LYNCH, J.

Antonio Gomes was indicted for the murders in the first degree of Basilisa Melendez, Joanna Aponte Rodriguez, and Kenneth Aponte Rodriguez, and for breaking and entering a dwelling house in the nighttime with intent to commit a felony and making an armed assault therein. The defendant filed a motion in limine to exclude evidence of blood enzyme testing. The motion was denied after hearing, but the defendant was granted the opportunity to present further evidence on the motion. The defendant was convicted and sentenced to three consecutive life sentences on the murder charges, and to a further concurrent life term on the breaking and entering charge. We affirm.

We summarize the relevant facts as the jury could have found them. On the morning of December 5, 1979, Eduardo Aponte Rodriguez (Aponte) took his common law wife, Basilisa, and two of their three children, Jacqueline and Kenneth, from their home at 12 Jacobs Street, Boston, to a hospital in his van. A third child, Joanna, was left with Aponte's parents. Aponte himself then went on to meet two friends, identified as Pepo and Papo. Sometime between 2:30 and 3:30 P.M. Aponte, Pepo, Papo, and another friend — identified as Harry — returned to Aponte's home to pick up a refrigerator left outside the house. Basilisa and the two children returned from the hospital about fifteen minutes later. Basilisa told Aponte to pick up Joanna at his parents' home. With the refrigerator in the back of the van, Aponte, Pepo, and Papo left. Harry stayed behind.

After unloading the refrigerator, Aponte, Pepo, and Papo drove to a junkyard to get an automobile part, but the yard was closed. At approximately 4:00 to 4:15 P.M. the three drove to Aponte's parents' home to pick up Joanna. Aponte dropped Joanna at home and then continued to bring his friends home. On the way the three again stopped at the junkyard and, after waiting about an hour, obtained the necessary part. Aponte took his friends home at about 6:00 to 6:15 P.M. and then returned home himself at about 6:25 or 6:30 P.M.

His landlord, Antonio Cardoza, was waiting outside the house. Aponte owed Cardoza money for rent. Aponte told Cardoza that Basilisa had the money and that he would go get it. After parking his van in the driveway, Aponte walked up the steps followed by Cardoza. Aponte put his key into the lock but the door would not open; the door or doorlock had been broken. Part of the door fell forward and Aponte pushed the door open.

Aponte saw his wife's body lying on the floor, and exclaimed, "Oh, my God, Bassi, what have they done to you?" He told Cardoza to call the police. He then went out on the porch and, holding onto one of the columns, screamed, "Oh, God, please help me, please help me, God." While he was calling out for help, Aponte saw three adults emerge from nearby 24 Jacobs Street, the building where the defendant lived. They looked at him, got into an automobile parked in front of 24 Jacobs Street, and drove away.

Boston police Officers Lawrence Fisher and Michael Cintolo arrived on the scene at 6:36 P.M. Aponte saw the officers and called out, in Spanish, "Help me." The officers got out of their police car, came up the stairs, and entered the house. There they observed the bodies of Aponte's wife and two of the children. The third child, an infant, lay in a crib in another room, unharmed. Aponte's wife was covered with blood, her face and head severely battered. She had been stabbed. She was naked from the breastline down. The children had also been stabbed. One had been thrown up against the wall; the other lay tangled up with a wooden chair. One of the children had been "almost decapitated" and her throat had been cut. Officer Cintolo radioed for ambulances.

Officer Fisher began to investigate the apartment. The master bedroom had been ransacked. Officer Fisher observed broken windows in the room. In the kitchen Fisher saw that a window was open about twenty-four inches with its curtain flapping in the wind. He glanced out the window into the dark and saw below the remnants of what appeared to be a broken screen propped up against the building.

Boston police Detective Thomas Cashman, who had arrived on the scene shortly after Officers Fisher and Cintolo, observed a brown paper bag in the front bedroom of the house. On the bag were some reddish stains, later determined to be blood. Inside were Christmas gifts that Aponte had bought two or three days earlier, some children's clothes.

Suffolk County medical examiner George Curtis, who had arrived on the scene at about 8:00 P.M., found that the victims had been stabbed and beaten, and that they had died "[o]ne or two hours, not more than three hours" before his arrival; specifically, he concluded that their deaths occurred roughly between 5:50 P.M. and 6:30 P.M.

Also arriving about 8:00 P.M. was Boston police criminalist Stanley Bogdan. He collected specimens of a number of reddish stains throughout the apartment. After chemical analysis he concluded that the specimens were blood stains of human origin. He tested each specimen to determine its blood type within the ABO blood grouping system.

The mother and children all had type O blood, as did Aponte and the landlord. Aponte's friend Harry had type B. Bogdan found certain specimens to be type O. ABO tests were inconclusive as to a number of other items, including stains collected from a chair in the doorway. However, Bogdan was able to determine that the stains from the chair were consistent with a mixture of two blood types: O and A. This was consistent with two people — one with type O blood, the other with type A — bleeding at the same time in the same immediate area. Chemical analysis revealed type A blood in the following items: reddish stains from the back of a bedspread, reddish spots from the front bedroom floor, stains from the bed, stains from the edge of the front bedroom door, stains from a hanging string of beads, and stains from the paper bag found in the front bedroom. Further tests revealed that the type A bloodstain on the paper bag was Rh positive. Bogdan sent the specimen from the paper bag to FBI Agent William McInnis for additional blood grouping tests, described in detail in the body of this opinion.

The defendant's activities on the night of the murders are described as follows. At 7:00 P.M. that night the defendant was admitted to the emergency room at Boston City Hospital complaining of a stab wound to his right forearm and a bruise on his right hand. He told the treating physician that he had sustained these injuries while punching an assailant. He said that he had been stabbed. The doctor testified that the wound was of the type that would have bled.

Boston police officers Francis Evans and Ronald Erickson responded to Boston City Hospital upon report of a stabbing. They did not know about the incident at 12 Jacobs Street. They arrived at 9:55 P.M. and went to the emergency room. In a trauma room they saw the defendant whose right arm was now bandaged from the elbow down, including his hand and wrist. When the officers, who were in uniform, entered the room, the defendant looked at them, "immediately straightened right up" or "popped his head up" and asked, "Why are you here?" Officer Evans told the defendant they had come to talk with him about his injury. The defendant said, "Who called you?" Officer Evans said he assumed that hospital personnel had called.

The police then asked the defendant his name and address and questioned him as to how he had been injured. The defendant said he lived at 24 Jacobs Street. He did not give clear answers to the police questions and fumbled with his words. When questioned as to the particulars of how his injury had occurred, the defendant "seemed to agree with whatever was suggested to him." He was anxious to leave, (he said) several times, "I have to go; I'm getting a ride." The defendant's account to the police at the hospital was essentially as follows: He had been at a trolley stop with his five year old son. Initially, he could not pinpoint the exact location of the stop, but was able to do so later when the police questioned him as to various landmarks. At the trolley stop a black man wearing a blue hat, blue jacket and pants approached and asked the defendant for a match. The defendant reached into his shirt pocket for a match. The man then displayed a large knife and demanded money. The defendant said he then punched the man with his right hand. Simultaneously, the man stabbed the defendant's right arm and ran away. The defendant said he then came to the hospital in a private automobile.

The police left the hospital and went to the trolley stop described by the defendant. They looked for a weapon or blood, but could find nothing to indicate that a crime had been committed there. Later that night, listening to a news broadcast on commercial radio, the officers heard a bulletin about the murders at 12 Jacobs Street. Recalling that the defendant had said he lived at 24 Jacobs Street, they informed officers of the homicide unit about their encounter with the defendant.

The next day, December 6, 1979, Boston police Detective Sergeant Robert Bird, Detective Warren DeLauria, and Detective John Green went to the defendant's house and spoke with the defendant and his girl friend, Donna Dailey. On this occasion the defendant's account of his activities on the night of the murder differed from the account he had given at the hospital. At the hospital the defendant had said he was attacked by a black man. To the police at his home, however, the defendant contended that his assailant was white, and that there were other white men with the assailant. He told the officers several times that the alleged attack had been "a racial incident." He also stated that he took a taxi to the hospital, whereas he had previously stated that he had come in a private car. The defendant himself then raised the subject of the three murders at 12 Jacobs Street. He began to yell, "If you want my ideas on this thing next door, I'll tell you right now that those Puerto Ricans are all f____ing each other and they're doing their relatives and everything else."

About midday on December 8, 1979, the same officers returned to speak further with the defendant. During the course of this conversation the defendant showed the officers the cut on his arm and said, "See, it's only a little scratch. . . . [About that] report I made to the police, it never happened." The defendant said he had cut himself. Then, fifty seconds to a minute later, he said, "I didn't cut myself. I had a fight with my girl and she stabbed me." Donna Dailey was present as he said this. The defendant again brought up the subject of the murders, saying "I hate those f____ing people anyway. [N]ow get the f____out of my house."

In August, 1982, Boston police detective Mark Madden obtained a warrant for a sample of the defendant's blood for chemical analysis. The defendant went with the police to the hospital where the blood sample was drawn. Test results for the defendant's blood and conclusive blood-grouping results obtained two years earlier from the blood-stained paper bag were identical.

On October 8, 1982, the defendant was arrested by Sergeant John Doris. After giving the defendant Miranda warnings, Sergeant Doris asked him about his activities on the day of the murder. The defendant responded that he had worked until 2:00 P.M. Two friends picked him up at work and they then drove to the defendant's home at 24 Jacobs Street. The defendant's girl friend, Donna, was not at home, so he went to his mother's house, where he watched television. The defendant stated that he watched the "six o'clock news" on channel 5. After the news began, the defendant claimed, a reporter named Jorge Quiroga interrupted to report, in a live broadcast from the scene, the murder of a woman and two children on Jacobs Street. The defendant said that his mother then suggested that he check on his girl friend and her two children.

The defendant told Sergeant Doris that he then left his mother's house. He stated that while running through a field he fell and cut his arm on a piece of glass. When he reached Jacobs Street, he saw Aponte on his knees on the porch yelling, "[T]hey've murdered my family. My wife and children are dead." The defendant then told Sergeant Doris that he entered his house and telephoned for a taxi to take him to Boston City Hospital for treatment of his injured arm.

After questioning the defendant was detained in a cell at Area B police headquarters. The next day, at about 6:05 P.M., Officer Paul Bankowski found the defendant hanging by the neck on a cord fastened to the wall of his cell, unconscious but still alive. The officer took him down and resuscitated him.

Several days later the defendant, still in his cell, engaged in a shouting argument with some recently arrested juveniles seated outside his cell. When Officer Bankowski intervened, the defendant said to him, "Tell them what I did. Tell them why I'm here. They don't want to mess with me."

At trial the defendant offered alibi testimony from his mother and his girl friend.

1. Admission of evidence of electrophoretic testing. The defendant claims that the judge erroneously admitted evidence of a genetic marker analysis performed upon bloodstains on the paper bag found at the crime scene because the Commonwealth failed to establish that the procedure employed to analyse the stain — electrophoresis — is generally accepted within the relevant scientific community. Commonwealth v. Neal, 392 Mass. 1, 12 (1984). Commonwealth v. Fatalo, 346 Mass. 266, 269 (1963). See Frye v. United States, 293 F. 1013, 1014 (D.C. Cir. 1923). There was no error.

"Electrophoresis is the movement of charged particles through a buffered conducting medium by application of a direct current. The term isozyme is used to describe enzymically active blood proteins which can be identified by their relative mobilities in an electric field. After separation of the proteins into marker bands by application of a current, specific chemicals are applied to make the proteins visible. Biology Methods Manual, Metropolitan Police Forensic Science Laboratory, London, England (1978). The relative distance of the bands from a common origin is compared with known standards, and evaluated by established guidelines. The results are then compared to population studies which show the known frequency of each factor in a given population. This produces a statistic which is representative of the percentage of the population that has that group and those factors in common. The more genetic markers identified, the smaller the population of persons who might possess a particular combination of factors" (footnote omitted). People v. Young, 425 Mich. 470, 515-516 (1986) (Boyle, J., dissenting). See Commonwealth v. Gliniewicz, 398 Mass. 744, 748 (1986). Thus, the electrophoresis procedure permits an investigator to type a blood sample with greater precision than is possible with the familiar ABO system, Correll v. State, 523 So.2d 562, 566 (Fla. 1988), and results of the test may serve to establish a "strong association between the bloodstain and its possible donor or the exclusion of the criminally accused as a donor of the bloodstain." Note, The Admissibility of Electrophoretic Methods of Genetic Marker Bloodstain Typing Under the Frye Standard, 11 Okla. City U. L.Rev. 773, 778 (1986) (hereinafter cited as Genetic Marker Admissibility).

The particular electrophoretic method at issue here is known as "multisystem" electrophoresis, so-called because it entails separating a number of enzymes simultaneously on the same sample. Such a method has the advantages of saving time and requiring less bloodstain material. Wraxall Stolorow, The Simultaneous Separation of the Enzymes Glyoxalase I, Esterase D and Phosphoglucomutase, 31 J. of Forensic Sci. 1439, 1439-1440 (1986). It also has been suggested that the multisystem approach provides "a substantial improvement of the resolution of the isozyme bands of [certain enzymes] compared to their respective single-system methods of conventional electrophoresis." Id. at 1440.

Both multisystem and conventional electrophoresis methods were employed in this case by FBI serologist William McInnis. McInnis received from the Boston police crime laboratory the paper bag recovered from the crime scene, on which he determined there were two bloodstains. McInnis applied the electrophoresis technique to the stains, testing for seven enzyme and protein systems, abbreviated as follows: PGM, EsD, GLO-1, EAP, ADA, AK, and Hp. With the exception of the Hp system, McInnis tested for all the systems using the multisystem approach. McInnis also performed the more traditional antigen antibody tests on the stains, testing Rh and Mn factors. As a result of these tests, in combination with testing earlier performed by the Boston crime laboratory, it was determined that one stain exhibited identifiable types in six systems of genetic markers: ABO (type A); Rh (type D positive); Mn (type M negative); EAP (type B); ADA (type 1); Hp (type 1). Of the United States population, McInnis testified, 0.6% of whites and 1.2% of blacks would present this particular combination of genetic markers. As noted previously, a sample of the defendant's blood was taken and McInnis performed thereon ABO testing, Rh, and Mn typing, and electrophoretic analysis for the seven enzyme and protein systems. The test results corresponded identically to the results obtained from the stain on the paper bag.

The defendant claims that electrophoresis may not be considered to be generally accepted in the scientific community because: the reliability of the multisystem approach is not agreed upon; there is disagreement as to the length of time that certain genetic markers can be read in dried blood; and there are questions as to the effect on the same of crime scene contaminants. We reject these claims.

"In determining whether experts generally accept the reliability of [electrophoresis], we may properly consider not only the testimony of experts in the record before us but also articles written by experts and the conclusions of other courts." Commonwealth v. Kater, 388 Mass. 519, 527 (1983). A perusal of relevant scientific and legal writings, decisions from other jurisdictions, and the expert testimony in the record reveals that electrophoresis in general, and the multisystem in particular, are generally accepted in the relevant scientific community.

The Commonwealth's expert, Mark Stolorow, testified that electrophoresis, including the multisystem, is generally accepted in the forensic science community. Stolorow is serology coordinator for the Illinois Department of Law Enforcement and holds a Master of Science degree in forensic chemistry. He has testified as an expert in forensic serology over one hundred times in six States, for both prosecution and defense. As serology coordinator, he is responsible for training new serologists, proficiency testing of staff serologists in seven crime laboratories, updating staff serologists on new developments in the field of blood analysis, and evaluation and research of new equipment in the field. His achievements and experience in the field of electrophoresis are extensive.

In 1972, Stolorow participated in an electrophoresis course taught by Brian Culliford of Scotland Yard, then recognized as one of the foremost experts in the field. In 1977, Stolorow participated in a research project at the laboratory of Dr. Benjamin Grunbaum at the University of California at Berkeley. The project goal was to improve the capability of crime laboratories in electrophoretic analysis of dried bloodstains. Stolorow spent approximately six months on the project, "participating in the developmental phase . . . inventing the method that ultimately resulted from that research." Initially, Grunbaum, Stolorow, and Brian Wraxall collaborated in the development of the multisystem. While Stolorow acknowledged that studies have been published pointing out problems in the use of electrophoresis, he indicated that such studies are intended to alert those using the technique to potential pitfalls, not to call into question the technique's underlying reliability. He knew of no scientific publication that had ever refuted the reliability of electrophoresis. He concluded that electrophoretic testing of dried evidentiary bloodstains "certainly has gained general acceptance in the forensic science community."

The defendant offered the testimony of Diane Juricek, Ph.D., a researcher in genetics. Dr. Juricek had performed electrophoretic testing on fresh materials, but not on dried evidentiary blood stains. She testified that electrophoresis is unreliable when applied to dried evidentiary blood because such blood not only degrades with age, but also may be subject to crime scene contaminants and adverse environmental conditions which, she claimed, may result in erroneous readings. Dr. Juricek also testified that the multisystem was unreliable because it compromises among optimum testing conditions in order to test several enzymes simultaneously. According to Dr. Juricek, the unreliability of the multisystem is illustrated by the lack of scientific publications affirming its reliability. Finally, she criticized the actual testing procedures in this case.

Also testifying as an expert for the defense was Dr. Benjamin Grunbaum, a biochemist. Grunbaum testified that electrophoresis is reliable for testing fresh blood and dried bloodstains of known origin prepared under laboratory conditions. However, Grunbaum contended that the reliability of multisystem electrophoresis for testing evidentiary bloodstains from a crime scene has never been independently verified.

A review of relevant scientific literature and court decisions reveals that, despite Grunbaum's and Juricek's criticisms, when applied properly by trained analysts cognizant of the scientific literature as to the warning signs of erroneous readings, conventional and multisystem electrophoresis are generally accepted within the scientific community. As was noted in People v. Reilly, 196 Cal.App.3d 1127, 1148 (1987), "Dr. Grunbaum stands virtually alone in his opposition to electrophoretic typing of dried bloodstain evidence." The Reilly court surveyed opinion of a number of experts. One of them, Dr. Edward Blake, testified that electrophoresis is generally accepted in the scientific community when performed properly, and that "[h]e was unaware of any dissension on the point until he read Dr. Grunbaum's amicus brief in [another case] and knows of no one who shares Grunbaum's views. Nor [was] he aware of any publications that indicate lack of reliability." Id. at 1144. Another expert, Dr. George Sensabaugh, testified in Reilly that Doctors Grunbaum and Juricek were the only scientists he knew of who questioned the reliability of electrophoresis. Id. at 1146. He, too, knew of no publications questioning the technique's reliability. Indeed, Sensabaugh earlier had published a refutation of Juricek's assertions of unreliability. See Sensabaugh, Response to "The Misapplication of Genetic Analysis in Forensic Science," 29 J. of Forensic Sci. 12 (1984) (concluding that Juricek's analysis evidenced "a naive and often erroneous characterization of genetic typing analysis . . . [and a] . . . disregard of pertinent literature [and] distortion of context of cited works").

As to the effects of adverse environmental factors and aging on the sample, the Reilly court noted that Dr. Grunbaum's "criticism [as to the effects of these factors] was repeatedly qualified by noting that well trained, competent analysts who use proper procedures and are aware of the published literature warning of typing problems can account for those possibilities" (emphasis deleted). Reilly, supra at 1141. See Genetic Marker Admissibility, supra at 787-790, and authorities cited (effects of some environmental factors have been studied and categorized, thus "alerting forensic serologists to the characteristic changes that genetic markers undergo as they become less detectable with age"); Budowle Allen, Electrophoresis Reliability: I. The Contaminant Issue, 32 J. of Forensic Sci. 1537, 1546 (1987) (effects of certain types of contaminants "are predictable from a knowledge of protein behavior and the individual marker systems"; "[b]asic scientific principles, the scientific literature, and practical experience enable the forensic scientist to interpret results confidently"). Thus, the above authorities indicate that, so long as the analyst is trained to recognize the signposts of adverse environmental factors, the reliability of the test is not compromised.

With the exception of the Michigan Supreme Court, People v. Young, supra, all courts considering the issue have held evidence of electrophoretic testing admissible. People v. Morris, 199 Cal.App.3d 377 (1988). Correll v. State, 523 So.2d 562 (Fla. 1988). State v. Adams, 418 N.W.2d 618 (S.D. 1988). People v. Reilly, 196 Cal.App.3d 1127 (1987). People v. Partee, 157 Ill. App.3d 231 (1987), cert. denied, 484 U.S. 1072 (1988). People v. Crosby, 116 A.D.2d 834 (N Y 1986). Plunkett v. State, 719 P.2d 834, 841 (Okla.Crim.App.), cert. denied, 479 U.S. 1019 (1986). Smith v. State, 62 Md. App. 627 (1985). Graham v. State, 168 Ga. App. 23 (1983). State v. Chavez, 100 N.M. 730 (Ct.App. 1983). People v. Borcsok, 114 Misc.2d 810 (N.Y.Sup.Ct. 1982). State v. Washington, 229 Kan. 47 (1981). Robinson v. State, 47 Md. App. 558 (1981). State v. Rolls, 389 A.2d 824 (Me. 1978). Of these, four jurisdictions have specifically held that the multisystem method is generally accepted in the relevant scientific community. See People v. Morris; State v. Adams; Plunkett v. State; State v. Washington. We conclude, therefore, that both multisystem and conventional electrophoretic testing of dried evidentiary bloodstains are generally accepted as reliable in the relevant scientific community.

However, the defendant contends, even if the procedure is generally accepted in the scientific community, evidence of the test results nonetheless should not have been admitted because the test was not properly performed and FBI Agent McInnis was not properly qualified as an expert. Testimony indicated that Agent McInnis was an experienced analyst, trained in the electrophoretic technique and that he carefully conducted the genetic marker typing and used appropriate standards and controls. He was aware of typing problems described in the relevant scientific literature. Mark Storolow testified that the technique used by the FBI in this case was reliable. On this evidence there was "sufficient basis for finding, as a preliminary question of fact, that this witness was qualified to testify as an expert" and that the procedures employed were performed properly and reliably. Commonwealth v. Shea, 356 Mass. 358, 361 (1969). Therefore, the defendant's various attacks alleging infirmities in the performance of the testing or the skill or knowledge of the witness go only to the weight of the evidence, not to its admissibility. Commonwealth v. Yameen, 401 Mass. 331, 336 (1987), cert. denied, 486 U.S. 1008 (1988). Commonwealth v. Shea, supra. United States v. Gwaltney, 790 F.2d 1378, 1382 (9th Cir. 1986), cert. denied, 479 U.S. 1104 (1988). P.J. Liacos, Massachusetts Evidence 439 (1981 1985 Supp.). See Commonwealth v. Beausoleil, 397 Mass. 206, 220-221 (1986). The evidence of electrophoretic testing was properly admitted; thereafter, any attacks on the evidence were for the jury to weigh.

2. Statistical evidence. The defendant claims that it was error for the judge to admit McInnis's expert testimony that, in the United States population, 1.2% of blacks present the particular combination of genetic markers found in the bloodstain on the paper bag recovered from the Aponte home, and that testing on the defendant's blood sample places him in that 1.2% of the black population. McInnis based his testimony upon a compilation of statistics delineating fractions of the general population exhibiting particular genetic characteristics. Under a statistical theorem known as the product rule, the fractions corresponding to the characteristics detected in the blood stain are then multiplied; the resulting fraction represents the portion of the population presenting all of those characteristics at once. In this case that fraction was 1.2% for the black population. The defendant contends that such testimony is not admissible because its probative value is outweighed by its potential to confuse or prejudice the minds of the jury. We disagree.

The relevance of the evidence is unassailable. "[P]opulation percentages on the possession of certain combinations of blood characteristics, based upon established facts, are admissible as relevant to identification." State v. Washington, 229 Kan. 47, 59 (1981). See Plunkett v. State, 719 P.2d 834, 841 (Okla.Crim.App. 1986); People v. Rolls, 389 A.2d 824, 830 (Me. 1978). "The significance of the similarity of blood types cannot be intelligently understood without knowledge of the frequency of that blood type in the relevant population. `Where reasonable estimates of the population frequencies are available, they should not be kept from the jury.'" Davis v. State, 476 N.E.2d 127, 136 (Ind.App. 1985), quoting McCormick, Evidence § 210, at 655 (3d ed. 1984). See State v. Joon Kyu Kim, 398 N.W.2d 544, 552-553 (Minn. 1987) (Kelley, J., dissenting), quoting Sensabaugh, Biochemical Markers of Individuality, Forensic Science Handbook 338, 403 (R. Saperstein ed. 1982) ("without being provided the appropriate statistical information [as to gene frequency], the triers of fact have no rational basis for deciding the significance of a type-for-type match"). Indeed, while we generally disfavor admission of statistical evidence, we have previously held such evidence admissible where paternity is sought to be established using the human leukocyte antigen (HLA) blood test. Commonwealth v. Beausoleil, 397 Mass. 206 (1986). Cf. Commonwealth v. DiMarzo, 364 Mass. 669, 677 (1974) (no error to admit evidence that bloodstains found in house were consistent with defendant's blood group).

Where courts and commentators have been reluctant to admit statistical evidence, that reluctance has stemmed largely from the fact that the probabilities on which the evidence depended were based on mere speculation or were characterized in such a way as to mislead or confuse the jury. See, e.g., Commonwealth v. Drayton, 386 Mass. 39, 50-51 (1982) (manner of presentation may make statistical evidence misleading); People v. Collins, 68 Cal.2d 319 (1968) (en banc) (prosecution presented probabilities without any underlying factual basis); People v. Harbold, 124 Ill. App.3d 363, 381-383 (1984) (statistical evidence must rest on adequate factual basis and, even then, potential for confusion outweighs minimal probative value). See also Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 Harv. L.Rev. 1329 (1971). Courts have legitimately feared that statistics might be employed as a way "to assign a number to the probability of guilt or innocence." People v. Collins, supra at 330. On the other hand, where the statistical evidence is shown to be based on accepted scientific principles, courts, including this one, have admitted such evidence. Commonwealth v. Beausoleil, 397 Mass. 206, 217 n. 15 (1986) (evidence as to probability of paternity using HLA test admissible where estimate is "based on accepted scientific principles"). People v. Alzoubi, 133 Ill. App.3d 806, 809 (1985) (same). Davis v. State, 476 N.E.2d 127, 134-135 (Ind.App. 1985) ("where probability testimony is based on empirical scientific data, rather than unsubstantiated estimates, the presentation and admission of probability testimony need not constitute error"). State v. Washington, 229 Kan. 47 (1981) (expert permitted to testify in a murder prosecution that only 0.6% of the population had same blood characteristics as defendant.

Here, Agent McInnis testified that the gene frequency percentages he had calculated were based on a compilation of sixty-five population studies in many localities throughout the United States. The statistical figure was presented as indicating that the defendant belonged to a population group exhibiting a certain genetic array; there was no attempt to use the figure as "odds" that the defendant was guilty. The calculations on which the probability determinations were based were explained in detail. Commonwealth v. Drayton, supra at 50. On 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 evidence was more probative than prejudicial. Therefore, the evidence was properly admitted.

3. Failure to photograph the electrophoretogram. Between April 3 and May 9, 1980, Agent McInnis performed electrophoretic testing on the bloodstains found on the paper bag recovered from the crime scene. When the tests were complete, the gel plates were not preserved. No photographs were taken of the gel plates. The defendant claims that the failure of the Commonwealth to photograph the electrophoretogram denied him his due process right to a fair trial. He concedes, however, that the Commonwealth provided him with FBI laboratory notes and reports. While defense counsel raised the issue of improper testing generally at the Frye hearing and during trial, she never specifically objected to the failure to photograph or to provide photographs of the electrophoretogram. Since we conclude that there was no error in the admission of the tests, counsel's failure to raise a specific objection is of no consequence.

"In this Commonwealth, when potentially exculpatory evidence is lost or destroyed, a balancing test is employed to determine the appropriateness and extent of remedial action. The courts must weigh the culpability of the Commonwealth, the materiality of the evidence and the potential prejudice to the defendant. . . . Where evidence is lost or destroyed, it may be difficult to determine the precise nature of the evidence. While the defendant need not prove that the evidence would have been exculpatory, he must establish `a "reasonable possibility, based on concrete evidence rather than a fertile imagination," that access to the [material] would have produced evidence favorable to his cause.'" (Citations omitted.) Commonwealth v. Willie, 400 Mass. 427, 432-433 (1987), quoting Commonwealth v. Neal, 392 Mass. 1, 12 (1984).

Applying the balancing test above, we note that the Commonwealth was culpable in some degree for failing to photograph the material. However, that culpability is mitigated to a great extent by the fact that the defendant has been provided with laboratory notes and reports of the test results from the FBI laboratory. Commonwealth v. Shipps, 399 Mass. 820, 835 (1987). Neither is this a case where the Commonwealth ignored or rejected a defense request to preserve evidence by special means. Commonwealth v. Willie, supra. Commonwealth v. Jewett, 17 Mass. App. Ct. 354, 360 (1984). Rather, the Commonwealth had completed its testing over two years before the defendant's arrest, so "there was no lawyer to whom notice could have been given concerning the testing." Commonwealth v. Shipps, supra at 834. Contrast Commonwealth v. Gliniewicz, 398 Mass. 744, 749 (1986) ("defendants received no notice of the impending tests, and thus were not able to have their own expert present to observe and potentially to refute the subjective aspects of the testing").

Furthermore, the defendant has failed to show how his case was prejudiced by the lack of photographs. The defendant had available Agent McInnis's laboratory report and notes, from which defense counsel conducted an extensive cross-examination. Moreover, that photographs of the test results might have been useful to the defense, does not rise to a showing of "a `reasonable possibility, based on concrete evidence . . .' that access to [a photograph] would have produced evidence favorable to his cause." Commonwealth v. Willie, supra.

Indeed, as one commentator has remarked: "Photography of electrophoretograms of ideal samples may be reliable for the purposes of leisurely scientific appraisal, however, I know of no such proven testing of samples of varying activities as does occur in forensic samples. A single photograph of such a separation could not adequately cover the range of such activity with the sensitivity of the human eye. Photography does not necessarily represent the true picture and can lead to artifacts." (Emphasis deleted.) Baxter, Electrophoresis in Forensic Sciences, 30 J. of Forensic Sci. 994, 995 (1985). Therefore, we conclude that the failure of the Commonwealth to provide a photograph of the electrophoretogram did not deprive the defendant of a fair trial.

4. G.L.c. 278, § 33E, review. After reviewing the record, we conclude that there is no reason to exercise our extraordinary powers under G.L.c. 278, § 33E.

Judgments affirmed.