
735 S.W.2d 831 (1987)
STATE of Tennessee, Appellee,
v.
James Allen SMITH, Jr., Appellant.
Court of Criminal Appeals of Tennessee, at Knoxville.
Decided April 14, 1987.
Permission to Appeal Denied June 29, 1987.
*832 W.J. Michael Cody, Atty. Gen. & Reporter, Bettye Springfield-Carter, Asst. Atty. Gen., Nashville, William E. Dossett, Dist. Atty. Gen., David Dake, Asst. Dist. Atty. Gen., Knoxville, for appellee.
Douglas L. Dunn, Lockridge & Becker, P.C., Knoxville, for appellant.
Permission to Appeal Denied by Supreme Court June 29, 1987.

OPINION
RICHARD R. FORD, Special Judge.
Charged in a two-count indictment with aggravated rape of a child less than thirteen years of age, and with aggravated rape resulting in the child's pregnancy, the appellant, James Allen Smith, Jr., was convicted of the later offense. As of right he appeals both his conviction and the resulting effective sentence of thirty (30) years imprisonment. He seeks relief on five grounds, including a challenge to the sufficiency of the convicting evidence. We affirm the judgment.
First, the record amply supports the verdict of the jury as approved by the trial judge. The victim was born July 17, 1972. She resided with her mother and grandfather in LaVergne, Tennessee. The victim was barely twelve years old when her grandfather took her and her seven-year-old cousin on a ten-day visit to her great grandmother's home in Knoxville. The visitation period included the dates of the Michael Jackson Concert given in Knoxville on August 10, 11 and 12, 1984. During the visit in her great grandmother's home, the victim noticed that the appellant would sometimes be present, particularly at breakfast time.
Because of the limited space of the great grandmother's two-bedroom home, the *833 sleeping arrangement required the use of the living room. The victim's great grandmother and an aunt slept in the bedroom which was separated from the living room by a curtain drawn over the doorway. An uncle slept in the other bedroom. On the night of the rape the victim's grandfather did not sleep in the house. He slept in his parked van, where he slept for a period of five nights during the visit. The appellant is the son of the aunt, who shared the bedroom with the victim's great grandmother.
The living room furnishings included a sofa and a love seat. On the night of the offense the victim had made her bed on the sofa. Her seven-year-old cousin had made his bed on the floor. Sometime between 1:00 and 3:00 a.m., the appellant awakened the victim and told her to get on the floor. Believing the appellant wanted to sleep on the sofa, the victim moved to the floor and went to sleep. Later, she felt something touching her vagina. She awakened and the appellant got on top of her. Her panties had been pulled down to her ankles. The appellant had an odor of alcohol about him.
The victim described the resulting act of forcible intercourse. She protested by shaking her head "no" as the appellant continued to sexually penetrate her. Although the appellant hurt her, and she cried, she was too scared to scream. After the appellant finished with her, she went to the bathroom and stayed awhile. When she returned to the living room, the appellant was asleep on the sofa. She lay down on the floor beside her cousin and went to sleep.
When the victim and the others awakened that morning she told no one because she was too scared. When the victim returned to her home in La Vergne, she did not tell anyone. She did not learn she was pregnant until January or February, 1985, when her mother took her to a physician because of an "overweight" problem.
Doctor James Lee Broerner, an obstetrician, delivered the victim's full-term baby on May 3, 1985. Although the victim had told her doctor that the incident with the appellant had occurred in October, the obstetrician testified that if conception had occurred a few days after August 10, 11 or 12, of 1984, such would be consistent with the gestation age of the baby.
The State's evidence included the appellant's voluntary statement written on April 24, 1985. He said that when he entered the living room, (the subject child) was asleep on the couch, and that his uncle was asleep on the other couch. The appellant said he went to sleep on the floor, and that he did not rape (the subject child).
Doctor Francis Jones, an anatomic, clinical pathologist, who has a special interest in immunol hematology, with twenty years experience in paternity testing, conducted paternity tests to determine the probability of the appellant's being the father of the victim's child. Doctor Jones described the taking of blood samples from the appellant, from the victim, and from her child. Each blood sample was subjected to tests which included six groups of testing involving red cell antigens. He listed these six procedures as "ABO, MNS, RH, Kell, Duffy, and Kidd." In addition to the six red cell procedures, he described a seventh test, a relatively new testing procedure, which he described as "HLA testing, white cell testing, as in white cells."
After comparing the results of the testing procedures, Doctor Jones concluded that the appellant could not be excluded as the father. On the contrary, Doctor Jones calculated, from the results of the testing procedures, "that James Allen Smith, Jr., had a 99.4 percent likelihood of being the father." Doctor Jones further testified that his calculations constituted biological evidence only, and that he knew nothing of what the victim had said about the offense.
In our consideration of the appellant's challenge to the sufficiency of the convicting evidence, we are guided by certain principles of settled law. On appeal the State is entitled to the strongest legitimate view of the evidence, and all reasonable and legitimate inferences which may be drawn therefrom. State v. Cabbage, 571 S.W.2d 832, 835 (Tenn. 1978). A guilty *834 verdict, approved by the trial judge, accredits the testimony of the State's witnesses and resolves all conflicts in the testimony in favor of the theory of the State. State v. Hatchett, 560 S.W.2d 627, 630 (Tenn. 1978). A verdict against a defendant removes the presumption of innocence and raises a presumption of guilt on appeal. State v. Grace, 493 S.W.2d 474, 476 (Tenn. 1973). A crime may be shown by circumstantial evidence alone if the circumstantial evidence sufficiently shows all the necessary elements of the crime and the appellant's connection therewith. Price v. State, 589 S.W.2d 929 (Tenn.Cr.App. 1979). Marable v. State, 203 Tenn. 440, 313 S.W.2d 451 (1958).
The relevant question on appeal is whether, after viewing the evidence in the light most favorable to the State, any rational trier of fact could have found the essential elements of the charged offense beyond a reasonable doubt. Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979); T.R.A.P. 13(e). The direct, as well as the circumstantial evidence, including the biological evidence, amply supports the verdict. The challenge to the sufficiency of the evidence is meritless.
Next, the appellant contends it was error for the trial court to permit Doctor Francis Jones (who had supervised certain biological tests) to state his opinion as to the percentage probability of the appellant's paternity. Quite properly, counsel for the appellant had raised the admissibility issue by a motion in limine.
After hearing the proposed testimony in the absence of the jury, the trial judge considered the appellant's contention that such proposed testimony would be irrelevant, immaterial and prejudicial, because the appellant could not be excluded (as the father) by such tests. Then, as now, the appellant argued that such evidence would "tend to make the jury attribute more weight to this evidence than the evidence would otherwise have."
The trial judge recognized the expertise of Doctor Jones. The trial judge found that the reliability of the tests, including the results thereof, had been established. Concluding that the proposed evidence was both relevant and material the trial judge permitted it to be introduced. The record amply supports his findings.
In our view such evidence is particularly relevant as to the identity of the perpetrator of the crime. That such evidence may also tend to prove biological fatherhood does not, per se, render it inadmissible on the issue of the identity of the perpetrator of the rape offense. It is the aggregate of a person's physical features, physical condition, marks and traits which serve to identify him. The weight to be accorded each such feature, condition, mark or trait is within the domain of the finders of fact.
We specifically note certain statutory changes affecting the admissibility of blood-grouping test results. As alluded to by Doctor Jones during the jury-out hearing, both the American Medical Association and the American Bar Association have recognized the recent advancement of medical science in paternity testing. Such advancement has resulted in the adoption of a pertinent uniform law of evidence in a number of states, including Tennessee.
Originally, Tennessee statutory law provided for the admission of qualified blood-grouping tests to disprove paternity. The results of such tests were originally admissible in both civil and criminal cases only in cases where the alleged person was excluded as being the biological father. See Chap. 30, § 1, Public Acts, 1957, encoded as T.C.A. § 24-716. In 1983, however, T.C.A. § 24-716 was amended to provide for the admission of the results of qualified blood-grouping tests, in both civil and criminal cases, as part of the proof of paternity. See Chap. 459, § 1, Public Acts, 1983, encoded as T.C.A. § 24-7-112. Subsection (b)(2) of the amended Act provides:
If the tests and comparisons do not exclude the defendant as the father of the child, the court, upon motion for the introduction of the results of such tests and comparisons by either party, shall determine whether such results may be admitted into evidence. In making such *835 a determination, the court shall consider the probative value of such tests and comparisons and the results thereof and whether or not they have been properly authenticated. If the court determines that the tests and comparisons should be admitted into evidence, such evidence shall be considered by the trier of fact along with all the other evidence of the defendant's paternity. (Emphasis added).
The trial jury was permitted to hear the expert witness, Doctor Jones, describe the seven different types of tests applied to the respective blood samples taken from the appellant, from the alleged victim, and from the victim's baby. After the jury heard the witness testify as to his calculation of the 99.4 percent likelihood of the appellant's being the biological father, the trial judge gave the jury the following unchallenged cautionary instruction:
THE COURT: Let me just say this. The Doctor is not stating, of course, that the Defendant  is this, I think this is what you are getting at  is the father of this baby, or that he impregnated this victim. That is a question you jurors must determine. That is within your domain. He has testified that his testing and calculation shows that there is a likelihood of 99.4 percent  but do not take that as being testimony that the Defendant is the father of the baby in this case. You must take this testimony, along with all the other testimony, before you reach your determination, determine your verdict in this case. Do you wish to add anything to that, Mr. Dunn?
MR. DUNN: No, Your Honor.
It is settled law that the admissibility of evidence rests within the sound discretion of the trial court which will be reversed only for an abuse of such discretion. State v. Banks, 564 S.W.2d 947, 949 (Tenn. 1978). The record shows no abuse of such discretion, but on the contrary, it shows that the trial judge carefully delineated the function of the witness from that of the separate fact-finding domain of the jury. This evidentiary issue affords no basis for appellate relief.
Next, we have found no merit to the appellant's insistence that the trial court erred by allowing rebuttal evidence as to the blood types of two other adult males, who were occupants of the home about the time of the offense.
As to the sleeping arrangement in the living room of the great grandmother's house, the defense had presented evidence that the grandfather was the one who slept on the couch (sofa); that the victim had slept on the love seat, and that the love seat and couch (sofa) were situated within touching distance of the occupants thereof. Photographs of the living room furniture arrangement were exhibited to the jury.
The defense presented evidence that one of the bedrooms was occupied by the other adult male (the uncle) resident of the home. The defense also presented evidence that the appellant did not reside there, but lived at another address with his girlfriend.
During the State's proof in chief, the appellant's attorney extensively cross-examined Doctor Jones. The cross-examination included questions as to whether paternity blood tests of the victim's "first order" relatives would produce a result similar to that of the appellant's test result.
At the conclusion of the defense proof, the State, in rebuttal, presented two medical records custodians from different hospitals. One custodian testified as to the recorded blood type of the victim's grandfather. The other custodian testified as to the recorded blood type of the victim's uncle. Doctor Jones, on being recalled in rebuttal, testified that given the blood type attributed to the grandfather, and to the uncle, neither of them could be the father of the victim's baby.
We have previously held that any competent evidence which explains or is a direct reply to, or a contradiction of, material evidence introduced by the accused, or which is brought out on his cross-examination, is admissible in rebuttal. Nease v. State, 592 S.W.2d 327, 331 (Tenn.Cr.App. 1979). The scope of rebuttal evidence lies within the sound discretion of the trial judge. Beasley v. State, 539 S.W.2d 820, *836 823 (Tenn.Cr.App. 1976). In this case we find no abuse of that discretion.
The appellant next insists the trial court erred by refusing to allow the defense to present evidence, through the victim's mother, that there was a motive for fabrication; further, that the trial court erred by refusing to allow the defense to make an offer of proof.
During a jury-out hearing the victim's mother, called by the defense, was asked whether she had made any statement by telephone to the effect that if the appellant is found not-guilty, she would go down the list until she found someone who is (guilty). The defense witness replied, "I have never said anything like that." Thereafter, the appellant sought to call two witnesses to impeach his witness. The impeachment was disallowed. The trial court also noted that the stated intended proof was immaterial.
On appeal the appellant cites no authority in support of this issue. Where an appellant fails to provide citations to appropriate authorities in support of his contentions as to an issue, the issue is waived. T.R.A.P. 27(a)(7); State v. Lunati, 665 S.W.2d 739, 749 (Tenn.Cr.App. 1983). We must and we do treat this meritless issue as waived.
Finally, the appellant contends that under the circumstances of this case, he was given an excessive sentence. After conducting the sentencing hearing, the trial judge found the appellant to be a standard offender, Range I. On the conviction of aggravated rape of a child less than thirteen years of age, resulting in pregnancy, a Class X crime, the trial court fixed the appellant's punishment at twenty-five years imprisonment for the aggravated rape, plus a consecutive five year sentence for impregnating his victim, an effective total sentence of thirty years.
In support of his contention of excessive punishment, the appellant argues that the offense was non-violent; that the victim did not have to carry the baby to full-term delivery, and that he should not be blamed for the victim's discomfort and pain.
For our determination of the sentencing issue, we have reviewed the record as mandated by T.C.A. § 40-35-402(d). In so doing, we have taken due notice of the provisions of T.C.A. § 40-35-102 and § 40-35-103. We also adhere to the guidelines of Moss v. State, 727 S.W.2d 229 (Tenn. 1986). We have made no presumption of correctness as to the sentencing decision of the trial judge.
For aggravated rape the statutory range of punishment is imprisonment for life, or for a period not less than twenty years. See T.C.A. § 39-2-603(a)(4)(b). Where the aggravated rapist, as here, has been determined to be a Range I offender, the sentence may be fixed at any determinate period of not less than twenty years nor more than forty years. T.C.A. § 40-35-109(a). In the event the victim becomes pregnant, the punishment shall be increased by five years. T.C.A. § 39-2-609.
The State gave no notice nor did it seek to have the appellant's punishment enhanced either as a persistent offender (T.C.A. § 40-35-106), or as an especially aggravated offender for his especially aggravated offense. (T.C.A. § 40-35-107). We find that the appellant is not an especially mitigated offender (T.C.A. § 40-35-108), and that none of the mitigating factors specifically enumerated in T.C.A. § 40-35-110 is applicable. The argument that the rape offense was non-violent, and that the child victim is responsible for her own pain and suffering is untenable.
The appellant has a very substantial criminal record. His numerous arrests and convictions, mostly for misdemeanor offenses, reflect a consistent pattern of misconduct. The appellant has learned little, if anything, from his previous periods of probation. Society has now been subjected to the appellant's deplorable offense of raping and impregnating a child.
The twenty-five year sentence, enhanced by the five year sentence for an effective total sentence of thirty years, as originally ordered by the trial judge, is lenient punishment. Far from being excessive, the sentence conforms to the purposes of the Tennessee Criminal Sentencing Reform Act *837 of 1982, as amended (T.C.A. § 40-35-101 et seq.). We adopt and approve the judgment of the trial court wherein the appellant's punishment as a Range I offender has been fixed at an effective total sentence of thirty years imprisonment.
The judgment of the trial judge is affirmed.
BYERS and CORNELIUS, JJ., concur.
