In this article, we present a self-contained review of recent work on complex biological systems which exhibit no characteristic scale. This property can manifest itself with fractals (spatial scale invariance), flicker noise or 1/f-noise where f denotes the frequency of a signal (temporal scale invariance) and power laws (scale invariance in the size and duration of events in the dynamics of the system). A hypothesis recently put forward to explain these scale-free phenomomena is criticality, a notion introduced by physicists while studying phase transitions in materials, where systems spontaneously arrange themselves in an unstable manner similar, for instance, to a row of dominoes. Here, we review in a critical manner work which investigates to what extent this idea can be generalized to biology. More precisely, we start with a brief introduction to the concepts of absence of characteristic scale (power-law distributions, fractals and 1/f- noise) and of critical phenomena. We then review typical mathematical models exhibiting such properties: edge of chaos, cellular automata and self-organized critical models. These notions are then brought together to see to what extent they can account for the scale invariance observed in ecology, evolution of species, type III epidemics and some aspects of the central nervous system. This article also discusses how the notion of scale invariance can give important insights into the workings of biological systems.

Insect societies – colonies of ants, bees, wasps and termites – vary enormously in their social complexity. Social complexity is a broadly used term that encompasses many individual and colony-level traits and characteristics such as colony size, polymorphism and foraging strategy. A number of earlier studies have considered the relationships among various correlates of social complexity in insect societies; in this review, we build upon those studies by proposing additional correlates and show how all correlates can be integrated in a common explanatory framework. The various correlates are divided among four broad categories (sections). Under ‘polyphenism’ we consider the differences among individuals, in particular focusing upon ‘caste’ and specialization of individuals. This is followed by a section on ‘totipotency’ in which we consider the autonomy and subjugation of individuals. Under this heading we consider various aspects such as intracolony conflict, worker reproductive potential and physiological or morphological restrictions which limit individuals’ capacities to perform a range of tasks or functions. A section entitled ‘organization of work’ considers a variety of aspects, e.g. the ability to tackle group, team or partitioned tasks, foraging strategies and colony reliability and efficiency. A final section, ‘communication and functional integration’, considers how individual activity is coordinated to produce an integrated and adaptive colony. Within each section we use illustrative examples drawn from the social insect literature (mostly from ants, for which there is the best data) to illustrate concepts or trends and make a number of predictions concerning how a particular trait is expected to correlate with other aspects of social complexity. Within each section we also expand the scope of the arguments to consider these relationships in a much broader sense of ‘sociality’ by drawing parallels with other ‘social’ entities such as multicellular individuals, which can be understood as ‘societies’ of cells. The aim is to draw out any parallels and common causal relationships among the correlates. Two themes run through the study. The first is the role of colony size as an important factor affecting social complexity. The second is the complexity of individual workers in relation to the complexity of the colony. Consequently, this is an ideal opportunity to test a previously proposed hypothesis that ‘individuals of highly social ant species are less complex than individuals from simple ant species’ in light of numerous social correlates. Our findings support this hypothesis. In summary, we conclude that, in general, complex societies are characterized by large colony size, worker polymorphism, strong behavioural specialization and loss of totipotency in its workers, low individual complexity, decentralized colony control and high system redundancy, low individual competence, a high degree of worker cooperation when tackling tasks, group foraging strategies, high tempo, multi-chambered tailor-made nests, high functional integration, relatively greater use of cues and modulatory signals to coordinate individuals and heterogeneous patterns of worker-worker interaction.

The human AIDS viruses – HIV-1 and HIV-2 – impose major burdens on the health and economic status of many developing countries. Surveys of other animal species have revealed that related viruses – the SIVs – are widespread in a large number of African simian primates where they do not appear to cause disease. Phylogenetic analyses indicate that these SIVs are the reservoirs for the human viruses, with SIVsm from the sooty mangabey monkey the most likely source of HIV-2, and SIVcpz from the common chimpanzee the progenitor population for HIV-1. Although it is clear that AIDS has a zoonotic origin, it is less certain when HIV-1 and HIV-2 first entered human populations and whether cross-species viral transmission is common among primates. Within infected individuals the process of HIV evolution takes the form of an arms race, with the virus continually fixing mutations by natural selection which allow it to escape from host immune responses. The arms race is less intense in SIV-infected monkeys, where a weaker immune response generates less selective pressure on the virus. Such a difference in virus-host interaction, along with a broadening of co-receptor usage such that HIV strains are able to infect cells with both CCR5 and CXCR4 chemokine receptors, may explain the increased virulence of HIV in humans compared to SIV in other primates.

Scientists observe nature, search for generalizations, and provide explanations for why the world is as it is. Generalizations are of two kinds. The first are descriptive and inductive, such as Boyle's Law. They are derived from observations and therefore refer to observables (in this case, pressure and volume). The second are often imaginative and form the axioms of a deductive theory, such as Newton's Laws of Motion. They often refer to unobservables (e.g. inertia and gravitation). Biology has many inductive generalizations (e.g. Bergmann's Rule and ‘all cells arise from preexisting cells’) but few, if any, recognized universal laws and virtually no deductive theory. Many biologists and philosophers of biology have agreed that predictive theory is inappropriate in biology, which is said to be more complex than physics, and that one can have nonpredictive explanations, such as the neo-Darwinian Theory of Evolution by Natural Selection. Other philosophers dismiss nonpredictive, explanatory theories, including evolutionary ‘theory’, as metaphysics. Most biologists do not think of themselves as philosophers or give much thought to the philosophical basis of their research. Nevertheless, their philosophy shows in the way they do research. The plethora of ad hoc (i.e. not universal) hypotheses indicates that biologists are reluctant inductivists in that the search for generalization does not have a high priority. Biologists test their hypotheses by verification. Theoretical physicists, in contrast, are deductive unifiers and test their explanatory hypotheses by falsification.

I argue that theoretical biology (concerned with unobservables, such as fitness and natural selection) is not scientific because it lacks universal laws and predictive theory. In order to make this argument, I review the differences between verificationism and falsificationism, induction and deduction, and descriptive and explanatory laws. I show how these differ with a specific example of a successful and still useful (even if now superseded as explanatory) deductive theory, Newton's Theory of Motion. I also review some of the philosophical views expressed on these topics because philosophers seem to be even more divided than biologists, which is not at all helpful.

The fact that biology does not have predictive theories does not constitute irrefutable evidence that it cannot have them. The only way to falsify this philosophical hypothesis, however, is to produce a predictive theory with universal biological laws. I have proposed such a theory, but it has been presented piecemeal. At the end of this paper, I bring the pieces together into a deductive theory on the evolution of life history traits (e.g. clutch size, mating relationships, sexual size dimorphism).