The Study of Prehistoric Birds Depends on Imprints of a Prehistoric

question 21

Essay

The study of prehistoric birds depends on imprints of a prehistoric creature's remains in
stone, commonly known as fossils. To study ancient ecosystems effectively it would be
useful know the actual mass of individual birds, but this information is not preserved in
the fossil record. It seems reasonable that the biomechanics of birds is much the same
today as in the past. For example, today's relationship between the wing length and total
weight of a bird should be very similar to that for birds from the distant past. The wing
lengths of ancient birds are readily obtainable from the fossil record, but the weight is
not. A regression model expressing the relationship between wing length and total
weight of modern birds could be used to estimate the mass of similar prehistoric birds.
Data for some species of modern birds of prey and are given below. Wing length and total weight of modern species of birds of prey
$\begin{array}{|l|c|c|}\hline {\text { Bird species }} & \begin{array}{c}\text { Wing length } \\(\mathbf{c m})\end{array} & \begin{array}{c}\text { Total weight } \\\text { (kilograms) }\end{array} \\\hline \text { Gyps fulvus } & 69.8 & 7.27 \\\text { Gypaetus barbatus grandis } & 71.7 & 5.39 \\\text { Catharista atrata } & 50.2 & 1.70 \\\text { Aguila chrysatus } & 68.2 & 3.71 \\\text { Hieraeus fasciatus } & 56.0 & 2.06 \\\text { Helotarsus ecaudatus } & 51.2 & 2.10 \\\text { Geranoatus melanoleucus } & 51.5 & 2.12 \\\text { Circatus gallicus } & 53.3 & 1.66 \\\text { Buteo bueto } & 40.4 & 1.03 \\\text { Pernis apivorus } & 45.1 & 0.62 \\\text { Pandion haliatus } & 49.6 & 1.11 \\\text { Circus aeruginosos } & 41.3 & 0.68 \\\text { Circus cyaneus (female) } & 37.4 & 0.472 \\\text { Circus cyaneus (male) } & 33.9 & 0.331 \\\text { Circus pygargus } & 35.9 & 0.237 \\\text { Circus macrurus } & 35.7 & 0.386 \\\text { Milvus milvus } & 50.7 & 0.927 \\\hline\end{array}$

-Biological theory suggests that the relationship between the weight of these
animals and their wing length could be
modeled using an exponential model.
Perform the appropriate transformation of
variable(s) and fit an exponential model to
the data.
a) What is the resulting best fit line using
the transformed data?
b) What is the predicted log of bird weight for a species with wing length L = 56.0 ?
Show your work below.

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