No, AE doesn't have any such thing. You could try the various particle systems and modulate particle sizes by keyframing some properties or using parameter maps, but outside that I don't see much. Even if you were to buy e.g. Plexus and use the various options there to control dot sizes it would still not compare to AI's function. Some of that stuff may of course also benefit from using expressions down to the point of manually placing individual circles and animating their scale...
The way to do this is to start in Illustrator, create your tapered lines there, Expand appearance in Illustrator, then import as a comp in AE and convert vector layers to shapes. There are two ways to animate the creation of a tapered line. If you use Offset Paths instead of Trim Paths then the line starts growing from the thinnest point and moves to the thinnest point. If you use Trim Paths then you must have a straight tapered line and you have to set the right first vertex and then animate both start and end values to make the line start at the thinnest end and extend to the thickest end.
Here's what a comp looks like:
Here's a zip file for you with both a CC and a CS6 project inside. Sometimes AE is buggy creating shape layers from vector layers. If that happens you can add a stroke, then just turn the stroke off in the AE project. I hope this helps. There is usually a way to do what you want in AE if you think outside the box. Here's what it looks like (Click on the animated gif to see it)
Thanks for the answers guys
It's unfortunate that AE doesn't do it as simply as Illustrator, but thank goodness for all the work-arounds
YOU CAN DO IT IN AE
I was looking for the same thing and found this!
You just manipulate the "Brush Time Properties" setting in the "Write On" effect.
i hope afte effects will include a stroke with width variation manipulation like anime studio software* not effect write on* i would like the stroke stays in footage all time.
You can with 3dstroke from trap code.