I have a plot like this in my paper, but one of the co-authors says The x-axis is backward. I think as long as keeping all figures in the same style, it is ok. But I am not sure if there is really such a rule that years should increase from left to right? My field is environmental science.
I think readers will be strongly expecting that time increases from left to right in a graph. It's probably not a "rule" that you'll find written down anywhere, but it's certainly the overwhelmingly common practice. Having time go from right to left will very likely confuse your readers, and I don't think it should be done unless there is a very strong reason for it.
The "rule" is that you should create figures that make it easy for readers to understand what you are showing. That's because we use figures to convey information. So, if your choice of axis is confusing readers, then you've violated the rule. Looking at your figure, I find it confusing, and several of the others here appear to have had the same reaction.
So yes, in this sense, there is a "rule" that years should increase left-to-right unless you have a very specific reason to it the other way around, and that reason is to make something easier to understand -- for example, if you were talking about what someone would experience who is traveling backward in time.
As others have already pointed out: The convention is that the numbers should increase from left to right. And even though it's not really a rule, but only a convention, it is so common that any deviation might be hard to justifiy.
However, it might be the case that you're just using inappropriate labels. You mentioned that your field is environmental science, but did not exactly say what the graph shows. For example, if your graph shows information about something like "How much of a certain substance that was emitted in year X can still be detected today", then the order might make sense. But then, the labels should be "The number of years that have passed", turning the absolute years into a duration, then being properly ordered:
^ | | +-------|----------------|------------...-----------------|-----------> after 1 year after 10 years ... after ~100 years (from 2017) (from 2007) (from 1917)
(That's only a wild guess, based on wondering why you chose the "wrong" direction in the first place - but you might think about it...)
It is most common to increase chronologically from left to right any time you plot a timeseries along an x-axis, so that would be the standard unless you have a good reason not to do it that way. You are certainly allowed to do it differently - but you should have a good reason.
If you didn't do it that way a reader will tend to assume there must be some specific reason you chose to do it in a non-standard way. Alternatively, they will assume this must be done in the usual way so many readers will initially interpret it as if it was done in the usual way.
For your example image, even though I knew to pay attention to the x-axis, I initially thought there was a decrease in whatever you were studying over time. It took me a few extra moments to go, "oh, right, its the other way around, so I have to flip the trend...so it's actually been increasing over time, yes?"
One way to think of it is: readers are accustomed to being right-ward facing, wondering what comes next in the series. If you were trying to estimate what the past must have been like, based on more recent times, then it makes sense to start with the most recent time period on the left. If you are trying to imagine how things will be in the future, it makes more sense to start with the oldest time period and work towards the future on the right of the scale.
The problem is that axes usually can be thought of a having an origin at 0 and extend from there in negative or positive directions. Normally on a horizontal axis the positive direction is to the right and negative is to the left. So moving from left to right moves to higher numbers. Of course time series plots don't usually show year 0, but you might want to think about where the origin (x=0) would be on your graph. It's true that this is really just a convention and probably one enforced by people who are used to left to right languages (not to mention people who think maps should have north at the top).
Backwards graphs are fairly common in some circles: Source
Is it acceptable?
If the paper is written in a right-to-left language - then yes, but then - please also place the Y axis labels on the right side of the figure.
Otherwise, it's only appropriate if:
you have a reason to plot your figures like this, and
you clearly indicate, graphically, the direction of progression along the X axis, with text or graphics or both, e.g.
(ugly PNG image, but you catch my drift); and it wouldn't hurt to switch the Y-axis labels to the right right in this case as well.
A graph axis is a (segment of a) number line. Numbers increase to the right on a number line. Not all variables are numerical and therefore not all variables support axes: categorical variables are a prominent example.
The first thing readers notice about your graph (even before meaningfully looking at it) is that there is a decreasing trend. Do you intend to convey that some quantity is decreasing? If so, then this graph conveys your intent.
Only after carefully inspecting the horizontal axis does a reader discover that you have a non-numerical independent variable (because your labels are not in number line order). Do you intend to treat years as non-numerical data? If so, then this graph conveys your intent.