How to produce desired type of trendline?

I'm using Microsoft Office Standard 2010 v. 14.0.7194.5000 (32-bit) (old, I know, I hope that won't be a problem with using this community).

For practice, I'm trying to recreate the following graph from the original data (produced and graphed in 2008 (by Hummel et al. 2008), but I'm not 100% certain which version of Excel was used, if it was used at all):

Thus far, I have generated the following:

As far as I can tell, all the data points match (which it should, because as I said, I have access to the original data), but as you can see, the trouble I'm having is with the trendlines. I've tried every trendline option available in my version of Excel. In the picture provided, I've used a logarithmic trendline, but as you can see, it doesn't have the same fit as the one in the graph I'm trying to recreate, as those rise rapidly and then level off. The ones in the smaller number range are very similar, but the upper most (especially the yellow "Angiopteris evecta" are very different. An exponential trendline would seemingly have the right shape, but of course it is "concave" whereas I need a "convex" curve. 

Does anyone have any suggestions for what my problem may be or what type of trendline might be in use in the example? Or is the upper one is clearly not from any version of Excel and I've no hope of getting a similar line?

I've attached a piece of the data I'm working with, if that's any help. Thank you!