Panting in Animals Animals use different strategies to control their internal temperature depending on how hot they are. When the core temperature of a dog, duck, or cat exceeds a critical value, it will start to pant (make quick, gasping breaths that increase evaporation of water from the tongue and mouth). Vieth (1989) studied heat loss as a function of the ducks’ core temperature,
. She found that different functions described heat loss below the temperature at which the ducks started to pant and above this temperature. If
is the rate of heat loss:
The Correct Answer and Explanation is:
To model heat loss in ducks with respect to their core temperature, we consider two different functions: one for when the ducks are below the panting threshold temperature and another for when they begin to pant.
Let H(T)H(T)H(T) represent the rate of heat loss as a function of core temperature TTT. According to Vieth (1989), heat loss changes behavior once the duck begins panting. Below a certain critical temperature TcT_cTc, the heat loss increases gradually. Once the temperature exceeds TcT_cTc, the duck starts panting and the heat loss rate increases more rapidly.
We can model this piecewise function as:H(T)={aT+b,for T≤TccT2+dT+e,for T>TcH(T) = \begin{cases} aT + b, & \text{for } T \leq T_c \\ cT^2 + dT + e, & \text{for } T > T_c \end{cases}H(T)={aT+b,cT2+dT+e,for T≤Tcfor T>Tc
Where:
- aT+baT + baT+b is a linear function representing the heat loss before panting begins
- cT2+dT+ecT^2 + dT + ecT2+dT+e is a quadratic function representing the accelerated heat loss due to panting
- The constants a,b,c,d,a, b, c, d,a,b,c,d, and eee are determined empirically
- TcT_cTc is the critical core temperature at which panting starts
Explanation
Animals maintain their internal temperature through a variety of physiological mechanisms. In birds like ducks, when the core body temperature begins to rise, the rate of heat loss through normal processes such as radiation or convection increases gradually. However, once the temperature exceeds a certain threshold, these methods become insufficient to regulate body temperature, and the duck begins to pant.
Panting is a form of evaporative cooling where water evaporates from the moist surfaces of the mouth and tongue, which absorbs a significant amount of heat and cools the body. This sudden shift in heat-loss strategy results in a noticeable change in the heat loss curve. Vieth’s 1989 study captured this shift by showing that the function representing heat loss is linear before panting starts, and becomes quadratic after panting begins.
This means that as core temperature increases slightly, heat loss also increases slightly until a certain critical temperature. Beyond that, panting kicks in, and heat loss increases much more rapidly to protect the animal from overheating. The quadratic nature of the post-threshold heat-loss function reflects the compounding effect of panting: not only is more water evaporated with each breath, but the breathing rate increases as well, amplifying the heat loss.
Understanding these functions helps scientists and veterinarians model thermoregulatory responses in animals under heat stress and design better strategies for animal care, especially in hot environments or during climate extremes.
