After a jury trial, the defendant was convicted of aggravated rape, kidnapping, assault and battery by means of a dangerous weapon, and assault and battery on one woman; he was also convicted of rape, as a lesser included offense of aggravated rape, on another woman. On appeal, he argues primarily that the judge’s instructions to the jury, which tracked the Superior Court model jury instructions, misstated the law of rape. Specifically, he maintains that the language “sexual intercourse is complete upon penetration, no matter how slight, of a person’s genital opening” precludes his conviction in a case where the victim withdrew consent during intercourse. The defendant also argues that the cases were improperly joined and that an expert witness failed to lay a sufficient foundation for the admission of deoxyribonucleic acid (DNA) evidence. We affirm.
Instructions. The jury heard evidence that one woman, victim 1, was a sex worker who initially agreed to sexual intercourse with the defendant for a fee. During intercourse, according to the victim’s testimony, the defendant became very aggressive and forceful. When she asked him to slow down, “he started becoming more aggressive.” She tried to squirm away, telling him to stop, that this was not what was arranged; in response, he “put more weight on top of [her], and wrapped his arm around [her] two arms and put his hand over [her] mouth” so that she could not scream. His weight restrained her so that she “couldn’t fight him off.” Afterwards, as she was crying and in pain, he took the money he had paid her from her pants pockets and left.
During his instructions at the end of the case, the judge told the jury, inter alla,
“Rape is natural sexual intercourse with another person by force and against that person’s will, or that compels a person to submit to such an act by threat of bodily force or violence. . . . ‘Natural intercourse’ . . . consists of inserting the penis into the female sex organ. Natural sexual intercourse is complete upon penetration, no matter how slight, of a person’s genital opening. . . . The [C]ommonwealth must prove that at the time of penetration the complainant did not consent, or in other words that the intercourse was against the complainant’s will.”
*659As there was no objection to any part of the charge, we review for a substantial risk of a miscarriage of justice. See Commonwealth v. Freeman, 352 Mass. 556, 563-564 (1967).
On appeal, the defendant argues for the first time that the jury could not reasonably have found him guilty of rape. He does not suggest that consent may not be withdrawn during intercourse or that the facts themselves are insufficient to support a charge of rape.1 Rather, he maintains that the judge’s instructions did not permit the jury to find him guilty on these facts. He argues that
“[ajssuming that consent can be withdrawn after consenting to penetration and that therefore the judge’s instruction was not an accurate statement of the law, the instruction became the law of the case. ... In the present case, at no point did the judge tell the jury that intercourse could become rape if the [victim] consented to being penetrated.”
The Massachusetts rape statute “follows the common-law definition of rape, and requires the Commonwealth to prove beyond a reasonable doubt that the defendant committed (1) sexual intercourse (2) by force or threat of force and against the will of the victim.” Commonwealth v. Lopez, 433 Mass. 722, 726 (2001). See Commonwealth v. Sherry, 386 Mass. 682, 687 (1982) (“The essence of the crime of rape, whether aggravated or unaggravated, is sexual intercourse with another compelled by force and against the victim’s will or compelled by threat of bodily injury”). “As to the first element, there has been very little disagreement. Sexual intercourse is defined as penetration of the victim, regardless of degree” (emphasis supplied). Commonwealth v. Lopez, supra at 726-727.
Appellate courts in other States have interpreted language similar to this jury instruction to permit a conviction on these facts. See McGill v. State, 18 P.3d 77, 84 (Alaska Ct. App. 2001) (“Our statutes do not limit ‘sexual penetration’ to the moment of initial penetration”); State v. Siering, 35 Conn. App. 173, 182 (1994) (“We construe the statutory reference to pene*660tration as establishing the minimum amount of evidence necessary to prove that intercourse has taken place. The statute does not read that ‘intercourse is complete’ upon penetration; rather it provides that ‘penetration, however slight, [is sufficient] to complete . . . intercourse’ ”); State v. Bunyard, 281 Kan. 392, 412 (2006) (“The defendant’s narrow definition of penetration fails to comport with the ordinary meaning and understanding of sexual intercourse, which includes the entire sexual act. . . . Rather than limiting the definition of intercourse, the phrase ‘any penetration, however slight, is sufficient to constitute sexual intercourse’ establishes the threshold of evidence necessary to prove that intercourse has occurred. . . . [The statute] proscribes all nonconsensual sexual intercourse that is accomplished by force or fear, not just the initial penetration”); State v. Robinson, 496 A.2d 1067,1069 (Me. 1985) (“In anybody’s everyday lexicon, the continued penetration of the female sex organ by the male sex organ, after the time either party has withdrawn consent, is factually ‘sexual intercourse’ ”); State v. Baby, 404 Md. 220, 260 (2008) (where the Court of Appeals of Maryland “agree[d] with the Connecticut appellate court [in Sierling, supra,] that concluding that the act of penetration ends the act of sexual intercourse would lead to absurd results not contemplated by the drafters of [the Maryland] rape statute”). Contrast State v. Way, 297 N.C. 293, 297 (1979) (“If the actual penetration is accomplished with the woman’s consent, the accused is not guilty of rape, although he may be guilty of another crime because of his subsequent actions”).2
In arguing that the judge’s instruction did not permit a conviction in the situation where consent at the initiation of intercourse was later withdrawn, the defendant reads the judge’s language too narrowly. The instruction that “[njatural sexual intercourse is complete upon penetration, no matter how slight, of a person’s *661genital opening,” means that initial penetration is sufficient to accomplish the act of intercourse; it does not imply that penetration, or intercourse, does not continue thereafter. In addition, the words “[t]he [C]ommonwealth must prove that at the time of penetration the complainant did not consent” were immediately followed by the clarifying language “or in other words that the intercourse was against the complainant’s will” (emphasis supplied). These instructions accurately described for the jury the elements of the crime of rape and cannot reasonably be read to exclude the facts of this case. Here, there was evidence that victim 1 consented at the time of the initial penetration but withdrew her consent during the subsequent intercourse. The defendant then forcibly continued to have intercourse with her, despite her pleas for him to stop and her efforts to get away from him. If the jury believed that evidence, the judge’s instructions permitted them to find the defendant guilty of rape. We see no error, and there was no substantial risk of a miscarriage of justice.
Joinder. The defendant next argues that his conviction should be reversed because the incident described should not have been joined for trial with a second rape case. The jury also heard evidence that, within weeks of the first incident, a second woman, victim 2, accepted a ride from a man she identified as the defendant.3 Instead of driving her home, the defendant drove her to the same location, an empty building, where he had taken victim 1. He told her to take her clothes off, and when she refused, he beat her repeatedly, kicking and punching her. He put a knife to her neck and threatened to kill her. Eventually, she agreed to have intercourse with him, and while he penetrated her from behind, he had the knife in one hand and her hair in another. Afterwards, when the two heard a noise in the building, the defendant ran away.
The defendant agrees “there were factors suggesting that the offenses against [the two women] were related. Specifically, both incidents occurred at 108 Grove Street [in Worcester]. During both incidents, the assailant used the bathroom after *662getting off of the elevator. Both [women] believed their attacker was involved with construction. Finally, in both incidents the sexual intercourse was from behind.” The Commonwealth adds that both women were sex workers and heroin addicts who worked in the same area of Worcester. In each case, the defendant took the woman to the Northworks Building on Grove Street, entering through an unlocked door and then boarding the freight elevator. He took each woman to a very dark room that was under construction and then blocked the door with an object described by one woman as a red canister and by the other as a fire extinguisher. Each act of intercourse was very forceful, and each woman identified the defendant as her attacker. Finally, the two crimes occurred very close to each other in time, no more than perhaps a month apart.
When offenses are related, “[t]he trial judge shall join the charges for trial unless he determines that joinder is not in the best interests of justice.” Mass.R.Crim.P. 9(a)(3), 378 Mass. 859 (1979). The decision whether to join the cases is a matter committed to the sound discretion of the trial judge. Commonwealth v. Sullivan, 436 Mass. 799, 803 (2002). “[T]o prevail on a claim of misjoinder, the defendant ‘bears the burden of demonstrating that the offenses were unrelated, and that prejudice from joinder was so compelling that it prevented him from obtaining a fair trial.’ ” Commonwealth v. Pillai, 445 Mass. 175, 180 (2005), quoting from Commonwealth v. Gaynor, 443 Mass. 245, 260 (2005).
“[T]he test is not whether we would have made a different decision. Rather, we will uphold the judge’s decision unless we are convinced that ‘no conscientious judge, acting intelligently, could honestly have taken the view [he] expressed.’ ” Pillai, supra at 181, quoting from Commonwealth v. Ira I., 439 Mass. 805, 809 (2003). In this case, as did the court in Pillai, we conclude that “the facts . . . ‘demonstrate the defendant’s participation in [two] criminal episodes that, despite slight factual variations, are sufficiently [related] to support the judge’s decision to allow the Commonwealth’s request for joinder.’ . . . The judge could have reasoned that the offenses were related because they showed a common pattern of operation.” Ibid., quoting from Commonwealth v. Walker, 442 *663Mass. 185, 200 (2004). In addition, “evidence of one offense likely would have been admitted at a separate trial of the other . . . not only to show a common pattern of conduct, but also ‘to corroborate!] the victim’s testimony’ and ‘render[] it not improbable that the acts charged might have occurred.’ ” Id. at 183, quoting from Commonwealth v. King, 387 Mass. 464, 472 (1982). See Commonwealth v. Zemtsov, 443 Mass. 36, 43-45 (2004); Commonwealth v. Aguiar, 78 Mass. App. Ct. 193, 198-204 (2010).
Expert testimony. For the first time on appeal, the defendant challenges the admission of evidence that DNA material consistent with the defendant’s profile was recovered from condom wrappers retrieved by the police from the room where the second victim said she had been raped. That argument was waived when it was not presented to the trial judge. See Commonwealth v. Bly, 448 Mass. 473, 489 (2007). Therefore, as with the defendant’s claim regarding the judge’s jury instructions, we review for a substantial risk of a miscarriage of justice.
Citing Commonwealth v. Gomes, 403 Mass. 258 (1988), the defendant argues that one of the expert witnesses did not explain to the jury the underlying calculations that led to her conclusions. In Gomes, the defendant’s argument was that “the judge erroneously admitted evidence of a genetic marker analysis performed upon bloodstains . . . because the Commonwealth failed to establish that the procedure employed to analyse the stain — electrophoresis — is generally accepted within the scientific community.” Id. at 265-266. That issue had been the subject of extensive pretrial litigation, and the court upheld the trial judge’s decision to admit the evidence. Id. at 273. The defendant in Gomes also challenged the judge’s decision to admit statistical evidence about the percentage of the African-American population that possessed the combination of genetic markers found in the defendant’s sample and the bloodstain retrieved from the scene. In a pretrial hearing, the expert witness had “explained in detail” the calculations that led to his statistical figures, and the court concluded, “[o]n this basis, the judge could find, as a preliminary finding of fact, that the statistical evidence presented was based on established, empirical data rather than speculation and that the *664evidence was more probative than prejudicial. Therefore, the evidence was properly admitted.” Id. at 275.
In the present case, the defendant did not contest at trial the admissibility of the challenged DNA evidence. He now argues that because the witness did not explain to the jury the underlying calculations for her statistics, the evidence should have been excluded; in his view, “the jury had no way of evaluating the validity of [the witness’s] claim that the DNA profile would not occur more often than 1 in 2.66 million for the African American population. The same is true [for the statistics relating to the two additional condom wrappers].”
We are not persuaded. Whether there was a scientific basis supporting the admissibility of the evidence was a matter for the trial judge to decide. See Commonwealth v. Durning, 406 Mass. 485, 490 (1990) (“The determination as to the admissibility of evidence is the responsibility of the judge and not the jury. However, if the judge makes a preliminary finding of fact that the scientific evidence is sufficiently reliable to be admitted, evidence attacking its reliability can be considered by the jury in determining the weight to be accorded the scientific evidence” [citations omitted]). See also Mass. G. Evid. §§ 104(a), 702 (2011).
In this case, the defendant was free to challenge the Commonwealth’s evidence by cross-examining the witness about her underlying calculations and the validity of her conclusions, and he did cross-examine her about the limitations of her evidence. However, by the time of closing argument, defense counsel essentially conceded that the DNA evidence was accurate.4 He does not, even now, present us with any reason to find that the judge’s decision to admit the evidence was erroneous. See Commonwealth v. Bizanowicz, 459 Mass. 400, 410-411 (2011). We see no error and certainly no substantial risk of a miscarriage of justice.
Judgments affirmed.
The defendant did make that argument to the jury at the trial: “But at the time of penetration, it’s not rape — it isn’t. That’s what she agreed to.”
In several of the cases from other States, the issue arose in the context of the trial judge’s response to a question from the jury. See, e.g., State v. Baby, 404 Md. at 260 (“[T]he trial court should have directly addressed the jurors’ confusion on the effect of withdrawal of consent during intercourse, rather than simply referring the jurors to previously provided instructions on the elements of rape”). In the present case, there was no question from the jury. When the facts call for such an explanation, it is preferable for the judge to address the issue in the final instructions, without waiting for a question.
This second woman testified that, although she had worked that day as a sex worker to support her drug habit, at the time she accepted a ride from the defendant, she had stopped working and was trying to get a ride home.
In his closing argument, counsel stated, “He handled the wrappers. I mean, come on — we all know that. That’s what the DNA shows. . . . Now, was he in the room? I think it’s fair that you could conclude that he was in the room. Was he in the room with [victim 1]? It’s probably fair that you conclude that. Did he pay her for sex? It’s probably fair that you could conclude that.”