convergent evolution

Examples of convergent evolution in the following topics:

• Convergent Evolution

  • Convergent evolution occurs in different species that have evolved similar traits independently of each other.
  • This phenomenon is called convergent evolution, where similar traits evolve independently in species that do not share a recent common ancestry.
  • Convergent evolution describes the independent evolution of similar features in species of different lineages.
  • Convergent evolution is similar to, but distinguishable from, the phenomenon of parallel evolution.
  • The opposite of convergent evolution is divergent evolution, whereby related species evolve different traits.

• Evolution of Reptiles

  • Pterosaurs had a number of adaptations that allowed for flight, including hollow bones (birds also exhibit hollow bones, a case of convergent evolution).

• CAM and C4 Photosynthesis

  • Over 90% of plants use C3 carbon fixation, compared to 3% that use C4 carbon fixation; however, the evolution of C4 in over 60 plant lineages makes it a striking example of convergent evolution.

• Processes and Patterns of Evolution

  • The evolution of species has resulted in enormous variation in form and function.
  • Sometimes, evolution gives rise to groups of organisms that become tremendously different from each other.
  • When two species evolve in diverse directions from a common point, it is called divergent evolution.
  • This phenomenon is called convergent evolution, where similar traits evolve independently in species that do not share a recent common ancestry.
  • These physical changes occur over enormous spans of time and help explain how evolution occurs.

• Evidence of Evolution

  • Evidence for evolution has been obtained through fossil records, embryology, geography, and molecular biology.
  • The evidence for evolution is compelling and extensive.
  • Another form of evidence of evolution is the convergence of form in organisms that share similar environments.
  • DNA sequences have also shed light on some of the mechanisms of evolution.
  • Explain how the fossil record has aided in the development of the theory of evolution

• Tips for Testing Series

  • Convergence tests are methods of testing for the convergence or divergence of an infinite series.
  • Convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence, or divergence of an infinite series.
  • When testing the convergence of a series, you should remember that there is no single convergence test which works for all series.
  • Here is a summary for the convergence test that we have learned:
  • Formulate three techniques that will help when testing the convergence of a series

• Absolute Convergence and Ratio and Root Tests

  • An infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute value of the summand is finite.
  • (A convergent series that is not absolutely convergent is called conditionally convergent.)
  • The root test is a criterion for the convergence (a convergence test) of an infinite series.
  • otherwise the test is inconclusive (the series may diverge, converge absolutely, or converge conditionally).
  • The red sequence converges, so the blue sequence does as well.

• Development of the Peripheral Nervous System

  • During neurulation, the borders of the neural plate, also known as the neural folds, converge at the dorsal midline to form the neural tube.
  • The emergence of the neural crest was important in vertebrate evolution because many of its structural derivatives are defining features of the vertebrate clade.

• Evolution of Angiosperms

• Comparison Tests

  • The limit comparison test is a method of testing for the convergence of an infinite series, while the direct comparison test is a way of deducing the convergence or divergence of an infinite series or an improper integral by comparison with other series or integral whose convergence properties are already known.
  • Example: We want to determine if the series $\Sigma \frac{n+1}{2n^2}$ converges or diverges.
  • In both cases, the test works by comparing the given series or integral to one whose convergence properties are known.
  • If the infinite series $\sum b_n$ converges and $0 \le a_n \le b_n$ for all sufficiently large $n$ (that is, for all $n>N$ for some fixed value $N$), then the infinite series $\sum a_n$ also converges.
  • The series $\Sigma \frac{1}{n^3 + 2n}$ converges because $\frac{1}{n^3 + 2n} < \frac{1}{n^3}$ for $n > 0$ and $\Sigma \frac{1}{n^3}$ converges.