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91Ó°ÊÓ

Among a population of tadpoles, the correlation coefficient for size at metamorphosis and time required for metamorphosis is \(-0.74 .\) On the basis of this correlation, what conclusions can you draw about the relative sizes of tadpoles that metamorphose quickly and those that metamorphose more slowly?

Short Answer

Expert verified
Larger tadpoles metamorphose more quickly, while smaller ones take longer.

Step by step solution

01

Understanding Correlation Coefficient

The correlation coefficient of \(-0.74\) indicates a strong negative relationship between the size of tadpoles at metamorphosis and the time they require for metamorphosis. This means that as one variable increases, the other tends to decrease.
02

Interpreting the Negative Correlation

Because the correlation is negative, we can conclude that larger tadpoles tend to require less time to metamorphose, whereas smaller tadpoles tend to take more time. The magnitude of \(-0.74\) indicates this relationship is strong.
03

Drawing Conclusions

In terms of relative sizes, tadpoles that metamorphose quickly are typically larger, while those that take longer to metamorphose are generally smaller. This conclusion is directly derived from the negative correlation between size at metamorphosis and time required for it.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Negative Correlation
In statistics, correlation is a measure that describes the extent to which two variables are related. A negative correlation means that when one variable increases, the other decreases, and vice versa. The range for the correlation coefficient is from -1 to 1. When you see a correlation of -0.74, it suggests a strong negative relationship.
This simply implies that there is a tendency for the variables to move in opposite directions with substantial strength. Understanding this helps in predicting one variable by observing changes in the other. A strong negative correlation, like -0.74, often inspires confidence in these predictions. Remember that correlation does not imply causation, meaning the decrease in one variable caused by another is not always confirmed.
Tadpole Metamorphosis
Tadpole metamorphosis is the process by which tadpoles transform into frogs. This is an important stage in the life cycle of amphibians. During metamorphosis, tadpoles undergo significant changes, such as the development of legs and the absorption of their tails.
  • Metamorphosis is crucial for the survival and adaptation of amphibians to a new habitat.
  • It involves a shift from an aquatic environment to a more terrestrial one.
Tadpoles may differ in size and the time they take to complete metamorphosis, and these factors can be influenced by various environmental and genetic factors. Understanding the relationship between size and metamorphosis time helps biologists study the effects of these factors on amphibian development and adaptability in their environment.
Biological Statistics
Biological statistics is the application of statistical analysis to biological data. These statistics help scientists understand complex relationships in living organisms. Through statistical methods, biologists can validate their hypotheses and draw accurate conclusions.
  • It allows for the interpretation and prediction of biological processes.
  • Researchers can assess the reliability of their data.
  • It aids in understanding relationships between different biological variables, such as size and development time.
In the context of tadpole metamorphosis, biological statistics help to analyze how various factors, such as size and metamorphosis time, are interlinked. This aids in making sound scientific conclusions that can influence conservation strategies and biological research directions.
Size and Time Relationship
The relationship between size and time in tadpole metamorphosis highlights the biological interplay between growth and developmental speed. A negative correlation was observed, which means that size and metamorphosis time have an inverse relationship.
  • Larger tadpoles tend to metamorphose faster than smaller ones.
  • Smaller tadpoles may require more time to complete their development.
This relationship can be profound for understanding survival strategies. Faster metamorphosing tadpoles might avoid predators longer by leaving the water sooner. Conversely, those that take longer might face more threats but gain other advantages.
Understanding these dynamics is essential for ecologists and conservationists in predicting species' responses to environmental changes.

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Most popular questions from this chapter

A rancher determines that the average amount of wool produced by a sheep in her flock is 22 kg per year. In an attempt to increase the wool production of her flock, the rancher picks the five male and five female sheep that produce the most wool; the average amount of wool produced per sheep by those selected sheep is \(30 \mathrm{~kg} .\) She interbreeds these selected sheep and finds that the average wool production among their progeny is \(28 \mathrm{~kg} .\) What is the narrow-sense heritability for wool production among the sheep in the rancher's flock?

Eugene Eisen selected for increased 12 -day litter weight (total weight of a litter of offspring 12 days after birth) in a population of mice (E. J. Eisen. 1972. Genetics 72:129-142). The 12-day litter weight of the population steadily increased but then leveled off after about 17 generations. At generation \(17,\) Eisen took one family of mice from the selected population and reversed the selection procedure: in this group, he selected for decreased 12 -day litter weight. This group immediately responded to the reversed selection: the 12 -day litter weight dropped \(4.8 \mathrm{~g}\) within 1 generation and dropped \(7.3 \mathrm{~g}\) after 5 generations. On the basis of the results of the reverse selection, what is the most likely explanation for the leveling off of 12 -day litter weight in the original population?

The following data are the numbers of digits per foot in 25 guinea pigs. Construct a frequency distribution for these data. $$ 4,4,4,5,3,4,3,4,4,5,4,4,3,2,4,4,5,6,4,4,3,4,4,4,5 $$

What information does the correlation coefficient provide about the association between two variables?

Many researchers have estimated the heritability of human traits by comparing the correlation coefficients of monozygotic and dizygotic twins (see pp. \(747-748\) ). One of the assumptions made in using this method is that monozygotic twin pairs experience environments that are no more similar to each other than those experienced by dizygotic twin pairs. How might this assumption be violated? Give some specific examples of how the environments of two monozygotic twins might be more similar than the environments of two dizygotic twins.

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