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[Prelude: The Meaning of Diversity, p.1]
p.7-8 most complex systems are not predictable. Owing to the interdependence of actions, complex systems can be predicted only in the very short run... are... not easily forecast even with abundant data (Orrell 2007). The particulars that emerge within complex systems are also difficult to predict... As for stability, though often robust, complex systems are also capable of producing large events, such as mass extinctions (Erwin 2006; Newman 1997) and stock market crashes. Owing to the interactions between entities, complex systems produce these large events far more often than would be predicted by "normal" that is, Gaussian fluctuations.
As a result, complexity creates problems for analysis.
p.8-10 some broad general claims do appear to hold across contexts. First, diversity often enhances the robustness of complex systems... Second, diversity drives innovation and productivity... Finally... diversity merits attention because, at least subjectively, it makes systems more interesting.
p.10-11 Many of the challenges that we presently face... involve complex systems. Each challenge involves anticipating and harnessing diverse, adaptive entities, with interdependent actions. These entities interact within contact structures or networks. Actions taken at one time and place often echo across networks of relationships. Small events can trigger large reactions... within diverse complex systems, large events can often be absorbed with minimal loss of function.
p.12 If we can understand how to leverage diversity to achieve better performance and greater robustness, we might anticipate and prevent collapses... if we hope to harness complexity , we need to identify lever points - points in time at which intervention can have large effects. To do that, we must undertake the relatively pedestrian exercises of defining the pieces and figuring out how those pieces fit together.
p.14 Understanding the relevance of diversity - especially to robustness - often requires thinking about complexity. By studying diversity and complexity together, we can start to say things about what kind of diversity, when, and under what conditions produces good outcomes (robustness) in systems with what kinds of characteristics.
p.14 A critic could argue that because complex systems differ in their particulars, we cannot expect that the functions of diversity in one complex system translate to others. My first response to that position is that we should not aim for a theory that gets the details correct in every specific case, but instead pursue the modest goal of identifying core functions of diversity - as responsiveness, as fuel, as insurance, etc. Those core insights will fan out across disciplines; they will apply within economics, ecosystems, and biological systems alike. [JLJ - perhaps even game theory]
p.15 This book asks more questions than it answers. I worry on its completion whether I've accomplished more than depositing puzzle pieces on the floor.
[Chapter 1: On Diversity and Complexity, p.16]
p.16 When scientists speak of diversity, they can mean any of three characteristics of a population. They can mean variation in some attribute... They can mean diversity of types... Or they can mean differences in configuration
p.17 complexity can be loosely thought of as interesting structures and patterns that are not easily described or predicted. Systems that produce complexity consist of diverse rule-following entities whose behaviors are interdependent. Those entities interact over a contact structure or network. In addition, the entities often adapt.
p.25 A complex system consists of diverse entities that interact in a network or contact structure... These entities' actions are interdependent... In navigating within a complex system, entities follow rules, by which I mean prescriptions for certain behaviors in particular circumstances. The rules might be fixed
p.25 Systems possessing diverse, connected, interacting and adaptive agents often prove capable of producing emergent phenomena as well as complexity... Emergence refers to higher order structures and functionalities that arise from the interactions of the entities.
p.26 Emergent properties can... be functional. Complex systems often prove robust to internal and external disturbances. This robustness emerges even though it was neither engineered from the top down nor an objective of the parts... individual pursuit of survival produces diverse interactions and behaviors that combine to form systems that can withstand mighty blows.
p.31 The fact that complexity, which is itself a complex idea, lacks a single definition should, thus, not be a surprise.
p.43 Here, then, is the takeaway: fundamental diversity is not required for complexity. Emergent diversity is.
p.44-45 Creating a complex system from scratch takes skill (or evolution). Therefore, when we see diverse complex systems in the real world, we should not assume that they've been assembled from whole cloth. Far more likely, they've been constructed bit by bit. Each step along the way, complex systems rely on their rule-based parts to adapt to changing surroundings... complex systems are assembled through selection. Only entities that function well within the system survive. This process of selection of the entities in a complex system can be thought of as a form of assembly... Assembly implies that the level of diversity in a system has survived some winnowing process.
p.46 In most complex systems, multiple factors influence the independent variable of interest.
p.49 In complex systems, (statistical) selection bias is caused by (evolutionary) selective pressures. The species that currently exist in the world have survived selective pressures.
p.52 Viruses' robustness stems from the fact that they present a moving target. We're not fighting a flu virus, we're fighting a diverse, fluctuating population of flu viruses.
[Chapter 2: Measuring Diversity, p.54]
p.55 To move beyond loose, informal characterizations of diversity requires formal measures... Counting the number of types is the most obvious way to measure diversity.
p.55-6 I make three observations about measures in general and diversity measures in particular. First, measures can be constructed from the ground up by experimenting with mathematical formulae, or they can be derived analytically from a list of desiderata... Second, diversity measures compress information... In the process... information gets lost in the translation... Finally, diversity measures can be applied to cultures, languages, makes of automobiles, ecosystems, and even toothbrushes. Each of these sets of types has distinct properties. One size can't fit all... Thus, we will need more than one measure.
p.77 The existence of multiple measures for diversity enables researchers to choose the measure that best captures the relevant diversity
[Chapter 3: The Creation and Evolution of Diversity, p.79]
p.93-94 My discussion of the evolution and creation of type diversity relies on the rugged landscape model and its offspring, the dancing landscape model. A rugged landscape is a graphical representation of a function defined over several variables in which the elevation of any type corresponds to its payoff or value. In biology, this payoff equals fitness
p.94 The rugged landscape model assumes that fitness does not change. That would be true if fitness did not depend on features of other species. In reality... interdependence means that the fitness landscape for a species will fluctuate due to adaptations by other species. I will refer to these coupled rugged landscapes as dancing landscapes. Dancing landscapes capture co-evolutionary processes.
p.94 In order to understand what causes diversity, we first need to understand what survives selection.
p.100 The first explanation for how selection can produce type diversity relies on different landscapes.
p.101 The second explanation for how selection creates type diversity relies on the existence of multiple peaks on the same rugged fitness landscape.
p.103-104 The third way in which selection can produce diversity is though coupled landscapes. Coupled landscapes capture interdependencies in payoffs... Biologists refer to coupled landscape models as co-evolutionary... In a co-evolutionary model, the species attributes evolve over time. In co-evolution, a species' fitness landscape depends on the actions, attributes, and population sizes of other species. This means that the landscapes of the interdependent species perform a coupled dance. Movements on one landscape shift the heights on other landscapes.
p.105-106 We've just seen how interdependent payoffs produce dancing landscapes using a model with only two actions. More realistic models of species adaptation... include multidimensional action spaces. Some choices of actions unilaterally improve fitness... I will refer to these as proficient adaptations... Most adaptations do not improve payoffs in all environments... The value of such an adaptation depends on the reactions of competitors.
p.106 Fitness, in an ecology (or market), depends on the actions of others. In other words, many adaptations are contextual - they produce benefits in some instances but not in others.
p.108 this example highlights a key point: complex systems that include local interactions may be more likely to support diversity.
p.110 The interim disturbance hypothesis states that diversity rises and then falls with the rate of temporal fluctuations.
p.121 Evolution tinkers (Jacob 1977). It has no intentionality, has little inherent bias in search direction, moves slowly, and has no foresight. Evolution wouldn't fail to try something because it thought it was unlikely. Nor would it try something because it anticipated that it would be useful in the future. Instead, evolution is a mindless process in which successful mutations and recombinations of genes increase their representations in the population.
p.122 evolution relentlessly plods along... Evolution locates solutions to problems that one would think would only happen in creative systems.
p.123 too much exploitation can result in stopping at a suboptimal solution. Too much exploration can prevent solutions from being implemented... This tradeoff makes for a delicate balancing act... that I should explore until it's time to exploit - seems like a compelling solution, but unfortunately it doesn't quite work when the landscapes dance. On dancing landscapes, the peaks change... Evolutionary systems also have to balance exploration and exploitation. Selection operators do exactly this.
p.124 evolution is constrained in that steps along the path to an improvement must be viable.
[Chapter 4: Constraints on Diversity, p.127]
p.145-125 In a complex organism with diverse interacting parts, sudden evolution of a new functionality seems unlikely. Darwin's solution to this problem was to distinguish between structural change, which must be continuous, from functional change, which need not be.
p.142 Evolution may... drive structural and functional characteristic to an efficient frontier... The flip side holds as well: a lack of functionality constraints produces abundant diversity.
p.143 Plasticity seems like a great idea. Species that can adapt to changing circumstances would seem to have a reproductive advantage. True enough, but adaptability comes at a cost.
p.144 the amount of plasticity depends on the extent to which exploration has limited range.
[Chapter 5: Variation in Complex Systems, p.148]
p.148 Every case of extinction of a species is a failure to provide any variations which could have been used to meet and overcome the circumstances which were leading the species downhill -H.G. Wells, Julian Huxley, and G.P. Wells, The Science of Life, 1930, p. 415
p.159 Given a rate of disturbance, there exists an optimal level of variation. Except in rare cases, the closer the level of variation is to the optimal level, the better the population will perform on average.
[Chapter 6: Diversity's Inescapable Benefits I: Averaging, p.167]
p.174 Portfolio theory was developed to show how diversification spreads risk.
p.181 diversification reduces performance variation and therefore contributes to robustness.
p.182 In a complex system... regardless of what the factors are, diverse systems should perform better because of the effect of averaging across all the factors.
[Chapter 7: Diversity's Inescapable Benefits II: Diminishing Returns to Types, p.183]
p.183 When diminishing returns to type are present, diverse collections do best... Diminishing returns to type exist if the contribution to some performance measure such as efficiency, robustness, or accuracy decreases with the amount of type. This... means that output rises at a diminishing rate. Diminishing returns are a widespread phenomenon in economics and ecosystems. [JLJ - perhaps also in complex games of strategy]
p.194 The results from this section do not imply that when confronted with a novel situation we should always choose a diverse collection. If we have enough information to know what drives performance, then we should select the best collection on the basis of that information. If not, and if we only get one try, then we should probably choose a diverse collection. This does not mean that diversity is always better, only that if we are not sure of what we're doing, we should err toward greater diversity.
[Chapter 8: Diversity's Impact in Complex Systems, p.196]
p.196 In this chapter, I describe the myriad ways in which diversity impacts complex systems when interactions are present.
p.200 Empirical evidence suggests that learning rates tend to decrease over time... It has everything to do with the fact that the easy improvements are found first and that, over time, improving becomes more difficult.
p.210 a key lesson: more diversity implies greater responsiveness.
p.211 The law of requisite variety provides an insight into well-functioning complex systems. The diversity of potential responses must be sufficient to handle the diversity of disturbances. If disturbances become more diverse, then so must the possible responses. If not, the system won't hold together.
p.230 In systems with capacity constraints a tradeoff arises between redundancy and diversity. Greater diversity entails more responsiveness... but increases the odds that the failure of any one entity could cause the system to collapse. Greater redundancy implies less ability to respond to new disturbances but a greater ability to withstand the loss of any one entity in the system... In systems that are not so constrained by capacity, the field tilts in the direction of greater diversity.
[Chapter 9: Parting Thoughts, p.249]
p.251 leveraging diversity requires an understanding of assembly.
p.253 an undeniable fact: the physical, ecological, economic, political, and social systems that we inhabit and interact with and within are complex and diverse.
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