Continuous Multi-Variable Timeline Graph

[ClaimQA122333]

Hello everyone! I am super new to Power BI, and therefore if what I ask is nonsensical or impossible, please forgive my ineptitude.

I am currently trying to see if Power BI will be able to help me simplify a lot of my work products that are currently done in Excel, but am running into some problems already.

For background: I measure file performance using 12 different categories, and want to show a continuous performance timeline for each of my file owners. To do that, however, I cannot find the right type of graph/plot. So before I launch into the actual data, I'll simplify it down for example's sake.

I created an example with dummy data to visualize what I mean. 

Let's assume that the file is called "Animals I've Seen This Year" and the categories are the animals. I can get the data to display showing "number of animals" on the Y axis (which I want to change) and "month" on the X axis (which is good).

My question is, is it possible for me to show "animal type" on the Y axis, keep "month" on the X axis, and show the bubbles as a fluctuating line for the duration of the graph? I know that "animal type" dictates the color of the bubbles, and "number of animals" dictates the size, but is there a way for me to show this data without the bubbles overlapping?

Something like this (forgive the crudeness of MS Pain):

I suppose this is a bit of a specific request for a graph, but my knowledge in this field is very lacking so it may actually exist.

Thank you to anyone who can help!

[lbendlin]

Assign your animals an index, and then use the index as the y axis.