I develop mathematical, computational, and conceptual models to study complex phenotypes.
Earlier in my career, I focused on how evolutionary and genetic processes shape reproductive and behavioral traits. It was necessary at that time to treat as a black box many of the genetical and physiological details that determine phenotypes, and to focus in a general way on how natural selection influences phenotypes over very broad assumptions about underlying mechanisms. Some examples can be found in my summary below on past research.
My research has changed in the past few years, following the great changes in modern biology. It is now possible to see below the surface of complex phenotypes to the biochemical and genetical mechanisms that control those characters. I have continued to focus on complex phenotypes as I did earlier in my career, but now with particular emphasis on how the quantitative dynamics of genetical, biochemical, and cellular mechanisms determine those phenotypes, and how evolutionary processes in turn shape the mechanisms and dynamics that give rise to phenotypes.
Virulence and mechanisms of pathogenesis
The problem of parasite virulence has developed into a major topic in evolutionary biology and infectious disease studies. There are two reasons for this. First, it is important to understand why parasites vary so much in the degree of harm they cause their host. Second, the concepts needed to analyze the evolution of virulence arise from fundamental aspects of sociality and life history. On the social side, parasites compete within hosts for limited resources. Outcompeting neighbors provides a benefit, but intensive competition may degrade the resource. In this case, degrading the resource means harming the host. On the life history side, harm to the host affects the parasites’ survival, altering the parasites’ balance between reproduction, measured as transmission to new hosts, and longevity, measured as how long the parasite survives before the host dies or before being cleared from the host. My 1996 review Models of parasite virulence brought together the problem of parasite virulence and the fundamental aspects of microbial sociality and life history (43).
Those theories of virulence arise from a basic understanding of evolutionary process. But the connection between abstract theories and how parasites actually make hosts sick remained vague until recently. Over the past few years, much has been learned about the biochemical mechanisms by which pathogens manipulate host tissues and host immunity. Those biochemical mechanisms of pathogenesis mediate most aspects of virulence. So the challenge becomes much richer. How do the general evolutionary processes shape the biochemical mechanisms of pathogenesis, which in turn play the direct mechanistic role in virulence? We do not know the answer, but this sort of connection between evolutionary concept and biochemical mechanism is the exciting prospect of modern biology.
We analyzed the relation between mechanism and evolutionary process in two preliminary papers. Our overview predicts how evolutionary process will shape the timing of expression of various pathogenic mechanisms in relation to the amount of harm those mechanisms cause to the host (111). We also apply this line of thought to one of the unsolved mysteries of infectious disease: why can some pathogens start an infection with a very low dose (number of cells or particles in the inoculum), whereas other pathogens require a high dose to start an infection (104)?
We predict that pathogens requiring only a low dose depend primarily on pathogenic mechanisms that act locally during invasion. For example, direct injection of molecules into neighboring host cells manipulates aspects of host physiology and immunity. This sort of local action requires only a few pathogens to alter host physiology. By contrast, we predict that pathogens requiring a high dose depend on pathogenic mechanisms that act at a distance. For example, secreted molecules must build up to sufficient concentration over long distances in order to manipulate the host immune response. Such manipulation may arise by altering host cytokine signaling or similar immune regulatory processes. Distant action typically requires larger pathogen populations during invasion to build up the concentration of a diffusible secretion. In general, the problem of relating biochemical mechanisms of pathogenesis to the population biology and evolution of infectious disease will be an important topic going forward.
Microbial life history and sociality
The theory of virulence is an example of the broader problems of sociality and life history. The application of sociality and life history concepts to microbes has grown rapidly in the past few years. For example, many bacteria secrete molecules to take up iron, which is often a limiting resource for growth. Similarly, many pathogens secrete molecules to manipulate host immunity or to create biofilms.
The secretions by an individual microbe typically act externally and benefit all members of the local group. Secreting imposes a cost in terms of growth, so cheaters that do not secrete gain by sharing the benefits without paying the costs. Microbial cheaters have been observed in several experimental and natural settings. Given that cheaters grow faster than secretors when in direct competition, what maintains the widely observed patterns of secretion?
Recent theory has emphasized the genetic structure of populations, in which secretors tend to associate spatially with other secretors, reducing direct competition and allowing highly secreting groups to share mutual benefits. Such kin selection can be a powerful force favoring cooperative traits. In my recent papers (116,117,119), I argue that, although kin selection is a factor, demographic processes often dominate in determining the relative fitness of secretors versus cheaters when measured over the full cycle of microbial life history. Key demographic factors include the local density of microbes at which secretion significantly alters the environment, the extent to which secretion enhances microbial growth and maximum local density, and the ways in which secretion alters colony survival and dispersal. I also show that, in long-lived colonies, competition of progenitors with their descendant mutants significantly alters evolutionary dynamics and degrades the level of cooperative secretion favored by natural selection.
This subject provides an opportunity to connect the fundamental concepts of sociality and demography that I helped to develop in my book, Foundations of Social Evolution, with many interesting and important microbial traits such as virulence (111) and metabolism (118). Because microbes can often be studied experimentally in controlled settings, there is much opportunity for testing theories and refining the way in which we understand microbial ecology, evolution, and virulence.
Epidemiology and evolution of infectious disease
The integration of mechanistic and evolutionary analyses is the theme of my book, Immunology and Evolution of Infectious Disease, and of my various recent studies on host-parasite interactions. At this point, I have finished much of the conceptual background and the first stages of quantitative modeling. I recently took the next step in this work through collaborations with an experimental laboratory that studies antigenic variation, using the mathematical and computational models to design experiments (103). The long-term goal is to understand how various mechanistic components determine complex aspects of host immunity and parasite escape, and how evolutionary processes have shaped the underlying mechanisms. We are also studying fundamental models to understand why some pathogens, such as influenza, vary so much, whereas other pathogens, such as the measles virus, vary so little (105).
Cancer, age-specific disease, and somatic genomics
Cancer might be described as an evolutionary process within individuals that changes the normal regulatory interactions governing cellular birth and death rates. This is a fascinating problem for an evolutionary biologist, because one must understand the short-term evolutionary processes within individuals that disrupt normal regulation, and the long-term evolutionary processes that have shaped the normal network of regulatory controls on cellular dynamics.
The great progress of modern biology at the genetical, biochemical, and cellular levels of cancer provides an opportunity to link mechanistic models of complex phenotypes to the evolutionary processes that shape mechanisms. My early work on cancer focused on epidemiological data, linking mechanistic, quantitative models of progression within individuals to rates of incidence in populations (93,96,98). In my recent book, Dynamics of Cancer: Incidence, Inheritance, and Evolution, I start with incidence rates in populations and then develop a deeper understanding of mechanistic details, quantitative models of phenotypes (cellular regulation and cancer progression), and evolutionary processes.
Recently, my interests in cancer have turned to two related topics. First, somatic mutation must be common in all individuals, because a human body contains approximately 10^13 to 10^14 cells, all descended from a single-celled zygote. To understand the relation between the number of somatic mutations that occur and the number of cells that carry a mutation, we must think of the body in relation to the lineage history descending from the single ancestral zygote and how mutations accumulate in that lineage history. This view of somatic evolutionary genomics led us to propose that a significant fraction of adult onset cancers may arise from somatic mutations early in development (86). New high-throughput genomic technologies are just opening up the possibility of directly measuring somatic variability and evolution (115). This new work will be one of the great biomedical topics in the coming years. I remain interested in placing the new data within the essential context of cell lineage history.
The second topic arises from thinking about cancer as the disruption of the normal checks and balances in the regulatory control of cells and tissues. This view leads to the more general problem of...
Robustness and regulatory networks
Our cells and tissues have multiple repair mechanisms and checks and balances on growth. Those multiple mechanisms buffer against most mutations and physiological disruptions, leading to a form of robustness against perturbation. Cancer arises only after the final protective mechanism fails. This sort of robustness leads to an evolutionary paradox.
Each additional protective mechanism reduces the impact of any single hereditary mutation and therefore allows the accumulation of more mutations in the population. The additional mutations allowed by robust buffering lead to significant mutational decay in the protection provided by each buffering component. In general, a robustness mechanism decreases the sensitivity of a character to perturbation and therefore reduces the intensity of natural selection on that character. Reduced selective pressure on the character may often favor a less costly, lower performance trait (108).
The paradox of robustness arises from evolutionary dynamics: enhanced robustness causes an evolutionary reduction in the adaptive performance of a character, leading to a degree of maladaptation compared to what could be achieved by natural selection in the absence of robustness mechanisms. Over evolutionary time, buffering traits may become layered on top of each other, while the underlying adaptive traits become replaced by cheaper, lower performance components.
I have established the basic logic of the paradox of robustness (108), and applied the idea in a simple model of cancer and the heritability of DNA repair defects (94). I believe the basic idea is quite general and has widespread implications for understanding organismal design. However, I am still searching for a clear way to connect this general concept of evolutionary dynamics to the empirical facts of evolutionary history.
Information, probability, and the common patterns of nature
The patterns of natural history tend to follow a few common probability distributions or their relatives: normal, gamma, power law, and so on. Within ecology and evolution, there is a long and developing line of neutral theory to explain the commonness of these patterns. The neutral theories show how small-scale random processes of mutation, birth, and death can, in the aggregate, lead to the observed distributions. These neutral theories do often come close to matching observations. The question is why. Are the small-scale processes of mutation, birth, and death truly neutral and purely random? Or, are there other reasons why the observed aggregate patterns follow these apparently neutral distributions, in spite of non-neutral processes acting at smaller scales? These questions touch directly on how we understand the patterns of nature.
I used the well developed concepts of entropy and information theory to discuss why the commonly observed aggregate distributions are in fact so common (114). We know from the central limit theorem that the summing up of many small-scale processes, each non-normal in distribution, leads nonetheless to the normal distribution at the aggregate, or summed, level of measurement. In effect, the non-normal fluctuations at the small scale cancel in the aggregate, leaving as the only signal, or information, the standard normal pattern. The same sort of canceling of non-neutral fluctuations at the small scale likely happens in many cases in which we measure at the aggregate level, for example, of nucleotide substitutions, species numbers in communities, number of ecological connections between species, and so on.
In my first contribution, I presented a broad synthesis of these concepts from other disciplines (114). I presented the ideas in a way that may help in applying the theory to biological problems and to understanding the role of neutral theories in ecology and evolution. Within that first synthesis, I also began to identify some of the weaknesses in the conceptual structure as it currently exists in physics and information theory.
I am now pursuing those weaknesses. In particular, we recently developed a new approach to measurement, information, and probability (121). An important component of the variation in observed pattern arises directly from the fundamental way in which measurement changes at different scales. As one brief example, measurements are often linear at small magnitudes but grade into relative or logarithmic scaling at large magnitudes. Such linear-logarithmic scaling leads naturally to normal distributions at small scales, power law distributions at large scales, and Student's distributions at intermediate scales.
More generally, there appears to be a simple way to relate the scaling of measurement to the common patterns of nature. We have used the relation between measurement scale and probability to provide a classification of common probability distributions (123). Our classification emphasizes that simple aspects of measurement and aggregation determine the form of the common probability distributions and their relations to each other. This understanding of the natural history of pattern provides an essential background to nearly all scientific studies. One must know the natural contours of pattern set by measurement and aggregation in order to analyze how particular processes cause deviations from those natural contours. I have illustrated the way in which measurement sets expected pattern by analyzing the simple biological example of species abundance distributions (122).
Through much of my career, I have been interested in coevolutionary interactions that lead to conflict or cooperation. These interactions occur at many different levels of biological organization: between members of the same population (social behavior), between different genetic elements within a genome, and between host and pathogen populations. This broad view led me to study coevolutionary interactions in a variety of systems.
Sex allocation and sociality
I have studied sex allocation, which is the division of resources to sons and daughters, or, more generally, to male and female reproductive function. Sex allocation has played an important role in the study of social behavior because (a) many aspects of reproductive competition affect the relative value of sons and daughters, for example, sexual selection or conflict among genetic relatives; (b) the methods required for analyzing sex allocation problems apply to several questions in adaptation, for example, frequency dependent selection or genetic constraints such as sex chromosomes; and most importantly, (c) numbers of males and females and investment in each are relatively easily measured traits. Perspectives on adaptation and social evolution can therefore be tested by studying sex allocation. My book Foundations of Social Evolution summarizes much of this work.
I have worked on theories of genomic conflict. Different parts of the genome are transmitted in different ways, and therefore may have conflicting reproductive interests. For example, mitochondria are transmitted mostly from mother to daughter, whereas autosomes are passed equally to both sons and daughters. Mitochondria and other matrilineal elements therefore favor a female-biased sex ratio, whereas autosomes tend to favor an equal sex ratio. Conflicting modes of genetic transmission cause many interesting traits, such as cytoplasmic male sterility in plants, sex ratio biasing bacterial and viral symbionts, and high frequencies of transposable genetic elements. Many aspects of genomic organization and patterns of genetic variation can only be understood in the context of genomic conflict.
I have developed theoretical models to analyze the coevolutionary genetics of hosts and parasites. Populations often contain high levels of genetic polymorphism for resistance to pathogens. The effectiveness of this resistance is limited because the pathogens are, in turn, widely polymorphic for host-range genes that can escape host resistance. In addition to the variability found within populations, the frequency of particular host and parasite genes may vary widely over small geographic areas (metapopulation dynamics).
Virulence, symbiosis, and sociality
The host-parasite work emphasizes evolutionary dynamics on the conflict side of my interest in conflict and cooperation. I have also studied the evolution of mutual harm or benefit in symbiosis. For example, the more a parasite harms its host (virulence) the more it damages its food supply. But the costs of virulence may be offset by increased competitive success against other parasites within the host or by greater transmission to other hosts. This problem of virulence can be generalized by considering parasite and host genes as replicators that live within a shared compartment (body). The different replicators have a shared interest in using the body's resources prudently, but also conflict over the distribution of resources. This general view of symbiosis applies to the evolution of protocells and genetic systems near the origin of life, to genomic conflict, to the evolution of ecological mutualisms, and to the evolution of group living and social behavior.
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