
1 . Such ecological dynamics of community assembly shape and characterize the pattern of macroevolutionary processes McPeek12 , in which the correlation be-tween ecological dynamics and diversification pattern has long intrigued biologists. Thus, in the context of dynamical processes, speciation and extinction represent this correlation and are naturally expected to be variable. ith the fast devel-opment of molecular phylogenetic techni ues and increasing availability of phy-logenetic comparative methods Felsenstein 2 , inference of the speciation and extinction rates from phylogenies has become possible Etienne et al. 1, Nee et al.
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1 ,1 ,1 ,1 , Pybus and Harvey1 .
One of the pervasive patterns observed in a majority of distinct clades is the slowdown of accumulation of lineages of a phylogeny of extant species McPeek
12 , which contradicts the phenomenon of the pull-of-the-present that describes an accelerating lineage accumulation pattern. The pull-of-the-present in the lineages-through-time plots is purely a theoretical outcome Etienne et al. 4, Jablonski and Roy 2, Nee 1 4 as the signature of the constant birth-death model. It results from the fact that under constant speciation and extinction rates lineages arising in the recent past have not yet had time to go extinct and therefore are prone to be represented in the phylogeny more than lineages arising in the more distant past. Thus, a more realistic model on diversification mechanism and explanation of the empirical pattern than the constant-rate model is imperative.
Among the various interpretations to this puzzle Moen and Morlon12 , three main explanations stand out. The first is that fractional sampling may cause the slowdown. This was first suggested in 1 4 Nee et al.1 . However, Phillimore and Price Phillimore and Price1 4 , conducting a meta-analysis of the distribution of speciation events through time, argued that random sampling cannot explain the slowdown in speciation if extinction rate approaches the speciation rate. Because with a constant extinction rate species in the deep past are more likely to go extinct than the species born close to the present, which leads to branching times close to the tips of the reconstructed phylogenetic tree of the extant species. As an alter-native explanation they proposed diversity-dependent diversification - the second main explanation -, which assumes a high rate of speciation due to exploration of new niches early in the history of a clade and a decrease of species accumula-tion due to the niches becoming filled with species as time passes. Although this provides a reasonable biological interpretation, it has also been argued that new species may actually create new niches F. et al. that may not decrease speci-ation rate. The third explanspeci-ation established in the standard birth-death model, is that speciation takes time. This indeed leads to slowdowns as observed Etienne et al. 4 .
A probabilistic model that accommodates diversity-dependence and non-zero extinction was published, which can be simulated and allows speciation and non-zero extinction rates to be estimated from phylogenies Etienne et al. 1 . Sim-ulations with a diversity-dependent speciation rate show a wide range of species accumulation patterns, from the pull-of-the-present resulting from a high level of extinction to the slowdowns of lineage accumulation resulting from low levels of ex-tinction. The parameter inference is more precise for trees with large crown ages, which contain more information. Nevertheless, when extinction rate is high, the speciation rate is likely to be overestimated and the carrying capacity is likely to be underestimated Etienne et al. 1 .
Our work Chapter 2 confirms the inference bias caused by extinction in a spatial community but relates it to the dispersal rate. Specifically, a high dispersal rate leads to upwards bias in the estimation of speciation rate and downwards bias in the estimation of extinction rate. The behavior of the parameter inference suggests that extinction and dispersal are correlated and should not be treated as
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two independent factors. If a species resides in multiple locations, it has a lower extinction rate as local endemic disasters or competition would only affect one local population at a time. Conse uently, a more widespread species has a lower chance to go extinct than an endemic species that exists in only one location Diamond
41 .
In Chapter 3, we also showed that high dispersal strengthens the sampling ad-vantage of the abundant species. Thus, the species with high mobile ability seems to have a high fitness, which attributes to that they can explore a wide range of natural resource. However, it is often argued that local species may be more com-petitive than the immigrants because their traits have adapted to the local habitats under stabilizing selection. This local adaptation predicts a local advantage in fit-ness. So there is a puzzle whether and how dispersal ability is related to niche breadth. It has been reported that more specialized species coexist when species have large dispersal abilities B chi and uilleumier 21 . That may imply a sce-nario in which successful invaders that used to be generalists and good dispersers eventually adapt to the local environment and become specialists. The intensity of local competition, thereby, determines the degree of difficulty of coexistence with other residents, which can be depicted by diversity-dependence, underscoring the importance of knowing local and regional carrying capacities.
Carrying capacity
A better understanding of the carrying capacity i.e. how many species a com-munity can sustain is key to the uestion whether diversity-dependence is de-tectable. Both the analysis of detecting diversity-dependence on a global scale Etienne et al. 2 and our analysis on the local scale suggest that the power to detect diversity-dependence is weak when the community is far away from satura-tion. This is reasonable because when the diversity is at a low level far below the carrying capacity, diversity-dependence is too weak to have any effect and hence cannot be detected. Here, low diversity may just be because the community is at the onset of species proliferation or just experienced an instant mass extinction. hen the community is close to saturation, diversity-dependence can be reliably detected by a model with global diversity-dependence even if diversity-dependence is actually local.
However, determining the carrying capacity empirically is a big challenge. In Chapter 2, we tried to estimate the carrying capacity from phylogenies using the likelihood formulation of the global model, but we found that the estimation of the carrying capacity on different spatial scales needs to be interpreted with caution. The regional carrying capacity is not simply the sum of the carrying capacities of its component locations. A widespread species counts once for the calculation of regional species richness while it counts twice if summing up local species rich-ness of two locations. This generates downward bias in the estimation of the total carrying capacity when dispersal is large, thereby leading to wrong predictions of the saturation level. e note that we only studied simple metacommunities with only two locations. The relationship between the carrying capacity and
diversity-5
dependence in a meta-community with many locations still remains to be studied. A local likelihood formulation that is directly derived from the spatial model may be a solution. In Box .1 I have written the master e uation for this model. A similar e uation can be derived to obtain the likelihood, using the so-called Q-approach
1 . However, increasing the number of locations increases the dimensions of species range categories. An accurate likelihood formulation for the spatial model with high dimensions is a difficult task.
Box 5.1. An example of diversity-dependent diversification model with two locations.
The probability of a community having𝑛 species in location A, 𝑛 species in location B and𝑛 species in both locations can be described by the following master e uation:
𝑑𝑃(𝑛 , 𝑛 , 𝑛 , 𝑡) 𝑑𝑡 = 𝜆 (𝑛 + 𝑛 − 1)𝑃(𝑛 − 1, 𝑛 , 𝑛 , 𝑡) + 𝜆 (𝑛 + 𝑛 − 1)𝑃(𝑛 , 𝑛 − 1, 𝑛 , 𝑡) + 𝜆 (𝑛 + 1)𝑃(𝑛 + 1, 𝑛 − 1, 𝑛 − 1, 𝑡) + 𝜇 (𝑛 + 1)𝑃(𝑛 + 1, 𝑛 , 𝑛 , 𝑡) + 𝜇 (𝑛 + 1)𝑃(𝑛 , 𝑛 − 1, 𝑛 + 1, 𝑡) + 𝜇 (𝑛 + 1)𝑃(𝑛 , 𝑛 + 1, 𝑛 , 𝑡) + 𝜇 (𝑛 + 1)𝑃(𝑛 − 1, 𝑛 , 𝑛 + 1, 𝑡) + 𝑀 , (𝑛 + 1)𝑃(𝑛 , 𝑛 + 1, 𝑛 − 1, 𝑡) + 𝑀 , (𝑛 + 1)𝑃(𝑛 + 1, 𝑛 , 𝑛 − 1, 𝑡) − [𝜆 (𝑛 + 𝑛 ) + 𝜆 (𝑛 + 𝑛 ) + 𝜆 𝑛 + 𝜇 (𝑛 + 𝑛 ) + 𝜇 (𝑛 + 𝑛 ) + 𝑀 , 𝑛 + 𝑀 , 𝑛 ] 𝑃(𝑛 , 𝑛 , 𝑛 , 𝑡)
where𝜆 and 𝜇 denote the speciation rate and extinction rate, respectively, for location𝑖, and 𝑀, is the dispersal rate from location𝑖 to location 𝑗.
𝜆 is the rate of allopatric speciation. In this model, widespread species present in both locations cannot become extinct in one step. Two extinc-tion events are re uired, first in one locaextinc-tion and then in the other without migration between these events.
An alternative techni ue that avoids analytical likelihood calculations in high di-mensions is approximate Bayesian computation, a techni ue we exploit in Chapter 3 for a different purpose. It seeks parameters that results in simulated patterns that are close to the observed pattern. One caveat is that different configurations of species across different subregions complicates the simulation process, increasing the demand on computational time. So, a reliable and precise inference method for the carrying capacity remains to be found.
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Diversity-dependence in dispersal
As an additional and realistic mechanism to the global approach Etienne et al.
1 , we implemented dependent dispersal in the model. This diversity-dependence refers to the diversity-dependence on the species richness of the dispersal destination. The idea behind this is simply that a saturated region will have in-tense competition and thereby constrains additional immigrants of the same trophic level that are competing for the same natural resource. So we assumed that diversity-dependence of immigration only exists in the destination location. How-ever, density-dependence in dispersal that is referred to as diversity-dependence at the macroevolutionary scale Sutherland et al. 1 can also occur in the loca-tion of origin. For example, territorial individuals can distribute over the available living places Fretwell and Lucas . As local density increases, which leads to an increase in competition intensity, individuals choose to settle in patches where only few other individuals are present. This mechanism leads to positively density-dependent emigration, that is, higher emigration rates as population densities in-crease Altwegg et al. . In Chapter 4, we investigate a negative density effect, which is the Janzen-Connell effect Connell 4, Janzen . The decrease of fitness when density increases can be interpreted as follows. The most abundant species is likely to attract natural enemies pathogens, parasites, pedators . As a result, the density of the species is constantly checked and constrained. The vacant space left by individual death is likely to be colonized by species that are phylogeneti-cally distantly related to the abundant species, which are not favored by the natural enemies of the abundant species which are only able to attack species that are phylogenetically related. This negative density-dependence forms a certain pattern of species-abundance distribution SAD , which informs us about commonness and rarity in ecological systems. Our study on an isolated region suggests that limited dispersal ability conserves rare species and thus promotes regional species rich-ness. In contrast, unlimited dispersal ability elevates the intensity of competition. Conse uently, the abundant species outcompete the rare species, dominating the community. This conclusion suggests that spatial structure and dispersal ability play an important role in competition, which is often ignored in the literature.
Future research should also focus on spatially explicit modelling. One spatial ex-tension to the trait evolution model with population dynamics would be to consider multiple locations or even multiple types of natural resources selecting different traits. In principle, modifying the Ricker-e uation of the fitness function Chapter 2 to accommodate species interactions in spatial geographic structures can achieve this goal:
𝜔(𝜇, ) =
𝑁,
𝑁,
∶= 𝑅(𝜇, )𝑒 (⃗⃗⃗,⃗⃗⃗⃗)/ . .1
The population growth ratio i.e. the fitness is thus proportional to the growth rate that is related to the mean trait𝜇, and an exponential term that accounts for
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kernel can be modified in a way to accommodate the spatial structure of interest as follows:
𝛽(⃗⃗⃗𝜇, ⃗⃗⃗𝑁) = ∑(𝑒 ( , ,) 𝐼
, 𝑁, ) .2
where 𝐼, = 1 if species 𝑖 and 𝑗 are interacting at the same location, otherwise 0 Drury et al.4 . This spatially explicit trait evolution model will address uestions such as repeated trait evolution, and correlation between different evolving traits.
Competition and fitness
Diversity-dependence is in essence a competition process among species. Lim-ited natural resources drive species to compete. The species with the morphological trait that can better utilize resources give more birth to offspring that inherit this advantage. Biologists often use the metaphor of a fitness landscape with fitness peaks in which species climb uphill van Doorn et al. 2 , eissing et al. 21 . However, this fitness landscape is an imaginary scene that never shows up con-cretely in reality, and therefore cannot directly be used to study the strength of stabilizing selection and competition. The morphological trait as a response to the virtual fitness landscape is the object of research.
In Chapter 3, we investigate how the trait pattern is formed under a certain level of stabilizing selection and competition in a Gaussian-like fitness landscape with a single peak one optimum trait and reversely whether we can infer the strength of stabilizing selection and competition from present-day trait data. It is intuitively clear that stabilizing selection attracts species to evolve towards the optimum trait while competition drives traits to evolve apart. Thus, the resulting traits eventually resemble a Gaussian shape to fit the natural resource distribu-tion eissing et al.21 . The population dynamics react accordingly so that the species with the trait closer to the optima is more abundant. However, when sta-bilizing selection is extremely weak the species with traits at the edge of the trait spectrum are more abundant, showing higher fitness. This implies a tendency to-ward exploration of new niches to avoid competition when local competition is too intense and the natural resource is evenly available across the trait dimension. This is similar to the diversity-dependent dispersal and the negative density effect men-tioned above, but now in trait space. In addition, the implementation of population dynamics provides a tool to assess whether the coexistence of species in the local ecosystem is stable or not. Our model applies to given phylogenies, which assumes traits of study are independent of diversification Drury et al.4 ,44,4 , Nuismer and Harmon14 . Thus, the species extant at any point of time are assumed to be known even though molecular phylogenies do not show the species that are now extinct . In the scenarios with a large competition coefficient that scales the in-tensity of competition, either a compromise is achieved among species where they have relatively low abundances or one of the competitors cannot maintain its popu-lation size and goes extinct. The latter scenario is inconsistent with the phylogeny,
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and then our model suggests that the generating parameters are not appropriate and terminates the corresponding simulation. Only the parameters that result in complete simulations are appropriate, i.e. represent a valid parameter domain of the strength of stabilizing selection and competition for the given trait pattern and phylogenies. The outcome of such complex trait evolution and population dynamics is the trait distribution and the abundance distribution. e found that the range of the traits is closely related to the width of the environmental resource niche while the width of the competition niche relative to the width of the resource niche de-termines how many species can coexist. The individual carrying capacity of the community serves as an indicator of how stable the system is. Because if there are too many species, competition forces them to have a low population size. If the individual carrying capacity is too small, limiting how large population can become, random demographic change may easily cause extinction, leading to incomplete simulations. This unstable behavior of simulations may lead to wrong predictions of the valid parameter domain. Thus,a prioriinformation of the individual carrying capacity helps improve the inference performance of the model. However, the indi-vidual carrying capacity is one of the most mysterious factors and hard to uantify. e had to set it to a n relatively arbitrary constant in our study. But we hope for a more thorough investigation in the future of empirical carrying capacities and the correlation between the individual carrying capacity and the species carrying capacity.
The rate of evolution plays a role in understanding species
interactions
The rate of evolution determines whether phylogenetic relationships among species are potentially informative to competition and stabilizing selection. A fast rate of trait evolution makes the ecosystem reach e uilibrium uickly. A vacant niche left by extinct species can be occupied immediately. The trait pattern is then informative for inferring the nature of the environment that determines the niche structure hosting species. As a conse uence, phylogenies may not be needed for inferring the rate of interaction Nuismer and Harmon 14 . However, if the rate of trait evolution is slow, a correct understanding of the rate of trait evolution is essential to reliably infer the strength of stabilizing selection and competition. An incorrect a priori assumption of a fast rate of trait evolution may result in over-estimation of the competition coefficient if the true rate of trait evolution is slow, because using fewer time steps in trait evolution to resemble the trait pattern that results from more time steps leads to inferring a higher competition coefficient that represents faster splitting up in competitive exclusion. Therefore, caution should be taken when making inference from different traits and different phylogenies.
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Trait-dependent speciation in trait evolution models
In trait evolution models, assuming evolutionary events such as speciation and extinction are independent of the focal traits seems to be conventional. This is pragmatic when the purpose of the research is to infer the role of the biotic and abiotic environment from the present traits and reconstructed phylogenies, because the extant species and their traits are the conse uence of natural selection. But the extant species only represent the winners of the evolutionary race. Using the present trait data and reconstructed phylogenies to infer species interactions should be done cautiously. Traits can play a key role in species proliferation Fitzjohn et al. . Researchers ask why some clade of species with similar traits shows a higher speciation rate than other clades, why there is repeated trait evolution in different regions. ith these initiatives, our work can be extended to generate phylogenies by modelling trait evolution and population dynamics. For example, speciation can be triggered when the trait variance increases to a threshold. Disruptive speciation van Doorn et al.2 may cause a species to split up into two specialists because specialists are more efficient in utilizing the resources without too much competition. Extinction results from a decrease in fitness and from demographic stochasticity. By this model, the generating phylogenies and traits can be compared with empirical data to infer underlying mechanisms of species interactions.
Modelling trait coevolution
hile we have shown in Chapter 4 that with the phylogenetic J-C effect re-alistic macroecological and macroevolutionary patterns can be obtained, further extensions may investigate trait coevolution of species based on this advantage. One possible direction is to explicitly incorporate the predator-prey or parasite-host mechanism in the population dynamics of the trait evolution model Chapter 3 . Then, a dynamical optimum trait system is expected for both types of species. For example, the optimum trait for the predator species would be the trait that many prey species or individuals develop while the prey species evolve away from that optimum trait in a finite trait space. Such complex systems prevent analytical like-lihood formulation. Hence, our ABC-SMC approach could still step in to help infer the role of species interactions.
Mathematical techniques in ecology and evolution
Across all my projects in the previous chapters, I have encountered substantial mathematical problems involving differential e uations and high dimensions. In the spatial diversity-dependent diversification model Chapter 1 , we track the num-ber of endemic species and of the widespread species in time. e sample the time to each event, and at each event, speciation, extinction or dispersal, the number of endemic and widespread species changes accordingly. One can describe the dynamics of the change of the probability through time with a differential e uation, reflecting how the events considered affect the likelihood of the model. e tried to
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write these e uations in the same way as for the global diversity-dependence diver-sification model Etienne et al. 1 , see Box .1. However, the consideration of two locations and the hidden species that are not observed in phylogenies substantially increases the size of the system of differential e uations. The classical numerical integration methods Etienne et al. 1 are then too time- and memory-consuming. I tried computing the integration using parallel programming with CPU and GPU. I did observe improvement the computation efficiency. However, the improvement is not substantial enough because the integration is se uential through time. In the trait evolution model with population dynamics Chapter 2 , we have the same is-sue. The trait of each species represents one dimension, mutually playing with the traits of other species and being affected by the abundance and the trait variance. Although we have a general mathematical formulation to express the mechanism, no analytical or numerical solutions, to my knowledge so far, can be applied to such a complex system. In particular, a recent techni ue that is reported to successfully obtain numerical solutions to the high dimensional stationary Fokker-Planck e ua-tions Sun and umar1 ,1 ,1 also failed in our case due to discontinuity and inseparability appearing in our model.
However, there may be alternative solutions. As our purpose in Chapter 1 was to test whether the global diversity-dependent approach is able to detect the signal of the local diversity-dependence, we performed a parametric bootstrapping analysis Etienne et al. 2 . The idea is to apply both the constant birth-death rate model and the global diversity-dependent model to the data simulated un-der the spatial diversity-dependent diversification model and obtain the maximum likelihood estimates of the parameters for each of the models and the likelihood ratio 𝐿𝑅 . These inferred parameters account for what the corresponding model recognizes as the most likely generating parameters for that model. Then, 𝐿𝑅 is compared to a set of likelihood ratios 𝐿𝑅s of the two models on the data sets generated under the constant birth-death rate model using its estimated param-eters. If the global approach can detect the signal of the diversity-dependence, 𝐿𝑅 would be significantly larger than most of the 𝐿𝑅s normally 95% of 𝐿𝑅s if setting the significant level as . . In Chapter 2, exploiting the power of ap-proximate Bayesian computation Toni et al. 2 , we developed an approximate Bayesian computation algorithm with a se uential Monte-Carlo optimization to per-form parameter inference and model selection. This type of algorithm is particularly designed to solve problems without analytical solutions. It takes the advantage of computer power to explore the goodness-of-fit of the simulations generated from randomly chosen parameters by comparing them with observations. The parame-ters that produce simulations that are most analogous to the observation are then assumed to best resemble the truth. Nevertheless, the efficiency of the algorithm depends on the prior information on the parameters and the evolutionary strategy of sampling across iterations of the algorithm. Many such strategies have already been developed Lintusaari et al.1 , Toni et al.2 . The prior relies on biological information. Therefore, a correct understanding of the data substantially improves the efficiency of the algorithm while a wrong understanding leads to bias.
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Conclusion
e are living on such a wonderful planet created by extraordinary biological events that generate fantastic biodiversity and phenomena. Biologists are fasci-nated by the mysterious puzzles and make great effort to understand the mecha-nisms behind them. To do that, the knowledge of multiple disciplines and collabora-tion among scientists in different fields are necessary. In this thesis, I explored how biological interactions on both species and individual scales influence the pattern of biodiversity, morphological traits, abundance structure in community, species accumulation through time, etc. I constructed mathematical models to uantita-tively describe the undergoing biological processes. Using computer simulation, I investigated the resulting patterns of the hypothesized biological mechanisms and assessed the validity of the hypothesis.
Biotic and abiotic interactions are the drivers of biological patterns and also the conse uence of themselves. Diversity-dependence constrains species diversity. In a spatially structured community, species are encouraged to disperse from regions with low carrying capacity to regions with high carrying capacity due to competition, for example, from temperate regions to tropical regions Brown2 , which may af-fect the efaf-fect of diversity-dependence on both local and global scales. Stabilizing selection and competition form morphological diversity and lead to population vari-ation, the process of which encodes the interplay of ecological and evolutionary dynamics. Competition provides explanations to a wide range of biodiversity pat-terns, serving as a theoretical support to, for example, hyperdiversity in the rain forest Clark and Clark2 , Levi et al.1 .
Testing creative hypotheses for biological patterns via computer science spurs the development of biology. However, ecosystems are so complex that biological patterns are the conse uences of multiple factors. Distinct conclusions may be drawn from studies from different angles. e are still on the way and will be long on this way of revealing the truth of the nature, which forms the fundamental meaning of a biological scientist’s work.
