Study Questions #8 (Lectures 4/5, 4/7) Due week of 4/17

Please write clear, complete (and brief) answers to the three starred questions. Please type. Drawings are ok if they help you explain.

1. In logistic population growth, DN is constantly changing as a function of N. Use the equation we discussed in class to say how this works. It will help you understand this if you consider what DN is when N is very low (near 0) or very high (near K). What happens if N > K?

Same as last week

* 2. What is the carrying capacity, K, and what factors influence its magnitude?

The carrying capacity is the number of individuals of a particular population that a certain environment can sustain. It is in the same units as N (numbers of individuals). K depends on how efficiently individuals use resources, and also on the level of resources available in a given environment. If a population becomes more efficient at using resources or the level of resources increases, then so will K.

3. What is exponential growth? Why is it not sustainable?

In exponential growth, populations grow following an exponential curve, that is, ever increasing. It can't be sustained because resources do not increase to keep pace, and eventually, every exponentially growing population will outstrip its resources.

* 4. What is rmax, and what is the difference between it and ractual? Which one determines the rate of population growth under density dependent conditions? Which one changes as a function of N? Which one remains constant?

Rmax is the rate of population increase that a population will show in the best of all possible conditions, ie., when resources are not limiting. ractual is the modified rmax that takes into account density effects. ractual = rmax((K-N)/K). So, ractual is always less than rmax.

5. If the length of an object increases, what happens to its ratio of surface area to volume? Describe two examples of how this causes problems in biology.

The surface area of an object is proportional to its squared length, while the volume is proportional to the cube of length. Thus, as length increases, volume increases faster than surface area, so the surface area/volume ratio declines. This causes problems in any situation where the rate of exchange is proportional to the surface area, but the need for exchange is proportional to the volume. For example, large animals need oxygen to supply their muscles according (in simplest terms) to their volume, but without modification, the surface area of respiratory membranes doesn't keep pace. Thus, large and active animals have highly elaborated areas for gas exchange. Heat exchange works the same way.

* 6. What are two engineering features of bone that increase its strength for a given weight?

Bone is stronger than it should be for a given weight because it

a. often has an I-beam shape

b. has internal buttressing at the ends for added strength

c. long bones have a cylindrical shape (very strong, and resistant to bending.

7. Which of these organisms has the most surface area of respiratory membranes, a cheetah or a frog? How might natural selection have favored a change during the evolution of vertebrates?

Cheetah. It, and other very active mammals need a lot of oxygen to fuel their rapid metabolism and muscle activity. Thus, mammalian lungs have an enormous amount of surface area-- much more so than an equivalently sized reptile, for example, which does not have the same high metabolic rate required in a warm-blooded animal.