Gary K. Greer, Associate Professor, Biology Department, Grand Valley State University
It is a long-standing tradition to begin an essay, particularly one regarding a scientific topic, with a quote – relevant by inference - from philosophy, literature, the arts, or Yogi Berra, that confers a courtier-like intellectual status or (as in my case) the veneer of it to the author. Far be it from me to break with the wisdom of Tevye the milkman (and fiddler with a penchant for roofs).
“Observe due measure, for right timing is in all things the most important factor.” - Hesiod
To my knowledge all ant species have castes, anatomically differing individuals that serve different roles in the colony. Some are workers that tend the queen and her eggs and larvae, others maintain the integrity of the nest or collect food, and there are soldiers that defend the nest. Anatomical differences among castes may be subtle or drastic, but, they are almost invariantly associated with their relative sizes. For example, soldiers are typically much larger than other castes and possess larger head-to-body and “skull”-to-jaw ratios (Figure 1). They are more than simply larger versions of the smaller castes, they are designed to deliver a bite that is a multiple of their increased size. Similarly, the depth of the skull of the great Cretaceous predator Tyranosaurus rex increased as it developed from a rather tiny hatchling to a nearly seven ton adult (Figure 2), a change that facilitated the development of large jaw muscles and a truly monstrous bite force (almost 13,000 pounds or 3.5 times that of an Australian crocodile 1). Ouch!
Figure 1. Pogonomyrmex badius, the Florida harvester ant by Alexander Wild; email@example.com.
Figure 2. Change in skull morphology in Tyranosaurus rex from juvenile (left) to adult (right); not at same scale. Permission via Palaeos.com.
Allometry is the study of size-dependent changes in form (allo- “different” and metry – “measurement”) such as those described above. Three terms relating to allometry are very useful. A trait that increases at the same tempo as total body size is said to be isometric (i.e., “same measurement”). Head size in most worker ants grows at the same pace as the entire body, resulting in an isometric head-to-body ratio throughout life. In contrast, a trait that increases faster than total body size is said to be positively allometric. Head size in soldier ants is such a trait. Conversely, traits that increase at a slower rate than the overall size of an organism are said to be negatively allometric. A head-to-body example of negative allometry can be observed in humans, wherein our heads grow at a slower rate than our bodies as we mature from infant to adult (Figure 3). Most animals and plants possess a number of traits that are allometric, some of which may be positively allometric while others negatively so in the same organism. My aim in this essay is to provide a few examples of the considerable insights in ecology, evolution, and medicine that can be gained from the study of allometry.
Figure 3. Change in head-to-body ratio in humans from birth to reproductive maturity; with permission from the Journal of Vertebrate Paleontology.
Let me show you a few examples of allometry that provide important ecological insight, beginning with changes in the body of the flying squid (Todarodes pacificus; aka Japanese common squid). The flying squid’s body width is negatively allometric resulting in a change from a rounded juvenile form to a streamlined adult form2 (Figure 4). Conversely, the length and width of the fins on the mantle are positively allometric, creating proportionally increasing steering planes that optimize the squid’s ability to swim backwards with great speed and even take flight – up to 100 feet. These body and fin changes are also associated with a switch in prey from primarily crustaceans (e.g., shrimp) to fish, minimizing competition for food among juvenile and adult flying squid 2.
Figure 4. Flying squid. Photo by Graham Ekins; permission via Flickr-The Commons.com. Idealized juvenile and adult body dimensions superimposed; L = length, W = width.
The allometry of a trait may be fairly rigid as is the case for flying squid body and fin dimensions, however, the allometry of other traits is sensitive to the environment, shifting to optimize survival and reproduction. This flexibility is technically known as adaptive (trait) plasticity. The early life of tadpoles provides a prime example that can be observed here in Michigan or easily replicated using experimental aquaria. Tadpoles that develop in ponds with high densities of diving beetle larvae possess high-profile tails conferring greater strength for escaping the clutches of these strong ambush predators. In contrast, tadpoles that develop in the presence of bluegills possess sleek, low-profile tails that confer the speed needed to escape these pursuit predators (Figure 5)3.
Figure 5. Tadpole tail depth in response to the presence of diving beetle larvae and bluegills. Photo from Benard 2006.
Plants are the masters of adaptive plasticity because allometry and plasticity are aspects of developmental processes and plants are composed of repeating shoot (stem + leaf) and root modules, each being born, developing and dying semi-autonomously. The primary appendage of a plant is the leaf and many plant species exhibit changes in the size and shape of their leaves as the plant gets larger. For example, tree ferns and white oaks produce increasingly large leaves as the tree increases in size with the obvious benefit of increased light capture. The successively larger leaves also become increasingly complex (i.e., lobed or dissected) such that the leaflets eventually have their own (sub)-leaflets which themselves become increasingly dissected (both positively allometric; Figure 6).
Figure 6. The twenty inch-long frond of a juvenile tree fern (top) and the eight foot-long frond of the tree-fern Cyathea aborea. Photos by G. Greer.
Similarly, the lobes of white oak leaves become deeper as one travels from base to uppermost-tip of the tree’s canopy (another positive allometry). The higher a leaf is located on a tree, the greater its distance from source of water (the soil) and the greater its exposure to heat and wind, which strip it of its water. The leaves at the top of an oak tree are the first to lose their water supply when the soil becomes dry and simultaneously the most vulnerable to water loss. The deep lobbing of these leaves minimizes the distance from a water-conducting vein (xylem) to water-demanding photosynthetic tissues and also minimizes the distance between these heat absorbing tissues and the leaf edge where heat is released4. Similar advantages are associated with plants that are partially submerged (e.g., Ranunculus aquatilis), where leaves that develop underwater will be deeply dissected, facilitating gas exchange, particularly absorption of carbon dioxide4. Leaves that develop above water will be fully “webbed” where carbon dioxide is easily acquired (Figure 7).
Figure 7. Illustration of Ranunculus aquatilis L., excerpted from Watson, L., and Dallwitz, M.J. 1992. The families of flowering plants: descriptions, illustrations, identification, and information retrieval. Version: 22nd July 2014. http://delta-intkey.com’.
The study of allometry also reveals key differences in major groups of organisms – in this case plants - and hence key differences in their ecological roles in the world today. A minimum size is required for reproduction, particularly among perennials. Investment into reproduction above this size-minimum is positively allometric and often adaptively plastic. For example, once a Christmas fern (Polystichum acrostichoides) reaches the minimum size required for reproduction, its investment into reproduction increases or decreases with its growth rate, which is an outcome of the quality of the environment5 (Figure 8).
Figure 8. Reproductive allometry of the Christmas fern, Polystichum acrostichoides. The arrow with an ‘R’ indicates the average minimum size necessary for reproduction and the arrow with an ‘S” indicates the size necessary for sequential (year-to-year) reproduction as a function of growth rate. From Greer and McCarthy, 1997, Patterns of Growth and Reproduction in the Christmas fern, Polystichum acrostichoides. American Fern Journal 90:60-76.
This “cautious” strategy maximizes the lifespan of the fern by minimizing the impact reproduction has on parent-plant survival. Because offspring survival is extremely low in ferns, this “cautious” strategy maximizes lifetime reproductive success (i.e., production of offspring that survive to adulthood) by giving an adult fern the maximum possible opportunities for reproduction. Not surprisingly, many fern species are very long-lived, from many decades to centuries. The opposite pattern occurs in many flowering plants. Species in the genus Pedicularis, a relative of snapdragons, invest more into reproduction at smaller sizes in stressful, high elevation environments where growth rate is slower than in favorable, low elevation environments where growth rate is higher6 (Figure 9). A very similar trend was observed by my 2012 Plant Ecology class of subpopulations of the smooth aster, Symphotrichum laeve, occurring at the droughty top versus the wetter, growth-favorable bottom of the old ski hill at GVSU’s Allendale campus (Figure 10). These positively-allometric shifts in reproduction in stressful, low growth, environments increase the likelihood of reproducing before death. The contrasting allometric responses by ferns and flowering plants reflects key differences in their physiology and reproduction. The comparatively low rates of resource acquisition and spore survival in ferns favors a strategy that maximizes survival of adult plants whereas the comparatively high rates of resource acquisition and seed dormancy in flowering plants, favor a strategy that maximizes reproductive output; exceptions not-withstanding.
Figure 9. Pedicularis kansuensis. Photo from 'eFloras (2008). Published on the Internet http://www.efloras.org [accessed 7 April 2008] Missouri Botanical Garden, St. Louis, MO & Harvard University Herbaria, Cambridge, MA.
Figure 10. Reproductive allometries for sub-populations of Symphotrichum laeve occurring on the upper-slope (red line) and lower-slope (blue line) of GVSU’s old ski run.
A considerable amount of macroevolutionary change in plants and animals (i.e., profound changes in form, anatomy, and physiology that typically manifest over a great number of generations) can be viewed as products of allometry. This macroevolutionary aspect of allometry is technically referred to as heterochrony (hetero = different, chrony = time); i.e., the speeding up or slowing down of development of different body parts between ancestors and descendants. Two notable examples of heterochronic evolution in plants include: (1) the evolution of lobed and dissected leaves4 (a very complicated tale that I confess to simplifying here, but, nonetheless true to the point), and (2) the very rapid evolution of single-stalked, soft kernelled maize (corn, Zea mays subsp. mays) from its still living, multi-stalked, hard kernelled, Central American ancestor, teosinte (Zea mays subsp. Parviglumis)7. Among animals, notable examples of heterochronic evolution include the increasing skull-height-to-skull-length ratio that followed increasing size in tyranosaurids, a cross-generational (and cross-species) reflection of the positive allometry individuals experienced from juvenile to adult described above1. Tyranosaurid skull evolution simply followed along and exaggerated a pre-existing allometry. Another example from animals is that of the modern horse hoof from a five-toed ancestor, wherein all toes but the center toe suffered a deceleration (i.e., negative allometry) compared to the limbs, while the center toe experienced an acceleration (i.e., positive allometry) that correlated with similar acceleration of the limb bones8. This complex set of macroevolutionary changes facilitated the evolution of increasing running speed, an adaptation for avoiding predation in grasslands, the new and rapidly expanding biome of the Eocene and Miocene9,10. Similarly, the independent loss of limbs in apodans (a group of amphibians), snakes (a group of reptiles), and whales (a group of mammals) were outcomes of heterochronic slowing (i.e., negative allometry) relative to body growth. We can also see the products of heterochronic evolution in ourselves. As I described above, the head-to-body ratio in humans decreases as we mature from fetus to adult, the product of a negative allometry of our head growth relative to our bodies (Figure 3). Nevertheless, development of our cranium – and brains within – expands at a faster rate than the rest of our skull, a positive allometry with a steeper slope than for any other primate11 (Figure 11). As a result, we humans possess exceptionally large brain-to-body size (weight) ratios, an important factor in the evolution of our high level of socio-technological intelligence that followed an initial reorganization of the brain in our early hominid ancestors11. The evolution of this remarkable trait, our brainy heads, the engine of our intelligence, creativity, and technical abilities, is the product of a positive heterochrony, that is, a cross-generational positive allometry.
Figure 11. Brain weight plotted against body weight for primates; both plotted in log10 scale. Figure from Holloway et al 2003.
Allometry has medicinal utility as well. A common attribute of many cancers is that the likelihood of metastasis (the spread of cancerous cells from its original site to another) increases much more rapidly than tumor size when tumors are small, that is, the likelihood of metastasis is positively allometric at small sizes (Figure 12). The likelihood of metastasis levels off with larger tumor sizes, indicating a negative allometry. In the case of the breast cancer study by Demicheli et al. (2006)12, a critical tumor size at which the likelihood of metastasis appears to switch from a positive to a negative allometry appears to be around 10,000mm3. When it comes to metastasis, small tumors are more dangerous than large tumors. This insight clarifies the importance of early detection of cancers and careful monitoring following removal of cancerous tumors.
Figure 12. Proportion of patients with lymph-nodes containing cancer cells based on the size (volume) of a patient’s initial tumor. From, Romano Demicheli, Elia Biganzoli, Patrizia Boracchi, Marco Greco, William J.M. Hrushesky, Michael W. Retsky. 2006. Allometric Scaling Law Questions the Traditional Mechanical Model for Axillary Lymph Node Involvement in Breast Cancer. Journal of Clinical Oncology, Vol 24: 4391-4396.
The underlying genetic basis of allometry is far beyond the scope of this essay, but, not surprisingly, it depends on the specific organism and the specific trait(s) concerned. In some cases just a few genes that orchestrate the activities of other genes and subsequently a number of “linked” traits appear to be involved. For example, the rapid evolution of the single-stalked form and soft kernels in maize from its ancestor teosinte, which is multi-stalked and possesses hard kernels, is the product of just a few regulatory genes, perhaps as few as two7. In other cases – as with leaves and their lobing and dissection – the underlying genetic mechanisms are complex, a cascading gene network characterized by numerous stimulating and repressing feedbacks (i.e., up-regulation and down-regulation of gene activity). In most cases, our understanding of the underlying genetic mechanisms is largely absent with only a few heavily research examples so far, some of which are presented above.
There is much yet to learn regarding allometry to much potential benefit, both in terms of basic and applied knowledge. I hope this is a source of inspiration for students considering a future in biology.