Critique of AIC usage This note https://www.significancemagazine.com/science/580-graphical-interpretations-of-data-walking-the-line provides an interesting interpretation of something that first looks likes a trend but also has an interpretation as a  step change.
The following questions are to understand AIC usage better by critiquing the article example.

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*The AICc (AIC with a correction for small sample sizes) must be used here? Although this is not stated and thus it is unknown whether it was.

*Is there a problem with checking all the partitions of the years and taking the best one?

*Are there better alternatives to using AIC as done in the article?

The use of AICc would be required over AIC, as commented by @usεr11852. Thus the answer to question one is “yes”.
The obvious caveats here are such a small sample size and we do not know the author’s working.
The first figure below was published in the journal British Birds, and includes a trend line. The second figure is the author of the article having an alternative interpretation. The utility of the author’s analysis is it asks the question of what happened to cause the step change. I do not think that the author’s step change figure is necessarily correct, but it does give a further avenue of research (was there a step change and if so is it possible to find plausible causes). I like the use of various scenarios being presented in analysis, so there is validity in both figures in my opinion, and both could yield further examination competing with each other, so for example collecting more data other sites or asking domain experts for their input of these figures.


Below is some text from the linked article:
I have no issues with the paper, but is linear regression the best choice? The slope is significant, but the assumption of normal errors for small counts might be a technical objection. Looking pragmatically at the data and considering the problems in the fieldwork (hobbies can be secretive, and a breeding pair that failed early would easily be missed), it seems unlikely that changes of one or two pairs would be important. On the other hand, roughly twice as many pairs bred during the last four years of the study compared to earlier years.
These articles set out to discuss graphs and not statistical methods, so details of the modelling process that can be found in many textbooks are omitted. Obviously this is post hoc modelling, which at this stage is descriptive. Having a count (of nests) as the response variable suggests Poisson rather than normal errors, hence a generalised linear model rather than simple regression. With just 10 years’ data I will ignore serial correlation and time series models. I used the glm command in Stata to compare the null model, simple linear, and step-change models with the break-point at each year in turn, then chose the model with the lowest value for Akaike’s information criterion (AIC).
The best fit (lowest AIC) was the two-means model shown in Figure 3. Purely subjectively, it seems to me a better interpretation of the data than the simple trend and raises the question of what might have happened between 1997 and 1998 to create or allow a step change. (The British Birds paper makes clear there was no change in field methods.)
 A: This is not exactly answering the question, but to me the major problem here is the obsession with finding "the best" and focusing on interpreting what "the best" is (and what may be a "correct" criterion to decide what is the best), while disregarding the simple truth that the data, particularly because of the small sample size, cannot distinguish between these proposals, whatever criterion was used to pick one over the other. Both approaches generate fits that are compatible with the data (quite certainly more can be had), and deciding between them is a pretty meaningless task.
On top of that, it isn't even clear what "best" means - what is the aim? Prediction (a two step model can hardly be used for reasonable prediction as another step may come at any point in the future)? Giving some knee-jerk pseudocausal interpretation (in which case one should probably discourage branding any of these as "best")? Dependence over time issues and more detailed knowledge on what causes whatever "trend" is seen will be important here, and I'm not sure whether anything ignoring this can lead to any insight.
In fact, regarding model selection, different methods come with different implicit definitions of what "best" actually means, and as there are different aims of model selection, this is legitimate. We should get off the idea that whatever method can make the data on their own tell us what "the best fit" is, without any input from our side such as a proper formalisation of what we want to achieve.
Actually for the given data I'd think it better to just show the points without any eye-guiding descriptive fit - I suspect they do more harm than helping. Alternatively one should show more than one.
