NB: Work in progress.
What is the relationship between the different types of working memory or short-term memory and other types of reasoning abilities (non-working memory reasoning tasks including verbal ability, numerical, spatial, etc.)? Are the different measures of short-term and working memory measuring approximately the same thing?
This is a good question, but you are a funny person: say hello to positive manifold.
The concept of the general factor of intelligence emerges from the observation that all cognitive tasks are positive correlated with one another, or display positive manifold. It's as though they're all tapping into this invisible phlogiston, the general factor of intelligence/psychometric g.
Is there a relationship between these variables?
As above. The reason why WM is most predictive of academic achievement is essentially because it's thought that it's tapping into the general factor most.
Somebody who has a strong verbal working memory may generally… Or on the other hand, if somebody has a strong visual-spatial working memory they may generally perform well on intelligence tests on other types of visual-spatial tasks
What you are saying sounds perfectly cogent, but you are making one important assumption here that I don't necessarily agree with: that visuo-spatial WM and verbal WM are so thoroughly dissociable that one can have one that is stronger than the other in the way that I kick a ball real good with my right foot, but am a total ponce with my left foot. Although they are considered separate cognitive structures, I would anticipate that they're still very highly correlated in most people, individual differences notwithstanding.
Of course, there are many other factors that affect ability and learning. Working memory would be a small determinant but a determinant nonetheless.
Here, I disagree. Have you ever attempted to entertain a complicated concept comprising multiple components, only to have it "fall out of your mind" for lack of a better word? In order to process complicated concepts, you need to have some. Working memory is king, and all other abilities are subservient to it.
How common is the occurance of individuals that have poor verbal working memory and high verbal reasoning scores on intelligence tests for example?
I am going to make a bold a priori claim: it is simply not possible for this to occur.
To argue my point, consider what you are implying: suppose someone was reading a passage of text with a long sentence. If they had very low verbal WMC, what would happen is that the beginning of the sentence would decay before they got to the end; they could never hold the information in the fore of the mind sufficiently long enough to process it, prod it, and synthesise an idea. Likewise for a sophisticated verbal reasoning task; a complex reasoning item has multiple components that must be considered simultaneously.
Effectively, what I am saying is that robust WMC is a necessary but insufficient component of verbal reasoning ability.
How about for visual-spatial working memory and non-working memory visual-spatial scores on intelligence tests?
I'm a little confused by this, but I think you're making the same analogy as above. Same deal. However, I will make the point that WMC would represent the bottleneck in cognitive resources that would predict performance.
Having made this claim simply from first principles, let me dig up some evidence for my claims.