"Lifetime prevalence rates of 53.5% for depressive disorder 73.5% for anxiety disorders and 37.5% for ADHD [attention-deficit hyperactivity disorder] were found."
Those were the figures arrived at by Alexandru Gaman and colleagues  who set about investigating the "prevalence rates of psychiatric co-morbidities" among other things in a cohort of over a hundred adults diagnosed with "high-functioning" autism via the quite recently revised DSM-5 criteria. I've stressed the words 'high-functioning' to denote this being the authors' words not mine (personally, I'm not so sure that general level of functioning is all that good as a descriptor).
Various other observations were made by authors such as the finding that: "Subjects with psychotic co-morbid symptoms had a more severe social deficit" which might tap into some other discussions being had on how some of the screening instruments talked about with autism in mind are seemingly not adverse from potentially picking up other labels with a psychosis element to them (see here). I say that also with the understanding that at least for some, autism and psychosis are not diagnostically unstrange bedfellows (see here).
I've zoomed in on the anxiety disorder(s) bit to the Gaman findings because of their very high lifetime prevalence and because, day-to-day, anxiety disorders can be absolutely disabling for many people on the autism spectrum (see here). Indeed, with all the very positive talk about things like employment and further education opportunities [slowly] increasing for autistic young people and adults, one of the details that does not seem to be talked about as much is how issues like anxiety can significantly hinder not only efforts to get a job/student place but also keeping that job/student place in the longer term (see here). Talent is being outshone by crushing anxiety in some cases.
Gaman and colleagues concluded by talking about how identification of something like anxiety disorder is "a crucial clinical issue." I would very definitely agree with this viewpoint but more than that, efforts now need to go into what can be done about treating/managing such anxiety to make people's lives easier (see here); accepting that we still have some distance to go in this process . I'd also like to see some kind of research parity being arrived at specifically with regards to the question: how prevalent and what effects does anxiety have for those NOT described as having 'high-functioning' autism?
To close, having recently been party to some interesting debate on social media about the ins-and-outs, rights-and-wrongs and positives-and-negatives of [exclusive] self-diagnosis with autism in mind, I'd like to link to a paper by Ashwood and colleagues  on how one of the premier 'are you autistic?' self-report schedules is not necessarily fit for purpose when it comes to a self-diagnosis of autism. Indeed pertinent to today's post, how "generalized anxiety disorder may ‘mimic’ ASD [autism spectrum disorder] and inflate AQ [Autism-Spectrum Quotient] scores, leading to false positives" echos a viewpoint that I championed: identity, emotions and politics aside, there is no substitute for a thorough professional assessment when autism is suspected. Outside of such an assessment being potentially pertinent to the idea that autism rarely appears in some sort of diagnostic vacuum (see here), it is perhaps even more important as the DSM-5 criteria for ASD and SCD [social (pragmatic) communication disorder] start to become even more mainstream and what it means/will mean to the concept of autistic identity too...
 Gaman A. et al. Psychiatric co-morbidities in a French cohort of adults with high-functioning autism (HFA). European Psychiatry. 2017; 41: S136.
 Lorenc T. et al. Support for adults with autism spectrum disorder without intellectual impairment: Systematic review. Autism. 2017 Jun 1:1362361317698939.
 Ashwood KL. et al. Predicting the diagnosis of autism in adults using the Autism-Spectrum Quotient (AQ) questionnaire. Psychological Medicine. 2016;46(12):2595-2604.