I wrote a reply, which may or may not make the cut for publication, so I will post it here for you to consider. Maybe you can submit your own reply to the article?
This is an interesting hypothesis, but the author has lost me in the second paragraph by saying that "rhythm" is the only method approved by the Catholic Church. Whether Bovins has confused rhythm with NFP or presumed the two methods are one and the same, it is an inexcusable error in a scientific report.
Rhythm is using a calendar, assuming the "standard" 28-day cycle, to guesstimate when ovulation occurs. It is highly fallible, most obviously because very few women actually experience the "textbook" 28-day model for the menstrual cycle promoted as part of the rhythm method.
Natural Family Planning, or NFP, on the other hand, depends on recognizing certain physical symptoms of fertility and approaching ovulation -- changes in quantity and quality of cervical mucus discharge, the shape, placement and consistency of the cervix itself, and a few more complicated techniques like basal body temperature. It can be used to try to achieve or avoid pregnancy.
NFP is approved by the Church for use in extraordinary circumstances (couple abstain from intercourse during the time a woman is fertile) because it does not interfere with a woman's natural cycles, because it is consistent with a respect for life, and (this is very important!) because it shows respect for the nature of the marital sexual union as an analogy of the mystical union between Christ and His Church. (People think the Church is anti-sex.... ahhhh, if only they knew!)
NFP is proven to be more than 98% effective, more effective than any other contraceptive measure. Of course, it involves the inconvenience of paying attention to fertility symptoms and of a degree of self-denial, but it is extremely effective. Moreover, every couple I know who have practiced NFP are enthusiastic advocates of it -- yes, that includes the men, who say that periods of abstinence enrich their elationships with their wives and make the times of intimacy more gratifying.
Oh -- some studies indicate that NFP couples actually engage in sexual intercourse more times per month than non-NFP couples.
Finally, I am not comfortable with the promotion of "assumptions" without a presentation of the basis from which said assumptions occur. One can easily dismiss the premise that rhythm leads to more deaths in consequence: embryonic deaths can occur from flaws resulting from unhealthy ovum or sperm (ostensibly because of "old" sperm left in the fallopian tube to fertilize the ovum), but they can also occur because of biochemical hostilities brought about by mechanical and/or chemical impositions of artificial birth control methods. However, the thing Catholic consider is that embryonic deaths due to lack of viability is not the result of a hostile act against life in general or the specific conception. This is of paramount importance.
I recommend Bovens and anyone else interested in the subject read Kippley and Kippley, The Art of Natural Family Planning, and the Papal Encyclicals: Pope Paul VI's Humanae Vitae and John Paul II's Evangelium Vitae: John Paul II's work on Theology of the Body (synthesized for easier mental consumption by Christopher West) is also seminal.