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In this alternate Earth, all the species of fish, amphibian, reptile, mammal and bird combine to make up only 0.5% of all animal life on the planet (presented on the pie chart in blue.) It doesn't sound much compared to the two or three percent back home, but it's still quite a lot of invertebrates!

As with back home, the other 80% of animals on this alternate Earth make up the arthropods.

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By merging the two presented pies into one, what would this new pie chart look like?

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    There is no well-defined way to "merge" them. You can merge them any way you want. Do you have an idea of how you want to merge them? – 2017-01-16
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    I don't know how. – 2017-01-16
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    Unless you have an idea of how you want to merge them (like any kind of specifications you would have for what the merged pie chart would look like), this isn't really a mathematics question. – 2017-01-16
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    Just the two pie charts presented here merged together so that the arthropods are highlit with the vertebrates. – 2017-01-16
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    I don't know, it seems doable to me. Comprising $99.5\%$ of life on Earth $1_B$ (that's the one that isn't our Earth), the invertebrates take up $0.995 \cdot 360^{\circ} = 358.2^\circ$ of the first chart. We could just keep dividing up the Invertebrate section: $80\%$ of that $358.2^\circ$, or $0.8 \cdot 358.2 = 286.56^\circ$, would be devoted to Arthropods, the other portion "Non-Arthropod Invertebrates" I guess (a new color). Then, you can subdivide this $80\%$ of $99.5\%$ according to how the Arthropods (yeah yeah, "arthropoda") divide up the 2nd chart, and so on. – 2017-01-16

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The logic behind a pie chart is that the ratios of areas representing populations is the same as the ratios of the populations themselves. I think the question is perfectly well-formed, if we impose a reasonable interpretation: That we would like to condense all of the given information into a single pie chart. And since it's all information about animals, and all animals are displayed in the first chart (albeit with much less detail than the second), we can incorporate the second chart into the first.

Pieces of a pie chart are represented by sectors, and to specify (the size of) a sector in a given circle, we need only specify its (central) angle. So: $\text{sectors} \longleftrightarrow \text{angles}$.

Since invertebrates make up $99.5\%$ of life on Earth A (that's the one that isn't our Earth; we live on Earth 1), they take up $99.5\%$ of $360^\circ$, so $0.995 \cdot 360^{\circ} = 358.2^\circ$ of the first chart.

Since we're given more information about the Invertebrate population than is displayed in the first chart, we can just keep dividing up the Invertebrate section:

  • $80\%$ of that $358.2^\circ$, or $0.8 \cdot 358.2 = 286.56^\circ$, would be devoted to Arthropods, the other portion "Non-Arthropod Invertebrates" I guess (a new color).

    • Then, you can subdivide this $80\%$ of $99.5\%$ according to how the Arthropods (yeah yeah, members of "Arthropoda") divide up the 2nd chart:

      • Suppose that on Earth A, $60\%$ of the Arthropods are Insects: that would be a sector with angle $0.6 \cdot 0.8 \cdot 0.995 \cdot 360^\circ = 171.936^\circ$.

      • If $20 \%$ of the Arthropods are Crustaceans like Zoidberg, that would be represented by a sector with angle $0.15 \cdot 0.8 \cdot 0.995 \cdot 360^\circ = 57.312^\circ$, and so forth for the rest (only Chilopods and Arachnids).

I've been making estimations about the exact percentages of how the Arthropods are broken up, but hopefully the example is illustrative. In this scenario, our sectors and their corresponding angles look something like

\begin{array}{ll} \rm Sector & \rm Angle \\\hline \rm Vertebrates: & 1.8^\circ \\ \text{Non-arthropod Invertebrates}\ : & 71.46^\circ \\ \rm Insecta : & 171.936^\circ \\ \rm Crustacea : & 57.312 \\ \rm Remaining: & (57.492^\circ \text{ remaining}) \end{array}

I don't have a great program for a quick drawing, but hopefully you get the idea. You could even do something fancy to draw attention to the fact that Arthropods fall into the Invertebrate category (like outlining their sectors with the Invertebrate color, or some kind of over-arching label saying that Insecta etc. are Arthropods, or that Arthropods are Invertebrate)