In the last posts, we described how evolutionary biologists theorized about modularity, a process in which a system of traits goes through parcellation and/or integration in order to become an integrated set of co-evolving traits. Modularity is an interesting solution to the problem of integrated systems, because it allows on trait to undergo evolutionary change, whilst the rest of the system is kept stable.

Modularity is hypothesized to be the result of many different processes, which can be mutually exclusive or not. Some of those processes are genetic in nature: it has been theorized ¹ that the equilibrium between pleiotropic effects (i.e., a single gene has a phenotypic effect on more than one trait) and epistasis (i.e., more than one gene have phenotypic effects on a single trait) can lead to modularization. Other processes are microevolutionary: the same author theorized that, in order for the modules to be “stable”, a combination between directional selection (natural selection for values of a trait that are either greater or smaller than the ancestral state) and stabilizing selection (selection against phenotypes which deviate in any directions from the optimal value of a trait) is necessary, with directional selection establishing the modularity, and stabilizing selection maintaining it in posterior generations. Yet another mechanism of modularity (which, again, does not exclude the other mechanisms) is developmental ². If a system is “undecomposable”, in the sense that the whole system is necessary for its functioning (for example, the visual system, which necessitates, in mammals, of the local circuits of the retina as well as posterior processing areas, such as the lateral geniculate nucleus and the visual cortex), this is a good indicator that the development of each trait that typifies the system is integrated. This kind of developmental modularity is what interests us here ³.
A good deal of morphological evolution (in our case, the evolution of brain morphology, such as the size of individual regions, or the types of cells which are found in it) can be described in terms of the alterations in the form of one or more individual elements. A (non-neural) good example is the shape of the wings of bats, which can be explained by the elongation of the phalanges ⁴. Almost all of those changes can be expressed mathematically as an alteration in growth duration or rate of a given dimension or body part in relation to others; those differential rates of growth for different measures of an organism are called allometric growth ⁵. Although allometric growth is sometimes alluded as an alternative explanation to adaptation (that is, as evidence that a given trait did not evolve as an adaptation for something, but simply as a consequence of the growth rules which govern the taxon in which the species is inserted), many allometric relationships are in fact adaptive; this is especially important in structures whose function is dependent on surface area, such as the intestine, or which are constrained by space, such as the brain.
Two allometrically related traits will have a genetic correlation if the genotypes vary in terms of form or in the age at which growth stops in a uniform growth curve. Evolutionary changes in the time it takes for a trait to be fully developed in a given organism are called heterochronies ⁶, and they can happen in various ways ⁷. To better understand this, we will borrow an example from Futuyma’s Evolutionary Biology.
Suppose that an ancestral species has a given trait with size y, and its body size has size x. This trait begins development at post-conception age a, and development stops at an age b. During this time interval, y and x grow at rates ky and kx, respectively. If the period of development for trait y is extended by a quantity Δb during evolution, its size at maturity will increase. The trait in the descendent species (that is, the species in which the trait now develops for more time) will have the same shape (expressed by a ratio y/x) that his ancestor had if the allometric coefficient a (a constant which describes the linear relationship between y and x) equals 1, but will have a different shape (y is bigger than x) if a > 1. The term hypermorphosis is used to describe the process through which development is extended during evolution, and peramorphosis is the morphological consequence (the exaggerated shape of the descendent in relation to its ancestor) ⁷. If, however, development is “truncated” during evolution by precocious maturation (that is, development ends at age b – Δb), the adult form of the descendent will be smaller and trait y will be less developed. This process is called progenesis, and its morphological expression is called pedomorphosis ⁷.
Peramorphosis and pedomorphosis can be generated by yet another process. Remember that we postulated that there are two points in time which are critical for heterochronic evolutionary changes: a point b, the age at which development stops; and a point a, the age at which development begins. It is predicted that, if the start point a of development for trait y is dislodged by a quantity Δa (post-dislodging), pedomorphosis ensues, and the trait y will be less developed, while pre-dislodging (development begins at age a – Δa) will result in peramorphosis. However – and this is the point which is most interesting for the late-equals-large rule –, if both the start point a and the end point b are post-dislodged – that is, if a quantity of time Δa is added to both the beginning and the end of development, conserving the amount of time it takes for a trait to develop, but not the point in time in which development begins – the reverse ensues, with peramorphosis happening. This is an extremely important consequence, because the late-equals large postulates that, during the evolution of brain region sizes in mammals, that is exactly what happened.

On the blogosphere:
The evolution of modularity, in my Principles of Neurobiotaxis

GP (1996). Homologues, natural kinds and the evolution of modularity. American Zoologist 36: 36-43. SJ, Lewontin RC (1979). The spandrels of San Marco and the Panglossian paradigm: A critique of the adaptationist programme. Proceedings of the Royal Society of London B 205: 581-598. C, Puelles L (2001). Modularity in vertebrate brain development and evolution. BioEssays 23: 1100-1111. KE, Behringer RR, Rasweiler JJ IV, Niswander LA (2006). Development of bat flight: Morphologic and molecular evolution of bat wing digits. PNAS 103: 6581–6586.

⁵ Gould SJ (1966). Allometry and size in ontogeny and phylogeny. Biological Reviews 41? 587-680. http://

⁶ Gould SJ (1977). Ontogeny and Phylogeny. Cambridge, MA: Harvard University Press.

⁷ Alberch P, Gould SJ, Oster GF, Wake DB (1979). Size and shape in ontogeny and phylogeny. Paleobiology 5: 296-317.