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Abstract:
Organisms on the earth have evolved into increasingly larger and more complex organ-
isations, reflecting a series of major evolutionary transitions. Here, I focus on the major
evolutionary transition from unicellular ancestors to multicellular organisms. Organisms
can have different life cycles in terms of cell numbers and composition during devel-
opment. The selection outcome is different when an organism undergoes different life
cycles. The rule of “survival of the fittest” from Darwin determines which life cycle sur-
vives. Organism competition relies on individuals’ fitness, which depends on the traits
of life cycles they undergo. Organisms mostly experience cell differentiation and include
different cell types. The transformation from phenotypically homogeneous organisms
into heterogeneous ones leads to the change in individuals’ fitness. Considering cellular
interactions among different cell types in an organism, the question then arises: what are
the effects of phenotypical heterogeneity for an organism?
In experiments, it is hard to investigate the way that cells interact and the effects
that cellular interactions yield in phenotypically heterogeneous organisms. Essentially,
these biological problems can be transformed into mathematical ones. We can address
these problems by mathematically modelling the interactive effects of individual cells on
the competitiveness of organisms. This idea leads to the thesis proposal of mathematical
models of life cycle competition in heterogeneous organisms. Here, I specifically pay attention to phenotypically heterogeneous organisms, because they could include diverse
cellular interaction forms. The mathematical models adopted in this thesis can depict the
underlying cell interacting forms and describe their effects quantitatively. Specifically,
I demonstrate the work in three chapters including the emergence of multicellular life
cycles, irreversible somatic differentiation and the evolution of reproductive strategies.
Firstly, since cellular interactions could be beneficial or adverse for organisms, we
ask which interaction form promotes the evolution of multicellularity? To answer this
question, I present a mathematical model considering stage-structured populations. Populations have different but unique reproductive strategies. I capture the effects of cellular interactions via evolutionary game theory by a payoff matrix. This payoff matrix determines population growth rates, which further determine the performance of popula-
tions. By comparing the growth rates between populations with unicellular organisms
and populations with multicellular organisms, I found the three most important char-
acteristics determining the emergence of multicellularity: the average performance of
phenotypically homogeneous groups, heterogeneous groups, and solitary cells.
Secondly, cellular interactions can lead to cell differentiation, resulting in multiple
cell phenotypes in organisms. Essentially, there are only two types in terms of reproduc-
tion: germ cells (for fertility) and somatic cells (for viability). Here, somatic cells perform
extreme altruistic behaviour in terms of viability and lose their fertility entirely. I refer to this extreme altruistic behaviour as irreversible somatic differentiation (ISD). To understand the evolution of ISD, I simulate the stochastic development of organisms, which includes the one for ISD. Considering different conditions in organism development, I seek stochastic development that has evolutionary growth advantages for ISD. Our results show that ISD emerges under the conditions of both somatic cells’ benefits and cell differentiation costs in larger multicellular organisms.
The forms of frequency-dependent cellular interactions are used in the first two
models. However, cellular interactions are frequently observed in a threshold form in
nature. These threshold effects depend on the minimum number of a certain cell type in
an organism. Thus, I extend the cellular interaction form from frequency-dependent to
threshold-dependent. An organism grows faster if the cells of a cell type meet a given
threshold. Meanwhile, the organism size effects have also been incorporated, which are
assumed as being neutral in the first model. Our results show that distinct reproductive
strategies could perform uniquely or equally best for populations under the effects of
sizes and thresholds. Among the unique optimal reproductive strategies, only binary-
splitting ones can be optimal.
In summary, I build mathematical models to address the biological problems of cellular interaction effects on multicellular organisms. The problems include the emergence of multicellular life cycles, irreversible somatic differentiation and the evolution of re-
productive strategies. The cellular interactions and organism size both determine the
growth rate of a population. The population growth rates are calculated by the character-
istic equations of different structured-population models. Besides, to build the stochastic trajectories for the development of multicellularity, stochastic sampling (Monte Carlo) methods are used to capture the potential cellular interaction forms.
