a) Contrary to what we may have grown up learning, only small animals hibernate

Question

a) Contrary to what we may have grown up learning, only small animals hibernate (not completely true…black bears are now believed to hibernate, however it’s a different mechanism than small animals-more on this later in the semester). Perhaps we can understand why this is, by considering stored energy and the rate of energy metabolism (utilization). Here, you will calculate whether hibernation is necessary by comparing a 1200 pound polar bear and a 1.5 pound grey squirrel (like those living here in Columbus). We can compare how long each could survive during a winter fast if they used only body fat as their energy source, and do not hibernate (which requires a drop in metabolism below the BMR). The weight-specific Basal metabolic rate (BMR) of mammals is 4.46 M-0.30 when expressed in units of mLO2consumed per gram of body tissue per hour and (importantly) weight is calculated in grams. For this simple estimate, you may use BMR, but keep in mind that small animals have a larger increase in metabolism with temperature than large animals. Calculate how long each animal could survive on stored fat equal to 20% of its total body weight (this is a fairly reasonable fat amount found in both squirrels and bears in nature). Make sure you keep all units very clear during this calculation, there are many steps.

Potentially useful information:

The value of energy content of fat is 9.3 kCal per gram of fat and 2.0 L of O2 are consumed per gram of fat metabolized. There are 5280 feet in a mile, and 1.0 foot = 0.3048 meters. One calorie = 4.184 joules. One pound (lb) = 454 grams and one ounce is 28.375 grams.

b) Given your results, what do you think might be the potential solutions for a) squirrels and b) polar bears for surviving through the winter (keeping in mind that food is scarce so they can’t just stay awake and look for food!) This should only be a FEW sentences!

Explanation / Answer

a) Weight of polar bear=1200 lb=454*1200 =544800 g=544.8 kg

stored fat=20% of 544800=108960 g=108.96 kg

total energy content =9.3*108960 =1013328 kcal =1013328000cal =1013328000*4.184 J=4239764352 joules

total O2 consumed=108960*2=217920L=217920000ml

BMR=4.46 M-0.3

or,joules per hour per kg body weight=4.46 M-0.3

or,J-1 * h * kg =4.46 M 0.3

or, h*kg=4.46*4239764352

or,h=18909349009.92/108.96

or, hours=173543952

or,mins=10412637120 (1h=60mins)

Weight of squirrel=1.5 lb=454*1.5 =681 g=0.681 kg

stored fat=20% of 681=136.2 g=0.1362 kg

total energy content =9.3*136.2 =1266.66 kcal =1266660cal =1266660*4.184 J=5299705.44 joules

total O2 consumed=136.2*2=272.4L=272400ml

BMR=4.46 M-0.3

or,joules per hour per kg body weight=4.46 M-0.3

or,J-1 * h * kg =4.46 M 0.3

or, h*kg=4.46*5299705.44

or,h=23636686.2624/0.1362

or, hours=173543952

or,mins=10412637120 (1hr=60mins)

b)

a)In squirrel,

O2 consumed per min=4.46 (BMR=mlO2/min)

O2 consumed in total minutes =10412637120*4.46=46440361555.2ml >272400ml

Hence,hibernation is necessary.

b)In bear,

O2 consumed per min=4.46 (BMR=mlO2/min)

O2 consumed in total minutes =10412637120*4.46=46440361555.2ml >217920000ml

Hence, hibernation is necessary.

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