AMERICAN JOURNAL OF HUMAN BIOLOGY 19:643–653 (2007)
Symposium Paper
Growth Chart Curves Do Not Describe Individual Growth Biology MICHELLE LAMPL* AND AMANDA L. THOMPSON Department of Anthropology, Emory University, Atlanta, Georgia 30322
ABSTRACT Growth reference tables present statistical distributions of size for age of individuals within a sample or population. As summaries of phenotypic variability at the group level, they document that individuals grow by different rates during similar time frames. The data are commonly fitted by mathematical functions to produce the convex curves of percentile distributions useful for infant and childhood growth monitoring. In this form, the growth chart appears to be a frame of reference for judging how well an individual infant/child is progressing through time by comparison with peers across ages. This has led to the assumption that individuals should track in these channels during growth. The interpolated lines between the statistical distributions of size for age at the level of the population do not, however, represent how individuals grow. Growing is an individual process characterized by nonlinear episodic saltatory increments that result in shifting size relationships among similarly aged peers over short time intervals. Data from a prospective, longitudinal study of infants illustrate the poor performance of growth chart curves as representations of individual growth. Clarification of the paradigms supporting perceptions of normal growth patterns is useful both practically and theoretically: growth chart patterns have important clinical sequelae when this informs feeding recommendations. Further characterization of individual growth patterns will contribute to increased understanding of both individual growth biology and the nature of adaptability. Am. J. Hum. Biol. 19:643–653, 2007. ' 2007 Wiley-Liss, Inc.
Growing is a major biological event of infancy; during the first year, body weight triples and by the end of the second year nearly one half of final height is achieved. More than a decade and a half is required to match this short period in terms of the changes that determine the average adult’s final size. Growing takes place in individuals: cell, tissue, and organ level processes mediate the interplay between genomics and local physiology to determine the specific paths by which the organism increases in size and immature systems age. Morphology reflects the integration of multiple signals in this dynamic process, and the flexibility and diversity of outcomes is documented by variability in phenotypic size that is characteristic of all human populations. POPULATIONS VS. INDIVIDUALS IN THINKING ABOUT ADAPTABILITY Theories of human adaptability and plasticity focus on growth as an important mechanism by which populations survive: alterations in growth rates and the associated effects on size and longevity are components
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of explanatory models describing strategies by which survival is mediated in challenging, or changing environments. The question of whether these population level ‘‘adaptive strategies’’ are beneficial at the level of local samples, or individuals, has itself a significant history of debate, as articulated by the ‘‘small but healthy’’ hypothesis controversy (Martorell, 1989; Messer, 1986; Seckler, 1982). Some of these tensions reflect the divergent foci of intellectual conceptual frameworks (e.g., evolutionary perspectives vs. public health goals). For example, a reduction in the size of individuals within one generation due to environmental insult may decrease the attainment of the optimal potential of this cohort in terms of size and/or functionality, while maintaining the long term survivability *Correspondence to: Michelle Lampl, Department of Anthropology, Emory University, Atlanta, Georgia 30322, USA. E-mail:
[email protected] Received 15 May 2007; Accepted 15 May 2007 DOI 10.1002/ajhb.20707 Published online 17 July 2007 in Wiley InterScience (www. interscience.wiley.com).
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of the population across generations. This adaptive flexibility in the growth process is not necessarily ‘‘beneficial’’ from the point of view of the stunted individuals; and in the extreme can result in pathology as the lower limits of the organism’s maintenance requirements are reached. Medical and public health domains are concerned with alleviating and aiding those affected. On the other hand, if the individuals survive the insult to successfully reproduce, the genetic options for larger size have been preserved and remain biological pathways by which subsequent generations may thrive at a wider range of phenotypic variability. This is a success from the viewpoint of the species. Any ‘‘restitution’’ may take multiple generations as repercussions of parental insults are expressed in offspring (e.g., Ramakrishnan et al., 1999), and/ or selection may result in a genetically-determined growth pattern that optimizes functional size and growth pattern to local environments. The proximal mechanisms that mediate any of these responses are not yet clearly defined. Viewed more broadly, the generalities of how the developmental process provides an adaptive framework within which populations carry on from one generation of reproductively successful individuals to the next reflect a lack of attention to individual biology in their details that is not insignificant. As a case in point, designed to explain taxa-wide variations in developmental tempo and body size, life history theory is often used to speculate about the selective pressures shaping the human growth curve. As originally described, life history theory postulates that animals in stable environments, characterized by reduced mortality from extrinsic forces such as inadequate energy availability and predation, grow more slowly, mature later and have larger body sizes at maturation (Stearns and Koella, 1986). While this model was originally conceptualized to describe potential species-level responses to environmental constraints, not a facultative shift in growth of an individual organism to lower mortality risk, it has been further extrapolated to suggest that growth rates will vary between human populations with different environmental risks of inadequate energy availability or high mortality risk (Hill and Kaplan, 1999). However, whether these predictions of life history theory created to describe taxa-wide variation in maturational timing and lifespan, apply to the variation
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seen within and among individuals of a single species remains an open empirical question. For example, the tempo of growth in humans, at first glance, seems to run contrary to these life history predictions; populations in marginal environments grow more slowly, mature later, and at a smaller size. In contrast, individuals in more resource-rich environments grow more quickly and mature earlier and at larger body sizes (e.g., Eveleth and Tanner, 1990). This contradiction of patterns as seen between species and those seen among individuals of a single species highlights the importance of level of inquiry and draws attention to the way in which large scale analyses may mask interindividual variation. As selection occurs at the level of the individual, explication of the processes by which differences in individual size and growth rate occur will be useful in further conceptualizing how adaptability is expressed in developmental process. GROWTH STANDARDS DOCUMENT INDIVIDUAL VARIABILITY Common observation provides documentation of the variability in growth throughout development: among groups of children, there are the ‘‘short’’ and ‘‘tall,’’ ‘‘skinny’’ and ‘‘plump’’ individuals. We rely on objective frames of reference to clarify the meaning of the size of any individual: a comparison group of similarly aged individuals provides a statistical context of ‘‘size for age,’’ with many extant data sets providing such referents (reviewed in Roche and Sun, 2003). The specific characteristics of the population frame of reference are an important metric. For example, significant effects on infant size for age are due to factors ranging from genetic predisposition to biological age (gestational age in young infants) (Casey et al., 1991), feeding style (Dewey, 1998), illness (Waterlow, 1994), and altitude (Haas et al., 1982), in addition to broader lifestyle variables such as socioeconomic level (Victora et al., 1987) and maternal education (Lartey et al., 2000), as these mediate availability to the infant of resources ranging from nutrition to health care. Thus a conclusion of ‘‘small for age,’’ ‘‘large for age,’’ or ‘‘appropriate for age’’ for any single individual is entirely contingent on the nature of the comparative framework. But what, exactly, does diversity in size for age mean in terms of the biological process by which this is achieved? The size-for-age statis-
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tics of growth references reflect individual differences in how much growth is accrued during the same time frame, revealing that growth velocity is a biological process with some bandwidth. The biomedical paradigm posits that the growth chart percentile lines are the manifestation of the genetics of growth rate differences: larger individuals grow along higher percentile trajectories than smaller individuals, (e.g., 90th percentile sized individuals grow at 90th percentile growth rates). If, as it is said, in optimal environments diversity in child size reflects genetics alone (WHO MGRS et al., 2006), what genetic mechanisms and downstream pathways are responsible for a 6-cm difference in body length separating the 5th and 95th percentiles at birth, a 150% difference in weight at 6 months and a near doubling of the ranges of both by 2 years of age (de Onis et al., 2006; WHO MGRS et al., 2006)? With the goal of better understanding how growth provides an adaptive scaffold, it is helpful to consider how growing occurs in individuals. GROWTH CURVES: VISUAL REPRESENTATIONS OF INDIVIDUAL GROWTH VELOCITY TRAJECTORIES? While growth references are designed to characterize the size of an individual relative to a group of peers, in practice they have become much more. Commonly used for monitoring growth ‘‘progress’’ in individuals, serial measurements are interpreted in terms of ‘‘growth patterns’’ that underlie normative concepts of growth, with ‘‘healthy’’ individuals expected to ‘‘track’’ along the percentile curves and ‘‘crossing of centile lines,’’ particularly downward, a source of concern. It certainly may be the case that extended shifts in centiles are harbingers of serious medical conditions that may first manifest themselves in infant growth patterns (e.g., congenital cardiac anomalies, endocrine imbalance, metabolic disturbances), but exactly when, for example, slow growth progress becomes a significant clinical condition in itself (e.g., growth faltering or failure to thrive) is not a prescriptive diagnosis. This graphical schema clinical model of healthy growth presumes that the growth chart lines accurately represent how the genetic potential of size is achieved and has been adopted as a framework for understanding growth progress: the common interpretation of downward centile line crossing is that
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growth potential has been detoured in the face of insults that inhibit it from unfolding. When this is followed by upward crossing of centiles, recovery has been established and ‘‘catch up growth’’ may be occurring (e.g., Tanner, 1981). This paradigm is problematic in terms of diagnostic sensitivity and specificity, however, as, for example, infants normally experience a ‘‘reassortment of relative sizes’’ (Tanner, 1981. p 236) as an expression of postnatal regression to the mean (e.g., Cameron et al., 2005) that takes place across the first year of life. Recent studies have documented that interpretive paradigms based on growth chart patterns need to be reconsidered: The highly variable growth rates of individual infants result in one-third of infants crossing two percentile lines in length during the first months and as many as one in five infants cross two percentile lines in length between 6 months and 2 years; more than 60% of infants cross two percentile lines in weight for height in the first 6 months and one in three do so between 6 months and 2 years (Mei et al., 2004). It is worth considering if all of these percentile shifts merely reflect postnatal reassortment as individuals ‘‘find their’’ genetic pathways after prenatal life. It is also possible that there is a significant contribution in these graphical patterns from the biology of growth itself. To interpret these results, it is useful to revisit the specifics of how growth curves are constructed and consider if they merit employment as growth pattern diagnostic tools for individual assessment. Statistical distributions of size for age are fitted with mathematically-derived smoothing functions to generate the convex-shaped curves characteristic of the growth charts, typically used in clinics and pediatric offices as references for the interpretation of ‘‘normal growth.’’ For example, the recently published revised WHO standards for infancy and early childhood are based on data from 882 infants measured longitudinally until 18 months and 6,669 infants measured cross-sectionally, aged 18–71 months (de Onis et al., 2006). The Box Cox power exponential provided the distribution statistics at the target ages (e.g., weeks 1, 2, 4, 6, monthly 2–12) and the cubic spline smoothing function with a power transformation applied to the age generated the curves connecting the age-specific statistical distributions for length- and weight-for-age (Borghi et al., 2006). In this way, a useful and carefully constructed statistical distribution of size for age has been generated.
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The resulting lines that provide the curves do not, however, document how individuals’ change in size from one age to the next, as is often assumed. They represent mathematical smoothing techniques that link the age-specific percentile distributions. If the curves on the charts were growth channels, individuals would grow both continuously and quite similarly, if along different trajectories. Neither of these are the case. According to statistics collected by both the World Health Organization (de Onis et al., 2006; WHO MGRS et al., 2006) and the American National Center for Health Statistics (Kuczmarski et al., 2000; Ogden et al., 2002), it can be said that during the first year of life the 50th percentile represents a difference in total body length, weight, and head circumference of about 25 cm, 6 kg, and 10 cm, respectively. This summary, however, does not refer to actual incremental growth of individual infants, but is the difference between statistical medians of size for age across the first year and provides a referent. BEYOND GROWTH CURVES: GROWING IS AN INCREMENTAL PROCESS As an incremental process through time, growth is only revealed by repeated measurements on individuals. The statistical distributions of size for age document that there is considerable diversity in how this change through time is accomplished. Expressed either as incremental change or growth rate, how much head circumference, length, or weight individual infants actually gain or lose across days, weeks, and months is an individual-specific indicator of growth biology and personal health status. While less common than those for size achieved, reference standards for incremental growth and growth rates have been generated from several data sources by different methods (e.g., Roche and Guo, 1992, van’t Hof and Haschke, 2000). One approach has been to derive growth velocities for shorter intervals than actual measurement assessments either by differencing the measurements and dividing by the time frame of interest or by fitting the longitudinal data with a mathematical function and estimating velocities by first derivatives. According to these approaches, infants are theoretically expected to grow, on average, a little more than 1 mm/day in length at 3 months of age and less than 0.5 mm from 6 to 24 months, while gaining about 30, 20,
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and 10 g/day at 3, 6, and 12–18 months, respectively (Roche and Guo, 1992). Alternatively, 2-, 3-, and 6-monthly increments expressed as monthly growth rates are available from the Euro-Growth Study of more than 2,200 infants collected at 22 sites in 12 European countries (van’t Hof and Haschke, 2000). Monthly growth rates for the European infants in these studies likewise characterize an overall negative trend in the velocity of infant growth in length, head circumference, and weight. These summaries, based on population level data, capture the general trends in infant growth and provide useful information for screening large groups of infants. But are these population level trends accurate reflections of how individuals grow? HOW INDIVIDUALS GROW When measured by trained personnel under research conditions, repeated measurements of individual infants identify that infants increase the measurable dimensions of their weight, length, and head circumference in spurts. In contrast to the image of slow and continuous size acquisition implied by the lines drawn on the graphical charts, the biology of infant physical growth is like many other physiological processes and proceeds in saltatory bursts of episodically timed growth events (Lampl et al., 1992). In fact, the incremental growth evident at traditional monthly or bi-monthly measurement intervals is accrued during discrete growth events that occur in a time frame of hours and physical growth proceeds by a series of bursts that are separated by intervals of no growth. These observations have been replicated at the level of individual limb lengths (Hermanussen, 1998) endochondral bone elongation (Noonan et al., 2004) and membranous bone across species (Goldsmith et al., 2003) and generate the hypothesis that cellular mechanisms, translated through hormonal and cytokine signals, integrate growth. These observations provide a mechanistic basis for the statistical distribution data documenting phenotypic variability in size for age. Individual differences in the timing of growth events, as well as the amount of growth at each growth saltation underlie variability in attained size for age among infants and explain growth rate variance. Infants of similar initial size can achieve different sizes through time by varying the timing and/or
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amount of growth saltations and infants of different initial sizes can end up at the same size through time by alternative pathways. Thus, being relatively short or long is achieved through more or less frequent growth events of greater and lesser amounts and the relative size among individuals may change quickly, depending on the timing of the growth saltations. INDIVIDUAL GROWTH PATTERNS VS. GROWTH CURVE REFERENCE FRAMES An understanding of how individual infants actually grow necessitates a reconsideration of how growth curves are used to compare individuals with their peers, and how these comparisons are construed as reflections of appropriate growth patterns, informing normative concepts of infant biology and adaptability. As an example of the potential problems in this practice, consider the case of the breastfed infant and the common practice of using infant growth patterns as assessed from data plotted on growth curves to drive intervention decisions. Lessons from breastfed infant growth patterns The most common interpretation of downward centile progress in an individual is insufficient nutrition and health personnel use these observations to guide feeding recommendations. The practical question regarding whether breastfed infants are ‘‘getting enough’’ to eat is addressed by reference to weight gain/loss patterns in actual quantitative terms, as well as by reference to centile crossing on growth charts. The appropriateness of using growth chart derived growth patterns as a nutritional guide, however, relies on several assumptions, not often considered. First, this assumes that the charts were devised with an understanding of how nutritional intake effects infant physical growth. Second, this comparison relies on the fact that the charts were constructed from data controlling for feeding patterns of the sample reference infants. Third, using a growth chart in this way assumes that the descriptive statistics of the pooled sample data accurately reflect the progress of individual infants. These may not actually be the case. Attention to growth-chart based growth patterns was augmented in the 1980s and 90s by studies of breastfed vs. formula fed infants: compared with formula fed infants, the breastfed infants’ weight-for-age exhibited
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downward progression across percentiles from about 3 months of age on the growth reference charts used in these studies (Hamill et al., 1979). This pattern might have suggested that breast milk was an insufficient source of nutrition to maintain growth and should be replaced and/or augmented with additional food sources. However, the researchers noted that the infants themselves were thriving and concluded that the apparently ‘‘slower weight gain’’ of breastfed infants after the first few months reflected the fact that the breastfed infants weighed less than the infants whose measurements were the source data for the charts. The gold standard reference at the time, the United States National Center for Health Statistics (NCHS) charts, adopted by the world health organization (WHO) for international use in 1978, were based on a limited sample of several hundred infants from the Fels longitudinal study in Ohio, who were predominantly formula fed (Roche and Sun, 2003). It was concluded that the ‘‘growth faltering’’ patterns of the breastfed infants were an artifact of the breastfed infants being smaller than the formula-fed reference sample infants. The WHO responded to these observations by initiating an infant growth study to generate data from breastfed infants and provide a reference standard based on the breastfed infant as the normative pattern. Data were collected between 1997 and 2003 in diverse ethnic and cultural settings (Brazil, Ghana, India, Norway, Oman, and the United States) from over 8,500 infants, all of whom were the result of healthy pregnancies among affluent, nonsmoking families who agreed to follow the WHO feeding recommendations (predominant or exclusive breastfeeding for at least 4 months, introduction of complementary foods by the age of 6 months, and continued partial breastfeeding until at least 12 months; accomplished by 20% of the sample). Known as the Multicentre Growth Reference Study (MGRS) these data were investigated for homogeneity of growth across populations. Length was chosen as the test parameter: interpopulation variance was found to be less than intrapopulation variance of total body length among the infants and it was decided that the population data could be combined to form a single reference sample (WHO MGRS et al., 2006). Published in 2006, these analyses aim to provide a single international standard for how infants and young children are expected to grow under optimal condi-
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tions. The proposition is that while the earlier reference charts were summaries of how children did grow, the new data provide a standard for how uncompromised infants should grow (WHO MGRS et al., 2006). This would seem to be a rational approach to resolving the problem of ‘‘the breastfed infant growth pattern.’’ Accepting that these standards are the normative model for breastfed infants, they were used to assess the growth of individual infants in a currently ongoing growth study of breastfed infants and the preliminary results are reported here. Case study Monthly weight data from a sample of 12 infants participating in an Emory University IRB approved weekly protocol longitudinal study of growth were assessed by reference to the MGRS standards (WHO Anthro, 2005; WHO MGRS et al., 2006). All of the infants in this sample were predominantly to exclusively breastfed for the first 4–6 months of life. As expected, the local sample means/medians fell close to the medians for the prescriptive sample (Fig. 1). Because of sample size, the local data were not analyzed by gender and the mean of the sample is closer to the 50th percentile of the WHO growth curve for female infants. These results may be a function of small sample size and/or the preponderance of females in the local data set (eight female infants, four male infants). As sample means do not reflect individual growth, it was of interest to further investigate if the individual study infants adhered to the prescriptive model of how infants should grow. Figure 2 investigates this perspective with serial growth measurements from three individuals. Each of these infants was a healthy term neonate of an uncomplicated pregnancy, predominantly or exclusively breastfed to 4 or 6 months of age. No confounding clinical conditions occurred during their development and each ended their first year as a healthy infant from an uncompromised environment, as per the samples from which the WHO standards were derived. The weight growth patterns of these individuals are both interesting and potentially alarming. Individual differences are strikingly documented, with an overall range in size for age between the 5th and 99th MGRS percentiles. This is not surprising considering the very real nature of individual variability, although it is a somewhat remarkable obser-
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vation among a sample of 12. Perhaps most interesting are the shapes of the individual curves. These three individuals are drawn from a sample whose mean weight mirrors the WHO distribution, but who individually differ in their progress from both the reference standard curve and from one another (Fig. 2). Female ‘‘7’’ and male ‘‘4,’’ for example, began postnatal life with roughly the same weight: the girl had a birth weight of 3.96 kg while the boy had a birth weight of 4.20 kg. Both of these weights are equivalent to the 95th percentile on the 2006 WHO sex-specific growth charts. By 12 months of age, however, the girl’s weight was dramatically different from the boy’s, at 12.4 and 8.13 kg, respectively. The difference in the percentiles represented by these weights is even more marked, with the girl above the 99th percentile and the boy, at the 5th percentile. From these graphical images, one might ask if the boy illustrates regression to the mean in the first few months, followed by canalization? This might explain his growth pattern by comparison with his ‘‘peers,’’ although the drop from the 95th to the 5th percentile could be considered more than a regression to the mean centile shift. This pattern is in stark contrast to the female, who did not experience the statistical adjustment of regression to the mean, but began at the 95th and continued to above the 99th percentile in her weight growth across the first year. Figure 2 further illustrates the reality of individually-based growth rates by a comparison between infant male ‘‘4’’ and another infant, female ‘‘9.’’ Male ‘‘4’’ ended the first year of life with a weight of 8.13 kg, a size that was nearly identical to that of female ‘‘9,’’ who had a weight at 1 year of 8.12 kg. The pattern of weight growth that led to this 1-year size, however, was quite different between the two infants: the female gained weight most rapidly within the first 6 months of life and more slowly thereafter. The male, on the other hand, gained very little weight in the first 4 months of life, gained weight more rapidly between 4 and 7 months, and slowly gained weight thereafter. Furthermore, it is notable that by comparison with this newly proposed normative standard for breastfeeding infants, female ‘‘9’’ experienced a decline in her ‘‘growth’’ from 4 months of age. In fact, she dropped from above the 50th percentile at 3 months of age to the 25th percentile by 6 months, and fell further, to the 15th percentile, by her 7-month mea-
Fig. 1. The study sample infants’ mean weight, sexes combined. The mean weight growth for the study sample (sexes combined due to sample size, n 5 12) is close to the WHO breastfed infant growth curve medians for males (triangle symbols) and females (square symbols) (de Onis et al., 2006; WHO Anthro, 2005). Study weights represent measurements from unclothed infants obtained with a SECA digital measuring scale. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]
Fig. 2. Population distribution curves versus individual growth patterns. Individual study infants’ monthly weight measurements by comparison with the WHO standards (de Onis et al., 2006; WHO Anthro, 2005). The standards’ medians for boys (single dotted line) and girls are illustrated. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]
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Fig. 3. Individual weight compared with the 5th, 15th, 25th, and 50th percentile WHO weight-for-age curves (de Onis et al., 2006; WHO Anthro, 2005). Monthly weight measurements for one female infant are illustrated to emphasize the effects of nonlinear growth biology on graphic growth patterns. The pattern identified by the squares results from plotting monthly measurements calculated from a 1-week lag interval compared with the pattern illustrated with the diamonds. The 1-week time interval results in as much as a 25 percentile drop in the size of the infant by comparison with her peers. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]
surement. This downward centile shift in weight from about three and a half months is in line with that reported by Dewey and others in their original studies of breastfed infants by comparison with the earlier NCHS/ CDC growth charts (eg. Dewey, 1998). What do these observations in Figure 2 mean? Why is a healthy infant ‘‘falling’’ across percentiles on the charts that aim to represent how healthy breastfed infants should grow? It was not due to differences in feeding, environment or general wellbeing of this infant, who is a healthy thriving individual. Is this an example of regression to the mean, or a readjustment to her genetic trajectory? Perhaps this ‘‘pattern’’ is not what it appears: the visual ‘‘decline’’ has no actual meaning in terms of her growth biology, albeit that she grows neither continuously nor according to the mathematical function that generated the curve. The chart is only designed to show the relative size of individual infants compared with their peers at static ages; it is not designed to show the actual change across time of growing infants. The
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graph illustrates that this child is relatively smaller compared with the infants in the reference sample between 5 and 7 months of age than she had been at younger ages. ‘‘Should’’ she be bigger between 5 and 7 months? No. The growth charts cannot capture the oscillation in relative sizes among peers that actually occurs due to differences in timing and amplitude of growth. It is likely that this graphic image is genetic variability in growth, as incremental growth saltations occur episodically across time. To investigate the effect that timing of individual growth events might have on the graphic image, infant ‘‘9’s’’ monthly weight growth data were replotted by a 1-week frame shift (Fig. 3). That is, as she was measured weekly, a plot using her weights taken closest to her monthly ‘‘birthdate’’ (the same graph shown for her in Fig. 2) was juxtaposed to the weight measurements taken at the next weekly measurement visit in the context of 5th, 15th, 25th, and 50th centiles of the MGRS weight-for-age growth curves. The timing of growth assessment against the back-
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ground of her actual growth identified a significant contribution from variability in weekly growth rates. While she still ‘‘drops in centiles’’ on the reference curves (is among the smaller children with age), the differences between the two time frame plots point out the effects that the nonlinear nature of weight gain and the timing of growth measurement can have on appearance of the growth pattern when plotted on centile charts. The nonlinear growth process results in more than a 25 percentile shift within 1 week, depending on whether a growth saltation occurred during the week or no change had taken place. Overall, even this small sample comparison identifies several salient points to consider when thinking about the meaning of how to interpret growth progress from a growth chart: individual growth proceeds by unique timing and incremental patterns that cannot be captured by a single mathematical model of central tendency and the timing of measurement of growth saltations relative to measurement has a significant effect on the individual’s percentile size ranking, with as much as a two centile shift in a short time span. IMPLICATIONS OF POPULATION-DERIVED TRENDS VS. ACTUAL INDIVIDUAL GROWTH The differences between individually-based observations of growth patterns and the trends that emerge from sample-level statistics have a significant impact on concepts concerning the biology of growth. Although the growth curve represents the distribution of size in populations of individuals at discrete points, nonetheless it is used to impute biological process from the slope that best fits the distribution of points. This description of what populations of individuals look like at various ages has become a prescriptive statement of what individuals should be doing. However, the process by which an individual gets from size A to size B is not knowable from this population distribution curve. Moreover, the methods of determining the statistical distributions of size for age on which the growth charts are based, followed by the smoothing linear interpolation functions, turn even longitudinally collected data into a cross-sectional comparison of size. The problems inherent in interpolating process from distance curves have long been recognized and were first described by Boas in the late 19th and early 20th centuries. As Boas documented, individual children grow at
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very different rates, making cross-sectionally derived charts inappropriate for assessing the growth of an individual. These points were most saliently directed to the loss of the adolescent growth spurt in cross sectional data due to the variability in the timing of onset among individuals (Boas, 1932), reiterated by Tanner and colleagues in the 1960s, who concluded that cross-sectionally constructed standards can ‘‘no longer represent correctly the growth of any individual . . .’’ (Prader et al., 1963. p 650). It is interesting that despite these repeated cautions, the WHO MGRS study proposes that their growth curves represent the ‘‘best description of physiological growth and should be applied to all children everywhere, regardless of ethnicity, socio-economic status and type of feeding’’ (WHO MGRS, 2006. p 64). As these growth charts are not designed to reflect individual’s longitudinal growth patterns and, therefore, cannot reveal how individuals are growing by comparison with their peers, it is difficult to justify interpretations of physiological growth biology from the growth charts. While the charts might be appropriately posited to describe a range of sizes that infants should be within for each age, as a percentile position depends on the timing of the measurement assessment relative to the timing of growth biology, it is beyond the scope of the evidence to posit that a growth reference pattern can reflect how infants should grow. PROXIMAL MECHANISMS FOR GROWTH PROCESS ADAPTABILITY ACT AT THE INDIVIDUAL LEVEL On a practical level, data derived from populations are not, perhaps, the best models for understanding adaptive responses in the growth process. As it is individuals who are growing, it is the biology of individual growth that is under selection; successful ‘‘growth patterns’’ in local ecologies are those that are compatible with survival of the fetus to successful reproduction. How individuals actually grow, in terms of discrete events, provides a focal point for investigating the nature of flexibility as variability in the amplitude and timing of saltatory growth events. The difference between a continuous and a discontinuous growth process has profound implications for our understanding of adaptation. When thinking about energy availability and use, for example, how growth actually proceeds is central to theoretical debates typi-
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cally constructed as narratives concerning biological trade-offs. To date, the continuous models have been employed to imply that growth is a declining drain on energy resources for the individual as the first year proceeds. The estimated energetic costs of growing come from longitudinal studies of weight change and body composition measured at 3month intervals. Daily weight velocities are interpolated, partitioned by age-appropriate percentages of lean and fat mass (Butte et al., 2000a) and energy equivalents for protein and fat deposition employed to calculate these theoretical estimates. Before 3 months of age, it is estimated that growth costs120 kcal/day (Butte et al., 2000b). This is based on an estimated 30-g/day weight gain, as interpolated from the 3-month interval data and a 20 kJ/g cost for this weight gain ‘‘growth.’’ After 3 months of age, interpolated daily weight gain drops to 12–20 g/day, and at an estimated 10 kJ/g weight gain, only 30–50 kcal/day are required for growth. From this viewpoint, a decreasing percentage of daily energy contributes to growth with age, from about 6% by 6 months to only 2–3% by the end of the first year. If this is the case, why are so many malnourished infants so small? The present estimates of metabolic requirements for growth are not likely to be correct estimates of a saltatory growth process. Among individuals, weight and skinfold changes accompany growth saltations (Lampl et al., 2005); these data suggest that a close relationship exists between energy stores and growth events at rates that may not be reflected by interpolated values. Further work is needed to re-evaluate these relationships with real ‘‘growth’’ values in lieu of interpolations. GROWTH BIOLOGY IS A FUNDAMENTAL INTERFACE BETWEEN THE SPECIES AND THE ENVIRONMENT It can be hypothesized that a saltatory growth process reflects a physiological cascade involving a biological clock acting through inhibitory and disinhibitory signals functioning at the level of gene expression and responsive to redundant sources of modulation downstream, including interference at the level of target cells/tissue. This may be an expression of ‘‘nested bow-tie’’ metabolic architecture (Csete and Doyle, 2004; Lampl, 2005), in which cross-talking chemical pathways permit multiple avenues for information about the
American Journal of Human Biology DOI 10.1002/ajhb
environment to have an impact on the amount and timing of growth events. With sufficient inhibitory feedback, a growth saltation will theoretically be suppressed. While it is tempting to suggest that a simple energetic signal system would drive and/or inhibit a growth saltation, interestingly, this is not necessarily the first principle: observational data identify that young infants grow in length even as they lose weight, illustrated by infants who are long and thin, not unusual among mothers with problems breastfeeding. The larger implication of this observation is that the biological clock timing length growth may be a driver in a dynamical system that actively tests the environment, rather than merely passively responds. Understanding the biology of growth is fundamental in thinking about adaptation. Conceptualizing growth as the slow, steady progression depicted on the growth curve leaves little room for individual adaptability; viewing growth as a curve on the chart relegates the potential for adaptation only to which channel an individual ends up on, the 5th vs. the 95th. By contrast, as a dynamic system, the pulsatility characteristics of saltatory growth events are able to change, providing flexibility that is ‘‘adaptive’’ at the species level as alternative paths are available for navigating from birth to reproduction through growth and development (Lampl and Johnson 1998). The environment is translated through body composition and hormonal signals, with the potential of altering the amplitude and frequency of growth saltations. Ultimately, patterns of growth events compatible with survival in an environment become the local growth pattern. Clarification of individual growth patterns has broad implications for our understanding of growth biology and the nature of adaptability, since it is precisely in this interindividual variability where selection may occur. LITERATURE CITED Boas F. 1932. Studies in growth. Hum Biol 4:307–350. Borghi E, de Onis M, Garza C, Van den Broeck J, Frongillo EA, Grummer-Strawn L, van Buuren S, Pan H, Molinari L, Martorell R, Onyango AW, Martines JC for the WHO Multicentre Growth Reference Study Group. 2006. Construction of the World Health Organization child growth standards: selection of methods for attained growth curves. Stats Med 25:247–265. Butte NF, Hopkinson JM, Wong WW, Smith EO, Ellis KJ. 2000a. Body composition during the first 2 years of life: an updated reference. Pediatr Res 47:578–585. Butte NF, Wong WW, Hopkinson JM, Heinz CJ, Mehta NR, O’Brian Smith E. 2000b. Energy requirements derived from total energy expenditure and energy deposition
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