#if p=q=0.5 then the difference is gone

[amber-tortoiseshell]

Hello! I just saw your cat colors master post and you seem very knowledgeable on the subject so I have a question. I was reading about the O/o gene for a little school assignment to talk about X linked genes. And since male cats only need one X to show orange color or black color. Wouldn't there be more orange and black male cats than female cats? I always hear people say an orange cat is more likely to be male than female but I never hear people say a black cat is more likely to be male than female. Is there some way for cats to be black that isn't linked to the O gene that changes the ratio of female to male black cats? Or are people just not noticing the ratio in black cats vs orange cats for some reason?

Yes, you're right, there are more black males than females, because the tortoiseshells are diminishing the numbers of both the black and and the red females.

Let's calculate the ratios; let p be the frequency of the black and q is the red allele. (This is also their probability: if you choose a random allele from the cat population, it'll be black with the chance of p and red with the chance of q.)

Black male: p/2 (1/2 of all cats are males and with p chance a male cat has the black allele therefore he is black)

Red male: q/2 (similarly)

Black female: p²/2 (both of her alleles need to be black, so we need to choose twice)

Red female: q²/2 (similarly)

Tortoiseshell female: pq (we need to choose a black and a red allele, and we can do it in two orders, so this is actually the more simple form of 2pq/2)

Let's check: p/2 + q/2 + p²/2 + q²/2 + pq = (p+q+p²+q²+2pq)/2 = 1, because p+q=1 and p²+2pq+q²=(p+q)²=1²=1. Good.

What could be the frequency of the red allele? I don't know, but for the sake of simplicity let's say it 0.2 (so every fifth male cat is orange).

Black male: p/2=0.8/2=0.4 (40%)

Red male: q/2=0.2/2=0.1 (10%)

Black female: p²/2=0.8²/2=0.64/2=0.32 (32%)

Red female: q²/2=0.2²/2=0.04/2=0.02 (2%)

Tortoiseshell female: pq=0.8*0.2=0.16 (16%)

So this means the male:female ratio in red cats is 10:2=5:1 (for every five males there's one female), while in blacks 40:32=5:4 (for every five male there're four females).

You see why it's much easier to notice.

[cryptobully-blog]

Markets Now: Dow Gets Whipsawed by Fed

http://cryptobully.com/markets-now-dow-gets-whipsawed-by-fed/

Markets Now: Dow Gets Whipsawed by Fed

The Dow Jones Industrial Average was sitting pretty at the end of January. And then it wasn’t, as a correction hit. Since then it’s gone up and down and up again, and the wild swings don’t seem likely to end any time soon. With that in mind, we’re keeping a semi-live look on the volatile markets. Here’s the latest from Barron’s reporters…

3:26 p.m. I hate using the word “whipsaw” to describe the market action, but there really is no better one today. The Dow was up. Then it was down. Now it’s up 72.34 points, or 0.3%, at 24,799.61. See, whipsawed. And I wouldn’t be surprised if the blue-chip benchmark finished up 200 points or in the red.

2:53 p.m. Wow. The Dow’s gone from 200 points up to down on the day in almost no time at all. Its fallen 14.17 points, or 0.1%, to 24,713.10, while the S&P 500 has, declined 0.2% to2,712.55 and the Nasdaq Composite has dropped 0.4% to 7,335.62. Could the Fed’s inflation expectation be the cause? “The most notable change to the economic forecasts was the shift higher in the inflation expectations, which show the central tendency above the 2.0% target in 2020,” writes Jefferies Senior Money Market Economist Thomas Simons. “This is something that we have not previously seen from the Fed’s forecast.”

2:07 p.m. Stocks are rising after the Federal Reserve lifted its benchmark interest rate by a quarter point but left its forecast for two more hikes this year unchanged.

The S&P 500 has risen 0.5% to 2,729.46, while the Dow Jones Industrial Average has gained 204.21 points, or 0.8%, to 24,931.48. The Nasdaq Composite has advanced 0.4% to 7395.29. The 10-year Treasury yield has ticked up 0.035 percentage point to 2.91%, while the US Dollar Index has slipped 0.3% to $90.13.

“Pretty much everyone saw this coming, but it’s still a significant event,” writes E*Trade’s Mike Loewengart. “We are another confident step closer to a normalized rate environment.”

Now we just need to see what Fed Chairman Jerome Powell says in his first Q&A.

12:12 p.m. Well, that was quite an hour. When I published my last update, nothing was happening. Then the Dow Jones Industrial Average decided to take off, at least a little bit. The Dow has gained 123.54 points, or 0.5%, to 24,850.81, while the S&P 500 has risen 0.4%, to 2728.02, and the Nasdaq Composite has advanced 0.3%, to 7386.09.

Maybe the market’s betting on a dovish surprise?

10:54 a.m. The stock market may not be doing much ahead of today’s Federal Reserve meeting, but that doesn’t mean there isn’t at least a little bit of action elsewhere. Sure, the S&P 500 has ticked up 0.1% to 2719.05, while the Dow Jones Industrial Average has dipped 10.76 points to 24,716.51, and the Nasdaq Composite has advanced 0.1% to 7373.21. That’s certainly nothing to write home about. But the U.S. Dollar Index has dropped 0.3% to 90.09 today, and we’ll be keeping a close eye on whether the currency leads to more dollar weakness or a rebound.

And then there’s the Treasury market. So far today, the 10-year Treasury yield has risen 0.025 percentage point to 2.901% and the 2-year Treasury yield has risen to 2.337%. The difference of 0.564 percentage point between the two is greater than yesterday’s close of 0.545 point–good news for those worried about the flattening yield curve. “If the net result of today’s FOMC meeting is that the 10’s -2’s spread drops to fresh lows (so below 0.50%) I’ll take that as a pretty significant caution signal on markets,” writes Sevens Report’s Tom Essaye.

6:57 a.m. It’s all about the Federal Reserve today, so it shouldn’t come as a surprise that the market isn’t doing much this morning. S&P 500 futures have ticked up half a point, while Dow Jones Industrial Average futures have risen 5 points. Neither is enough to move the indexes by more than a fraction of a percentage point. Nasdaq Composite futures have fallen 0.3%, but probably would be right around flat if it weren’t for the Facebook (FB) saga.

So what’s the Fed going to do? We know one rate hike is priced into the market, so anything beyond that would be a shock, and few appear to expect that. Instead, all eyes will be on the Feds “dots,” the individual forecasts that can be extrapolated into a prediction for the number of rate hikes to come. Right now, the dots suggest three hikes in 2018 and two in 2019, and the market will be watching to see if those change, says Jones’ Trading’s Michael O’Rourke. “From our perspective, there has been just enough weakness and there are still enough doves at the Fed to keep the forecast at 3 hikes, although many in the market are expecting the upward shift to four,” he says.

Now we just have to wait to see how the market responds.

Markets