Scientific studies suggest that some animals regulate their

Scientific studies suggest that some animals regulate their intake of different types of food available in the environment to achieve a balance between the proportion, and ultimately the total amount, of macro-nutrients consumed. Macro-nutrients are categorised as protein, carbohydrate or fat/lipid. A seminal study on the macro-nutrient intake of migratory locust nymphs (Locusta migratoria) suggested that the locust nymphs studied sought and ate combinations of food that balanced the intake of protein to carbohydrate in a ratio of 45:55 [1]. Assume that a locust nymph finds itself in an enivronment where only two sources of food are available, identified as food X and food Y . Food X is 27% protein and 73% carbohydrate, whereas food Y is 73% protein and 27% carbohydrate. Assuming that the locust eats exactly 100 mg of food per day, determine how many milligrams of food X and food Y the locust needs to eat per day to reach the desired intake balance between protein and carbohydrate. [1] D Raubenheimer and S J Simpson, The geometry of compensatory feeding in the locust, Animal Behaviour, 45:953–964, 1993.

Solution

Let the quantities of food X and food Y eaten by the locusts be p and q miligrams respectively. Also, let the sum of the daily intake of protein and carbohydrate by the locusts be r. Then p +q = 100...(1) , 0.27p + 0.73q = 0.45r or, 27p+ 73q = 45r...(2) and 0.73p+ 0.27q = 0.55r or, 73p + 27q = 55r....(3). On multiplying both the sides of the 2nd equation by 55 and the 3rd equation by 45, we get 1485p + 4015q = 2475r...(4) and 3285p + 1215q = 2475r...(5). Now, on subtracting the 4th equation from the 5th equation, we get 3285p+ 1215q - 1485p - 4015q = 0 or, 1800p - 2800q = 0...(6). From the 1st equation, we have q = 100 - p. On substituting this value of q in the 6th equation, we get 1800p - 2800(100- p) = 0 or, 1800p + 2800p = 280000 or, 4600p = 280000 so that p = 280000/4600 = 60.87 (approximately). Then q = 100 -p = 100- 60.87 = 39.13. Thus, the locusts need to eat 60.87 milligrams of food X and 39.13 milligrams of food B daily to reach the desired intake balance between protein and carbohydrate.