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Epistasis is caused by genetic interactions among mutations that affect fitness. To characterize properties and potential mechanisms of epistasis, we engineered eight double mutants that combined mutations from the rho and rpoB genes of Escherichia coli. The two genes encode essential functions for transcription, and the mutations in each gene were chosen because they were beneficial for adaptation to thermal stress (42.2 °C). The double mutants exhibited patterns of fitness epistasis that included diminishing returns epistasis at 42.2 °C, stronger diminishing returns between mutations with larger beneficial effects and both negative and positive (sign) epistasis across environments (20.0 °C and 37.0 °C). By assessing gene expression between single and double mutants, we detected hundreds of genes with gene expression epistasis. Previous work postulated that highly connected hub genes in coexpression networks have low epistasis, but we found the opposite: hub genes had high epistasis values in both coexpression and protein-protein interaction networks. We hypothesized that elevated epistasis in hub genes reflected that they were enriched for targets of Rho termination but that was not the case. Altogether, gene expression and coexpression analyses revealed that thermal adaptation occurred in modules, through modulation of ribonucleotide biosynthetic processes and ribosome assembly, the attenuation of expression in genes related to heat shock and stress responses, and with an overall trend toward restoring gene expression toward the unstressed state.

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The "leafing intensity premium" hypothesis proposes that leaf size results from natural selection acting on different leafing intensities, i.e., the number of leaves per unit shoot volume or mass. The scaling relationships among various above-ground functional traits in the context of this hypothesis are important for understanding plant growth and ecology. Yet, they have not been sufficiently studied. In this study, we selected four bamboo species of the genus Indocalamus Nakai and measured the total leaf fresh mass per culm, total non-leaf above-ground fresh mass, total number of leaves per culm, and above-ground culm height of 90 culms from each species. These data were used to calculate leafing intensity (i.e., the total number of leaves per culm divided by the total non-leaf above-ground fresh mass) and mean leaf fresh mass per culm (i.e., the total leaf fresh mass per culm divided by the total number of leaves per culm). Reduced major axis regression protocols were then used to determine the scaling relationships among the various above-ground functional traits and leafing intensity. Among the four species, three exhibited an isometric (one-to-one) relationship between the total leaf fresh mass per culm and the total non-leaf above-ground fresh mass, whereas one species (Indocalamus pumilus) exhibited an allometric (not one-to-one) relationship. A negative isometric relationship was found between the mean leaf fresh mass per culm and the leafing intensity for one species (Indocalamus pedalis), whereas three negative allometric relationships between mean leaf fresh mass per culm and leafing intensity were observed for the other three species and the pooled data. An exploration of the alternative definitions of "leafing intensity" showed that the total number of leaves per culm divided by the above-ground culm height is superior because it facilitates the non-destructive calculation of leafing intensity for Indocalamus species. These results not only confirm the leafing intensity premium hypothesis for bamboo species but also highlight the interconnected scaling relationships among different functional traits, thereby contributing to our understanding of the ecological and evolutionary significance of leaf size variation and biomass investment strategies.

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There is a lack of research on whether tree size affects lamina and petiole biomass allocation patterns, whereas the trade-off between leaf biomass allocated to the lamina and the petiole is of significance when considering the hydraulic and mechanical function of the leaf as a whole. Here, Camptotheca acuminata Decne was selected for study because of the availability of trees differing in size growing under the same conditions. A total of 600 leaves for two tree size groups and 300 leaves per group differing in height and trunk diameter were collected. The lamina fresh mass (LFM), lamina dry mass (LDM), lamina area (LA), petiole fresh mass (PFM), and petiole length (PL) of each leaf was measured, and reduced major axis regression protocols were used to determine the scaling relationships among the five functional traits. The bootstrap percentile method was used to determine if the scaling exponents of the traits differed significantly between the two tree size groups. The results indicated that (i) there was a significant difference in the LFM, LDM, PFM, PL, LMA, LFMA and PFM/LFM between large and small trees, but no significant difference in LA; (ii) the LA versus LFM, LA versus LDM, LFM versus PFM, LA versus PFM, and PL versus PFM scaling relationships of the two groups were allometric (i.e., not isometric); (iii) there were significant differences in the scaling exponents of LA versus LFM, LA versus PFM, PL versus PFM between the two groups, but there was no significant difference in the LFM versus PFM scaling relationship between the two groups of trees. The data were also consistent with the phenomenon known as "diminishing returns". These data indicate that tree size influences leaf biomass allocation patterns in ways that can potentially influence overall plant growth, and therefore have an important bearing on life-history strategies.

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According to Michener's paradox, most altruistic groups in nature should be small and large groups should not exist. This is because per capita productivity is thought to decrease as groups get larger, meaning that the share of indirect fitness available to each group member declines, which favours dispersal. The empirical evidence for a decrease in per capita productivity is contradictory, however, and limited to the social Hymenoptera. I report that per capita reproductive success decreased with increasing group size across 26 cooperatively breeding bird species. Small groups comprising two or three individuals were the most common (79% of 16,101 groups), and these had the highest per capita reproductive success. This close fit between per capita reproductive success and the distribution of group sizes in nature suggests that it may indeed be difficult for large groups to evolve through indirect fitness benefits alone.

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Cognitive-achievement relations research has been instrumental in understanding the development of academic skills and learning difficulties. Most cognitive-achievement relations research has been conducted with large samples and represent average relations across the ability spectrum. A notable gap in the literature is whether these relations vary by cognitive ability levels (IQ). This study examined cognitive-achievement relations across different general ability levels (Low, Average, and High) to fill this gap. Based on Spearman's Law of Diminishing Returns, it would be expected that general intelligence would be a stronger predictor of academic skills at lower levels of IQ, and more specific abilities would be stronger predictors of academic skills at higher levels of IQ. To test this, multi-group path analysis and structural equation modeling were used to examine whether integrated models of cognitive-reading relations are differentiated by IQ levels in the Woodcock-Johnson III and Woodcock-Johnson IV standardization samples. Global and broad cognitive abilities were used as predictors of basic reading skills and reading comprehension for elementary and secondary school students. The magnitude of prediction differed across ability groups in some cases, but not all. Importantly, the variance explained in basic reading skills and reading comprehension tended to be larger for the Low group compared to the Average and High groups. When variance accounted for by general intelligence was removed from the broad abilities, the effects of the broad abilities were similar across ability groups, but the indirect effects of g were higher for the Low group. Additionally, g had stronger relative effects on reading in the Low group, and broad abilities had stronger relative effects on reading in the Average and High groups. The implications and limitations of this study are discussed.

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PURPOSE: Traditional coronal-plane vertical spine height measurements, such as T1-T12 and T1-S1 spine height, are influenced by 3-dimensional spinal deformity. Therefore, they are unreliable indicators of true spine growth. The novel 3D true spine length (3D-TSL) technique assesses spine growth regardless of the presence of 3D spinal deformity. This study evaluates the effect of growth friendly surgery on spine growth using the 3D-TSL technique at two years follow-up. METHODS: Radiographs of early onset scoliosis (EOS) participants undergoing growth friendly surgery at a single institution were evaluated at pre-index, post-index, and at 2-year follow-up. Scoliosis, kyphosis, traditional coronal height and 3D-TSL were measured. RESULTS: Twenty-four EOS patients (14 female) with a mean age of 6.3 years were included. Scoliosis improved from 77.8 ± 18.7° pre-index to 56.0 ± 17.8° post-index (p < 0.001); but increased at 2 years to 65.9 ± 20.1° (p < 0.05). Kyphosis improved from 56.0 ± 20.7° pre-index to 39.3 ± 13.8° post-index (p < 0.001); and increased again at 2 years to 48.6 ± 16.4° (p < 0.05). Traditional T1-S1 height increased from pre-index to post-index, to 2-year follow-up (245.5 ± 37.2 mm to 275.8 ± 42.7 mm; p < 0.001, to 288.0 ± 41.7 mm; p = 0.005). As expected, T1-S1 3D-TSL did not change from pre to immediately post-index (305.6 ± 43.9 mm vs 306.5 ± 44.0 mm); there was a significant change from post-index to 2-year follow-up (334.1 ± 48.0 mm; p < 0.001). CONCLUSIONS: Out of plane changes in scoliosis and kyphosis over time justify the use of the 3D-TSL for this cohort of patients. There was no significant change in 3D-TSL from pre-index to post-operatively; however, during the growth phase of treatment 3D-TSL increased significantly by 27.6 mm.

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Foliage leaves are the primary photosynthetic organ of the majority of vascular plants, and their area vs. biomass scaling relationships provide valuable insights into the capacity and investment in light interception, which is critical to plant growth and performance. The "diminishing returns" hypothesis (DRH), which is based primarily on data from gymnosperms and angiosperms, posits that leaf (lamina) area scales with leaf dry mass. on average with a scaling exponent less than 1.0. However, it remains uncertain whether DRH applies to ferns or whether ecological factors affect the scaling exponents governing fern leaf morphometrics. To address this issue, 182 individuals of 28 subtropical ferns species were studied at low, medium, and high elevations (i.e., 600 m, 900 m, and 1200 m, respectively) in Mount Wuyi National Park, Jiangxi Province, China. The scaling relationships between leaf area and leaf biomass for individual and total leaf of ferns at different elevations were examined by using standardized major axis regression protocols. Analyses of the 28 fern species (using Blomberg K-value protocols) indicated no phylogenetic biases among the species compositions of the three different elevations. In addition, at the individual plant level, individual leaf area (ILA) did not differ significantly among the three different elevations (P > 0.05). However, individual leaf mass (ILM) was significantly higher at 900m than at 1200m (P < 0.05), resulting in a significantly higher leaf mass per area (LMA) at the 900m elevation than at the 600m and 1200m elevations (P < 0.05). The ILA and ILM at the 900m elevation were significantly higher than at the 600m elevation (P < 0.05). At the species level, ILA and ILM did not differ significantly among the three elevations (P > 0.05). The total leaf area per individual (TLA) did not differ significantly across the different elevations (P > 0.05). However, total leaf mass per individual (TLM) did differ significantly (P < 0.05). At the individual plant level, the scaling exponents for ILA vs. ILM and TLA vs. TLM at the three different elevations were all significantly less than 1.0 (P < 0.05), which was consistent with the DRH. At the species level, the scaling exponents for the ILA vs. ILM were significantly less than 1.0 at the middle and high elevations, but not at the low elevation. The scaling exponents of the TLA and TLM were numerically highest in the middle elevation, and all were less than 1.0 for the three elevations. These results indicate that the scaling relationships of leaf area versus mass of subtropical ferns at different elevations support the DRH hypothesis. The study further informs our understanding of the resource allocation strategies of an ancient and diverse plant lineage.

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Evolution can be contingent on history, but we do not yet have a clear understanding of the processes and dynamics that govern contingency. Here, we performed the second phase of a two-phase evolution experiment to investigate features of contingency. The first phase of the experiment was based on Escherichia coli clones that had evolved at the stressful temperature of 42.2 °C. The Phase 1 lines generally evolved through two adaptive pathways: mutations of rpoB, which encodes the beta subunit of RNA polymerase, or through rho, a transcriptional terminator. We hypothesized that epistatic interactions within the two pathways constrained their future adaptative potential, thus affecting patterns of historical contingency. Using ten different E. coli Founders representing both adaptive pathways, we performed a second phase of evolution at 19.0 °C to investigate how prior genetic divergence or adaptive pathway (rpoB vs. rho) affects evolutionary outcomes. We found that phenotype, as measured by relative fitness, was contingent on founder genotypes and pathways. This finding extended to genotypes, because E. coli from different Phase 1 histories evolved by adaptive mutations in distinct sets of genes. Our results suggest that evolution depends critically on genetic history, likely due to idiosyncratic epistatic interactions within and between evolutionary modules.

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We live in times when our culture is obsessed with happiness. The value of almost every aspect of our lives is increasingly judged in terms of their contribution to our happiness. Happiness has become the ultimate goal by which values and priorities are constructed and the only thing for which any action in pursuit of does not require justification. In contrast, sadness is increasingly abnormalized and pathologized. In this paper, an effort is made to counteract the narrative that sadness, a critical aspect of human life is abnormal or a pathological condition. The evolutionary benefits of sadness and its place in human flourishing are discussed. A rebranding of sadness is proposed that emphasizes the free expression of sadness in everyday greetings to remove it from its current negative state and promote many of its benefits including post-traumatic growth and resilience.

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The universal phenomenon of evolution consists of change after change in flow configuration in a time direction that is perceptible to the observer. This reality clashes with the doctrine of precise optima, minima, and maxima, now rigidly in place because of calculus and computational simulations of all kinds of flowing and changing configurations. With two dissimilar examples, access on an area (a human settlement) and along a line (animal locomotion), it is shown that even a 1-percent imperfection in performance is accompanied by a sizable bandwidth of freedom to hit the 'target', that is, an easily accessible design with close to perfect performance. The evolutionary designs reveal the physics behind the phenomenon of diminishing returns in the vicinity of the mathematical optimum. In evolution what works is kept.

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Background: Numerous studies show that increasing levels of education, income, assets, and occupational status are linked to greater improvements in White adults' health than Black adults'. Research has yet to determine, however, whether there are racial differences in the relationship between health and debt and whether this relationship varies across cohorts. Methods: Using data from the 1992-2018 Health and Retirement Study, we use survival analyses to examine the link between debt and heart attack risk among the Prewar Cohort, born 1931-1941, and Baby Boomers, born 1948-1959. Results: Higher unsecured debt is associated with increased heart attack risk for Black adults, especially among Baby Boomers and during economic recessions. Higher mortgage debt is associated with lower risk of heart attack for White but not Black Baby Boomers. The relationship between debt and heart attack risk remains after controlling for health behaviors, depressive symptoms, and other economic resources that are concentrated among respondents with high levels of debt. Conclusion: Debt is predictive of heart attack risk, but the direction and strength of the relationship varies by type of debt, debtors' racial identity, and economic context.

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Foliage leaves are essential for plant survival and growth, and how plants allocate biomass to their leaves reveals their economic and ecological strategies. Prior studies have shown that leaf-age significantly influences leaf biomass allocation patterns. However, unravelling the effects of ontogeny on partitioning biomass remains a challenge because it is confounded by the effects of environmental factors. Here, we aim to elucidate whether leaf-age affects the allocation to the lamina and petiole by examining leaves of known age growing in the same general environmental context. We sampled 2698 Photinia serratifolia leaves developing in the same environment from April to November 2021, representing eight leaf-ages (n > 300 for each leaf-age). Petiole and lamina biomass, and lamina area were measured to evaluate the scaling relationships using reduced major axis regression protocols. The bootstrap percentile method was used to determine the differences in scaling exponents among the different leaf-ages. ANOVA with Tukey's HSD was used to compare the ratios of petiole and lamina biomass to lamina area across the leaf-ages. Correlation tests were used to determine if exponents, intercepts, and ratios differed significantly across the different leaf-ages. The data indicated that (i) the ratio of petiole and lamina biomass to lamina area and the scaling exponent of lamina biomass versus lamina area correlate positively with leaf-age, and (ii) the scaling exponent of petiole biomass versus lamina area correlates negatively with leaf-age. Leaf maturation process involves an inverse proportional allocation between lamina and petiole biomass for expanding photosynthetic area. This phenomenon underscores the effect of leaf-age on biomass allocation and the importance of adopting an ontogenetic perspective when entertaining plant scaling theories and unravelling the principles governing shifts in biomass allocation throughout the leaf lifespan.

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"Diminishing returns" in leaf economics occurs when increases in lamina mass (M), which can either be represented by lamina dry mass (DM) or fresh mass (FM), fail to produce proportional increases in leaf surface area (A), such that the scaling exponent (α) for the M vs. A scaling relationship exceeds unity (i.e., α > 1.0). Prior studies have shown that FM vs. A is better than DM vs A in assessing diminishing returns in evergreen species. However, the superiority of FM vs. A over DM vs. A has been less well examined for deciduous species. Here, we applied reduced major axis protocols to test whether FM vs. A is better than DM vs. A to describe the M vs. A scaling relationship, using a total of 4271 leaves from ten deciduous and two evergreen tree species in the Fagaceae and Ulmaceae for comparison. The significance of the difference between the scaling exponents of FM vs. A and DM vs. A was tested using the bootstrap percentile method. Further, we tested the non-linearity of the FM (DM) vs. A data on a log-log scale using ordinary least squares. We found that (i) the majority of scaling exponents of FM vs. A and DM vs. A were >1 thereby confirming diminishing returns for all 12 species, (ii) FM vs. A was more robust than DM vs. A to identify the M vs. A scaling relationship, (iii) the non-linearity of the allometric model was significant for both DM vs. A and FM vs. A., and (iv) the evergreen species of Fagaceae had significantly higher DM and FM per unit area than other deciduous species. In summary, FM vs. A is a more reliable measure than DM vs. A when dealing with diminishing returns, and deciduous species tend to invest less biomass in unit leaf light harvesting area than evergreen species.

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Leaf lamina mass and area are closely correlated with the photosynthetic capacity and competitive ability of plants, whereas leaf age has been demonstrated to affect physiological processes such as photosynthesis. However, it remains unknown whether the lamina mass vs. area scaling relationship is influenced by leaf age, which is important for understanding plant adaptive strategies and, more broadly, resource utilization and growth. We measured the leaf functional traits of five leaf-age groups of Photinia × fraseri for a total of 1,736 leaves. ANOVA followed by Tukey's honestly significant difference test was used to compare the functional traits among the five leaf-age groups. Reduced major axis regression protocols were used to fit the scaling relationship between lamina mass and area, and the bootstrap percentile method was used to compare the lamina mass vs. area scaling relationships among the leaf-age groups. Lamina area, and the ratio of lamina dry mass to lamina fresh mass increased with increasing leaf age. Lamina fresh mass per unit area, and lamina dry mass per unit area both exhibited a parabolic-like trend as leaf age increased, i.e., at the leaf maturation stage, it showed a slight but significant decline. The phenomenon called diminishing returns were confirmed by each of the five leaf-age groups, i.e., all of the numerical values of the scaling exponents of lamina mass vs. area were significantly greater than 1. There were significant differences in the scaling exponents of lamina mass vs. area for the leaves across different sampling times. The scaling exponents were lower at the early rapid growth stage, indicating a lower cost for increasing leaf area compared to the leaf maturation stage. These data are consistent with leaves undergoing a transition from resource acquisition to resource conservation in the process of their development and growth.

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The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz and Schrödinger, that perceived color space is not Euclidean but rather, a three-dimensional Riemannian space. We show that the principle of diminishing returns applies to human color perception. This means that large color differences cannot be derived by adding a series of small steps, and therefore, perceptual color space cannot be described by a Riemannian geometry. This finding is inconsistent with the current approaches to modeling perceptual color space. Therefore, the assumed shape of color space requires a paradigm shift. Consequences of this apply to color metrics that are currently used in image and video processing, color mapping, and the paint and textile industries. These metrics are valid only for small differences. Rethinking them outside of a Riemannian setting could provide a path to extending them to large differences. This finding further hints at the existence of a second-order Weber­Fechner law describing perceived differences.

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PREMISE: The phenomenon called "diminishing returns" refers to a scaling relationship between lamina mass (M) vs. lamina area (A) in many species, i.e., M ∝ Aα>1 , where α is the scaling exponent exceeding unity. Prior studies have focused on the scaling relationships between lamina dry mass (DM) and A, or between fresh mass (FM) and A. However, the scaling between petiole mass and M and A has seldom been investigated. Here, we examine the scaling relationships among FM, DM, A, and petiole fresh mass (PFM). METHODS: For each of 3268 leaves from nine Lauraceae species, FM, DM, A, and PFM were measured, and their scaling relationships were fitted using reduced major axis regression protocols. The bootstrap percentile method was used to test the significance of the difference in α-values between any two species. RESULTS: The phenomenon of diminishing returns was verified between FM vs. A and DM vs. A. The FM vs. A scaling relationship was statistically more robust than the DM vs. A scaling relationship based on bivariate regression r2 -values. Diminishing returns were also observed for the PFM vs. FM and PFM vs. A scaling relationships. The PFM vs. FM scaling relationship was statistically more robust than the PFM vs. A scaling relationship. CONCLUSIONS: "Diminishing returns" was confirmed among the FM, DM, A, and PFM scaling relationships. The data collectively indicate that the petiole scales mechanically more strongly with lamina mass than with area, suggesting that static (self) loading takes precedence over dynamic (wind) loading.

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OBJECTIVE: Several studies of nurse staffing and patient outcomes found a curvilinear or U-shaped relationship, with benefits from additional nurse staffing diminishing or reversing at high staffing levels. This study examined potential diminishing returns to nurse staffing and the existence of a "tipping point" or the level of staffing after which higher nurse staffing no longer improves and may worsen readmissions. DATA SOURCES/STUDY SETTING: The Readiness Evaluation And Discharge Interventions (READI) study database of over 130,000 adult (18+) inpatient discharges from 62 medical, surgical, and medical-surgical (noncritical care) units from 31 United States (US) hospitals during October 2014-March 2017. STUDY DESIGN: Observational cross-sectional study using a fully nonparametric random forest machine learning method. Primary exposure was nurse hours per patient day (HPPD) broken down by registered nurses (nonovertime and overtime) and nonlicensed nursing personnel. The outcome was 30-day all-cause same-hospital readmission. Partial dependence plots were used to visualize the pattern of predicted patient readmission risk along a range of unit staffing levels, holding all other patient characteristics and hospital and unit structural variables constant. DATA COLLECTION/EXTRACTION METHODS: Secondary analysis of the READI data. Missing values were imputed using the missing forest algorithm in R. PRINCIPAL FINDINGS: Partial dependence plots were U-shaped, showing the readmission risk first declining and then rising with additional nurse staffing. The tipping points were at 6.95 and 0.21 HPPD for registered nurse staffing (nonovertime and overtime, respectively) and 2.91 HPPD of nonlicensed nursing personnel. CONCLUSIONS: The U-shaped association was consistent with diminishing returns to nurse staffing suggesting that incremental gains in readmission reduction from additional nurse staffing taper off and could reverse at high staffing levels. If confirmed in future causal analyses across multiple outcomes, accompanying investments in infrastructure and human resources may be needed to maximize nursing performance outcomes at higher levels of nurse staffing.

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Adaptation to mechanical loading is critical to maintaining bone mass and offers therapeutic potential to preventing age-related bone loss and osteoporosis. However, increasing the duration of loading is met with "diminishing returns" as the anabolic response quickly becomes saturated. As a result, the anabolic response to daily activities and repetitive bouts of loading is limited by the underlying mechanisms that desensitize and render bone unresponsive at the cellular level. Osteocytes are the primary cells that respond to skeletal loading and facilitate the overall anabolic response. Although many of osteocytes' signaling mechanisms activated in response to loading are considered anabolic in nature, several of them can also render osteocytes insensitive to further stimuli and thereby creating a negative feedback loop that limits osteocytes' overall response. The purpose of this review is to examine the potential mechanisms that may contribute to the loss of mechanosensitivity. In particular, we examined the inactivation/desensitization of ion channels and signaling molecules along with the potential role of endocytosis and cytoskeletal reorganization. The significance in defining the negative feedback loop is the potential to identify unique targets for enabling osteocytes to maintain their sensitivity. In doing so, we can begin to cultivate new strategies that capitalize on the anabolic nature of daily activities that repeatedly load the skeleton.

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RNA evolves by adding substructural parts to growing molecules. Molecular accretion history can be dissected with phylogenetic methods that exploit structural and functional evidence. Here, we explore the statistical behaviors of lengths of double-stranded and single-stranded segments of growing tRNA, 5S rRNA, RNase P RNA, and rRNA molecules. The reconstruction of character state changes along branches of phylogenetic trees of molecules and trees of substructures revealed strong pushes towards an economy of scale. In addition, statistically significant negative correlations and strong associations between the average lengths of helical double-stranded stems and their time of origin (age) were identified with the Pearson's correlation and Spearman's rho methods. The ages of substructures were derived directly from published rooted trees of substructures. A similar negative correlation was detected in unpaired segments of rRNA but not for the other molecules studied. These results suggest a principle of diminishing returns in RNA accretion history. We show this principle follows a tendency of substructural parts to decrease their size when molecular systems enlarge that follows the Menzerath-Altmann's law of language in full generality and without interference from the details of molecular growth.