To develop properly, bird embryos must maintain a high and steady body temperature. They do not generate sufficient heat to manage this themselves, however, and so they must rely on a heat subsidy from the parent, delivered when the parent broods the egg. The heat is generally delivered through a specialized patch of skin on the parent's breast known as the brood patch.
It seems a simple matter to warm an egg by pressing a warm body against it. This assumption of simplicity has led biologists to imagine that the warming of an egg can be analyzed with very simple models of heat transfer. However, the transfer of heat between a parent and its egg is a complex process with many interesting subtleties, both physical and biological.The assumption that it is simple has led students of avian incubation seriously astray, for two reasons. First, these interesting subtleties tend to be 'simplified away' by the prevailing simplistic models of egg warming. Second, it is a safe bet that birds that can exploit these subtleties will enjoy a selective advantage over those that do not. Consequently, any inference about avian ecology or reproductive ecology that depends upon these simplistic models will likely be seriously in error.
In addition to being a fascinating problem in biophysics, the energetics of egg incubation provides a compelling case study of how the uncritical application of Occam's Razor (the assumption that the simplest explanation must be the best) can impose blinders rather than enlighten. Realizing this started me questioning the prevailing reductionist mindset of modern biology, which has fulminated into full-blown obsession with my studies on "emergent physiology" in social insect colonies.
I became interested in eggs because they offered a useful model system for exploring how variation of body size affects how heat is exchange with the environment. My work on blood-borne heat exchange in reptiles had convinced me that body size affected the ability to exchange heat in some complicated and unexpected ways.
I thought that bird eggs could help clarify this because they are simple in shape (all are spheroidal), varied tremendously in "body size" (2 g to over 1500 g, nearly 3 orders of magnitude), and they contain living things that generate heat and circulate blood. In short, bird eggs represent the perfect experimental model for sorting out the complex scaling of heat exchange with size.
I first undertook to measure eggs' thermal conductance, Kt, that quantifies how readily heat moves between the egg and environment. Prevailing dogma was that this quantity scaled to body size by a power relationship, i.e.
Kt = a Mb
where b is the scaling exponent. Rather, I found that thermal conductance scaled in a complex composite power curve that reflected the varying dominance of the various modes of heat flow (convection, radiation, conduction and blood-borne) at different egg sizes. To ignore this complex scaling is to simplify away much interesting thermal biology.
J S Turner. 1985. Cooling rate and size of birds’ eggs - a natural isomorphic body. Journal of Thermal Biology 10: 101-104. [pdf]
H Tazawa, J S Turner and C V Paganelli. 1988. Cooling rates of living and killed chicken and quail eggs in air and in helium-oxygen gas mixture. Comparative Biochemistry and Physiology 90A: 99-102. [pdf]
J S Turner. 1988. Body size and thermal energetics. How should thermal conductance scale? Journal of Thermal Biology 13: 103-117. [pdf]
A warm egg in air loses heat uniformly over its surface. When an egg is warmed by a brood patch, however, heat flows non-uniformly from the warmed patch through the egg to the exposed surface. This means that an egg has very different thermal properties depending upon whether it is sitting in air or is being warmed by a brood patch. Eggs warmed by a brood patch contain substantial temperature gradients within, while eggs in air are nearly uniform in temperature throughout. The diagrams to the right show the portion of the egg near the brood patch (top) is warmer (red) than the egg's opposite pole (blue) [based upon model calculations of heat flow through contact-incubated eggs]
Most models of incubation energetics have assumed that the cost of contact incubation can be inferred from the properties of eggs in air. This assumption has allowed serious errors to permeate our thinking about what it costs to incubate an egg. Among the more serious errors has been the notion that the embryo is a mere passive recipient of heat from the parent, at most contributing heat as it grows. In fact, the embryo has striking physiological capabilities for managing the flow of heat into its egg, most notably through the developing embryonic circulation of blood. This is evident in the temperature maps to the right. At the end of incubation, heat is distributed more widely through the egg than at the beginning. This capability emerges only when the egg is contact-incubated.
Among the interesting surprises to emerge when these capabilities are accounted for: as the embryo matures, incubated eggs require more heat from the parent to keep warm. Failure of simpler models to account for this long led people to assume that parental costs declined with age of the embryo.
J S Turner. 1987. Blood circulation and the flows of heat in an incubated egg. Journal of Experimental Zoology (Supplement 1): 99-104. [pdf]
H Tazawa, G C Whittow, J S Turner and C V Paganelli. 1989. Metabolic responses to gradual cooling in chicken eggs treated with thiourea and oxygen. Comparative Biochemistry and Physiology 92A: 619-622. [pdf]
H Tazawa, Y Suzuki, J S Turner and C V Paganelli. 1988. Metabolic compensation to gradual cooling in developing chick embryos. Comparative Biochemistry and Physiology 89A: 125-129. [pdf]
J S Turner. 1990. The thermal energetics of an incubated chicken egg. Journal of Thermal Biology 15: 211-. [pdf]
J S Turner. 1991. The thermal energetics of incubated birds’ eggs. In: D C Deeming and M W J
Many birds incubate their eggs intermittently, sitting on them for a time, then leaving the eggs to cool while the parent forages for food or defends territories. This imposes complex regimes of heat flow on the eggs, and analyzing these properly requires complex models of heat flow.
These complex heat flows can be analyzed by measuring a quantity called the thermal impedance, a transient-state analog of the thermal resistance. Put simply, thermal impedance depends upon the time-dependency of transient heat inputs to the egg. Rapidly-changing heat heat inputs to the egg face a larger thermal impedance than do more slowly-changing heat inputs. Practically, this can be demonstrated by imposing sinusoidally-varying heat inputs to the egg through an artificial brood patch. The thermal impedance is calculated from the amplitude and phase delay of the sinusoidally-varying temperature.
On the left curve, a rapidly varying heat input from a brood patch elicits only small variations of temperature in the egg center (middle curve). On the right, a slowly-varying heat input from the brood patch produces larger fluctuations of egg temperature in the center. The left curve represents high-impedance warming, while the right curve represents low-impedance warming.
This means that incubating birds can manipulate how effectively heat penetrates the egg simply by varying the frequency of intermittent incubation. Many short visits will result in high impedance warming of the egg, whilst few long visits will produce low-impedance warming, and more effective penetration of heat into the egg.
Impedance also affects the egg's fundamental thermal properties. For example, the egg's thermal capacity is the heat input required to raise the egg temperature by some amount. Many think this is a physical property of the egg, specifically the product of the egg's specific heat and its mass. An impedance-limited regime, on the other hand, means that some parts of the egg exchange heat more readily than others. Consequently, an egg will have an apparent thermal capacity that varies with frequency of heat input: low-impedance warming will produce a larger apparent thermal capacity than will low-impedance warming.
J S Turner. 2002. Maintenance of egg temperature. In: Avian Incubation: Behaviour, Environment And Evolution, D C Deeming (ed).
J S Turner. 1994. Time and energy in the intermittent incubation of birds’ eggs.
J S Turner. 1997. On the thermal capacity of a bird’s egg warmed by a brood patch. Physiological Zoology 70: 470-480.
J S Turner. 1994. Transient thermal properties of contact-incubated chicken eggs. Physiological Zoology 67: 1426-1447. [pdf]
J S Turner. 1994. Thermal impedance of a contact-incubated bird’s egg. Journal of Thermal Biology 19: 237-243. [pdf]