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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Introduction
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A
biological interaction is the effect of the activities of one organism on anotherorganism. It has been widely recognized as the fundamental basis of avari-ety of ecological and evolutionary phenomena. On the species scale, a biological interaction among species is known as interspecific interaction, and includes mutu-alism, commensmutu-alism, parasitism, amensmutu-alism, neutralism and competition, which are classified by distinct degrees of benefit or harm species cause to others. The interspecific interactions often have a long-term effect, affecting, for instance, bio-diversity and morphological trait evolution. Thus, studying the underlying mecha-nisms how species interact helps us to understand species assemblages. Biological interactions also happen on the individual scale within species, which is normally known as intraspecific interaction. This type of interaction is mainly due to mem-bers of the same species competing for limited resources such as food, water, living space and mates etc. The conse uence of this competition is the slowdown of population growth that ultimately leads to an e uilibrium population size if the environment does not change, although competition may also result in population cycles or chaos. Biologists use carrying capacity to express the number of in-dividuals or species that a stable environment can maintain on the corresponding scales. The interactions of both scales can operate and interplay on the same time scale, resulting in a complex process influencing biodiversity.
Ecologists and evolutionary biologists have made a great effort trying to re-veal the underlying mechanisms of biological interaction that explains biodiversity. However, while significant progress in understanding biological processes has been achieved, our knowledge is still limited by the large spatial and temporal scales involved in those processes. For example, ecological process occurs anywhere and anytime such that it is usually difficult to fully track. Macro-evolutionary changes that are significant enough for detection often take a large amount of time, for instance, in unit of million years for speciation and extinction. Thus, a practical method that is able to tackle uestions on large spatial and temporal scales is imperative. Theoretical approaches along with the development of computer sci-ence make this possible. Theoreticians exploit mathematical modelling to study the fundamental interaction patterns hidden in empirical data, which is collected from the extant species and from the fossil record that stores information of the extinct species in the past.
Modelling macroevolution
In 1 4 , based on Corbet’s work on the distribution of butterflies Corbet and illiams’ data of numbers of moths of different species caught in a light-trap
Fisher et al. Part 2 , Fisher Fisher et al. developed a mathematical the-ory to predict the relative numbers of animals of different species obtained when sampling at random from a ecological community. Later on, illiams illiams
21 ,21 showed that the logarithmic series used to address the problem of the fre uency of occurrence of species in a random sample from a mixed population can also be applied to a great variety of other biological distributions. These suc-cesses in phenomenological descriptions by mathematics drew people’s interest to
Introduction
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3
developing theoretical models to explain the biological distributions. Soon, in 1 4 , endall endall tried a number of discontinuous Markov processes that lead to distributions of negative binomial and logarithmic series forms and hoped future researches may find some biological meaning in them. One of the stochastic pro-cesses is a birth-death immigration process, which became the basis of theoretical models of species diversification.
In 1 4, inspired by endall’s work, Nee et al. Nee et al. 1 described a probabilistic null model appropriate for molecular phylogenies, which records lin-eages that have given rise to at least one contemporary descendant. For this model, which is also called the reconstructed process , Nee et al. derived a geometric distribution for the number of lineages existing at any particular time in the recon-structed process, and the distribution of waiting times between birth events, and generalized the results to time-dependent birth and death rates. A likelihood func-tion for a reconstructed phylogeny is derived to estimate the speciafunc-tion rate and extinction rate. However, the diversification rate was not yet related to other biolog-ical processes, such as trait evolution. Almost at the same time, Pagel Pagel 144
noticed the importance of trait evolution and presented a new statistical method for analysing the relationship between two discrete characters that are measured across a group of hierarchically evolved species or populations. Although likeli-hood calculations for models involving speciation and extinction rates Moore et al.
12 , Nee et al. 1 and rates of character state change have been described separately Pagel 144 , they have not yet been fully integrated. But biologists’ attention started to be drawn towards this direction. In the next decade, based on Neeet al.’s work some research on the state-dependent speciation rates was done by Pagel Pagel 14 , Paradis Paradis 14 and Ree Ree 1 . Pagel’s model allows different rates of speciation to different character states, but it assumes no extinction and states change only at speciation events. Paradis Paradis 14 and Ree Ree 1 presented likelihood-based methods that use reconstructed ances-tral states to compare speciation rates between states but also excluded extinction. Shortly after, the gap was filled. In 2 , Maddison et al. Maddison et al.
11 developed a binary-state speciation and extinction model BiSSE that allows speciation and extinction rates to depend on the character state of a lineage at each point in time and allows the character state to change over time. A method to calculate the likelihood with two states was presented. They showed how this calculation leads to new methods for parameter estimation and hypothesis testing of a binary character’s effect on diversification along a full phylogenetic tree that contains extinct species. The BiSSE model soon attracted biologists’ interest and inspired many other trait-dependent diversification models, becoming the basis of these models.
However, the BiSSE model assumes that the phylogenetic tree is complete and fully resolved, and that all character state information is known. These assump-tions restrict its applicability as few published phylogenies are both complete to the species level and large enough to detect differential diversification. So, FitzJohn Fitzjohn et al. improved the model to make it applicable to incomplete phylo-genies. He developed likelihood calculations that compensate for incomplete
phy-1
logenetic knowledge in two cases: 1 incomplete random sampling of all extantspecies within a group and 2 unresolved clades instead of tips in phylogenies. In2 1 , FitzJohn FItzJohn 4 described a new comparative phylogenetic method, the uantitative state speciation and extinction QuaSSE model, which is based on the BiSSE model, for inferring the effect of uantitative traits on speciation and extinction rates. Also, the likelihood of a phylogenetic tree and the distribution of character states among species are derived. FitzJohn’s work promoted the devel-opment of macroevolution models in trait-dependent diversification rates, opening a door for biologists to further focus on a variety of trait types.
Among the traits of interest studied by the invoked trait-dependent diversifica-tion research trend, geographic traits that crucially influence diversificadiversifica-tion rates stand out. Several researches emerged to study geographic range as traits that are likely to influence speciation and extinction Cardillo et al. 2 , Jablonski and Roy 2 , Mckinney 122 , Pigot et al. 1 , Ribera et al. 1 . Mc inney Mck-inney 122 found that species with larger ranges are commonly considered less prone to extinction than those with smaller ranges. Range contraction events will therefore increase the rate of extinction, and they may cause anagenetic speciation stochastic extirpation of local populations or cladogenetic speciation speciation fragmenting an ancestral range into smaller descendant ranges . These effects are counterbalanced by range expansion, achieved through dispersal events that estab-lish new populations. Rosenzweig, Chown , Gaston and Chown Chown 2 , Gaston and Chown , Rosenzweig 1 showed that changes in range size may have a variety of effects on speciation rates.
There are many uestions related to geography and diversification. Are regional differences in species richness and endemism driven by spatial asymmetries in spe-ciation and extinction rates, or by asymmetries in direction of lineage dispersal Chown and Gaston 2 , Mora and Chittaro 12 , Stebbins 1 4 ? How do range size and range evolution affect speciation rate Gaston and Chown , Jablonski and Roy 2 , Pigot et al. 1 , agner and Erwin 21 ? hat are the most common modes by which speciation divides ancestral ranges in terms of range size or degree of sympatry Anderson , Barraclough and ogler 11 , Gaston , Phillimore et al. 1 , Pigot et al. 1 ? How do speciation rates compare on the mainland, within an island, and directly after dispersal to the island Gillespie and Roderick , Ricklefs and Bermingham 1 ? Are specialists more likely to arise from generalist ancestors or directly from other specialists Barnett and Simp-son 1 , Nosil et al. 141 ? The need for phylogenetic models to infer these interactions has been raised previously in the context of biogeographic frameworks that assume constant speciation and extinction rates and hence allow consideration of geographic characters only on a static tree Lamm and Redelings 1 , Ree and Smith 1 , Ree and Sanmart n 1 1 .
In 2 11, Goldberg et al. Goldberg et al. developed a model for geo-graphic traits that encapsulates the basic concepts introduced above. The model is also based on the mathematical framework of the BiSSE model Maddison et al.
11 , modified to include biogeographic parameters and to allow state change at speciation and through local extinction. The geographic state speciation and
ex-Introduction
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tinction GeoSSE model specifies the states as the geographic traits and uses the new likelihood-based approach to estimate region-dependent rates of speciation, extinction, and range evolution from a phylogeny. Also, Goldberg et al. applied it to the evolution of habitat occupancy in Californian plant communities, where they found higher rates of speciation in chaparral than in forests and evidence for expanding habitat tolerances.
However, in this series of speciation and extinction models, diversity-dependent diversification rates are rarely considered. Empirically, palaeontological evidence for diversity-dependence has been found from the relatively constant diversity within numerous higher taxa over millions of years Alroy , Ezard et al. , Gould et al. , Rabosky and Sorhannus 1 4 , Raup et al. 1 , Stanley 1 . If diversity-dependence and non-zero extinction are true, models of diversification should in-clude both processes. Several existing models incorporate diversity-dependence but without extinction. This is in part because simulations reveal that extinc-tion erases the signature of a reducextinc-tion in the speciaextinc-tion rate through time Liow et al. 1 , Quental and Marshall 1 , Rabosky and Lovette 1 2 , leading to the suggestion that extinction rates have probably been low in clades that show slowdowns in lineage accumulation Rabosky and Lovette 1 2, 1 . Another explanation is just for convenience to compute likelihood Bokma 1 , Rabosky and Lovette 1 2 . In 2 12, Etienneet al. Etienne et al. 1 used a hidden Markov model HMM considering diversity-dependence in speciation rate and con-stant non-zero extinction rate to numerically compute the likelihood of a phylogeny. They considered incomplete sampling of species and presence of other species that have gone extinct but affected diversification rates in the past. The model was applied to the phylogenies of clades with an existing fossil record Cetacea and Cenozoic of macroperforate planktonic foraminifera and clades without fossil ev-idence Dendroica, Plethodonand Heliconius. They concluded that the method performs uite well in estimating a non-zero extinction rate from molecular phylo-genies with and without fossil record in some case studies. They suggested that the diversity-dependent diversification model with extinction should be preferred over the constant-rate birth-death model or pure birth model as a more biologically realistic model for macroevolution.
Nevertheless, the diversity-dependence diversification model is designed as a simple model of diversity-dependence, serving more like a null model. It assumes a global scenario, thus, ignores spatially distributed clades that do not interact but may have different influence on clade-specific speciation. In addition, the spatial structure of the community is widely recognized as an essential driver of biodiversity Chown 2 , Gaston and Chown , Rosenzweig 1 . Thus, this simplification may reduce the power of the likelihood formulation for parameter inference.
Modelling trait evolution
Although evolutionary biologists have long been fascinated by paleontology, sys-tematics, morphology, and genetics, the interactive dynamics of ecological and evo-lutionary processes received little attention Schoener 1 . Only recently people
1
started to realize the substantial effect of both directions between ecology andevolution. In fact, the influence of ecological processes on evolution has beendoc-umented by many empirical phenomenons. One of the best known instances is the evolution of Gal pagos ground finches, which are also called Darwin’s finches to memorize Darwin’s study by Lack in his book Darwin’s Finches Lack 1 2
in 1 4 . Darwin’s Finches comprise a group of about 1 species. Their beak sizes are evidenced to associate with the size of seeds that are available in environment, showing apparent evolutionary evidence responding to ecological changes. In the speciesGeospiza fortis, people found that the beak size of the birds is larger when large seeds are more available Grant and Grant . Conversely, when small seeds become more available for some years, small beaks are pervasive in the pop-ulation. The study of the other direction, i.e. of evolution affecting ecology, is tricky because such processes were believed to be too slow to observe. However, recent studies have looked at ecological and evolutionary processes at similar time scales Hairston et al. 2 , Reznick et al. 1 , Reznick and Ghalambor 1 4 , showing that evolution can be fast, thus, plays a role in ecological processes. One empirical example is the evolution of Caribbean lizards Strauss et al. 1 . Before preda-tors invaded the community, the small lizards Anolis sagrei were happy living on the ground and tree trunks. The invasion of the predatorLeiocephalus carinatus -a l-arge liz-ard with curly t-ail th-at feeds onAnolis sagrei- results in reduction of the population size ofAnolis sagrei. Few small lizards with shorter limbs that better fit the higher branches of the trees where the predator cannot reach, survive. After a few generations, this selection rapidly caused the shift of the limb size distribution towards shorter limbs and increased the abundance ofAnolis sagrei.
The first theoretical attempts to model trait evolution occur in the 1 s. In 1 2, right right 21 developed a model to illustrate a basic principle of the evolution of gene fre uencies. The model describes that in a static environment with random mating, selection causes the gene fre uency at a locus to change in order to maximize the mean fitness of individuals in the population until e uilibrium where the fitness reaches a maximum. The fitness here means that how individuals are adapted to the environment thus have a higher chance to survive and give birth to offspring.
In 1 , Lande Lande 1 4 clarified the concepts and constructed a mathe-matical model to describe an adaptive topography for the average phenotype in a population:
Δ ̄𝑧(𝑡) = ℎ 𝜎 𝜕𝑙𝑛 ̄𝑊
𝜕 ̄𝑧(𝑡) 1.1
where ̄𝑧(𝑡) denotes the mean phenotypic trait value of the population at time 𝑡. The change of the mean traitΔ ̄𝑧(𝑡) is affected by the change of the mean fitness with respect to the mean trait. The formula uantitatively measures how the mean trait of a population changes to better fit the environment. In addition, it consid-ers population genetics. The heritability ℎ is determined by the genetic system, the breeding structure of the population and the environment. It measures the proportion of the variation in a given trait within a population that is explained by inheritance from the parent generation instead of the environment or random
Introduction
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chance. The variance of the trait is denoted by 𝜎 , which is normally assumed to be constant and independent from the mean trait Falconer . However, Simpson Barnett and Simpson 1 and an alen an alen 2 in their case studies also argued that this may not be the case. A changing variance in the cause of evolution is more realistic but also leads to a much more complex system. Nevertheless, Lande’s formula provides a uantitative tool to model trait evolution. In fact, at the meantime, there are two alternative models dominating the trait evolution studies even till now, i.e. Brownian motion process and Ornstein Uhlenbeck O-U process. hile the Brownian motion process mimics random walks of traits in evolution Felsenstein and the O-U process describes a selective force pulling traits towards an optimum, they assume independent evolution for each species and thus do not account for species interactions Pennell and Harmon
14 . Nevertheless, because of analytical tractability, they are majorly favored to study trait evolution. Apart from these two models, Lande’s model is well biolog-ically interpretable. It assumes a fitness landscape such that species struggle to climb up the hills of the fitness landscape via evolving their traits to better fit the environment.
However, early studies of trait evolution ignored phylogenetic information. Only in 1 Felsenstein Felsenstein 1 introduced a phylogenetic independence con-trasts method to test hypothesis of modes of trait evolution. Felsenstein pointed out that given the fact of species being part of a hierarchically structured phylogeny, if the traits are drawn independently from the same distribution they cannot be used for statistical tests among models. This can be circumvented by considering the phylogenetic relatedness of the species in traits. The novel idea of integrating phylogenetic information opened a new era and spawned a family of uantitative methods to apply models of population and uantitative genetics, paleobiology, and ecology to data including a phylogenetic tree, the family of which is now well known as phylogenetic comparative methods PCMs . In fact, the models mentioned in Section Modelling macroevolution all fall in this family, normally regarded as model-based approaches to investigate rates of diversification and the influence of characters on diversification.
Nowadays, the progress and directions of PCMs start to move towards a more integrative comparative biology. Phylogenetic community ecology is one of the ar-eas in which PCMs have played an incrar-easingly important role Pennell and Harmon
14 . The study of phylogenetic community ecology is to exploit the phyloge-netic relatedness among species in traits to explore how the community structure and patterns are formed ebb et al. 211 . However, species differences in rela-tive abundance, competition and community functioning are rarely incorporated in phylogenetic comparative methods.
Fortunately, the mismatch between community ecology and phylogenetic com-parative methods has started to attract theoreticians’ attention. In 2 1 , Nuismer & Harmon 14 presented a model that allows the traits of species to evolve along a phylogeny in an interactive manner to infer the rate of trait evolution and inter-action. Later on, Druryet al. Drury et al. 4 ,44 derived a likelihood function to the spatial extension of the Nuismer & Harmon’s model for estimating
parame-1
ters of interest and tested the statistical power among several relevant models ofdetecting the impact of species interactions on trait evolution. Their work filled thegap of trait evolution among interacting species. However, the influence of distinct species abundances is still not accounted for.
Modelling individual interactions in community ecology
Ecologists have spent decades on studying species abundance distributions while phylogenetic comparative methods usually assume an e ual population size for all species under consideration Pennell and Harmon 14 . To study the influence of differences in species abundances on community ecology, individual-based simula-tion models that make use of individual properties are thus a powerful approach. Through simulating ecological processes such as birth, death, migration and specia-tion on an individual basis, one can track the populaspecia-tion size of species and therefore assess its impact on interspecific and intraspecific interactions, and further study how community patterns are formed. One of the studies of individual-based com-munity ecology traces back to Hubbell’s neutral theory in 2 1 Hubbell , which borrowed the idea of the neutralist theory of evolutionary genetics developed by imura, Crow, Ewens Ewens , imura , imura and Crow and built upon MacArthur and ilson’s theory of island biogeography MacArthur and ilson114 . Neutrality means that all individuals in the community share identical rates of birth, death and migration regardless of their species identities. The neutral the-ory has achieved a great success in explaining species abundance distributions in some empirical cases. hilst it opened a door to modelling the change of species abundances along with producing a phylogeny. However, there are mismatches of neutral theory’s predictions and observed empirical patterns. For example, it cannot produce highly diverse communities while at the same time having very dominant species, and it produces phylogenies that show a strong pull-of-the-present. hile neutralists have sought the explanation of these mismatch in simplifications of the model with respect to speciation mode and the way of modelling space, many ecol-ogists argue that this happens because neutral theory ignores differences between species and among individuals.
Speaking of species differences, the negative density effect proposed by Janzen Janzen and Connell Connell 4 independently is a well-known explanation of the maintenance of high biodiversity and species heterogeneity, which is also known as the Janzen-Connell hypothesis. The theory states that the most abundant species are at a disadvantage because they are more prone to be explored and attacked by natural enemies. Thus, rare species have more chance to grow in the vacant sites, promoting species richness. One might think that combining of the Janzen-Connell hypothesis and the neutral theory may resolve the insufficient power of the neutral theory to explain high biodiversity in communities. In 2 1 , Leviet al. Levi et al. 1 presented a model with similar initiatives to study whether Janzen-Connell effect can maintain a practical species diversity and to answer how strong Janzen-Connell effects must be to maintain observed levels of tree species richness.
Introduction
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However, pathogens and herbivores are rarely monophagous and usually at-tack several closely related hosts Agrawal and Fishbein 2 , Gilbert and ebb
4 , Novotny et al. 142 . Thus, closely related species should have a greater negative effect on the survival rate of each other than distantly related species. This mechanism has been demonstrated by several observations in tropical rain forest Gilbert and ebb 4 , Novotny et al. 142 , ebb et al. 211 . For example, from the perspective of the host, ebbet al. ebb et al. 212 used community-wide seedling mortality data to analyze the relationship between seedling survival and phylogenetic neighborhood effects in a tropical rain forest. They found that seedling survival was enhanced in a more heterogeneous neighborhood where phylodiver-sity is high. They further suggested that interactions with pathogens may explain positive effects on seedling survival. From the perspective of the natural enemy, by experimental inoculation of plant leaves with fungal pathogens in a tropical rain for-est, Gilbert & ebb Gilbert and ebb 4 found that the chance that a pathogen is able to infect two different plant species increases with increasing phylogenetic relatedness.
Furthermore, the spatial structure of the community and dispersal ability of in-dividuals play an important role in biological interactions. Not all inin-dividuals of a species can invade suitable habitat patches within a community. Many species are strongly dispersal-limited Clark and Clark 2 , Seidler and Plotkin 1 . The geographical distribution of a species depends on its dispersal ability. Dispersal limitation determines patterns of diversity and can be used to explain species co-existence in neutral theory Etienne et al. , Macdougall and Turkington 11 . However, the conse uences of dispersal limitation for species diversity depend on the processes that determine the diversity and abundance of species within sites and exhibit a complex effect on species diversity Cadotte 22 , Schuler et al. 1 . Tilman applied experimental introductions to relax dispersal limitation and demon-strated that species diversity increases with the introduction of species in a grass-land community Tilman 2 4 . It might be because that the increase of dispersal helps species invade empty sites. In contrast, Mou uet and Loreau Mou uet and Loreau 1 found that species diversity declines as dispersal increases because of increased homogenization of the metacommunity. That is to say, the influence of dispersal on diversity patterns may differ for different spatial scales. In addi-tion, the density of a species is not constant in areas with different distances to an empty site. Thus, the J-C effect should show spatial pattern Hubbell , Levi et al. 1 .
Both the negative density effect Janzen-Connell hypothesis and the phyloge-netic relatedness effect contribute to biodiversity where dispersal ability and spatial pattern of the effect play a role. hile empirical evidence of the combining effects has been found recently Liu et al. 11 , theoretical analysis is still lacking. Fur-thermore, to what extent the phylogenetic J-C effect could make realistic predictions on macroevolutionary and macroecological patterns is still unclear.
1
Thesis outline
Closely bonded to the three sections of the introduction aforementioned, the fol-lowing chapters study the mechanism of biological interactions from the perspective of macroevolutionary diversification on species level, the perspective of the inter-and intra-specific eco-evolutionary interactions on trait evolution inter-and the perspec-tive of individual’s birth, death and migration processes. All results and conclusions are summarized in Synthesis.
The slowdown of species accumulation is a widely observed phenomenon in reality. The hypothesis of diversity-dependence diversification is one of the expla-nations that achieve a great success in interpreting such pattern. However, current diversity-dependence diversification models ignore the geographic spatial structure, thus, can only assess the diversity-dependence signal on a global scale. In Chapter
2, I develop a spatial extension to the global diversity-dependence diversification
model to mimic macroevolutionary events such as speciation, extinction, migration and contraction on species scale. I generate evolutionary history stored in a phy-logenetic form and apply the global analytic likelihood formulation to estimate the macroevolutionary rates, i.e. speciation rate and extinction rate. Furthermore, I exploit bootstrapping techni ue to examine whether the global approach is capable to detect the diversity-dependence signal on a region of different spatial levels.
As species abundance plays a role in species interaction, thus, further helps form trait evolution, which is usually ignored, in Chapter 3, I introduce a trait evolution model that takes population dynamics into account during the cause of the trait evolution. The model allows traits to evolve along a phylogeny and un-der environmental attraction towards an optimum trait and competitive repulsion. An approximate Bayesian computation evolutionary algorithm is applied to inves-tigate the strength of stabilizing selection and competition. I, later on, illustrate our method on the body size of the baleen whales and compare the results with a trait evolution model without population dynamics and a trait evolution model with metabolic dynamics. Our work induces such a family of trait evolution models that can accommodate any type of species interactions in the trait evolution process.
In Chapter 4, I follow the intuition of the mechanism of the phylogenetic Janzen-Connell hypothesis in an explicitly spatial model and develop a mathematical formulation to calculate the colonization probability of individuals that reflects the essence of the phylogenetic Janzen-Connell mechanism in a spatial manner. I con-duct substantial simulations under different parameter combinations that account for different strengths and interaction distances of negative density effect, phylo-genetic relatedness effect and individual dispersal ability. I am interested in the resulting species-abundance distribution, species distribution, characters of phylo-genetic trees and species richness. The comparison of the results among a variety of parameter explorations reveal the underlying mechanism of how those effects affect species assemblage.
