Echolocation in Bats The
bats (Chiropterans) of Pennsylvania are insectivorous. They locate their
prey by means of sonar. The bat emits a high frequency squeak and listens
for an echo. The time interval between the time the call is given and the
time the echo is heard is directly proportional to the There are many questions we can ask about a bat's echolocating abilities. For instance, can bats detect small objects as well as large objects? Do bats of different species echolocate equally well? Does a bat echolocate poorly if it is tired? In the laboratory we will construct a flyway (Figure 1). This structure simply confines the bat to a small area and thus makes our study easier. Within the flyway are rows of hangers. From these we can suspend objects of different sizes that the bat must dodge as it flies around the small area in the flyway. Figure 1. Schematic of experimental bat flyway. The flyway is long and narrow so the bat must pass through rows of obstacles that will be suspended from the hangers. If it strikes one of the obstacles, it will swing. Although the objects are weighted so that they will hang straight, they are movable. Each time the bat flies through a row of obstacles, it will pass between two objects. Since the objects are farther apart than its wingspan, it can only encounter one of them in each row. Now we have a way of measuring the bat's performance. All we need do is count the number of obstacles it misses (each row counts as 1) and the number that it hits during a series of flights. If the bat flies through a series of obstacles of one size in a series of flights and through a series of obstacles of smaller size in a second series of flights, then we can measure if or how its behavior changed. Obviously if the bat has more difficulty detecting the smaller objects, then it should make more errors. Suppose we get the following results:
We see that the bat made more errors when confronted with the small objects. This is the expected result, but does it indicate that the behavior of the bat has changed or does it mean that it did poorly on one run, and by chance did better on the second run, and that size of the objects had nothing to do with it? We need to have something to compare our results against, some baseline data. Let's take a look at another example before we return to the bat. Suppose that I spent 2 hours flipping a coin to see whether it came up heads or tails. Suppose we get the following outcome:
Is it a dishonest coin? Here we can
answer the question because if it were an honest coin we would expect, on
the average, 50 heads and 50 tails from 100 tosses. Notice that I said "on
the average". When a coin is " on the average" we will call it honest and
we can determine how far a coin's performance can deviate from 50:50 and
still be "on the average". The way we do that is by means of a Chi-square
analysis. A Chi-square (sometimes written as X _{
}X expected In our example we observed 70
heads when we expected 50, and 30 tails when we expected 50. Since the
capital sigma means to add up all of the terms, we sum all the (obs-exp) _{
}X2= 50 50 As the difference between the observed outcome and the expected outcome increases, the Chi-square statistic also gets bigger. A Chi-square table indicates when a Chi-square value is too big to be "on the average". By international agreement, a Chi-square value is "too big" when it would be expected to occur less than 5 times in 100. For our example, a check with a statistical table tells us that the maximum Chi-square value we will accept is 3.84. Our calculation of a value of 16 is 'too big' and we would infer that the coin is dishonest. Someone was using a loaded coin. In this case we have 1 "degree of freedom" because once we determined how many heads to expect, we know how many tails there had to be. All of this may be familiar to you since most introductory biology courses use this technique to analyze genetics problems. Suppose we repeat the coin experiment and the outcome is 85 Heads and 15 Tails. Obviously this outcome is worse than the first. Is this more "dishonest" than the first? Thinking back to the bats, we are asking "has the behavior of the bat (that is, its ability to echolocate) changed?" We can analyze this problem in exactly the same way as the first coin experiment except we need to review how we got the first set of expected values. That is, how do we determine how many times we "expect" the bat to hit the objects? An expected value is the product of the probability of an event happening and the total number of chances it has had to occur. For example, with the coin the probability of a Head is 1 out of 2, or 0.5, and we flipped it 100 times, so 0.5 x 100 gives an expected frequency of 50. The probability of an event is the number of ways an event can occur divided by the total number of outcomes. With a coin there is one way to get a head and there are only two outcomes--a head or a tail. So, the probability of a head is 1/2. An alternate way to estimate the probability of a head is to flip the coin many times and divide the number of times a head turned up by the total number of flips. To apply this method to the
bats we have to set up an hypothesis, H
Our best estimate of the probability of a miss is 417/450; the probability of a hit is 33/450; the probability of encountering a large obstacle is 200/450; the probability of encountering a small object is 250/450. Therefore, using the methods of we did with the coins, the probability of hitting a large obstacle is 33/450 x 200/450, and the expected frequency of hits of large obstacles is (33/450 x 200/450), or (33 x 200)/450 = 15. What is the expected probability for each of the other possibilities? Large Miss___________________________________________________ Small Miss___________________________________________________ Small Hit____________________________________________________ Large Hit____________________________________________________ What are the expected frequencies of each of the following? Large Miss___________________________________________________ Small Miss___________________________________________________ Small Hit____________________________________________________ Large Hit____________________________________________________ This set of experiments is designed to stimulate your thoughts about the way that bats use echolocation to perceive their environment. Think about the following questions when interpreting your analyses. Were the bats echolocating? Was there an effect of obstacle distribution on bat performance? Which obstacle density (2- or 3-string set) gave the bats more trouble? Do you think that this was the result of inability to "see" the strings, or of maneuverability? What was the effect of size of the object on performance? Can you ascertain the limit of size perception from your analyses? Was there some size above which performance was uniformly good? What were the effects of individual differences among the test subjects? Did all the bats perform equally well? Was there as much variability among the bats as you would expect there to be in the visual abilities of your classmates? Did any of the bats show evidence of learning during the course of the experiments (e.g., can you separate any effects due to learning the flyway from effects due to obstacle size)? Did the bats appear to tire? How do your estimates of bat perceptual ability compare with those reported by other researchers? How would you expect the feeding habits (prey, foraging habitat, foraging time) of a bat to affect its perceptual abilities? Link to table of Chi-square Critical Values
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Brown, Luther and Jerry F. Downhower. 1988. |