Fruit Fly Forces

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The Spotted wing drosophila, Drosophila suzukii, is a small fruit fly similar to the model organism Drosophila melanogaster. However, D. melanogaster will only infest fruit that is rotting or past its prime. D. suzukii infests ripe, healthy fruit, lays eggs in it, and destroys its commercial value. Estimates are that hundreds of millions of dollars are lost each year to D. suzukii in the US, where it is an invasive species first observed in California in 2008. (It's been spreading since then.)

Insects have a specialized organ called an ovipositor which they use to lay eggs. In this problem, we will study the mechanics of the ovipositor to get insight into why D. suzukii infests ripe blueberries whereas D. melanogaster and related native species do not. (Another reason some scientists study ovipositors is that they are mechanically similar to microsurgical probes being developed for minimally-invasive surgery.)

Here's a photo of a female D. suzukii, total body length about 2.5mm.

The ovipositor is at the rear of the fly, and you can see closer views in these images. The first compares the ovipositor from D. suzukii (left image) to D. simulans, another common species in the US which does not infest ripe fruit.

Here is an electron microscope image of the D. suzukii ovipositor.

Do

1. There is no simple, complete theory of when a knife will penetrate a piece of leather or an insect ovipositor will penetrate the skin of a fruit. However, the pressure applied is generally more useful than the force in these situations. Explain why you think this is the case. (Compare the problem: Stiletto heels.)

2. Estimate the length of the D. suzukii ovipositor, in mm. Please explain your reasoning.

3. The ovipositor has numerous sharp, serrated edges which it uses to cut into the skin of fruit such as blueberries. Estimate how many times as large is the force D. suzukii can apply with the serrated edges, as compared to a smooth ovipositor. Please explain your reasoning.

4. Estimate how many times as large the pressure is that D. suzukii can apply due to serrations. Please explain your reasoning.

5. It appears that a critical factor in whether an insect oviposits in a particular fruit is the difficulty of penetrating the fruit’s skin. In a series of trials, scientists at Maryland used a device called a penetrometer to measure force needed for a certain pin to penetrate blueberries that D. suzukii often infests. They found that it takes 27 ± 3 centiNewtons of force to penetrate a blueberry skin with a pin similar in shape to the D. suzukii ovipositor, but unserrated. In a similar study, scientists in Mexico found that ripe guavas that D. suzukii infests take a force of 53 ± 2 centiNewtons to penetrate, but also that D. suzukii only rarely infests early-ripe, firmer guavas with a penetration force of 89 ± 3 centiNewtons.

Across the animal kingdom, muscles work pretty much the same way everywhere. Every muscle can generate a force per unit cross-sectional area of roughly 200 kPa. Could the insect reasonably generate the amount of force scientists used to penetrate a blueberry or guava? To answer this, think about how big a muscle would it likely need in relation to its body size. What does this tell you about the value of the serrations? Please explain your reasoning.

Alyssa Truong & Mark Eichenlaub  9/17/17