東北大学機関リポジトリTOUR

Repeatability of phenotypic evolution of

tree-like organisms.

著者

Nonoyama Tomonobu

学位授与機関

Tohoku University

学位授与番号

11301甲第19372号

URL

http://hdl.handle.net/10097/00127818

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博士論文

Repeatability of phenotypic evolution of tree-like organisms.

令和元年度

東北大学大学院生命科学研究科 生態システム生命科学専攻

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Contents

Summary

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1. General Introduction

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2. Contingency of history: repeatability of phenotypic evolution of

tree-like organisms

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Abstract

... 8

2.1 Introduction ... . 8

2.2 Methods ... 10

2.2.1 Tree growth ... 11

2.2.2 Reproduction and evolutionary process ... 13

2.2.3 Phenotypic difference ... 16

2.3 Results ... 17

2.4 Discussion ... 19

Figure ... 24

3. Extinction dynamics in models of communities with interacting

species

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3

Figure ... 56

4. Evolutionary patterns of resource use efficiency and phenotypic

plasticity in model communities

61

Abstract ... 61 4.1 Introduction ... 62 4.2 Methods ... 64 4.3 Results ... 65 4.4 Discussion ... 67 Figure ... 70 Acknowledgements 75 References 76

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Summary

The evolutionary patterns of geological time scale have been studied in order to document the processes underlying the dynamics. A number of studies have examined how adaptation, interaction among lineages, and stochastic process yield temporal and spatial patterns in phenotypic, genetic and taxonomic diversity. However, it still remains unclear how long term evolutionary dynamics of phenotypic diversity are created in ecosystems.

First, I examine whether evolutionary history is mostly contingent or deterministic has been given much focus in the field of evolutionary biology. In the present study, to incorporate the effects of phenotypic plasticity, we constructed a model using tree-like organisms. In this model, the basic rules used to develop trees are

genetically determined, but tree shape (described by the number and aspect ratio of the branches) is determined by both genetic components and plasticity. The results of the simulation show that the tree shapes become more deterministic under higher mutation rates. However, the tree shape became most contingent and diverse at the lower

mutation rate. In this situation, the variances of the genetically determinant characters were low, but the variance of the tree shape is rather high, suggesting that phenotypic plasticity results in this contingency and diversity of tree shape. The present findings suggest that plasticity cannot be ignored as a factor that increases contingency and diversity of evolutionary outcomes.

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Second, by using the same model, I examine how patterns of extinction are affected by mutation rates (speciation rate in macro level). The result shows that, in the systems with interaction among individuals, a pattern of extinction similar to “mass extinction” is observed under moderate levels of mutation rates (speciation rates). In addition, extinction rates decrease through time.

Finally, I examine how phenotypes and their fitness archived after a long time evolution change depending on mutation rates, interactions among individuals and plasticity. The result shows that low level of mutation rates and plasticity promotes adaptation to distinctive environments and creates distinctive morphology.

Discontinuous evolutionary patterns appear through the effects of plasticity. These findings reveal the usefulness of simulation to understand the causes of the patterns of long term evolution. The implication and limitation of the present model and insight obtained are discussed.

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1. General Introduction

Long term evolution of organisms exhibits patterns specific to phenotypes, genetic variations and taxonomic diversity. Majority of the molecular level evolution show mostly stochastic dynamics. A temporal pattern of phenotypic evolution is characterized by a long time stasis of the phenotype interrupted by a short period during which the phenotype shifts rapidly from one state to another state (Gould & Eldredge 1977; Benton & Harper 2009; Hunt & Rabosky 2014; Landis & Schraiber 2017; Jackson 2019). Temporal patterns of taxonomic diversity show pseudo-replication of rapid increase of extinction of lineages followed by rapid increase of taxonomic diversity (Raup & Sepkoski 1982; Harnik et al 2012; Foster & Twit ch et t 2014; Stanley 2016).

The evolutionary patterns of geological time scale have been studied in order to document the processes underlying the dynamics. A number of studies have examined how adaptation, interaction among lineages, and stochastic process yield temporal and spatial patterns in phenotypic, genetic and taxonomic diversity. However, it still remains unclear how long term evolutionary dynamics of phenotypic diversity are created in ecosystems (Jablonski 2017). One of the major reasons of this difficulty is that long term evolution in empirical system is generally difficult to observe. For examples, fossil records have been used for observation of long term trends of phenotypic and

taxonomic diversity. Temporal patterns of extinction and origination of lineages have been observed, and a number of studies addressed the question of how environmental

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changes have affected the temporal dynamics of diversity (Foster & Twit ch et t 2014; Stanley 2016.). However, fossil records are difficult to detect detailed causes of the patterns (Kidwell & Holland 2002). Fossils records are generally rough records of formerly existed diversity and what we can observe is only a small part of the information of the past. In addition, it is impossible to obtain replicate of the

evolutionary episodes, and it makes difficult to test particular causal hypotheses (Gould 1990).

Alternatively, observation of evolutionary changes using microcosm has contributed much in understanding causes of temporal dynamics in phenotypic evolution. For examples, experimental study of bacteria has suggested that different experiments might lead populations along different evolutionary paths (Blount et al 2008). However, temporal scale and complexity of interaction among organisms of observation is still limited in microcosm.

Another method to address the issue of long term evolutionary dynamics is theoretical analyses using simulation models. Although this sort of studies have limitation in complexity and reality, it is useful to estimate essential factors affecting long term dynamics because it enable to test hypotheses by using enough numbers of replicates. It has been studied theoretically how temporal dynamics of taxonomic diversity are regulated by species interaction and how extinction and origination patterns are created by stochastic processes (Raup & Gould 1974; Newman 1997; Kärenlamp 2016)

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In the present study, I focus on the effects of contingency, mutation rates, plasticity and interaction between different phenotypes on long-term evolutionary dynamics of phenotypes and taxonomic diversity on the basis of theoretical models and simulation. In chapter 2, I address the issue of predictability of evolution by considering the effects of plasticity. There have been debates on predictability of evolution: whether adaptive evolution leads phenotypes to a same adaptive peak on the adaptive landscape or it leads to different peaks if evolutionary histories are repeated? In this study, I construct simulation model for hypothetical tree-like organisms that are composed of clone individuals, and investigate how mutation rates and phenotypic plasticity affects the predictability of the outcomes of adaptive evolution.

In chapter3, I focus on temporal dynamics of lineage diversity and extinctions using the same model of chapter 1. I examine how extinction rates of lineages differ by the changes of mutation rates on the basis of the models considering complex

interaction among clone individuals. In chapter 4, I focus on how interaction among individuals, phenotypic plasticity and mutation rates affect evolution of phenotypic traits. These findings reveal the usefulness of simulation to understand the causes of the patterns of long term evolution. The implication and limitation of the present model and insight obtained are discussed.

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Chapter 2

Contingency of history: repeatability of phenotypic evolution of

tree-like organisms

Abstract

Whether evolutionary history is mostly contingent or deterministic has been given much focus in the field of evolutionary biology. Studies addressing this issue have been conducted theoretically, based on models, and experimentally, based on

microcosms. It has been argued that the shape of the adaptive landscape and mutation rate are major determinants of replicated phenotypic evolution. In the present study, to incorporate the effects of phenotypic plasticity, we constructed a model using tree-like organisms. In this model, the basic rules used to develop trees are genetically

determined, but tree shape (described by the number and aspect ratio of the branches) is determined by both genetic components and plasticity. The results of the simulation show that the tree shapes become more deterministic under higher mutation rates. However, the tree shape became most contingent and diverse at the lower mutation rate. In this situation, the variances of the genetically determinant characters were low, but the variance of the tree shape is rather high, suggesting that phenotypic plasticity results in this contingency and diversity of tree shape. The present findings suggest that

plasticity cannot be ignored as a factor that increases contingency and diversity of evolutionary outcomes.

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2.1. Introduction

There has been much debate as to whether the evolutionary history of life is mostly contingent or more or less deterministic (Gould 1990; Vermeij 2006; Morris 2003; Powell 2012). A metaphor of “replaying life’s tape” (Gould 1990) was used to emphasize the preeminent role of contingency in the evolutionary process (Gould 1990). In this view, the outcome of evolution could be dramatically different if it was replayed, because evolution is essentially a stochastic phenomenon whereby trajectories that start close to each other soon diverge. Experimental study of bacteria has suggested that different experiments might lead populations along different evolutionary paths (Blount et al 2008). Empirical and theoretical studies suggest that natural selection constrains organisms to a relatively few highly adaptive options (Morris 2003). Furthermore, constraints might come from developmental, processes and environmental, physical and chemical biases (Gould et al 1979). In these views, the evolutionary routes are many, but the destinations are limited. In the present study, we examine relative contributions of determinism and stochasticity in evolution. This has not been addressed directly, and the quantification of the predictability of evolution remains elusive.

The concept of a fitness landscape (Wright 1932) has been used to address this issue. This concept has influenced many research fields on evolution and much effort has been spent to understand the characteristics of empirical landscapes (Weinberger & Kauffman 1989; Dawid et al 2010; Lobkovsky et al 2011). The base concept of a fitness landscape assumes that there is a functional relationship between the genome of an

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organism and its growth rate and fitness (Gavrilets 2004). The model of the fitness landscape describes how some phenotypes are more likely to evolve than others, and how developmental mechanisms could limit the evolutionary change (Beldade et al. 2002). In this situation, multiple evolutionary trajectories are accessible, but evolution might be strongly constrained to a particular adaptive peak (Lobkovsky & Koonin 2012).

However, in many real-world scenarios, fitness evaluations are not trivial (Jin 2005) and experimental evolution involving sexual reproduction and multicellular organisms with long life timescale is difficult (Orgogozo 2015), so that sometimes it is difficult to apply the fitness landscape into real biological systems. Also, phenotypic changes are often largely affected by phenotypic plasticity. The shape of the adaptive landscape might largely be affected by phenotypic plasticity, while such effects of plasticity have not been considered in the studies of repeatability of phenotypic

evolution. In the present study, we simulate parallel evolution experiments that focus on the predictability of evolution while also considering the effects of plasticity.

To address this subject, a community of dendritic organisms (e.g., tree, coral, sponge, Stromatoporoidea) provides an excellent model (Niklas 1997; Perttunen et al. 1998; Fourcaud et al. 2003; Nikinmaa et al. 2003). We assume hypothetical tree-like organisms and simulate their evolution and plastic change using the Honda model (Honda 1971). Using this model, we construct an individual-based model in which individuals compete with each other for light. We assume organisms are growing under

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direct ambient light, and we are not strictly concerned about the weight of their body. The morphology of the organisms was assumed to be determined by plastic change as a response to environmental condition and by genetic change as a result of genetic drift, mutation, and natural selection. For example, the morphology of coral is determined by both environmental factors, particularly light environment (Graus & Macintyre 1976; Merks et al. 2004) and genetic components (Sentoku & Ezaki 2012). We assume that the common evolutionary patterns can be found by simulating the shape of the hypothetical tree-like organisms (Ohno et al. 2016).

This study aims to explore the factors that affect the evolutionary contingency and determinism. We test whether, after sufficient time, the same phenotypes evolve in the model community within every simulation. Particularly, we focus on how mutation rates affect the contingency of the evolutionary history and how plasticity is associated with the phenotypic diversity patterns.

2.2. Methods

Here we constructed an individual-based model, in which dendritic-shaped individuals compete for light with other individuals and evolve through mutation and natural selection. Each individual was described by simple branching rules and parameters (e.g., Honda 1971). Using these models, the optimal branching rule to minimize the overlapping of leaf clusters was obtained (Honda & Fisher 1978, 1979). For convenience, the organism in the model was called a “tree” and its single

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component was called a “branch”. In the present tree model, we tentatively call the clusters of trees a “forest”.

In this model, the branch development process was deterministic. The variety of tree shapes was produced by the growth of branches to adapt to the

surrounding light environments. To describe how leaves receive light and how it inhibits other leaves from receiving light, a leaf ball model was used (Kanemaru et al. 1992). This model considers a leaf cluster as a ball and the branch according to the brightest vector. The influence of the local light environment on branch growth is an essential process determining the dynamics of tree crown architecture (Koike 1989;

Sorrensen-Cothern et al. 1993). Using these methods, we developed the simulation model, incorporating the dependence of the number and size of new shoots on the photosynthetic production of parental shoots. This model describes the growth of trees by branch developments, which is determined by the light condition. Accordingly, in this study, we used a previous 3D tree growth model (Honda 1971; Takenaka 1994) by incorporating a leaf ball model and reaction process of branch developments against the photosynthetic condition.

2.2.1 Tree growth

The tree morphology is determined by 11 parameters (Table 1). These parameters are all used by Honda(Honda 1971) and Yoshizawa (Yoshizawa & Yokozawa 2007) and the basic relationships between these parameters and the tree

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shape were shown in these papers. Thus, details of this relationship were not analyzed in this paper. The exact description of the branching geometry is as follows. A parent branch diverges into two offspring branches through one branching process. The

bifurcation process is repeated 5 times until the growth is over. The length of each of the two offspring branches is determined by the ratio of and , respectively, to the length of the parent branch. The angle between the mother branch and two offspring branches are described as and respectively. In the case of the trunk, when the

or equal to zero, one of the offspring branches grows vertically. Another branch was assumed to form a divergence angle alpha with the sister branch of its parent branch (i.e., the offspring branch is rotated with angle alpha around the trunk from the sister branch of its parent branch).

It is assumed that the branches search for the direction of light in the

surrounding environment. To describe a cluster of leaves, this model places a ball at the distal end of each branch. This ball is used to determine the brightest direction by making a map of the shadow of the other branches on the ball surface. The direction in which the branches will grow was determined according to the incoming light vector. is the average vector of light. is calculated by the following equation (Kanemaru et al, 1992):

where is the brightness per area, is the vector from the center of the ball to each cell on the ball surface, and is the area on the ball surface. n and m describe longitude and latitude. The light amount (Le) received by the leaf is calculated

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by the following equation: . Once the amount of the light

received by the tree is calculated, branches adjusted their positions according to V. The considered branch is rotated around the point where it attaches to its parent branch, toward brightest direction. The actual angle used for changing branch direction, , is calculated by , where is the angle between and original direction of the branch to grow. cr is the constant rate of bending the branch. In the case of , there is no influence of the phototropism in the simulation. After all branches change their direction, those branches that cannot capture sufficient light do not extend and become lost. Even if the branches can capture sufficient light to grow, the growth rate of the sister branch changes with the ratio of ra (Yoshizawa & Yokozawa 2007). The amount of light captured by an individual tree is calculated by summing all light captured by the survived branches of the individual tree. The light amount captured by the Nth tree is calculated by the equation . Trees are placed in a square area at an even interval. The ground of the area is assumed to reflect light at a fixed rate. Light is considered as ambient light.

2.2.2 Reproduction and evolutionary process

The simulation area is divided into the number of square cells. Each tree grows within a cell of the simulation area. The trees produce seeds and have the same lifespan. There is no overlap of generations among individuals. In the model, we assume that one tree produces one seed (offspring), and individuals with low fitness cannot produce seed

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(offspring). The total number of individuals is assumed to be constant. We assume that the trees are all clones, and the 11 variables

determining tree morphology are the same between offspring and its mother, except in cases of mutation, which occurs with a defined probability. A change of the value of each variable by mutation is described by adding a random value having a Poisson distribution with a mean of 0 and a standard deviation of 1.

After each generation, all of the cells are assumed to become empty. All offspring are ranked by fitness. Offspring in the bottom 20% rank do not survive. Each cell is placed by an individual randomly chosen from the survived offspring. If the fitness is equal, the offspring is selected at random and placed on the cell. The fitness of the Nth individual is calculated using the following

equation: where are the constant, is

the light amount captured by Nth individual, is the whole length of the individual, and is the value calculated by multiplication of the size of the tree and efficiency of the light. Durable construction and efficiency cannot be achieved at the same time (Onoda et al. 2017). In this paper, we consider the durability of leaves to be correlated with the size of leaves; because it seems that a large leave needs a structure to support it.

2.2.3 Phenotypic difference

We evaluated the tree phenotypes using two parameters, the aspect ratio of the branches and the number of branches of each individual. These two parameters are

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considered to be independent values. These parameters were calculated for all

individuals, and their variance and average were obtained. Also, we examined changes in 11 genetically-determined variables, and calculated the average and variance for each variable. After sufficient generation times, the phenotypes of the evolved trees were compared among the different simulation runs, and thus, we can investigate if similar phenotypes evolve independently in the different simulation runs. At the end of each simulation run, the values of the above two parameters were plotted in the

two-dimensional space.

We compare the patterns and position of the plots among different simulation runs. We calculated overall phenotypic difference among different simulation runs with same values of the parameters, and used D as an indication of repeatability of the simulation run. Thus, low implies that the simulation tended to yield the same result. The overall phenotypic difference between the Ath simulation run and the Bth

simulation run are calculated as , where is the shortest vector from nth plot in the Ath run to the mth plot in the Bth run. The average of the shortest distance of this vector represents the overall phenotypic difference between the different simulation runs.

2.3. Results

The shape of the organisms after 2500 generation is shown in Fig.1. We examined the aspect ratio and number of the branches of the all trees generated after 2500 generations

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(Fig. 2). The number of types with different values for the aspect ratio of the branches and number of branches was larger with the higher mutation rate, and every individual has unique values for these traits at . Due to plasticity, there is no fixed form tree. The shape of the individuals is highly influenced by their surrounding

environment. The relationship between mutation rate and average minimum distance of the phenotypic distribution among the different simulation runs (D) is shown in Figure 3. The differences in the phenotypic distribution among the different simulations (D) represented a hump-shaped relationship with the mutation rate, but its peak is located near the lowest mutation rate (5 × 10-5). The difference became the lowest at the highest mutation rate.

Both of the variances of the aspect ratio of the branches and number of the branches became the lowest at the intermediate level of mutation rate (Fig. 4). In contrast, the variance of the 11 characters showed a hump-shaped or monotonical increase with increasing mutation rate (Fig. 5). The differences among these patterns of variance reflect the differences in the variances of phenotypic plasticity. Thus, the variance of phenotypic plasticity became rather high at low mutation rates (5× 10-5 – 5 × 10-6). The shape of the tree was the most complex at the 5 × 10-5 mutation rate, and became rather simple at the high mutation rate.

We also examined the examined in the lower mutation rate in longer generations. We set the simulation for 225 individuals, and 40000 generations (Fig. 6). The trend does not change from 5000 generations results. We show the highest fitness change over

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generations in Fig.7. The value reaches attenuation with the progress of generation (5× 10-2 – 5 × 10-5). In lower mutation rate, highest fitness jumps by the mutation in

contingency (5× 10-6 – 5 × 10-7). Furthermore, the mutation that brings the fitness jump to the organisms does not occur in the lowest mutation rate. We examined the aspect ratio and number of the branches of the all trees generated after 5000 generations (Fig. 8). We also examined two traits change until end of the simulation (Fig. 9-15) in typical cases. The phenotypic tendency already determined until around 1500 generations in most of the cases. The change of the phenotypic divergence is shown in the typical cases are shown in Fig.16.

Phylogenetic relationships among lineages survived after 40000 generations showed that all of these lineages diverged after or around 39600 generations (Figs. 17). .

2.4. Discussion

The phenotypic patterns observed at 5000 generations are regarded as mostly equilibrium, because the trends observed through 40000 generations are mostly consistent after around 5000 generations. The phylogenetic relationships among the lineages survived at particular generations are mostly diversified from a single lineage before less than 400 generations. Although lineages are constantly replaced by newly evolved lineages, phenotypes distributions of the lineages are mostly stable through time. Thus, it is unlikely that the phenotypic patterns reflect long-term interactions among a few numbers of long lived lineages.

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A high mutation rate enables the phenotype to more easily move on the surface of the adaptive landscape. Under the high mutation rate, the population consists of multiple competing clones that differ genetically from each other (Fogle et al. 2008; Keller et al. 2012). In these cases, the phenotype reaches a global peak in the adaptive landscape (Lobkovsky & Koonin 2012). Therefore, it is expected that the same

phenotype evolves at the end of all simulations when the mutation rate is high. In terms of the two phenotypic characters, including both effects of genetic components and plasticity (aspect ratio of branches and number of branches), the results of the present simulation are consistent with this expectation. However, in this simulation, the variances of these traits are the highest at the highest mutation rate. The variances of many of the genetically determined characters also became highest at the highest mutation rate. These findings mean that phenotypic characteristics are mostly determined by the genetic component when the mutation rate is very high. A high mutation rate (e.g., 5 × 10-3 and 5 × 10-4) causes a decrease of branch number and aspect ratio, resulting in thin and sparse individuals. Thin and sparse trees are the least

susceptible to plastic change because these trees have potentially few chance to interact with other individuals than thick trees. Furthermore, high dense trees also have high plasticity, and the light amount they can get is easily increase or decrease due to light environment by chance. The number of branches is higher at the mutation rate of 5 × 10-2 than at lower mutation rate. Quite small and many branches were developed in several trees under the condition of this mutation rate, so that aspect ratio has not much

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changed relative to the lower mutation rates. Because small branches hardly interfere with the other branches, this type of tree also does not represent plastic change. In this case, the mean phenotype evolved is mostly equal among the different simulations (low

D), but the variation of the phenotype is high due to the high mutation rate.

In contrast, a high variety of phenotypic distribution patterns (large D) arises at the mutation rate of 5 × 10-5. A low mutation rate implies that it is difficult to move a long distance on the fitness landscape (Franke et al. 2011). The dominant phenotypes of the two traits (aspect ratio of branches and number of branches) that appeared in each simulation differ among the simulations. This pattern implies that phenotypes are trapped at particular adaptive peaks, and cannot reach a global peak of the adaptive landscape. However, in this simulation, the variances of these traits, particularly of the aspect ratio of branches, becomes rather high at the mutation rate of 5 × 10-5. Also, variances are low in most of the genetically determined characters at this mutation rate. Thus, the phenotypic variances arising at this level of mutation rate are mainly

attributed to phenotypic plasticity. Yokozawa demonstrated that crown architecture traits are important for the pattern of species coexistence in trees (Yokozawa et al. 1996). Complex tree shape and high variability in tree morphology are maintained due to the plasticity.

In this paper, we assume that the traits determined by plasticity and the genome-determined traits are separated. Numbers of studies have been conducted to identify the relative contribution of genes and environment. However, developmental

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plasticity is partly affected by gene networks(Pigliucci et al. 2006), therefore it is, in general, difficult to separate these two aspects(秀一 2017). Although it is difficult to classify the observed patterns in nature to either deterministic or non-deterministic, and to either genetic or environmental(Aerts 1999)., we tentatively used the model that can separate these processes to evaluate the importance of each factor for simplicity. Future studies incorporating more continual and complex situation of deterministic-contingent processes and plastic-geneme-determined traits.

In this simulation, phenotypic plasticity results from the interactions among branches attempting to obtain light. Such interactions among branches might yield the unique shape of the tree by chance. When the mutation rate is 5 × 10-5, the shape of the tree becomes complex. This suggests that strong and high frequency of interactions occur among the branches, resulting in the complex shape of the tree. Under such conditions, small spatial differences in the light environment appear by chance as a result of interaction among branches of the same and different trees. These differences might change the shape of the adaptive landscape. Thus, such plasticity is likely to promote the evolution of divergent phenotypes. Also, plasticity increases contingency, resulting in less repeatability of the evolutionary outcome among the different

simulations.

When the mutation rate is very low (i.e., 5 × 10-6), the repeatability of the phenotypic distribution remains low. This low level of repeatability and high level of contingency are supposedly derived from the effect of phenotypic plasticity. This is

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because variances of the genetically determined characters are very low and near zero, but variances of the two phenotypic traits, which include variance due to plasticity, are relatively high. Thus, phenotypic plasticity again increases the contingency and yield different phenotypic distributions at the end of the different simulations.

In the present simulation, we could not separate the phenotypic variance into genetic variance and environmental variance. We estimated the effect of the plasticity on the phenotypic variance by comparing the patterns of relationship between variables to develop the tree and parameters describing the tree shape. Although the former is determined only genetically and reflects genetic variance, the latter includes both genetic and environmental variance. Therefore, to better estimate the effects of plasticity in future studies, it is necessary to develop a model that can separate genetic variance and phenotypic variance. Furthermore, the regeneration niche has been regarded as an important factor for coexisting of species (Fox 1977; Grubb 1977). The overlap of individual rearrangement and generation change might also affect the coexistence of species. However, the present findings still suggest that phenotypic plasticity cannot be ignored as a factor to enhance the diversity of phenotypes through the increase of contingency. Plasticity potentially plays a major role in producing phenotypic diversity with relatively low mutation rates.

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Figure legends

Fig. 1. The 3-D shape of the results.

Each map is one experiment result. The six columns represent the mutation rates. The mutation rates were 5.0e-1, 5.0e-2, 5.0e-3, 5.0e-4, 5.0e-5, 5.0e-6, from the left. The three rows represents the individual number. The bottom row is the result which contains 225 individual and other rows are in the result containing 400 individuals. All results are after 2500 time steps.

Fig. 2. The histogram of the whole result.

Each map is one experiment result, and the horizontal axis represents aspect ratio, which is calculated by , where is the distance from the root to the most furthest branch, and small v and h denote the horizontal distance and vertical distance. The vertical axis represents the number of the branches in the individual. The six columns represent the mutation rates. The mutation rates were

from the left. The three rows represents the individual number. The bottom column is the result which contains 225 individual and other rows are in the result containing 400 individuals. All results are after 2500 time steps. The color bar of the figures are limit at 10 individuals.

Fig. 3. The average of the minimum distance.

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of the minimum distance cases of the same mutation rate. The green line represents for the simple average of four cases including results in 400 individuals and 225 individuals, and the blue line represents for the average which is considering the number of the individuals and weight. The orange line represents for the result only in 400 individuals. If the simulations all end at the same result, all points in the histogram become the same, and the minimum distance equals zero because all points are overlapped.

Fig 4. The Variance of the result in aspect ratio and branch number.

The horizontal axis represents the mutation rate. The left vertical axis represents the aspect ratio dispersion, and the right vertical axis represents the branch number dispersion. Both lines are a downward convex.

Fig 5. The variance of the parameters.

The parameter meanings are shown in Table 1. The horizontal axis represents the mutation rate. The vertical axis represents the variance of each parameter.

Fig.6. The highest fitness in each results after 5000 generations. Horizontal axis

represents the generations, and vertical axis represents the fitness. Each dot in the graph represents the highest fitness in each generations. The fitness is sampled in every 100 generations.

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Fig. 7 The phenotypic change through 40000 generations. (a) Horizontal axis represents the generations, and vertical axis represents the aspect ratio. which is calculated by

, where is the distance from the root to the furthest branch, and small v and h denote the horizontal distance and vertical distance. (b) Horizontal axis represents the generations, and vertical axis represents the branch number. The results are sampled every 100 generations from 100 generations until 40000 generations. Mutation rates are indicated in each panel.

Fig. 8. The phenotypic histogram of the whole result. Each map is one experiment result, and the horizontal axis represents aspect ratio, which is calculated by , where

is the distance from the root to the most furthest branch, and small v and h denote the horizontal distance and vertical distance. The vertical axis represents the number of the branches in the individual. The six columns represent the mutation rates. The mutation

rates were from

the left. Every result contains 225 individuals after 5000 generations. The color bar of the figures are limit at 10 individuals.

Fig. 9. Phenotypic change along the generations when the mutation rate is . Each map of the Figure is the midway results. The results are sampled every 500 generations from 100 generations until 4900 generations. the horizontal axis represents aspect ratio, which is calculated by , where is the distance from the root to the

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most furthest branch, and small v and h denote the horizontal distance and vertical distance. The vertical axis represents the number of the branches in the individual. The six columns represent the mutation rates.

Fig.10. Phenotypic change along the generations when the mutation rate is .

Fig.11. Phenotypic change along the generations when the mutation rate is .

Fig.12. Phenotypic change along the generations when the mutation rate is .

Fig.13. Phenotypic change along the generations when the mutation rate is .

Fig.14. Phenotypic change along the generations when the mutation rate is .

Fig.15. Phenotypic change along the generations when the mutation rate is . Details are the same as in Figure 10 except for mutation rate.

Fig. 16. The phenotypic divergence change along the generations. The horizontal axis represents the mutation rate. The vertical axis represents the coefficient of variance of the aspect ratio and number of the branch in each individuals. The Variance of the result in aspect ratio and branch number. Orange point and line represents the aspect ratio and blue line represents the branch number. Each map represents the result in another

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mutation rate. The mutation rate is

, in order from the upper left.

Fig. 17 Phylogenetic relationships among lineages generated during 40000 generations. Horizontal axis represents generations. Horizontal lines indicate lineages that survived after 40000 generations. The vertical positions of the lineages do not reflect phenotypic differences among the lineages. The number on each panel indicates mutation rates. The phylogenies obtained when the mutation rates were 5× 10-5, 5 × 10-6 and 5 × 10-7are not shown, because only single lineage survived in these cases. Other parameters are same as the simulation in Fig. 7.

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Table 1. Parameters used in the simulation.

Parameter Description Range

Branching angle 1 Branching angle 2 Branch attenuation rate 1 Branch attenuation rate 2 Rotation angle

Leaf radius

Leaf absorption rate Tendency to move Avoid threshold Rate of avoid reaction Death threshold

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Chapter 3

Extinction dynamics in models of communities with interacting species

Abstract

Current much focus has been placed on how environmental changes have yield

extinction dynamics during Phanerozoic era, while very few studies have considered a role of biological interactions as a cause of these extinction dynamics, particularly of mass extinctions. On the basis of a theoretical model using tree-like organisms, I examine how biological interactions cause extinction dynamics similar to those in the fossil records, and how mutation rates (speciation rate, see chapter 1) affect the

extinction dynamics. In this model, the basic rules used to develop trees are genetically determined, but tree shape is determined by both genetic components and plasticity. The hypothetical organisms are assumed to compete individually for light. The results of the simulation represented patterns of extinction similar to those with mass extinction and decline of background extinctions. This suggests that mass extinction can be arisen by interactions among species in the ecosystem without catastrophic environmental changes. In addition, decline of extinction rates can occur by long-term adaptation, and is not necessarily artifacts arisen in interpretation of fossil records. Although further studies treating more realistic and complex systems are needed, the present study suggests that the patterns identical to those observed in fossil records can be arisen in a simple hypothetical ecosystem.

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3.1. Introduction

Long term evolution of organisms exhibits specific patterns of phenotypic and taxonomic diversity. A temporal pattern of phenotypic evolution is often characterized by a long time stasis of the phenotype interrupted by a short period during which the phenotype shifts rapidly from one state to another state (Gould & Eldredge 1977; Benton & Harper 2009). Temporal patterns of taxonomic diversity show

pseudo-replication of rapid increase of extinction of lineages (i.e. mass extinction) followed by rapid increase of taxonomic diversity (Raup & Sepkoski 1982; Harnik et al 2012; Foster & Twit ch et t 2014; Stanley 2016) (Fig. 18). The evolutionary patterns of geological time scale have been studied in order to document the processes underlying the dynamics. A number of studies have examined how environmental changes,

interaction among lineages, and stochastic process yield temporal and spatial patterns in taxonomic diversity.

Current much focus has been placed on the cause of mass extinction (Raup & Sepkoski 1982; Sepkoski 1984; Harnik et al 2012; Foster & Twit ch et t 2014; Stanley 2016) and trend of decline of background extinction through time (Flessa & Jablonski 1985; Newman & Eble 1999; Alroy 2014). Mass extinctions have been regarded as qualitatively different from background extinctions. It is proposed that the former is caused by catastrophic environmental changes, and the latter caused by the processes other than serious environmental changes (Raup & Sepkoski 1982). Some studies assume that background extinctions are caused by stochastic environmental perturbation

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(Flessa & Jablonski 1985; Newman & Eble 1999), or loss of reproductive fitness (McKinney 1993; Wiens & Slaton 2011). However, there is little evidence for the processes and mechanisms of background extinction. Researchers considering biological interactions as major mechanisms of extinctions argue that magnitudes of both mass extinction and background extinction follow a same power law or exponential curve, and these two types of extinctions cannot be qualitatively separated (Sol´e & Bascompte 1996; Newman 1997) (Fig. 18). There is no comprehensive theory that characterizes extinction (Wiens & Slaton 2011).

Background extinction is known to have shown decline through time (Flessa & Jablonski 1985; Alroy 2010; Harnik et al 2012) (Fig. 18). However, the cause of this decline remains unclear. Community filter by loss of extinction-prone lineages

(McKinney 1993; Alroy 2010), or stochastic processes (Ma cLeod, 2004) can cause this decline, while it may be due to artifact in interpreting taxonomic diversity from fossil records (Alroy 2014).

In the present study, I examine whether these patterns of extinctions can be observed in the model used in chapter 1, which is the model of a community of

dendritic organisms (e.g., tree, coral, sponge, Stromatoporoidea). I assume hypothetical tree-like organisms and simulate their evolution and plastic change. Using this model, I construct an individual-based model in which individuals compete with each other for light. Both patterns of mass extinctions and decline of background extinctions are known in fossil records of dendritic marine organisms such as coral, sponge and

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Stromatoporoidea (Sepkoski 1984; Flessa & Jablonski 1985; Vien 2008). Thus, this model can be used to understand the cause of background extinctions and relationships between mass and background extinctions.

In the present study, I examine how patterns of extinction are affected by mutation rates (speciation rate in macro level). In the systems with interaction among individuals and plastic changes of phenotypes, patterns of extinction similar to those with mass extinction and decline of background extinctions are observed. I discuss the relationship between mass and background extinctions and whether decline of

background extinction is artefacts in interpretation of fossil records or is potentially reflecting existing pattern.

3.2 Methods

I used the individual-based model, in which clone dendritic-shaped individuals compete for light with other individuals and evolve through mutation and natural selection. The detailed structure of the model is described in chapter 2. The tree

morphology is determined by 11 parameters. The details of the branching geometry are described in chapter 2. We set the simulation for 400 individuals, and 2500 generations. The mutation rates are same as those in chapter.1. Individuals that appear during

simulation are recorded as single species if they have any different parameters from other individuals. All the simulations start with same parameters except for mutation rates.

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Phylogenetic relationships among the lineages arisen in the simulation are constructed. Survival or extinction of each lineage is recorded at every 10 generations. The patterns of phylogeny and temporal patterns of species diversity are observed for each simulation run. Extinction rate at every 10 generations (number of lineage that become extinct / number of lineages existed before 10 generations) is measured. The temporal patterns of extinction rates are observed for each simulation run.

3.3 Results

Number of species arisen in the simulation increased with increase of mutation rate (speciation rate). Level of fluctuation in the species diversity and

extinction were greater when mutation rate (speciation rates) was smaller, while only few species evolved when mutation rate was smaller than 5x10-6. Species diversity and intensity of extinction were temporally constant when mutation rate was very high (Fig. 19).

Phylogenetic relationships among lineages survived after 2500 generations showed different patterns among the simulation with different mutation (speciation) rates. When the rate was larger than 5x10-5, frequent extinction and diversification occurred and the clades dominated at particular generations were replaced by other clades diversified after this period (Fig. 20). In contrast, numbers of short lived species evolved from a single stem lineage when mutation rate was 5x10-6. When mutation rate was from 5x10-5 and 5x10-4, extinctions of particular clades followed by rapid

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diversification of survived lineages were observed repeatedly through the simulation run.

Extinction rates tended to decrease through time when mutation rate was 5x10-4 (r = -0.29, p<0.001) and 5x10-3 (r = -0.24, p<0.001) (Fig. 19). However, no decline of extinction rate was observed when mutation rate was lower than 5x10-5 and higher than 5x10-2. Frequency distribution of extinction magnitude showed a bell curve or normal distribution when mutation rate was relatively high (Fig. 21). However, it showed a monotonic distribution pattern when mutation rate was 5x10-5 and 5x10-4 ( Fig. 21). Magnitude of extinction was mostly constant through time when mutation rate was high, but episodes of extinctions were composed of frequent low-magnitude extinctions and rare high-magnitude extinctions when mutation rate was 5x10-5. Thus, the pattern corresponding to mass extinctions was observed when mutation rate was 5x10-5.

3.4 Discussion

The patterns of Phanerozoic extinction episodes have provided controversial issues. There has been much debate about the causes of five mass extinctions identified from the fossil records of marine invertebrates such as corals, molluscs, arthropods and sponges over 500 million years (Harnik et al 2012; Foster &

Twitchett 2014; Stanley 2016). Although catastrophic environmental changes are thought as major causes for mass extinctions (Schulte et al 2010; Kravchinsky 2012; Long et al

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2015; Sprain et al 2019), biological interactions are also considered as a cause (Bak 1997; Jain & Krishna 2002; Kärenlamp 2016) except for the extinction event at the end of the Cretaceous, which was induced by meteoric strike (Schulte et al 2010). The frequency distribution of magnitudes of extinction rates in the fossil records fit a power-law or exponential distribution (Sol´e & Bascompte 1996; Newman 1997) (Fig. 18), and simple models assuming positive and negative interactions among hypothetical species yield a frequency distribution of extinction rates similar to that found in the fossil records. These studies suggest that mass extinctions are not qualitatively different from background extinction, and the patterns of magnitudes of extinctions represent statistical nature of perturbation caused by species interactions (SOC model) (Sole´ & Manrubia 1996; Bak 1997). If this is the case, mass extinctions can be arisen as a result of species interactions.

In the present study, I show that the frequency distribution in magnitude of extinctions changes by increase of mutation rates (= speciation rates in this model, see chapter 2). A few serious extinction episodes and many minor extinction episodes were detected in the simulation under fairly low mutation rates. This sort of frequency distribution in extinction rates was not found in the simulation under high mutation rates. In the previous SOC models of extinctions (Sole´ & Manrubia 1996; Kärenlamp 2016), frequency distributions of extinction rates always show a power-law relationship regardless of mutation rates or speciation rates. In the present study, however, frequency distributions of extinctions differ among the species with different

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mutation (speciation) rates. So far, it is difficult to examine which frequency distribution model (e.g. power law, exponential, weibull distribution) is the best fit model for the distribution of these extinction rates, because these datasets are not much enough to conduct model selection analyses. Although further analyses are needed, the present findings suggest that the patterns of mass extinction can be arisen by

interactions among species in the ecosystem without catastrophic environmental changes.

There are controversies about the cause of decline of background extinctions detected in Phanerozoic. The decline of magnitude of extinction can be detected in the patterns of extinctions even if both episodes of mass extinction and background extinctions are included (MacLeod, 2004). The present study suggests that decline of magnitude of extinction can occur as a result of adaptation to interacting ecosystems. This sort of decline of extinction rates have not been observed in the previous models considering only biological interaction as a cause of extinctions. It is presumably that this decline of extinction rate reflects evolutionary trends of phenotypes that approach adaptive peaks on the adaptive landscape (see chapter 2). Because the organisms are assumed to be clones in this model, the patters of species diversity and extinctions correspond to those of genetic variations. Although further analyses are required to examine whether patterns of speciation in sexually reproducing organism differ from those of clone organisms, the present study suggests that decline of

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extinction rates can occur and is not necessarily artifacts arisen in interpretation of fossil records.

The system assumed in this study would be overly simplified and interactions assumed are limited to competition for light. However, the tree-like marine organisms (e.g. corals, sponges) are major elements of marine ecosystems, and fossil records of these organisms represent patterns of mass extinctions and decline of extinction rates (Sepkoski 1984; Vien 2008). Although further studies treating more realistic and complex systems are needed, the present study suggests that the patterns identical to those observed in fossil records can be arisen in a simple hypothetical ecosystem. The present findings shed light on the cause of long term patterns of diversity and extinctions, which are difficult to obtain replicates to test specific hypotheses.

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Figure legends

Fig.18. (A) Temporal patterns of extinctions of genera and decline of extinction rates detected from Phanerozoic fossil records (after Harnik et al 2012). (B) Frequency distribution of extinction rates during the Phanerozoic with the best fitting power-law (solid line) and exponential (dashed line) curves (after Sol´e & Bascompte 1996).

Fig. 19. Temporal patterns of species diversity, numbers of extinctions and extinction rates appeared in the simulations. Results for the different mutation rates are given.

Fig. 20. Phylogenetic relationships among species and lineages appeared in the simulations. Results for the different mutation rates are given.

Fig. 21. Frequency distributions of extinction rates. Results for the different mutation rates are given.

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Fig. 18. (A)

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Chapter 4

Evolutionary patterns of resource use efficiency and phenotypic

plasticity in model communities

Abstract

A large number of studies have been conducted to investigate how plasticity evolves and how it contributes phenotypic evolution. However, there are few studies addressing the question of how plasticity contributes to produce long time evolutionary patterns. In the present study, I examine temporal patterns of phenotypic changes and performance of resource use by mean of the simulation of the model communities used in chapter 2. It is investigated how plasticity caused by competitive interaction among individuals affect evolutionary patterns and how evolution through plasticity affect adaptation to novel environments. When mutation rates were low (effects of plasticity are high), discontinuous patterns of evolution were found in the morphological traits and light amount capture by individuals. The individuals grown in competitive environments became taller than those grown alone due to the effects of plasticity. At the end of the simulation, the individuals growing in competitive environments became taller and more efficient to capture light than those of the initial condition as a result of adaptation to competitive environments. However, if these individuals obtained at the end of the simulation grow alone, they become rather flatter and more efficient to capture light than those obtained at the initial stage and grown alone. Although further detailed

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analyses are required, these findings partially support plasticity first hypothesis. Evolutionary processes enabling plastic responses to distinctive environments and adaptive response to novel environments are discussed.

4.1 Introduction

Evolution dynamics through time have been a major concern in evolutionary biology for long time. A long-term pattern of phenotypic evolution is often characterized by a pattern of punctuated equilibria, that is a long time stasis of the phenotype interrupted by a short period during which the phenotype shifts rapidly from one state to another state (Gould & Eldredge 1977; Benton & Harper 2009; Hunt & Rabosky 2014; Landis & Schraiber 2017; Jackson 2019). Most of the examples of this discontinuous

evolutionary pattern are observed in fossil records and molecular phylogenetic analyses and therefore, it is difficult to understand why stasis of the phenotypes is maintained and how the relatively rapid phenotypic shifts occur. A number of empirical and theoretical studies have investigated processes that yield discontinuous evolutionary patterns of phenotypes, while exact mechanisms remain unclear (Futuyma, 2015; Jablonski 2017).

Recent progresses in developmental biology and ecology have given a new insight on the processes of discontinuous evolutionary patterns. Long-term evolutionary stasis can be led by developmental constraints that are created by complex and highly controlled global interactivity of development, because mutations that affect such global interactivity have deleterious pleiotropic effects, and such mutation will be

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strongly selected (Galis et al 2018). In most cases, phenotypic shift is not truly discontinuous but is relatively rapid continuous change. However, there are many examples of true discontinuous evolution called as “saltation”, which is sudden and large mutational change from one generation to the next (Chouard 2010; Szathmáry 2015; Katsnelson et al 2019). The saltation is close relevance to evolutionary

developmental genetics. Recent studies combining views of developmental biology and paleontology suggest that manifestation of phenotypic plasticity in the fossil record causes a radical phenotypic change similar to saltation, and therefore outcome of

plasticity-led evolution resembles punctuated equilibrium (Webster 2019; Jackson 2019). Although large number of studies have been conducted to investigate how plasticity evolve and how it contributes phenotypic evolution, there are very few studies

addressing the question of how plasticity contribute to produce long time evolutionary patterns.

Relationships between phenotypic plasticity and evolution by genetic mutation remain unclear and controversial, while one of the plausible idea (plasticity first hypothesis) is that plasticity initiates and accelerates the rate of phenotypic change, in that plastic adaptive phenotypes can emerge earlier and faster than phenotypic

changes due to genetic mutation (Levis & Pfennig 2016; Lafuente & Beldade 2019). This suggests that phenotypic changes are potentially accelerated by saltationary jumps due to plasticity, and subsequently phenotypic evolution is promoted by genetic changes. Thus, saltation is most likely to be observed in plastic traits under a low mutation rate.

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To test this hypothesis, patterns of phenotypic changes are observed in the model used in chapter 1, which is the model of a community of dendritic

organisms (e.g., coral, sponge). I assume hypothetical tree-like organisms and simulate their evolution and plastic change. Using this model, I construct an individual-based model in which individuals compete with each other for light. Discontinuous

evolutionary shifts are commonly found in fossil records of corals (Schwartz et al 2012). Coral represents high phenotypic plasticity by difference of environments and

interaction among other species, and variation in potential of plasticity is determined genetically in coral (Kenkel & Matz 2016).

In the present study, I examine temporal patterns of phenotypic changes and performance of resource use by mean of the simulation of the model communities. It is investigated how plasticity caused by competitive interaction among individuals affect adaptation and evolutionary patterns. In addition, the individuals of the same genotype are grown alone to observe how phenotypic change occurs in novel environment due to plasticity and adaptation. The relationships between effects of plasticity and genetic mutation on trait evolution are discussed.

4.2 Methods

I used the individual-based model, in which clone dendritic-shaped individuals compete for light with other individuals and evolve through mutation and natural selection. The detailed structure of the model is described in chapter 2. The tree

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morphology is determined by 11 parameters. The details of the branching geometry are described in chapter 2. We set the simulation for 400 individuals, and 2500 generations. The mutation rates are same as those in chapter.1. Individuals that appear during

simulation are recorded as single species (variant) if they have any different parameters from other individuals. All the simulations start with same parameters except for mutation rates.

Height, width, number of branches and light amount captured are recorded for each individual. After 2500 generations, all of the variants (species) appeared in the simulations are re-grown alone without interactions with other individuals to observe how plasticity due to interaction with other individuals cause changes on these traits. The traits of the individuals grown in the community and those grown alone are compared, and these are also compared among ancestral-descendent species.

4.3 Results

Height, width, and branch numbers of individuals and light amount captured by the individuals showed differences between the most ancestral and the most descendant species. The light amount captured by individuals increased through generations (Fig. 22). Under low mutation rates (5x10-6 - 5x10-5), the light amount captured became generally smaller when the individuals grew alone than when they grew at the presence of other individuals, which yield plastic growth of the branches to avoid competition (Figs.22, 23). Under moderate mutation rates (5x10-4 - 5x10-3), the maximum light

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amount captured when they grew at the presence of other individuals was greater than the amount captured when they grew alone, whereas the minimum light amount of the former was much smaller than the latter (Figs. 22, 23). Under high mutation rates (5x10-2 - 5x10-1), no difference was found in the light amount captured between these two growing conditions (Figs. 22, 23).

Changes in mutation rates caused differences in the temporal patterns of increase of the maximum light amount captured when the individuals grew at the presence of other individuals. Discontinuous increases of the values were found in the simulation with low mutation rates (5x10-6 - 5x10-5) (Fig. 22). Single event of the mutation yielded a saltational increase in the value, even when the same mutation event did not change the value of the individual growing alone. However, such “jump” was not found in the simulations with higher mutation rates (Fig. 22). Although

discontinuous increase was also found in the amount of light captured when the individuals grew alone, the level of the jump of the value was minor.

The organisms became lower when they grew alone than when they grew at the presence of other individuals via phenotypic plasticity (see chapter 2) (Fig.24). In the simulation with low mutation rates, width, height and branch numbers of the organisms represented discontinuous patterns of evolution. The organisms grown with other individuals become taller at the end of the simulation than those grown in the same environment at the initial stage. However, if these individuals obtained at the end of the simulation grow alone, they become rather flatter than those obtained at the initial stage

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and grown alone. These patterns were not detected or unclear in the simulations with high mutation rate (5 x 10-4 - 5x10-2). The evolutionary patterns of width of the

individuals were highly variable depending on mutation rates (Fig. 25). However, in the case of low mutation rates, overall difference in width and height between the same individuals grown in the distinctive environments (presence or absence of competitiors) became greater at the end of the simulation than at the initial condition (Fig. 25).

4.4 Discussion

Phenotypic plasticity is commonly found in nature and potentially superior to non-plastic solutions for a wide range of conditions. When individuals encounter multiple environments within their life spans, it is likely that natural selection yield that a plastic organism is adapted to more environments than a non-plastic one (Moran 1992). However, the ability of organisms to modify their phenotypes in

response to environmental conditions may reduce the efficacy of selection by disrupting the associations between phenotypes and genotypes (Ghalambor et al 2007), suggesting that plasticity may impede adaptive evolution. In contrast, phenotypic plasticity may produce an initially suboptimal adapted organism in a novel environment, but it causes survival of individuals and enables trait refinement by subsequent natural selection (Levis & Pfennig 2016; Lafuente & Beldade 2019). Thus, primarily plastic phenotype may become genetically reinforced in later stage. This plasticity first hypothesis also suggests that a large phenotypic change i.e. saltationary jump, can occur by plasticity

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with minor modification of developmental architecture via a small effect of mutation. The result of the present simulation partially supports this hypothesis.

It is likely that lower mutation rates increase the effect of plasticity. Under low mutation rates, light amount captured is greater when the individual grows with other individuals than when it grows alone. However, this difference disappears under high mutation rates. These suggest that plasticity contributes adaptive increase of the amount of light captured in this situation. Saltationary changes of the light amount captured are observed when mutation rates are low, suggesting that changes by mutation are intensified by plasticity. Temporal increase of light amount captured is found in also individuals growing alone, suggesting that adaptation through plasticity in competitive environment enhance fitness of the individuals growing without competition.

The patterns of temporal changes in morphological traits consistently support the above hypothesis. Under low mutation rates, the differences between

maximum and minimum trait values, which reflect the effect of plasticity, increase through time, and subsequently decrease. This pattern is consistently found in width and height, suggesting that effects of plasticity increase at first, but subsequently they become to be regulated genetically as a result of adaptation.

In this simulation, the individuals grown with other individuals become taller than the individuals grown alone by plasticity as a result of competition. This result is consistent with patterns generally observed in corals and sponges.

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trend as that by plasticity. Despite natural selection should operate on individuals only in the environment with competitors, it promotes divergence between the morphology of the individuals grown in competitive environments and the morphology arising when the same individuals grow alone. Thus, adaptation can create a genotype that displays divergent phenotypes through plasticity when it experiences different environments.

Branch numbers also contribute to enhance the effect of plasticity as well as width and height, but the patterns of evolution are not clear. There are

potentially complex relationships among the branch numbers and other traits as shown in chapter 2. In addition, some traits other than width, height and branch numbers should also affect light amount captured by individuals. More detailed analyses are required to clarify the relationships among traits, efficiency of obtaining resources and plasticity in this system.

Although the present model has numbers of limitations and issues of oversimplification, the observed patterns represent how plasticity is related to

adaptation, and how adaptation to novel environments is promoted by plasticity. Further studies are needed but the present findings shed new light on the issues of evolutionary novelty.

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Figure legends

Fig. 22. Results of the simulation showing temporal patterns of light amount captured by individuals. The values of individuals grown alone and maximum values of

individuals grown with other individuals are shown.

F ig. 23. Results of the simulation showing temporal patterns of light amount captured by individuals. The maximum and minimum values of individuals grown with other

individuals are shown.

F. 24. Shape of the representative individual grown with other individuals (upper) and that grown alone (lower).

F. 25. Temporal changes in height, width, and numbers of branches of the hypothetical organisms appeared in the simulation. The values of individuals grown alone and maximum and minimum values of individuals grown with other individuals are shown.

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