As far as breeding with EEs, there is really no way to tell, but he might be able to past the color to his children. Here's some of my experiances:
First Generation: The Start
I started out with Douglas. When I got him, I got him and a Barred Rock rooster. No hens. Douglas was an EE. Here's a picture of him:
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Second Generation:
The second generation was his children. I kept all his daughters, which was four in all, and one of his sons. All the hens layed blueish-green eggs. I had bred Douglas with some brown egger hybrids. All his daughters came out as EE hybrids. Here's some pictures of the second generation:
Douglas' son Jose`:
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Douglas' daughter Marvalo:
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His daughter Shiloh. Her eggs were more blue than green:
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His daughter Chenoa:
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His daughter Vienna. She layed more of green eggs than blue:
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Third Generation: Jose`'s Daughters
For the third generation, I bred Jose` with brown egger hens. He had two daughters, Cave and Bailey. They had single combs and layed brown eggs. Here's a picture of them:
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Fourth Generation:
The fourth generation was Vienna's daughter with a NHR rooster. Sorry, this probably been in third generation now that I think about it.... It came in fourth somewhere, but you can look at it as third. Vienna's daughter Katie layed green eggs. Here's a picture of her:
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That was my experiance with the EE generations. I called the group Douglas Whites after Douglas. They were hybrid EEs that were pretty good egg layers with the "dual-purpose" weight.
If I was you, I'd breed your rooster with a white-egger to preserve the pigment. If you breed him with brown eggers, you might get olive eggs. What gene he carries will be passed down. Now, I don't know how "culling" him would tell you what egg color gene he's carrying. Either way, if he is dead, how would that help you? As far as I know, you can't breed a dead rooster. That's kinda confusing me. Perhaps you can post a picture of him? I used to figure out what a EE was going to lay for a color of egg by looking at them. (This turned out to be 50/50. Not very accurate at all. I was right once. Ok, I just like looking at pictures of people's roosters. I love roosters, and I love EEs.

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