Question

In addition to biology, evidence drawn from many different disciplines, including chemistry, geology, and mathematics, supports models of the origin of life on Earth. In order to determine when the first forms of life likely formed, the rate of radioactive decay can be used to determine the age of the oldest rocks (see optional problems C and D, below) exposed on Earth’s surface. These are found to be approximately 3.5 billion years old. The age of rocks can be correlated to fossils of the earliest forms of life. A. The graph compares times of divergence from the last common ancestor based on the fossil record with a "molecular time" constructed by comparing sequences of conserved proteins to determine a mutation rate (after Hedges and Kumar, Trends in Genetics, 2003). Explain how such a molecular clock could be refined to infer time or the evolution of prokaryotes. B. Using a molecular clock constructed from 32 conserved proteins, Hedges and colleagues (Battistuzzi et al., BMC Evol. Biol. 2004) estimated the times during which key biological processes evolved. A diagram based on their work is shown. Connect the time of the origin of life inferred from this diagram with the age of the oldest fossil stromatolites and the age of the oldest exposed rock to show how evidence from different scientific disciplines provides support for the concept of evolution. Evaluate the legitimacy of claims drawn from these different disciplines (biology, geology, and mathematics) regarding the origin of life on Earth. The oldest known rocks are exposed at three locations: Greenland, Australia, and Swaziland. The following application of mathematical methods provides the essential evidence of the minimum age of Earth. The mathematics is appropriate for students who have completed a second year of algebra. However, it is not illustrative of the type of item that could appear on the AP Biology Exam. The exposed rocks contain a radioactive isotope of rubidium, 87 Rb, which decays into a stable isotope of strontium, 87 Sr. An $^{87}$ Rb atom with 37 protons and 50 neutrons decays when a proton is converted into a neutron to produce an atom, 87 Sr, with 36 protons and 51 neutrons. As time passed, the number of each isotope changed from its initial value. When a crystal containing $^{87}$ Rb atoms formed from the molten surface of the hot, early Earth during the Hadean eon, the number of these atoms at that initial time can be represented as $\mathrm{N}_{87 \mathrm{Rb}, 0} .$ As time passed, the number of atoms of this isotope changed to $\mathrm{N}_{87 \mathrm{Rb}}$ . C. Justify the relationship between the number of each isotope at any time and the number of each at the time that the molten rock solidified (denoted by the subscript 0): $N_{87}_{S r}=N_{87}_{S r, 0}+N_{87}_{R b, 0}-N_{87}_{R b}$ The decay of unstable radioisotopes is exponential with a half-life of $\mathrm{T}_{1 / 2},$ which for $^{87} \mathrm{Rb}$ is $4.88 \times 10^{10} \mathrm{years}$ : $$N_{87_{R b}}=N_{87_{R b, 0}} e^{-0.693 t / T_{1} / 2}$$ This can be used to replace the initial number of 87 bb atoms, which cannot be measured, with the present-day value: $$\frac{N_{87_{s r}}}{N_{86_{s r}}}=\frac{N_{87_{s r, 0}}}{N_{86 r}}+\left(e^{-0.693 t} / T_{1 /}^{2}-1\right) \frac{N_{87_{R b}}}{N_{86 r}}$$ When the measurements of the numbers of $^{87} \mathrm{Rb}$ and $^{87} \mathrm{Sr}$ were made (Moorbath et al, Nature, 1972), measurements of a second stable isotope of strontium, 86 $\mathrm{Sr}$ , were also made. The ratio of the initial number of 87 Sr and 86 $\mathrm{Sr}$ atoms is the same as today, since the isotopes are both stable. The value of this ratio is $0.71 .$ This is a linear equation in the form $y=a x+b,$ where a is the term in parenthesis containing the half-life of $^{87} \mathrm{Rb} .$ If $Y=N_{87}_{S r} | N_{86}_{S r}$ is graphed versus $N_{87}_{R b} / N_{86} s r^{\prime}$ the slope can be used to determine the time, t, that has passed since the rock formed from melting: $a=e^{0.683 t / T_{1} / 2}-1,$ so $$t=\ln (a+1) \bullet T_{1 /} \quad 2 / 0.693$$ D. Data on the rubidium and strontium isotopes at Isua in Greenland are provided in the table. Analyze these data to obtain the age of formation of these rocks. The solidification of the molten surface of Earth at the end of the Hadean eon (4 to 4.6 billion years ago) and the condensation of liquid oceans provided a medium from which life emerged. The most ancient fossils are colonial, photosynthetic cyanobacteria called stromatolites. As climate change melted the perennial snow covering Greenland, new geologic evidence of the time of that origin was obtained (Nutman et al., Nature 2016) with the discovery of the most ancient stromatolites. These fossils record communities of photosynthetic bacteria embedded in Isua sediments 3.7 billion years ago. Worldwide stromatolite fossils show a decline between 1 and 1.3 billion years ago.

Name: Problem 72, Chapter 18: Biology for AP Courses
Uploaded: 2019-08-02T02:23:05-08:00
Duration: 5 min 53 s
Channel: Grant Castaneda

   In addition to biology, evidence drawn from many different disciplines, including chemistry, geology, and mathematics, supports models of the origin of life on
Earth. In order to determine when the first forms of life likely formed, the rate of radioactive decay can be used to determine the age of the oldest rocks (see optional problems C and D, below) exposed on Earth’s surface. These are found to be approximately 3.5 billion years old. The age of rocks can be correlated to fossils of the earliest forms of life.
A. The graph compares times of divergence from the last common ancestor based on the fossil record with a "molecular time" constructed by comparing sequences of conserved proteins to determine a mutation rate (after Hedges and Kumar, Trends in Genetics, 2003). Explain how such a molecular clock could be refined to infer time or the evolution of prokaryotes.
B. Using a molecular clock constructed from 32 conserved proteins, Hedges and colleagues (Battistuzzi et al., BMC Evol. Biol. 2004) estimated the times during which key biological processes evolved. A diagram based on their work is shown. Connect the time of the origin of life inferred from this diagram with the age of the oldest fossil stromatolites and the age of the oldest exposed rock to show how evidence from different scientific disciplines provides support for the concept of evolution. Evaluate the legitimacy of claims drawn from these different disciplines (biology, geology, and mathematics) regarding the origin of life on Earth.
The oldest known rocks are exposed at three locations: Greenland, Australia, and Swaziland. The following application of mathematical methods provides the essential evidence of the minimum age of Earth. The mathematics is appropriate for students who have completed a second year of algebra. However, it is not illustrative of the type of item that could appear on the AP Biology Exam. 
The exposed rocks contain a radioactive isotope of rubidium, 87 Rb, which decays into a stable isotope of strontium, 87 Sr. An $^{87}$ Rb atom with 37 protons and 50 neutrons decays when a proton is converted into a neutron to produce an atom, 87 Sr, with 36 protons and 51 neutrons. As time passed, the number of each isotope changed from its initial value. When a crystal containing $^{87}$ Rb atoms formed from the molten surface of the hot, early Earth during the Hadean eon, the number of these atoms at that initial time can be represented as $\mathrm{N}_{87 \mathrm{Rb}, 0} .$ As time passed, the number of atoms of this isotope changed to $\mathrm{N}_{87 \mathrm{Rb}}$ .
C. Justify the relationship between the number of each isotope at any time and the number of each at the time that the molten rock solidified (denoted by the subscript 0):
$N_{87}_{S r}=N_{87}_{S r, 0}+N_{87}_{R b, 0}-N_{87}_{R b}$
The decay of unstable radioisotopes is exponential with a
half-life of $\mathrm{T}_{1 / 2},$ which for $^{87} \mathrm{Rb}$ is $4.88 \times 10^{10} \mathrm{years}$ :
$$N_{87_{R b}}=N_{87_{R b, 0}} e^{-0.693 t / T_{1} / 2}$$
This can be used to replace the initial number of 87 bb atoms, which cannot be measured, with the present-day value:
$$\frac{N_{87_{s r}}}{N_{86_{s r}}}=\frac{N_{87_{s r, 0}}}{N_{86 r}}+\left(e^{-0.693 t} / T_{1 /}^{2}-1\right) \frac{N_{87_{R b}}}{N_{86 r}}$$
When the measurements of the numbers of $^{87} \mathrm{Rb}$ and $^{87} \mathrm{Sr}$
were made (Moorbath et al, Nature, 1972), measurements of a second stable isotope of strontium, 86 $\mathrm{Sr}$ , were also made. The ratio of the initial number of 87 Sr and 86 $\mathrm{Sr}$ atoms is the same as today, since the isotopes are both
stable. The value of this ratio is $0.71 .$ 
This is a linear equation in the form $y=a x+b,$ where a is the term in parenthesis containing the half-life of $^{87} \mathrm{Rb} .$ If
$Y=N_{87}_{S r} | N_{86}_{S r}$ is graphed versus $N_{87}_{R b} / N_{86} s r^{\prime}$
the slope can be used to determine the time, t, that has passed since the rock formed from melting:
$a=e^{0.683 t / T_{1} / 2}-1,$ so
$$t=\ln (a+1) \bullet T_{1 /} \quad 2 / 0.693$$
D. Data on the rubidium and strontium isotopes at Isua in Greenland are provided in the table. Analyze these data to obtain the age of formation of these rocks. The solidification of the molten surface of Earth at the end of the Hadean eon (4 to 4.6 billion years ago) and the condensation of liquid oceans provided a medium from which life emerged. The most ancient fossils are colonial, photosynthetic cyanobacteria called stromatolites. As climate change melted the perennial snow covering Greenland, new geologic evidence of the time of that origin was obtained (Nutman et al., Nature 2016) with the discovery of the most ancient stromatolites. These fossils record communities of photosynthetic bacteria embedded in Isua sediments 3.7 billion years ago. Worldwide stromatolite fossils show a decline between 1 and 1.3 billion years ago.

Biology for AP Courses

Julianne Zedalis,…

Chapter 18, Problem 72

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Solved by Expert Grant Castaneda

08/02/2019

Step 1

This is possible because there are only 20 amino acids that can form a protein, and these amino acids are derived from DNA. Therefore, by comparing the sequences of these amino acids, we can determine the mutation rate and infer the time of evolution. Show more…

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In addition to biology, evidence drawn from many different disciplines, including chemistry, geology, and mathematics, supports models of the origin of life on Earth. In order to determine when the first forms of life likely formed, the rate of radioactive decay can be used to determine the age of the oldest rocks (see optional problems C and D, below) exposed on Earth’s surface. These are found to be approximately 3.5 billion years old. The age of rocks can be correlated to fossils of the earliest forms of life. A. The graph compares times of divergence from the last common ancestor based on the fossil record with a "molecular time" constructed by comparing sequences of conserved proteins to determine a mutation rate (after Hedges and Kumar, Trends in Genetics, 2003). Explain how such a molecular clock could be refined to infer time or the evolution of prokaryotes. B. Using a molecular clock constructed from 32 conserved proteins, Hedges and colleagues (Battistuzzi et al., BMC Evol. Biol. 2004) estimated the times during which key biological processes evolved. A diagram based on their work is shown. Connect the time of the origin of life inferred from this diagram with the age of the oldest fossil stromatolites and the age of the oldest exposed rock to show how evidence from different scientific disciplines provides support for the concept of evolution. Evaluate the legitimacy of claims drawn from these different disciplines (biology, geology, and mathematics) regarding the origin of life on Earth. The oldest known rocks are exposed at three locations: Greenland, Australia, and Swaziland. The following application of mathematical methods provides the essential evidence of the minimum age of Earth. The mathematics is appropriate for students who have completed a second year of algebra. However, it is not illustrative of the type of item that could appear on the AP Biology Exam. The exposed rocks contain a radioactive isotope of rubidium, 87 Rb, which decays into a stable isotope of strontium, 87 Sr. An $^{87}$ Rb atom with 37 protons and 50 neutrons decays when a proton is converted into a neutron to produce an atom, 87 Sr, with 36 protons and 51 neutrons. As time passed, the number of each isotope changed from its initial value. When a crystal containing $^{87}$ Rb atoms formed from the molten surface of the hot, early Earth during the Hadean eon, the number of these atoms at that initial time can be represented as $\mathrm{N}_{87 \mathrm{Rb}, 0} .$ As time passed, the number of atoms of this isotope changed to $\mathrm{N}_{87 \mathrm{Rb}}$ . C. Justify the relationship between the number of each isotope at any time and the number of each at the time that the molten rock solidified (denoted by the subscript 0): $N_{87}_{S r}=N_{87}_{S r, 0}+N_{87}_{R b, 0}-N_{87}_{R b}$ The decay of unstable radioisotopes is exponential with a half-life of $\mathrm{T}_{1 / 2},$ which for $^{87} \mathrm{Rb}$ is $4.88 \times 10^{10} \mathrm{years}$ : $$N_{87_{R b}}=N_{87_{R b, 0}} e^{-0.693 t / T_{1} / 2}$$ This can be used to replace the initial number of 87 bb atoms, which cannot be measured, with the present-day value: $$\frac{N_{87_{s r}}}{N_{86_{s r}}}=\frac{N_{87_{s r, 0}}}{N_{86 r}}+\left(e^{-0.693 t} / T_{1 /}^{2}-1\right) \frac{N_{87_{R b}}}{N_{86 r}}$$ When the measurements of the numbers of $^{87} \mathrm{Rb}$ and $^{87} \mathrm{Sr}$ were made (Moorbath et al, Nature, 1972), measurements of a second stable isotope of strontium, 86 $\mathrm{Sr}$ , were also made. The ratio of the initial number of 87 Sr and 86 $\mathrm{Sr}$ atoms is the same as today, since the isotopes are both stable. The value of this ratio is $0.71 .$ This is a linear equation in the form $y=a x+b,$ where a is the term in parenthesis containing the half-life of $^{87} \mathrm{Rb} .$ If $Y=N_{87}_{S r} | N_{86}_{S r}$ is graphed versus $N_{87}_{R b} / N_{86} s r^{\prime}$ the slope can be used to determine the time, t, that has passed since the rock formed from melting: $a=e^{0.683 t / T_{1} / 2}-1,$ so $$t=\ln (a+1) \bullet T_{1 /} \quad 2 / 0.693$$ D. Data on the rubidium and strontium isotopes at Isua in Greenland are provided in the table. Analyze these data to obtain the age of formation of these rocks. The solidification of the molten surface of Earth at the end of the Hadean eon (4 to 4.6 billion years ago) and the condensation of liquid oceans provided a medium from which life emerged. The most ancient fossils are colonial, photosynthetic cyanobacteria called stromatolites. As climate change melted the perennial snow covering Greenland, new geologic evidence of the time of that origin was obtained (Nutman et al., Nature 2016) with the discovery of the most ancient stromatolites. These fossils record communities of photosynthetic bacteria embedded in Isua sediments 3.7 billion years ago. Worldwide stromatolite fossils show a decline between 1 and 1.3 billion years ago.

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Key Concepts

Molecular Clock

A molecular clock uses the mutation rates of biomolecules, such as proteins or DNA, to estimate the time in prehistory when two species diverged from a common ancestor. By comparing conserved sequences across different organisms, scientists can infer evolutionary relationships and the timing of evolutionary events, further refining our understanding of the pace of prokaryote evolution.

Fossil Record Analysis

The fossil record provides tangible, physical evidence of past life forms and their evolutionary transitions. By correlating fossil data with other forms of geological and molecular evidence, scientists can create a timeline of life’s history on Earth, validating models that span from the origin of life to the evolution of complex organisms.

Radioactive Decay and Half-Life

Radioactive decay is a process where unstable isotopes transform into stable ones at a constant rate, described by their half-life, which is the time required for half of the original quantity to decay. This principle is fundamental in dating ancient rocks and geological formations, offering a timeline for the formation of the Earth and the emergence of early life.

Isotope Ratio Dating

Isotope ratio dating involves measuring the ratios of parent to daughter isotopes in a rock sample. Since these ratios change predictably over time due to radioactive decay, they provide a reliable mathematical method for determining the age of rock formations and constraining the timeline for the origin of life.

Mathematical Modeling in Geochronology

Mathematical modeling in geochronology applies algebraic and exponential decay equations to data from isotope measurements. By establishing linear relationships between isotope ratios, scientists can extract precise time estimates, thereby integrating quantitative methods with geological and biological evidence to date significant events in Earth’s history.

Multidisciplinary Evidence Integration

The integration of evidence from biology, geology, chemistry, and mathematics is critical for developing a comprehensive model of the origin and evolution of life. Each discipline contributes complementary methods and perspectives, from the molecular clocks of biology to the radioactive dating techniques of geology, ensuring that conclusions are supported by converging lines of independent analysis.

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