Impact of Solitary Involved Lymph Node on Outcome in Localized Cancer of the Esophagus and Esophagogastric Junction

Node-positive esophageal cancer is associated with a dismal prognosis. The impact of a solitary involved node, however, is unclear, and this study examined the implications of a solitary node compared with greater nodal involvement and node-negative disease. The clinical and pathologic details of 604 patients were entered prospectively into a database from1993 and 2005. Four pathologic groups were analyzed: node-negative, one lymph node positive, two or three lymph nodes positive, and greater than three lymph nodes positive. Three hundred and fifteen patients (52%) were node-positive and 289 were node-negative. The median survival was 26 months in the node-negative group. Patients (n = 84) who had one node positive had a median survival of 16 months (p = 0.03 vs node-negative). Eighty-four patients who had two or three nodes positive had a median survival of 11 months compared with a median survival of 8 months in the 146 patients who had greater than three nodes positive (p = 0.01). The survival of patients with one node positive [number of nodes (N) = 1] was also significantly greater than the survival of patients with 2–3 nodes positive (N = 2–3) (p = 0.049) and greater than three nodes positive (p < 0001). The presence of a solitary involved lymph node has a negative impact on survival compared with node-negative disease, but it is associated with significantly improved overall survival compared with all other nodal groups.
Introduction
Carcinoma of the esophagus carries a dismal prognosis, and for patients presenting with localized resectable disease, multivariate analysis has established that the presence or absence of involved lymph nodes confers the greatest prognostic significance.1 In surgical management, the extent and type of lymphadenectomy undertaken varies from no formal lymphadenectomy to two and three field dissection.2–5 The presence and extent of lymph node involvement is important as selective approaches may be considered depending on the nodal stage at presentation. In early tumors, for instance, the sentinel node concept initially developed in melanoma and breast cancer was explored to help identify patients who may not require lymph node dissection.6–8 The advent of minimally invasive esophagectomy may also highlight the need to subselect patients for lymphadenectomy.9
In the observations of the senior author (JVR), patients with solitary involved lymph nodes may achieve good outcomes, and this hypothesis was evaluated in this analysis of a large prospective database. We report herein that the cohort with a solitary node involved had cancer outcomes closer to node-negative disease than other node-positive subgroups, and suggest that this represents a distinct prognostic subgroup.
Patients and Methods
The study population consisted of all patients with tumors of the esophagus and esophagogastric junction who underwent surgical resection, either alone or preceded by neoadjuvant chemoradiation, between 1993 and 2005. Patients receiving multimodal therapy received cisplatin, 5-fluorouracil, and external beam radiotherapy (40–44 Gy, 2–2.67 Gy/fraction) as previously described.10 Data concerning the clinical and pathologic parameters for all patients was obtained from a detailed prospective database maintained by a full-time data manager. Pathologic parameters analyzed included the location of the tumor, tumor morphology, i.e., adenocarcinoma or squamous cell carcinoma, histological differentiation (grade), TNM staging, number and site of involved lymph nodes, and R classification after surgical resection. Staging of tumors was performed according to the American Joint Committee on Cancer TNM system.11
A subtotal esophagectomy was performed with a sutured anastomosis either in the right thorax (two-stage) or neck (three-stage). All cases underwent a formal abdominal lymphadenectomy and mediastinal lymph node dissection up to and including the subcarinal nodes. Thoracic nodes were submitted separately to abdominal nodes.
Statistical Analysis
Data are presented as frequencies, means, and percentages. ANOVA was used for comparison of the four demographic groups. Survival probability was estimated using the Kaplan–Meier method. Survival was calculated from the date of clinical diagnosis to date of death or date last seen. In the multivariate analysis, independent prognostic factors for survival were determined by using a Cox regression hazard model. Two analyses were performed, one for all patients and the other exclusive to node-positive patients. All statistical analyses were performed using Stata software (version 9.1 for Windows, Statcorp, TX). A p value <0.05 was considered statistically significant.12
Results
Patients/histology
Six hundred and four patients underwent surgery for localized malignancy of the esophagus or esophagogastric junction. The mean age was 62 ± 10.4 (median = 64, range 56 to 70). Four hundred and twelve (68%) patients were men. The mean number of lymph nodes examined per specimen was 12 ± 6 (median = 10, range = 6 to 55). Two hundred and eighty-nine patients (48%) had node-negative disease [number of nodes (N) = 0], 84 (14%) had one node positive (N = 1), 84 had two or three nodes positive, and 147 (24%) had greater than three nodes positive (N > 3). In patients with one involved node, in all cases the node was adjacent to the tumor, mediastinal for esophageal tumors, and periesophageal or along the left gastric artery for junctional tumors (Tables 1 and 2).
Table 1Demographics of Nodal SubgroupsHistologic DataN = 0 (n = 289)N = 1 (n = 84)N = 2–3 (n = 84)N > 3 (n = 147)Tumor site (%)Lower esophagus138 (47)39 (46)37 (44)57 (39)EG junction80 (28)35 (42)33 (39)75 (51)Middle esophagus55 (19)10 (12)12 (14)11 (7)Upper esophagus16 (6)02 (3)4 (3)Morphology (%)Adenocarcinoma140 (48)51 (61)57 (68)113 (77)Squamous cell carcinoma140 (48)29 (35)25 (30)32 (22)Others9 (4)4 (5)2 (1)2 (1)Treatment (%)Multimodal therapy129 (44)28 (33)24 (29)21 (14)Surgery alone161 (56)56 (76)60 (71)125 (86)Residual tumor (%)R0: no residual tumor250 (86)71 (85)64 (76)108 (73)R1: residual tumor found39 (13)13 (15)19 (23)39 (27)Rx: unknown1 (1)–1 (1)–Pathological stage (%)Stage 053 (18)–––Stage I59 (20)1 (1)––Stage II170 (59)21 (25)25 (30)16 (11)Stage III5 (2)58 (29)53 (63)110 (76)Stage IV1 (1)4 (5)6 (7)20 (13)pT stage (%)Tx3 (1)02 (3)1 (0.5)Tis12 (4)000T040 (14)1 (1)2 (3)2 (1)T156 (19)5 (6)4 (5)3 (2)T235 (12)16 (19)18 (21)12 (8)T3138 (48)60 (71)54 (64)120 (82)T46 (2)2 (3)4 (5)8 (5)EG = esophagogastricTable 2Histology of Nodal SubgroupsHistologic DataN = 0N = 1N = 2–3N > 3AdenoSCCAdenoSCCAdenoSCCAdenoSCCn = 140N = 140n = 51n = 29n = 57n = 25n = 113n = 32No%No%No%No%No%No%No%No%Tumor siteLower Esophagus64(46)66(47)19(52)15(52)23(40)13(52)39(35)17(53)EG Junction73(52)6(4)31(10)3(10)33(58)0074(65)1(3)Middle Esophagus3(2)52(37)1(28)8(28)1(2)10(40)0010(31)Upper Esophagus0016(11)0(10)3(10)002(8)004(13)TreatmentMultimodal80(57)46(34)23(45)5(17)20(35)4(16)19(13)3(10)Surgery alone60(43)93(66)28(55)24(83)37(65)21(84)94(87)28(90)Path stageStage 029(21)18(13)000000000000Stage 142(30)15(10)1(2)0000000000Stage 266(47)102(73)15(29)4(14)19(33)5(20)15(13)1(3)Stage 32(1)4(3)32(63)24(83)35(61)17(68)82(73)27(84)Stage 4001(1)3(6)1(3)3(6)3(12)16914)3(10)Unknown1(1)0000000000001(3)pT stageTx2(1)1(1)0000002(8)001(3)Tis9(6)0000002(4)000000T019(14)17(12)1(2)003(5)002(2)00T139(29)15(11)4(8)0014(24)003(3)00T216(11)19(14)12(23)3(10)36(63)4(16)11(10)1(3)T353(38)84(60)33(65)26(90)2(4)17(68)91(80)28(88)T42(1)4(2)1(2)00002(8)6(5)2(6)Adeno = adenocarcinoma, SCC = small cell carcinoma, EG = esophagogastric
Two hundred and two patients (33%) had multimodal therapy and 402 patients (67%) had surgery alone. Of the multimodal cohort, 129 (64%) were ypN0 on histopathologic assessment, 28 (14%) had one node positive, 24 (12%) had two to three positive nodes, and 21 (10%) had greater than three positive nodes. The attainment of an R0 resection was significantly greater in patients with none or one node involved compared with both other groups (p < 0.05). The majority of patients in all groups had pT3 tumors, 48% in the pN0 group compared with 71, 64, and 82% in the N = 1, N = 2–3, and N > 3 groups, respectively (p < 0.05). One hundred and forty (62%) of the squamous cell carcinoma cohort were node-negative (N = 0) compared with 140 (39%) of cases with adenocarcinoma (39%) (p < 0.05).
Survival
The median survival for all patients was 20 months at a median follow-up of 19 months (3–167). Patients who were node-negative (N = 0) had a median survival of 26 months (Table 3), compared with 16 months when one node was positive (p = 0.03). Patients who had two to three nodes positive had a median survival of 11 months, and 8 months in patients who had greater than three nodes positive (p = 0.01; N = 2–3 vs N > 3). The survival of patients with one node positive (N = 1) was significantly greater than the survival of patients with 2–3 nodes positive (p = 0.04) and the cohort with greater than three involved nodes (p < 0.0001).
Table 3Univariate and Multivariate Analysis: All PatientsVariablesNo. of PatientsMedian Survival (moths)p Valuea (Univariate)HR95% CIap valueb (Multivariate)HR95% CITreatmentSurgery only401130.0771–––Multimodal203190.840.69–1.02Tumor siteUpper esophagus25160.3711–––Middle esophagus87140.9460.980.58–1.66Lower esophagus268140.6581.160.69–1.81EG junction224140.6241.130.69–1.84Depth of invasionT05755<0.00110.6521T168260.5371.160.73–1.830.4720.710.21–2.3T281260.4191.200.77–1.850.5731.110.31–3.94T337311<0.0012.281.60–3.260.8711.400.79–2.41T4197<0.0014.342.46–7.680.6492.591.42–4.08No. of nodes028926<0.0011<0.00110.63–1.87184160.0381.361.02–1.820.7741.080.83–2.432–38411<0.0011.911.45–2.520.2021.421.07–3.18>31478<0.0012.612.08–3.290.0271.84HistologySquamous361140.9161Adenocarcinoma224130.5961.050.87–1.28–––Other19260.4830.800.44–1.48Stage05355<0.00110.1181I63550.7470.920.56–1.510.5760.680.18–2.59II230200.0371.491.02–2.170.5081.550.42–4.69III22510<0.0012.711.86–3.950.5271.680.34–5.58IV316<0.0016.163.72–10.20.1823.141.14–7.76Residual tumorR049217<0.00110.0521R111081.701.37–2.121.250.99–1.58aχ2bCox regressionHR = hazard ratio, CI = 95% confidence intervals, EG = esophagogastric
The 1-, 3-, and 5-year survival of the pN0 group was 78, 51, and 44%, respectively (Fig. 1). Where one node was involved, survival was 67, 41, and 35%, respectively. Where two to three nodes were involved, the 1-, 3-, and 5-year survival was 57, 25, and 13%, respectively, and where greater than three nodes were involved, this was 40, 14, and 8%, respectively.
Figure 1Overall survival by number of nodes positive.
Univariate analysis (Table 3) revealed nodal status, pT stage, pathologic stage, and R status as predictors of survival. Multivariate analysis revealed nodal status alone to significantly (p < 0.0001) impact on survival. By this analysis the hazards ratio increased from 1.08 for one involved node to 1.42 for two to three involved nodes, and 1.84 for greater than three nodes.
Excluding node-negative patients, univariate analysis (Table 4) revealed pT stage, pathologic stage, R status, and number of nodes as predictive of survival. By multivariate analysis (Table 5), pathologic stage (p = 0.010) and number of nodes were significant determinants of survival. Compared with the cohort with one involved node, the hazard ratio for two to three nodes was 1.56 (p = 0.049) and 2.06 (p = 0.007) for greater than three nodes.
Table 4Univariate Analysis: Node-positive AloneVariablesNo. of PatientsMedian Survival (moths)p valuea (Univariate)HR95% CITreatmentSurgery only241110.23410.63–1.11Multimodal74110.84Tumor siteUpper esophagus9180.6501Middle esophagus32100.5561.310.54–3.18Lower esophagus130100.1831.750.77–3.98OG junction144120.3501.480.65–3.36Depth of invasionT05110.0011T11280.9171.060.33–3.41T246240.1761.120.43–1.78T3235110.7571.430.74–2.14T41450.1572.230.74–6.78HistologySquamous86110.6381Adenocarcinoma221110.6381.070.81–1.40Other830.8481.070.49–2.35Stage1–II6319<0.0011III–IV251102.011.43–2.83Residual tumorR0259120.0351R16191.331.02–1.73No. of nodes18417<0.00112–384130.0211.671.06–2.29>31479<0.0012.531.50–3.62aχ2HR = hazard ratio, CI = 95% confidence intervalsTable 5Mutivariate Analysis: Node-positive OnlyVariablesp valuea (Multivariate)HR95% CIDepth of invasionT01T10.5440.820.31–1.75T20.6791.230.74–1.81T30.3131.490.99–2.21T40.2021.831.39–3.24StageI–II0.0101III–IV1.590.82–3.06No. of nodes112–30.0491.561.21–2.35>30.0072.061.51–2.82Residual tumorR00.2831R11.220.80–1.79aCox regressionHR = hazard ratio, CI = 95% confidence intervals
Discussion
Cancers of the esophagus and esophagogastric junction are aggressive tumors, which are typically diagnosed at an advanced stage of disease progression.13 This large retrospective review of a tertiary center’s experiences over 12 years highlights the importance of lymph node involvement in the prognosis of these tumors. The study shows that the presence of a solitary node, although a significantly negative factor compared with pN0 disease, is associated with significantly improved median and 1-, 3-, and 5-year survival compared with cohorts of patients with greater nodal involvement. The 5-year survival, for instance, was 35% compared with 13 and 8%, respectively, for cohorts with two to three positive nodes and greater than three positive nodes.
There is no uniform consensus on the number of lymph nodes that must be sampled. In a study by Ito et al.,3 the median number of lymph nodes examined per specimen was 6 (range 0 to 35) and only 20% of patients had at least 15 lymph nodes examined. In this study, the median number of lymph nodes examined per specimen was 12 (range 6 to 55), and 24% of the patients had at least 15 lymph nodes examined. These results appear consistent with practice in the United States where an analysis of the National Cancer Database indicated that only 18% of patients undergoing surgery for gastric cancer have more than 15 lymph nodes analyzed.14 In this Unit, lymph node clearance involves a D2 dissection of abdominal nodes, and wide mediastinal clearance to the carina and paratracheal node dissection if they appear involved. No cervical dissection is performed, consistent with recommendations from another group.15 It is acknowledged that variation in lymph node yield may mask stage migration, particularly in a retrospective analysis, but the standardization of lymphadenectomy is likely to minimize the impact of this potential bias.
The association between extent of nodal involvement and outcome is well described.16–18 No study to our knowledge has previously focused on the impact of one positive node on outcome in esophageal cancer. The observation, however, of the unique prognostic significance of a solitary involved node was recently reported.19 In a study of 187 patients with esophageal adenocarcinoma treated with neoadjuvant chemoradiotherapy, Gu et al.19 at the MD Anderson observed from their analysis that patients with a solitary involved node had better overall and relapse-free survival compared with other nodal groups. Moreover, the 5-year survival outcomes and 2-year relapse-free survival was not significantly different from the node-negative cohort. Although in our series survival figures were better for node-negative patients than patients with a solitary involved node, the overall pattern of outcome data in our series is consistent with the report from the Anderson group, with prognosis in this cohort closer to node-negative than other node-positive subgroups.
The clinical implication of this finding is not clear at this time, but it should, at minimum, encourage a more optimistic view of patients who have a solitary lymph node identified after adequate lymphadenectomy, as approximately 35% of patients with this pathologic stage may be cured. In the future, it is possible that advances in endoscopic US staging, fluorodeoxyglucose PET, and sentinel node assessment may improve pre- and intraoperative assessment of nodal involvement, defining node-negative, solitary involved node and micrometastatic-involved subgroups, and selective lymphadenectomy and minimally invasive approaches may be evaluated in these situations. This demands prospective evaluation, but it may be noteworthy that all involved nodes in the solitary involved node cohort were close to the primary site and may possibly have been identified as sentinel nodes.
In conclusion, this study shows that in a large cohort of patients, lymph node status and the number of lymph nodes positive at the time of surgical resection is directly linked to survival. Extensive nodal involvement is confirmed as carrying a dismal prognosis, but greater optimism is justified where a solitary involved lymph gland defines the pN stage after an adequate lymphadenectomy.

lymph node
survival
lymphadenectomy
esophagectomy


Increasing overall physical activity and aerobic fitness is associated with improvements in metabolic risk: cohort analysis of the ProActive trial

Aims/hypothesis Our aim was to examine the association between change in physical activity energy expenditure (PAEE), total body movement (counts per day) and aerobic fitness (maximum oxygen consumption []) over 1 year and metabolic risk among individuals with a family history of diabetes.
Introduction
The metabolic syndrome has been defined as a cluster of closely related cardiovascular risk factors including visceral obesity, insulin resistance, hyperglycaemia, hypertension, hypertriacylglycerolaemia and low HDL-cholesterol [1]. The combination of these risk factors has been shown to predict type 2 diabetes, cardiovascular disease and all-cause mortality [2], with physical inactivity identified as a major underlying risk factor. Given the rising prevalence of obesity and type 2 diabetes, the metabolic syndrome represents a potentially large public health burden [3, 4]. Previous research has shown that low levels of physical activity are associated with the metabolic syndrome [5, 6], and that objectively measured physical activity energy expenditure (PAEE) predicts progression towards the metabolic syndrome independently of obesity [7], with some evidence of interaction by cardiorespiratory fitness [8, 9]. Additionally, lifestyle interventions targeting physical activity as a modifiable risk factor have shown positive effects upon various metabolic components [10]. However, physical activity remains poorly measured in most epidemiological studies, with many relying on self-reporting [11]. Furthermore, it is unclear whether metabolic risk is most effectively reduced by increases in overall energy expenditure (EE), fitness or total body movement. A better understanding of these relationships would inform the development and targeting of individual and population-based interventions to reduce risk of diabetes and related metabolic disorders.
The ProActive (UK) trial is an explanatory trial of a theory-based intervention to promote physical activity among individuals reporting low levels of activity and who are at increased risk of the consequences of a sedentary lifestyle due to their family history of type 2 diabetes. The main trial results are presented elsewhere [12]. We recently observed a cross-sectional association between total body movement and clustered metabolic risk in this cohort [13] and are now extending these observations to examine the association between change in objectively measured PAEE (measured by individually calibrated heart rate [HR] monitoring), physical activity (total body movement measured by accelerometry) and aerobic fitness and clustered metabolic risk in the ProActive trial cohort over a period of 1 year.
Methods
The ProActive trial Full details of the study have been reported elsewhere [14]. In brief, ProActive aimed to evaluate the efficacy of a theoretical, evidence- and family-based intervention programme to increase physical activity among individuals defined as high-risk through having a parental history of type 2 diabetes. Potential participants were identified via diabetes registers and medical records of family history in 20 general practices in the East Anglia region of the UK. Three hundred and sixty-five individuals aged 30–50 years and reporting low levels of activity were randomly assigned to one of three interventions: brief written advice (control group), or a behavioural-change programme at two levels of intensity delivered either by telephone (distance) or face-to-face in the family home. The theory-based intervention programme [15] was delivered by trained facilitators and aimed to support increases in physical activity through the introduction and facilitation of a range of self-regulatory skills. Main trial results indicated no significant difference in the 1 year change in objectively measured daytime physical activity expressed as a ratio to resting EE between the three trial arms [12]. Consequently, the three trial arms were pooled and a cohort analysis conducted. Complete data on PAEE, aerobic fitness, anthropometry and biochemistry were available in 365 participants at baseline and 321 participants at follow-up, in addition to socio-demographic information. Total body movement measured by accelerometry was also assessed in a subsample of participants (n = 192) at baseline and follow-up and the data were included in these analyses. The measure of socioeconomic status (SES) was based on age at finishing full-time education (above or below 16 years). Ethics approval was obtained from the Eastern England Multi-centre Research Committee (MREC) and all participants gave written informed consent.
Anthropometric and metabolic tests Participants attended the study centre after an overnight fast and a sample of venous blood was taken. Fasting plasma glucose, serum insulin levels and lipid profiles (cholesterol, triacylglycerol, HDL- and LDL-cholesterol) were measured using the hexokinase method and standard enzymatic methods, as described previously [14]. Weight was measured on standard calibrated scales and height was measured using a rigid stadiometer. BMI was calculated as weight (kg) divided by height (m) squared. Waist circumference (cm) was measured over light indoor clothing as the mid-point between the lower costal margin and the level of the anterior superior iliac crests. Body fat percentage was measured by bio-electrical impedance (Bodystat, Isle of Man, UK), and systolic and diastolic blood pressures were measured using an automated Accutorr sphygmomanometer (Accutorr, Cambridge, UK).
Assessment of aerobic fitness, PAEE and total body movement Aerobic fitness (maximum oxygen consumption []) was predicted as oxygen uptake at maximal HR (220 minus age [years]) by extrapolation of the regression line established during the individual calibration for the relationship between oxygen consumption and HR during a submaximal graded treadmill exercise test. O2 uptake and CO2 production was measured continuously by indirect calorimetry throughout the test (Vista XT metabolic system; Vacumed, Ventura, CA, USA).Resting EE (REE) was calculated by the Weir formula [16] using  and  measurements obtained in the fasting state, after approximately 10 min of supine rest using the same indirect calorimetry system as previously described. PAEE was measured using the flex HR method [8]. Flex HR was calculated as the mean of the highest resting HR and the lowest HR while exercising. This point was used in the analysis of free-living minute-by-minute HR data to discriminate between rest and exercise. Below the flex HR point, EE was assumed to be equivalent to REE. EE above the flex point was predicted from the individual HR–EE regression line. Participants wore HR monitors (Polar Electro, Kemple, Finland) continuously during the waking hours over the following 4 days. PAEE was calculated by subtracting REE from the estimated average daily EE, and thereafter averaged over the 4 day period. PAEE is body size dependent, e.g. it requires more energy to move a heavier body. Similarly, aerobic fitness is highly correlated with body size or mass, e.g. larger individuals have a higher absolute aerobic capacity. Therefore, body size is a confounding factor that needs to be normalised for when analysing associations between EE variables and metabolic outcomes [17]. As such, both baseline and follow-up measures of aerobic fitness and PAEE were expressed relative to fat-free mass (FFM; kJ kg−1 FFM min−1) to adjust for between-individual differences in body size [17, 18].Free-living total body movement was assessed with an MTI Actigraph (formerly known as the CSA activity monitor) model WAM7164 (Manufacturing Technology, Fort Walton Beach, FL, USA). The accelerometer was worn over the same 4 day period as the HR monitor. Participants who did not manage to record at least 500 min/day of activity for at least 3 days were excluded from analyses. A customised program was used for data reduction and further analyses (MAHUffe; http://www.mrc-epid.cam.ac.uk). The outcome variable derived from accelerometry presented in this study is total body movement (counts per day), adjusted for monitored time, which is an indicator of the overall level of physical activity.
Calculation of the metabolic syndrome z score A summary score of clustered metabolic risk based on WHO criteria [1] was calculated by summing standardised values for waist circumference, triacylglycerol, fasting insulin and glucose, systolic blood pressure and the inverse of HDL-cholesterol [7–9]. Variables were standardised by subtracting the sample mean from the individual mean and dividing by the SD. Baseline and follow-up z scores were computed with the same transformation, e.g. using the mean and SD of baseline values. This continuously distributed metabolic risk variable (zMS) was also calculated without the adiposity component (i.e. waist circumference, zMS-ob). This clustered metabolic risk score increases statistical power as variables were not dichotomised, and includes a continuous measure of glycaemia (unlike some other measures of vascular risk [19]). Additionally, the International Diabetes Federation criteria were used to define metabolic syndrome as a dichotomous variable [1]. This score predicts hard clinical endpoints [20].
Statistical analyses Descriptive summary statistics were calculated separately for men and women using means and SDs at baseline and follow-up. t tests were used to examine whether there were any differences in baseline characteristics between those with and without follow-up data, as well as those with missing accelerometer data. Fasting insulin and triacylglycerol values were log transformed (ln) due to their non-normal distribution. In order to characterise change in physical activity and fitness in the ProActive cohort, we described the association between exposure variables using correlation coefficients. We then examined the proportion of metabolic syndrome and the mean clustered metabolic risk score among participants who increased and decreased their PAEE, fitness and total body movement over 1 year. We used linear regression to model change in PAEE and fitness (both per unit FFM), and total body movement ([total counts per day]/1,000, adjusted for monitored time), against individual subcomponents of the clustered metabolic risk score at follow-up (waist circumference, blood pressure, fasting triacylglycerol, insulin and glucose, and the inverse of HDL-cholesterol). These models were adjusted for age, sex, waist circumference (except when waist circumference was modelled as the outcome), smoking status, SES (assessed by self-reporting) and baseline phenotype, and were presented as standardised β-coefficients. We then tested whether change in PAEE, fitness and total body movement was associated with the clustered metabolic risk score at follow-up. The first model (obesity dependent) included all metabolic subcomponents (zMS) and was adjusted for age, sex, smoking status, SES and baseline zMS, while the second model excluded waist circumference from the zMS (obesity independent zMS-ob) and was adjusted for age, sex, smoking status, SES, baseline zMS-ob and waist circumference. Finally, we examined whether there was evidence of interaction between change in PAEE, total body movement and aerobic fitness and clustered metabolic risk, as well as interaction by age and sex. All data were analysed in continuous form, although some data were dichotomised for illustrative purposes. All analyses were completed using Stata Version 8.0. (STATA, College Station, TX, USA).
Results
Table 1 shows the anthropometric and metabolic characteristics of participants with complete data for baseline and follow-up (n = 321) stratified by sex. More women met the inclusion criteria and agreed to take part in the study than men. Participants with missing data at follow-up were slightly shorter than those with complete data (difference = 3.1 cm, p < 0.05) but not significantly different for all other baseline variables. There were also no significant differences in baseline characteristics between participants with and without accelerometer data (data not shown). In general, men were significantly taller and heavier than women but had a lower percentage body fat at baseline. In terms of the six metabolic syndrome subcomponents, waist circumference, systolic blood pressure, triacylglycerol, fasting glucose and insulin were all significantly higher in men, while HDL-cholesterol was significantly higher in women. Statistically significant differences were also observed for PAEE (kJ kg−1 FFM min−1) and  (ml kg−1 FFM min−1), with men achieving higher levels of physical activity and fitness even after adjustment for FFM. There were no significant differences in total body movement between men and women at baseline.
Table 1Anthropometric and metabolic characteristics of ProActive participants with complete baseline and follow-up data (n = 321), stratified by sex MenWomenBaseline (n = 129)Follow-up (n = 129)Baseline (n = 192)Follow-up (n = 192)Age (years)40.2 (5.8)N/A40.8 (6.1)N/AHeight (cm)177.8 (6.8)177.8 (7.0)163.4 (6.1)a163.2 (5.9)cWeight (kg)89.3 (15.5)89.5 (15.6)73.7 (14.6)a74.0 (15.2)BMI (kg/m2)28.2 (4.3)28.3 (4.4)27.6 (5.2)27.8 (5.4)dBody fat (%)25.6 (5.3)25.8 (5.2)34.6 (6.9)a34.8 (7.1)Waist circumference (cm)100.3 (11.1)100.9 (11.5)87.9 (11.8)a89.2 (12.5)cSystolic blood pressure (mmHg)127.1 (11.3)124.5 (11.3)d120.6 (13.8)a116.8 (13.3)cDiastolic blood pressure (mmHg)81.4 (8.8)79.6 (9.7)d76.2 (9.3)a73.9 (9.9)cTriacylglycerol (mmol/l)1.8 (1.6)1.7 (1.3)1.2 (0.6)a1.1 (0.7)Total cholesterol (mmol/l)5.2 (1.0)5.3 (1.0)5.1 (0.9)5.2 (1.0)HDL-cholesterol (mmol/l)1.2 (0.3)1.2 (0.3)1.6 (0.4)a1.6 (0.4)Fasting plasma insulin (mmol/l)70.2 (71.6)72.2 (52.3)55.0 (35.6)b56.3 (35.4)Fasting plasma glucose (mmol/l)5.1 (0.9)5.2 (1.0)4.7 (0.5)a4.8 (0.5)dPAEE (kJ kg−1 FFM min−1)0.13 (0.07)0.14 (0.08)d0.10 (0.08)b0.11 (0.07) (ml kg−1 FFM min−1)60.7 (10.54)61.2 (11.42)57.10 (10.72)b58.06 (10.38)Daily physical activity (total count)e265,000 (79,000)275,000 (106,000)269,000 (109,00)280,000 (110,000)Data are means (SD)ap < 0.001, bp < 0.05 for women vs men at baseline; cp < 0.001, dp < 0.05 for baseline vs follow-up (separately in men and women)eThese values are based on data from n = 192 ProActive participants for whom accelerometer data were available at baseline and follow-up
For men, there were no significant differences in mean height, weight, BMI, body fat, waist circumference, triacylglycerol, HDL-cholesterol, fasting insulin and glucose from baseline to follow-up. The only metabolic subcomponent that changed significantly over time was systolic blood pressure, which reduced from 127.1 to 124.5 mmHg. In terms of the activity variables, men significantly increased their physical activity (PAEE) from 0.125 to 0.139 kJ kg−1 FFM min−1, but increases in fitness and total body movement did not achieve statistical significance. For women, there were no significant differences in mean weight, body fat, triacylglycerol, total cholesterol, HDL-cholesterol and fasting insulin from baseline to follow-up. Mean height decreased very slightly, while BMI increased from 27.6 to 27.8 kg/m2 and waist circumference increased from 87.9 to 89.2 cm. Values for both diastolic and systolic pressure decreased significantly, while fasting plasma glucose increased slightly from 4.7 to 4.8 mmol/l. Increases over the year in PAEE, total body movement and fitness did not reach statistical significance. There was no significant change in the use of cardiovascular therapies during follow-up (data not shown).
There was no evidence for a correlation between change in fitness and change in PAEE (r = 0.1) or total body movement (r = 0.0). There was limited evidence for a positive correlation between change in PAEE and total body movement (r = 0.3). The overall prevalence of metabolic syndrome was 20% at both baseline and follow-up, although there was some movement between groups. The proportion of metabolic syndrome at follow-up was higher among participants who failed to increase their PAEE, fitness and total body movement over 1 year (Fig. 1a). Similarly, clustered metabolic risk scores were lower among individuals who managed to increase their PAEE, fitness and total body movement during follow-up (Fig. 1b). None of the differences between these groups reached statistical significance but were in the expected direction of effect.
Fig. 1a Proportion of ProActive participants with metabolic syndrome at 1 year follow-up by those who increased and decreased their PAEE, fitness and total body movement. b Mean metabolic summary score for ProActive participants at 1 year follow-up by those who increased and decreased their PAEE, fitness and total body movement (bars represent 95% CIs)
Table 2 shows the crude and adjusted associations between change in PAEE (kJ kg−1 FFM min−1),  (ml kg−1 FFM min−1) and total body movement ([counts per day]/1,000) with standardised subcomponents of the clustered metabolic risk score and the whole score (zMS) at follow-up. As all outcomes are expressed in the same unit (SD), it is possible to directly compare the magnitude of associations between the different components of activity with each of the outcomes, assuming they are measured with the same degree of measurement error. In adjusted analyses, fasting glucose, insulin and HDL-cholesterol at follow-up were significantly associated with a change in fitness over time; on average, individuals who increased their fitness had reduced levels of glucose and insulin, and increased levels of HDL-cholesterol at follow-up. Similarly, fasting glucose and insulin were associated with change in total body movement over time. All other subcomponents of the clustered metabolic risk score failed to show an association with change in either physical activity, fitness or total body movement. In adjusted analyses, change in fitness, but not change in PAEE, was associated with clustered metabolic risk at follow-up with (zMS; p = 0.034) and without the obesity component (zMS-ob; p = 0.04). In addition, change in total body movement from baseline to follow-up was associated with clustered metabolic risk in both the overall (zMS; p = 0.004) and obesity-independent score (zMS-ob; p = 0.01).
Table 2Crude and adjusted associations (standardised β-coefficients) between change in PAEE,  and total body movement with standardised subcomponents of the metabolic summary score and the whole score (zMS) at follow-up in the ProActive cohort over 1 yearOutcome (SD)Standardised β-coefficient (95% CI)Change in PAEE (n = 318)Change in  (n = 318)Change in total body movement (n = 191)CrudeAdjustedaCrudeAdjustedaCrudeAdjustedaWaist circumference−0.061 (−0.172, 0.051)−0.025 (−0.065, 0.016)−0.074 (−0.185, 0.037)−0.017 (−0.058, 0.024)−0.117 (−0.261, 0.027)−0.019 (−0.071, 0.032)Systolic blood pressure0.062 (−0.047, 0.171)0.074 (−0.004, 0.152)−0.017 (−0.126, 0.093)−0.035 (−0.113, 0.044)−0.017 (−0.158, 0.125)0.012 (−0.094, 0.118)Logged triacylglycerol−0.008 (−0.127, 0.110)−0.024 (−0.100, 0.051)−0.059 (−0.178, 0.060)−0.009 (−0.084, 0.067)−0.026 (−0.180, 0.128)−0.054 (−0.149, 0.041)Logged fasting insulin−0.064 (−0.175, 0.046)−0.024 (−0.093, 0.045)−0.094 (−0.203, 0.016)−0.069 (−0.137, −0.002)b−0.097 (−0.239, 0.045)−0.101 (−0.186, −0.017)bFasting plasma glucose−0.005 (−0.133, 0.123)−0.024 (−0.114, 0.067)−0.139 (−0.266, −0.012)b−0.090 (−0.180, 0.000)b−0.163 (−0.328, 0.002)−0.147 (−0.259, −0.035)bHDL-cholesterol (inverse)−0.053 (−0.165, 0.059)−0.056 (−0.125, 0.014)−0.115 (−0.227, −0.004)b−0.097 (−0.166, −0.029)b−0.027 (−0.167, 0.113)−0.026 (−0.121, 0.069)zMS−0.031 (−0.112, 0.050)−0.017 (−0.054, 0.020)−0.081 (−0.160, −0.001)b−0.056 (−0.093, −0.020)b−0.074 (−0.176, 0.028)−0.066 (−0.111, −0.021)bzMS-ob−0.023 (−0.103, 0.058)−0.012 (−0.053, 0.029)−0.083 (−0.163, −0.004)b−0.062 (−0.102, −0.022)b−0.065 (−0.166, 0.037)−0.068 (−0.119, −0.016)baAll coefficients adjusted for age, sex, smoking status, SES, waist circumference and baseline phenotype, except for waist circumference, which was adjusted for age, sex, smoking status, SES and baseline phenotypebp < 0.05
There was no evidence of interaction between change in EE and aerobic fitness (p = 0.28), EE and total body movement (p = 0.13) and aerobic fitness and total body movement (p = 0.13) with clustered metabolic risk at follow-up. While there was no evidence of a significant interaction between age or sex and change in the activity variables, the β-coefficients for change in PAEE appeared stronger in men than in women, and also in older rather than younger individuals.
Discussion
Our results suggest that small increases in physical activity, measured using accelerometry and aerobic fitness, were associated with improvement in clustered metabolic risk over a 1 year period in middle-aged individuals at high risk of developing type 2 diabetes. Our results were independent of age, sex, smoking status, socioeconomic group and baseline phenotype. This confirms our earlier cross-sectional result [13] in a prospective analysis, which provides stronger inferential evidence for the association between total body movement and metabolic risk. Further, this result is supported by our finding that the proportion of metabolic syndrome at follow-up was higher, albeit non-significantly, among groups who failed to increase their PAEE, fitness and total body movement over 1 year.
Although PAEE was not significantly associated with clustered metabolic risk in our analyses, we were able to demonstrate an association between overall body movement (i.e. physical activity) assessed by accelerometry and clustered metabolic risk. This is a novel finding given that previous prospective associations between objectively measured physical activity and metabolic risk were observed in a population of healthy middle-aged Europids [7], rather than the overweight, sedentary younger adults with a high risk of developing type 2 diabetes described in this cohort. We also observed that the benefits of increased fitness and total body movement acted primarily through changes in serum glucose, insulin and HDL-cholesterol, which may suggest that blood pressure is less sensitive to changes in activity and fitness. In a comparable study, Ekelund et al. [21] observed that an increase in activity was associated with fasting insulin, triacylglycerol, 2 h glucose and clustered metabolic risk but not with systolic or diastolic blood pressure. Contrary to our findings, previous literature has shown an association between PAEE and clustered metabolic risk, both cross-sectionally [8] and prospectively over a period of 5.6 years, independently of fitness [7]. This apparent discrepancy might be explained in a number of ways. First, while the trial was powered to detect a difference in physical activity-related EE between trial arms equivalent to 2 metabolic energy equivalent (MET) h/day or approximately 30 min of brisk walking, the sample size was relatively small for a cohort analysis and may not have been large enough to detect smaller but still biologically important differences. Nonetheless, all the PAEE β-coefficients were in the same direction of effect as those for the accelerometry data but they did not reach statistical significance.
Second, the precision in the methods we used to assess PAEE and body movement may affect the observed associations. PAEE from individually calibrated HR monitoring is an integrated measure of EE above rest calculated from free-living HR data. In sedentary populations, much of the daytime is spent in the region around the flex HR, which is used to discriminate between rest and physical activity. The association between HR and EE is less precise in this region, which may influence the accuracy of predicted PAEE on an individual level. Furthermore, the flex HR method may be sensitive to the fitness level of the people under investigation [22]. In contrast, accelerometry measures the vertical accelerations of the body, i.e. physical work, and is likely to be less sensitive to the characteristics of the population in terms of a sedentary lifestyle and fitness level. If most of the activities performed are locomotor activities, such as walking, measurement of body movement by accelerometry may be superior to HR monitoring when examining associations with disease risk. Ideally, the two different measurement techniques should be combined into one single piece instrument [23].
Finally, by standardising the clustered metabolic risk score, we assumed each component made an equal contribution towards defining metabolic risk. It is unlikely that each component is equally strongly associated with metabolic risk and some variables will be more important that others in different populations. It would therefore be ideal to weight each component of the score, but data are currently unavailable.
Our results suggest that small, feasible changes in physical activity (total body movement) and fitness in an at-risk population may prevent progression towards the metabolic syndrome. This supports previous literature, which has demonstrated an inverse relationship between fitness, physical activity and risk of developing metabolic syndrome in a number of settings [5, 24–26]. At a population level, our findings have important implications. This group of middle-aged, slightly overweight individuals, identified through primary care registers via their first degree family history of diabetes, represents an accessible population who might benefit from increased physical activity and fitness levels. Primary care or public health practitioners might target this group for preventive action. Findings can also be extrapolated to inform the characteristics of public health initiatives. Increasing total body movement can be achieved through small changes in lifestyle activity, such as taking the stairs and parking the car further away from work, which may be more palatable to sedentary and at-risk populations than targeting changes in moderate to vigorous intensity activities. Regular physical activity participation also has multiple positive effects upon other diseases in addition to metabolic syndrome, such as stroke, coronary heart disease and cancer [27, 28]. However, currently there is limited evidence regarding the effectiveness of lifestyle interventions for individuals, at-risk groups or populations in the treatment and prevention of metabolic syndrome and this is an area of research that warrants further investigation. It is important to clarify whether metabolic risk is most effectively reduced by increases in overall EE, fitness or total body movement to inform the development and nature of preventive interventions.
This study had several methodological strengths. The ProActive trial allowed objective measurement of several components of physical activity and fitness over a period of 12 months in a well-defined group of individuals accessed through primary care who were at risk of diabetes. There was a high follow-up rate (88%) and standardised measures were used throughout. We used objective measures of physical activity, which reduces the error and bias commonly associated with self-report measures and our objective measures of EE, physical activity (PAEE, total body movement) and fitness have been extensively validated in the laboratory and during free-living conditions [18].
In conclusion, small increases in physical activity assessed by accelerometry and in aerobic fitness were associated with improved metabolic risk over 1 year. Further research is needed to clarify the relationship between physical activity, EE, fitness and metabolic risk to inform advice and intervention development. We may need even more precise methods of measurement to capture the true dose effect of such relationships.

physical activity
fitness
metabolic risk
metabolic syndrome
cardio-respiratory fitness
syndrome x


Scaling of offspring number and mass to plant and animal size: model and meta-analysis

The scaling of reproductive parameters to body size is important for understanding ecological and evolutionary patterns. Here, we derived allometric relationships for the number and mass of seeds, eggs and neonates from an existing model on population production. In a separate meta-analysis, we collected 79 empirical regressions on offspring mass and number covering different taxa and various habitats. The literature review served as a validation of the model, whereas, vice versa, consistency of isolated regressions with each other and related ecological quantities was checked with the model. The total offspring mass delivered in a reproductive event scaled to adult size with slopes in the range of about 3/4 to 1. Exponents for individual seed, egg and neonate mass varied around 1/2 for most heterotherms and between 3/4 and 1 for most homeotherms. The scaling of the progeny number released in a sowing, clutch or litter was opposite to that of their size. The linear regressions fitted into a triangular envelope where maximum offspring mass is limited by the size of the adult. Minimum seed and egg size scaled with weight exponents of approximately 0 up to 1/4. These patterns can be explained by the influence of parents on the fate of their offspring, covering the continuum of r-strategists (pelagic–aquatic, arial, most invertebrates, heterotherms) and K-strategists (littoral–terrestrial, some invertebrates, homeotherms).
Introduction
Scaling of processes and patterns to body size has fascinated biologists for centuries (e.g., Peters 1983; Damuth 2007). Plant and animal characteristics have been correlated to organisms’ body mass (m) by simple scaling relationships of the form a·mb or, if log transformed, log(a) + b log(m). Properties include various reproductive parameters, such as the mass and number of the offspring, important for understanding life history strategies of species. The scaling of reproduction reflects several important trade-offs, e.g., investment of energy in somatic versus gonadic growth, in continuous or intermittent release and in many small or a few large offspring.
Studies have derived empirical regressions for offspring mass and number within one taxon (see review by Peters 1983). In addition, several partly contradictive physical, biochemical and ecological constraints related to parental energy investment, have been hypothesized to be responsible for the observed patterns (May 1978; Gordon 1989; Reiss 1989; Charnov and Downhower 1995; Hendry et al. 2001; Charnov 2001, 2002; Aarssen 2005). Although the trade-offs in reproductive investment reflect universal dilemmas that every species has to face, most work so far has covered either several progeny characteristics within a single species group or a single offspring parameter within at most two taxa (Moles et al. 2005a; Grubb et al. 2005).
In the present paper, we will focus on the relationship of offspring mass and number to adult weight for miscellaneous groups of species. The aim is to obtain a set of straightforward equations that are coherent with allometric theory and underpinned by empirical regressions available in literature. To this end, we will first derive body-size functions for the mass and number of offspring delivered in a reproductive event which comply with allometric macroecology (e.g., West et al. 1997; Hendriks 1999). Next, we will compare the acquired relationships to independent empirical regressions collected in a meta-analysis. Separating model development and testing allows for a comparison of theoretical and empirical evidence, reducing weaknesses of both. In this approach, model predictions of, e.g., offspring mass, are underpinned by independent measurements. Likewise, isolated empirical regressions for this reproductive parameter are checked for consistency with body-size dependence of related ecological factors, such as population production or survival.
In our analysis, we will seek a balance between model transparency and accuracy, needed for underpinning assumed mechanisms and identifying exceptions. The equations are not intended to cover detailed or speculative differences, observed in empirical regressions for sufficient taxa. In our interpretation, we will follow the classical distinction between r-strategists and K-strategists (MacArthur and Wilson 1967; Pianka 1970) as well as more recent applications thereof (Winemiller and Rose 1992; McCann and Shuter 1997; Cox and Moore 2005). However, it should be emphasized that the traditional classification of many small offspring versus few large offspring as used in the present paper is no more than a convenient way to structure the discussion.
Materials and methods
Regression collection and treatment
Allometric regressions derived from data before 1983 were collected from an extensive review (Peters 1983). Papers published afterwards were obtained by screening books and by an electronic literature search in Web of Science in 2006. All body-size correlations acquired for the meta-analysis were checked in the original papers. Collection and treatment of data by the authors was assumed to be adequate. Where multiple types of regressions were reported, we took the least-squares equations, to increase compatibility with the other studies. If regression characteristics were not given or suspected to be wrong, we derived them from the original data or digitized graphs.
To allow for comparison, all values were converted to fresh biomass, using dry–wet weight fractions. A database containing dry matter fractions of 110 species, collected by the present authors for various purposes, yielded averages (with 95% confidence intervals) of 20% (18–22%) for herbs, 22% (19–25%) for invertebrates, 25% (18–32%) for cold-blooded vertebrates and 30% (21–39%) for warm-blooded vertebrates. In addition, the literature reports means of 53% for wood, 15–21% for fruit, 87% for seeds, 23 for insects, 19% for marine invertebrates, 25% for fish and 29% for birds and mammals (Peters 1983; Suzuki 1999). Although the samples may be somewhat biased towards particular taxa, average levels do not deviate substantially. In the present analysis, we therefore used dry–wet weight fractions of 20% for fruits, forbs, herbs and invertebrates, of 25% for cold-blooded vertebrates, of 30% for warm-blooded vertebrates, of 40% for shrubs and trees (wood and leaves together) and of 80% for seeds. Differences between species around these values have, on average, a negligible influence on the intercept of the regressions. Even more apparent, conversion does not affect the slope of the allometric relationships. Seeds mass was multiplied by 80/20% = 4 to arrive at the fresh weight of sprouts with a water content that is comparable to that of eggs and neonates. Since total plant weight is not used as the independent variable for vegetation regressions, we took the closest alternatives, being the above-ground or stem mass. In one study on insects, animal size was expressed on a length basis instead of a weight basis (Berrigan 1991). For these regressions, length (m) was converted to weight (kg) as mass = 1/152π × 103 length3, assuming that the total size equals 1.5 times the elythra length and twice the abdomen length.
Rate constants for reproduction of plants were reported as annual standing reproductive mass delivered by all plants, including both reproducing and non-reproducing individuals. We assumed that the seed and fruit mass are renewed each year. For animals, total clutch mass reflected the total reproductive mass released in an event or present in ovaries, sometimes calculated in the original studies as a product of the total number of eggs (neonates) in a clutch (litter), the number of eggs per clutch (neonates per litter) and the egg (neonate) weight.
To allow for comparison between plants, invertebrates, cold-blooded vertebrates and warm-blooded vertebrates, we calculated the arithmetic average of all slopes (b) reported for each taxonomic group. To correct for differences in the amount of information included in the regressions, we also computed an average weighted by the number of data. For instance, the weighted average of a regression with b = 0.5 and n = 10 and another with b = 0.3 and n = 20 was calculated to be 0.5 × 10/30 + 0.3 × 20/30 = 0.37. As we are interested in both the absence and presence of links to organism mass, weak and insignificant correlations were included in the analysis as well. Where used, however, they will be explicitly mentioned in the text.
Model development
The relationship of offspring mass and size to adult weight can also be derived theoretically from previous modeling efforts (Hendriks 2007). The starting point in this model is production because coefficients and slopes of allometric regressions for this parameter differ only slightly for various groups of species. The rate constant for population turnover (production kp), measured as the production/biomass ratio (P/B) (kg kg−1 day−1) is related to adult mass (m) as:
The exponent (κ) was close to 1/4 for a wide range of cold-blooded species but tended to be somewhat higher for homeotherms (Peters 1983; Hendriks 1999, 2007). The coefficient (γp) represents the intercept at the standard temperature of 20°C and has a universal value of 7.5 × 10−4 kgκ day−1 for all species (Hendriks 2007). Following biochemical reaction kinetics, the intercept increases by a factor of qT as a function of temperature (Gillooly et al. 2001). Production kp by warm-blooded species with a body temperature of 37° is qT = 3.5 times higher than that of equally sized cold-blooded species at 20°C (Hendriks 2007).
Production kp is allocated to somatic and gonadic growth. We will consider the rate constant for reproduction (reproduction kpr) to be a fraction (prp) of total production kp according to:
In Spermatophyta, 7% of the total dry weight production is diverted to reproduction via seeds (Niklas and Enquist 2002). After correction to a dry–wet weight fraction of 20% as described in the methods section, the reproductive fraction (prp) equals 28% (Table 1). In animals, prp varies between 0 for juveniles and 1 for adults without somatic growth. Filling in the slope and the intercepts, yields the reproduction rate constant as a function of m (Fig. 1).
Table 1Main factors used in the equationsSymbolDescriptionUnitValuea, sourceγpScaling coefficients for productionkgκ day−17.5 × 10−4 (Hendriks 2007)kp, kprRate constants for production and reproductionday−1Equation 1κScaling exponent–p,c,w1/4, w1/3 (Hendriks 2007)mAdult masskgVariablemrTotal reproductive mass in a batchkgEquation 5meSeed, egg or neonate masskgmin(me) = 10−10, i10−10, p,acv10−7, tcv10−3… mr/3prlFraction inter-reproductive period of average life time–0.2prpFraction of production directed to reproduction–p0.28 (Niklas and Enquist 2002), i,v1R0Fecundity, number of offspring released in a reproductive eventno. individual−1Equation 6qTTemperature quotient–p,c1, w3.5 (Hendriks 2007)τrInter-reproductive perioddayEquation 4aSuperscripts: p plants, c cold-blooded, w warm-blooded, i invertebrates, v vertebrates, a aquatic, t terrestrialFig. 1Reproduction rate constants (kpr) (kg kg−1 day−1) decrease with adult mass (m) (kg) to the power of about 1/4–1/3. Model estimations (thick lines with letter) as well as empirical regressions (thin lines) for vascular plants (A, green dotted), invertebrates (B, yellow dashed-dotted), cold-blooded vertebrates (C, blue dashed) and warm-blooded vertebrates (D, red solid), as listed in Table 2. d−1 Day−1
Usually seeds, eggs and neonates are not delivered continuously but released in discrete batches, i.e., sowings, clutches and litters. The total offspring mass (mr) accumulated in a period between two successive reproductive events (τr) equals:
The inter-reproductive interval (τr) might be related to the organisms’ metabolism and to environmental conditions. Initially, we did not find empirical regressions that link τr to organism size. However, many other biological time parameters, including gestation and weaning time of homeotherms, scale to m with an exponent of κ (Peters 1983; Hendriks 1999). For an average mammal, the age at birth, weaning off and average death is at about 2, 3, 50% of the total period from conception to death, respectively (Peters 1983). τr, covering at least gestation and weaning (2 + 3%), thus equals at least (2 + 3%)/50% = 10% of the average lifetime τl, i.e., τr = prl·τl > 10%·τl. To allow for additional time to recover and mate we set the inter-reproductive period at a fraction (prl) = 20% of the average lifetime τl. This lemma is indirectly demonstrated by one long-term study on metabolism, reproductivity and average lifetime (τl) of earthworms (Mulder et al. 2007). In fact, although no evidence of a correlation between τr and the offspring was found, τl and m were strongly correlated. Following a more general theory, τl can indeed be defined here as the mean residence period in the population and can thus be replaced by 1/kp (Odum 1983). In this way, τr can now be assumed to equal:
Filling in the parameter values for mammals yields τl = 0.3/(3.5 × 7.5 × 10−4 m−1/4) = 114 m1/4. This is a factor of 2 larger than the value of 55 m0.23 (r2 = 0.37, n = 41) derived from a compilation of data on South American mammals that was published after our estimation (Pereira and Daily 2007). Obviously, this relationships needs to be confirmed for other species groups.
Substituting Eq. 4 into Eq. 3 yields the reproductive mass (mr) accumulated between batches as a linear function of adult size (m) as (Fig. 2): Fig. 2Clutch or litter (reproductive) mass (mr) (kg) increases with m (kg) to the power of about 3/4 to 1. Legend as in Fig. 1. Regressions listed in Table 3
The total reproductive mass derived from Eq. 5 can be divided into many small or a few large young. At one end of the interval, species called “r”-strategists here, maximize the number of young per female (R0) up to a limit set by the absolute minimum size [min(me)] of a seed, egg or neonate. The existence of such a threshold has been attributed to various restrictions but, to our knowledge, supporting quantitative evidence is still lacking. Since each individual starts off as a single cell, the average size of parental cells may serve as a first indication for the minimum egg or seed mass (me). The weight of a cell is reported to be in the range of 10−15–10−11 kg for plants and animals (Raven 1998; West et al. 2001; Mulder et al. 2005). Lower taxa with multi-cellular organization, such as mycorrhizal conidia and fruit bodies of basidiomycetes, actually release offspring as single cells (Mulder et al. 2003). Higher species reproduce by multi-cellular sexual spores, seeds, eggs and neonates, with sizes at or above that range. With this variability in mind, min(me) was tentatively set at the minimum observed for the taxon covered (Table 1). At the other side of the range, “K”-type organisms invest all reproductive mass into a few young. In this strategy, seed, egg and neonate mass are maximized by dividing the total reproductive mass over a few offspring. Low values are noted for, e.g., birds with an average of 4.8 eggs per clutch and for mammals with means of 2.7–2.8 neonates per litter (Blueweiss et al. 1978; Ernest 2003). Apparently, the risk of premature death is typically spread over, on average, at least three young, so that the maximum mass of individual offspring [max(me)] is calculated as max(me) = mr/3 = prp·prl·m/3. With seed, egg and neonate mass ranging between min(me) and max(me), we can now derive R0 as:
The number of seeds, eggs and neonates (R0) is thus expected to scale to m with exponents in the range of 0–1, for K-strategists and r-strategists, respectively. The corresponding intercepts are prp·prl/min(me) and 3, respectively. Intermediate values indicate that both types of species are present in the sampled taxon. If strategies are uniformly distributed among species, one expects a mean slope of 1/2, with the geometric average of prp·prl/min(me) and 3 as a coefficient. Vice versa, the mass of a seed, egg or neonate (i.e. me) varies between min(me) ∝ m1 and max(me)  ∝ m0, also with an average at m1/2 (Figs. 3, 4).
Fig. 3Egg or neonate mass (me) (kg) increases with m (kg) to a power varying around 1/2 for cold-blooded animals and in the range of 3/4–1 for warm-blooded animals. Legend as in Fig. 1; in addition, model estimations for organisms in general (E, dashed-dotted, me = 0.0000046 m1/2, me = 0.2 m). Regressions listed in Table 3Fig. 4Seed, egg or neonate number in ovaries, clutch or litter (R0) (young/individual) increases with m (kg) to a power varying around 1/2 for cold-blooded animals and close to 0 for warm-blooded animals. Legend as in Fig. 1; in addition, model estimations for organisms in general (E, dashed-dotted, R0 = 45,000 m1/2, R0 = 1). Regressions as listed in Table 3
Equations 4–6 apply to cases where τr is related to the metabolism of the organisms. Alternatively, τr may depend on cyclic processes in the environment. Since optimal conditions for offspring usually occur in specific seasons, synchronization of reproduction to annual cycles of temperature, light or food availability by e.g., hibernation or fetal growth retardation, is most likely. With τr = 365 days, Eq. 3 becomes: indicating that the mass released in a yearly sowing, clutch or litter (mr) scales to m with an exponent of 1−κ. Organisms with an intrinsic τr close to 1 year can exploit such synchronization most readily. Smaller species may somewhat postpone their reproduction, increasing the gonadic mass released. Larger species may do the opposite, decreasing the slope of the regression towards 3/4. Fitting Eq. 1 into 4 and writing m explicitly gives:
Using the typical values for the parameters (Table 1), cold-blooded and warm-blooded organisms with a τr of 365 days are expected to have an m of about 4 and 500 kg, respectively. Organisms that are much smaller mature sufficiently fast to allow multiple generations within a year or growing season. Species which are substantially larger need more than 1 year to produce one egg or neonate.
Results
Reproduction rate constant
We will now compare the derived equations to the empirical regressions obtained in the meta-analysis. The few correlations available for gonadic growth show that reproduction kpr indeed decrease significantly with increasing adult mass (P < 0.0001…<0.002, Table 2). Average slopes for plants and animals are in the range of −0.16 to −0.39 (Table 4). Slopes for warm-blooded species tend to be steeper than those for cold-blooded species. The empirical regressions for seed plants were derived from one study, with annual reproductive mass expressed as a function of foliage and stem mass because total weight correlations were not provided (Fig. 1; Niklas and Enquist 2003). The invertebrate regressions apply to short-term studies on different types of copepods. The outlier noted in field experiments with sac spawners was not confirmed by other correlations, including those for high food levels (Hirst and Bunker 2003, p 1,995). Low intercepts for fish and mammals apply to long-term observations, including intervals without gonadic growth (Charnov 2001; Charnov et al. 2001). High values were noted for reproductive growth in gestation periods (Payne and Wheeler 1968; Blueweiss et al. 1978). Reproduction within primates is slower, as earlier noted for production (Table 2, no. 34; Western and Ssemakula 1982; Hendriks 2007).
Table 2kpr (kg female kg−1 day−1) as a function of m (kg) according to empirical regressions (y = amb) collected in the meta-analysis. For abbreviations, see Table 1NoTaxonabnr2PSource1Spermatophyta1.8 × 10−4−0.162790.75<0.0001Niklas and Enquist (2003)2Spermatophyta3.0 × 10−4−0.334180.75<0.0001Niklas and Enquist (2003)11Copepoda9.7 × 10−4−0.2530810.06<0.001Hirst and Bunker (2003)12Copepoda1.3 × 1000.174520.05<0.001Hirst and Bunker (2003)13Copepoda2.7 × 10−3−0.26350.320.002Kiørboe and Sabatini (1995) 14Copepoda1.2 × 10−3−0.26100.720.002Kiørboe and Sabatini (1995)21Osteichthyes3.0 × 10−4−0.191390.74<0.0001Charnov et al. (2001)31Mammalia4.9 × 10−4−0.331920.89<0.0001Charnov (2001)32Mammalia1.9 × 10−3−0.43920.65<0.0001Blueweiss et al. (1978)33Mammalia3.6 × 10−3−0.40300.90<0.0001Payne and Wheeler (1968)34Primates8.4 × 10−4−0.44150.93<0.0001Payne and Wheeler (1968)
The differences between regressions for the reproduction kpr (kg kg−1 day−1) follow the trends expected from the model, based on average turnover kp (Eq. 2). That is to say, slopes −κ for both reproduction and production tend to be close to −1/4 for heterotherms and at or below −1/3 for homeotherms (Table 4; White and Seymour 2004; Hendriks 2007). Intercepts for seed growth in plant populations, including all life stages, follow Eq. 2, independently confirming the value of 28% for the prp. The reproduction rate regressions for animals are expressed on a female basis. With the exception of deviations noted for some regressions on copepods and primates, levels for true gonadic growth in heterotherms are within a factor of 3 of the model, based on a γp of 7.5 × 10−4 kg kg−1 day−1 previously derived for production (Fig. 1). In general, the variability of the intercepts for reproduction reflects differences in methods, conditions and species and is similar to the variability observed for, e.g., individual growth or consumption (Hendriks 2007). Keeping this variability in mind, we might approximate reproduction by 0.28 kp in plants and 1 kp in adult animals as predicted by Eq. 2 of the model.
Total offspring mass in a reproductive batch
With average production kp as a predictor of reproduction, we can now compare measurements and estimations for the reproductive masses and numbers (Fig. 2). Regressions indicate that total seed, egg and neonate weight increase with parent size (P < 0.0001…<0.05 in Table 3, Fig. 2). Most 95% confidence intervals for the average of the slopes encompass 3/4 or 1, but the whole animal size range can only be covered by an exponent of 1 (Table 4). The outcome for plants is dominated by a regression with a slope of 0.67 observed for fruit versus stem mass (1 in Table 3). Expressed on leaf mass, annual standing reproductive weight in plants scaled to 0.84 (Niklas and Enquist 2003). Comparing weighted averages, the mean slope for invertebrates 0.95 is significantly higher than the confidence interval calculated for plants and cold-blooded vertebrates (Table 4). The confidence intervals noted for exponents of birds and mammals cover 3/4 but not 1. All intercepts for cold-blooded and warm-blooded species are close to each other with the exception of one low value noted for fish (Fig. 2, Table 3; Stolz 2005). This outlier, however, reflects year-round observations while other regressions apply to peak gonad mass. Similar intercept differences were noted for the reproduction kpr.
Table 3Reproductive mass [sowing, clutch, litter (mr); seed, egg, neonate (me)] (kg) as well as the number of offspring (seed, egg, neonate; R0) as a function of m (kg), according to empirical regressions (y = amb) collected in the meta-analysis. Values in italics approximated by us because not/wrongly reported in the original study. Offspring mass or number measured in event (clutch, litter) or organ (ovary, fruits). n.a. Not available, n.s. not significant; for other abbreviations, see Tables 1 and  2No.Taxone, omr (kg)me (kg)R0 (no./female)Sourceabnr2Pabnr2pabnr2P1Spermatophytaao1.1 × 10−10.674180.75<0.0001Niklas and Enquist (2003)2Angiospermaeao1.1 × 10−11.02150.87<0.00015.8 × 10−60.23150.080.302.1 × 1051.01150.490.004Aarssen and Jordan (2001)3Spermatophytao5.7 × 10−21.08130.94<0.00011.0 × 10−50.60130.260.076.3 × 1020.43130.200.13Greene and Johnson (1994)4Angiospermaeo5.5 × 10−20.95570.68<0.00011.4 × 1030.562200.38<0.0001Shipley and Dion (1992)5Spermatophytao8.0 × 10−50.472240.43<0.001Moles et al. (2005b)6Spermatophytao4.6 × 10−60.602260.25<0.0001Grubb et al. (2005)11Rotifera–3.6 × 10−50.60430.550.001Walz et al. (1995)12Copepoda–4.0 × 10−30.93210.87<0.001Kiørboe and Sabatini (1995)13Copepoda–1.2 × 10−50.62410.75<0.001Kiørboe and Sabatini (1995)14Crustaceae2.5 × 10−21.16230.99<0.00015.2 × 10−80.24220.82<0.00012.5 × 1040.59230.59<0.0001Blueweiss et al. (1978)15Dipteraao6.7 × 10−11.00480.75<0.052.1 × 10−60.31480.19<0.052.1 × 1050.62480.19<0.05Berrigan (1991)16Hymenopteraao1.1 × 10−10.96310.80<0.051.4 × 10−30.89310.75<0.057.9 × 1010.07310.02n.s.Berrigan (1991)17Coleopteraao6.7 × 10−20.79560.82<0.051.5 × 10−30.69560.72<0.054.6 × 1010.10560.05n.s.Berrigan (1991)18Araneomorphaee1.3 × 1001.09130.900.00012.7 × 10−50.43330.620.00014.7 × 1040.66390.700.0001Marshall and Gittleman (1994)19Aphidaee1.2 × 1030.161370.35<0.0001Llewellyn and Brown (1953)20Cephalopoda–2.2 × 10−50.26180.080.25Wood and O’dor (2000)21Osteichthyeso1.3 × 10−21.04200.85<0.001Stolz (2005)22Osteichthyes-Reptiliaoe1.1 × 10−10.92850.86<0.00011.2 × 10−50.43630.820.00071.2 × 1040.551210.56<0.0001Blueweiss et al. (1978)23Osteichthyeso1.5 × 10−11.0890.91<0.0001McCann and Shuter (1997)24Osteichthyeso4.4 × 10−20.86200.91<0.0001McCann and Shuter (1997)25Osteichthyese4.7 × 1040.791080.62<0.0001Winemiller and Rose (1992)26Osteichthyese1.4 × 1050.781080.35<0.0001Winemiller and Rose (1992)27Salamandraee2.2 × 10−20.64740.89<0.012.0 × 10−50.25250.190.027.1 × 1020.31250.250.01Kaplan and Salthe (1979)28Salamandrae–1.8 × 10−40.37250.58<0.0001Kaplan and Salthe (1979)29Salamandrae–7.2 × 10−40.49210.550.0001Kaplan and Salthe (1979)30Reptiliae1.5 × 10−10.88350.96n.a.7.5 × 10−30.42350.70<0.00012.1 × 1010.48540.78<0.0001Blueweiss et al. (1978)31Avese2.9 × 10−10.641140.69<0.0016.9 × 10−20.67760.88<0.0014.1 × 100−0.081140.10<0.001Cabana et al. (1982)32Avese2.1 × 10−10.742200.85<0.00015.3 × 10−20.771600.83<0.00014.9 × 100≈01000n.a.Blueweiss et al. (1978)33Avese1.9 × 10−10.723500.79n.a.5.4 × 10−20.772300.93n.a.Western and Ssemakula (1982)34Mammaliae1.1 × 10−10.84760.93<0.0014.0 × 10−20.941140.94<0.001Cabana et al. (1982)35Mammaliae1.6 × 10−10.821100.97<0.00015.6 × 10−20.922000.94<0.00012.7 × 100≈01000n.a.Blueweiss et al. (1978)36Mammaliae1.1 × 10−10.79920.95n.a.5.1 × 10−20.94910.94<0.00012.4 × 100−0.14910.74<0.0001Western and Ssemakula (1982), Sacher and Staffeldt (1974)37Mammaliae2.7 × 10−20.71950.88<0.013.9 × 1000.001000n.s.Millar (1977)38Mammaliae3.4 × 100−0.16290.54<0.001Millar and Zammuto (1983)39Mammaliae2.2 × 1020.9540.98<0.00012.8 × 100−0.12630.32<0.0001Purvis and Harvey (1995)40Primatese8.3 × 10−20.851000.93<0.0001Ross (1998)Table 4Allometric scaling of reproductive parameters as listed in Tables 2 and 3 plotted in Figs. 1–4. Measured arithmetic mean and data-weighted mean (in italics) for the regression exponent b with 95% confidence interval and model values. For abbreviations, see Tables 1 and  2ParameterReproduction rateBatch massOffspring massOffspring numberSymbolpap·kpmrmeR0mr/meUnitd−1kgkgNumber of individualsEmpirical averagePlants−0.33, −0.160.93 (0.65–1.22)0.48 (0.20–0.75)0.66 (−0.10 to 1.43)0.450.78 (0.65–0.91)0.53 (0.45–0.60)0.58 (0.38–0.78)0.25Invertebrates−0.15 (−0.49 to 0.19)1.00 (0.83–1.17)0.55 (0.35–0.75)0.32 (−0.04 to 0.68)0.45−0.20 (−0.33 to −0.07)0.95 (0.87–1.03)0.56 (0.51–0.62)0.27 (0.13–0.42)0.39Cold-blooded vertebrates−0.190.90 (0.74–1.06)0.39 (0.28–0.50)0.58 (0.26–0.91)0.510.85 (0.78–0.91)0.40 (0.27–0.53)0.67 (0.54–0.81)0.45Birds0.70 (0.56–0.84)0.74 (0.59–0.88)−0.04 (−0.55 to 0.47)−0.04Mammals−0.39 (−0.53 to −0.25)0.82 (0.75–0.88)0.88 (0.77–1.00)−0.08 (−0.28 to 0.11)−0.06Model valueCold-blooded−1/411/21/2Warm-blooded−1/4 to −1/3(3/4)–1(3/4)–10
For the overall range, empirical slopes for heterotherms approach the value of 1 expected from Eq. 5 of the model. In addition, the intercepts for plants and animals are at the level expected from the coefficients prl·prp of Eq. 5. Exponents collected for homeotherms and some large-sized heterotherms tend towards 3/4, suggesting synchronization to annual cycles as explained by Eq. 7. The steep lines observed for invertebrates in comparison to the flatter slopes of cold-blooded vertebrates confirm the prediction that heterotherms of ca. 4 kg are likely to experience some kind of synchronization. In addition, exponents for mammals, including large species weighting up to 500 kg, are close to 3/4. Exponents for birds are smaller and obviously their weight range does not include this value.
Seed, egg and neonate mass
Regressions show that seed and egg masses are significantly related to adult size for most heterothermic species groups (P < 0.05, Table 3). Exceptions are noted for some correlations that cover a small size range or a few data (P ≥ 0.07;Table 3, nos. 2 and 3 and 20). The slope varies within a small interval around the mid-point value of 1/2 (Fig. 3). Averages for invertebrates are higher than those for plants and cold-blooded vertebrates, mainly because regressions on egg-carrying copepods and wasps have slopes closer to 1 (Table 3, 12 and 16; Berrigan 1991; Kiørboe and Sabatini 1995). The egg and seed masses (me) for plants, invertebrates and (semi-)aquatic vertebrates of the same size are within 1 order of magnitude of each other (Fig. 3). Eggs of aquatic crustaceans tend to be smaller than those of terrestrial spiders and insects with equal body size (Table 3, nos. 12–14 < 14–18). Likewise, intercepts for cold-blooded vertebrates increase in the sequence of fish, water-bound salamanders, land-dwelling salamanders and reptiles (Table 3, 22 < 27 < 28 ≤ 29 < 30; Blueweiss et al. 1978; Kaplan and Salthe 1979). Warm-blooded animals distribute their reproductive effort over a small and size-invariant R0, leading to exponents for egg and neonate mass (me) between 3/4 and 1 (Fig. 3).
The partitioning of the reproductive mass over seeds, eggs and neonate thus follows a combination of both strategies distinguished in the model. The empirical regressions collected are within the minimum and maximum boundaries set by Eq. 6 of the model (Fig. 3). The slopes for plants, most invertebrates and all cold-blooded vertebrates vary around ½ indicating some intermediate value between min(me)–m0 and max(me)–m1. Egg-carrying copepods, wasps, birds and mammals largely consists of K-strategists, with egg and neonate mass (me) exponents near those noted for clutch and litter mass (mr). Almost all regressions are above the intermediate intercept calculated by the model for an overall minimum offspring size min(me) of 10−10 kg (Table 1). Using typical minimum values min(me) of 10−7 kg for plants, fish and amphibians and of 10−3 kg for reptiles rather than the overall 10−10 kg gives a better fit of the model.
Seed, egg and neonate number
The number of seeds and eggs released by heterotherms scales to size with exponents largely between 1/2 and 1 (Table 4, Fig. 4). The difference between intercepts reflects the fraction of the lifetime covered, being near 100% for herbs and a few percent of less for trees, reflecting lifetime and batch fecundity (R0), respectively (Table 3, 2 vs. 3–4; Shipley and Dion 1992; Greene and Johnson 1994; Aarssen and Jordan 2001). The amount of eggs delivered by crustaceans, flies, spiders and aphids is significantly correlated to adult size but those for wasps and beetles are size-independent (Table 3, nos. 14–15, 18–19 vs. 16–17; Llewellyn and Brown 1953; Blueweiss et al. 1978; Berrigan 1991; Marshall and Gittleman 1994). The low intercept for vertebrate heterotherms applies to reptiles (Table 3, 30; Blueweiss et al. 1978). The clutch and litter size of warm-blooded species does not increase with adult size. In fact, four out of seven regressions have slightly negative slopes.
As expected, average slopes of regressions for R0 are in the same range as those calculated for the ratio of total and individual offspring mass (mr/me) (Table 4). The largest deviation between arithmetic means is noted for plants and equals 0.66−0.45 = 0.21. However, this difference is due to one study in which sowing weight and number but not seed weight scale significantly to m (b = 1.01…1.02, P < 0.00001…0.004, vs. b = 0.23, P = 0.30). With parameters set at typical values, the model follows these trends (Table 1).
Discussion
Data variability
The meta-analysis yielded regressions for various species groups. However, important phylogenetically lower taxa, such as bacteria, algae, fungi, mosses, ferns, Protozoa and annelids have not been included in allometric relationship on reproductive parameters. Budding or binary fission in unicellular organisms yields new cells that become independent at about 30–50% of the parent cell volume, respectively (Woldringh et al. 1993). Unicellular taxa thus maximize the mass rather than the number of their offspring. Fungi, mosses and ferns release spores that are at the lower end of the palynological range noted for seed plants (e.g., Nilsson 1983; Haig and Westoby 1991; Moore et al. 1991; Mulder and Janssen 1999). Their strategy is thus comparable to that of some seed plants, such as orchids. Additional study of the size-related reproduction of these cryptogams is required.
Plant offspring is characterized by seed and fruit mass with or without ancillary tissues, while adult mass refers to leaves and/or stems. Animal studies either cover the whole annual cycle or reproductive periods only. In addition, deviations from average values of other factors, such those for length–weight conversion or life-stage may increase variability.
Slopes on the trade-off between reproduction and production
Despite uncertainties, clear patterns on the average trends emerge (Fig. 5). Reproduction kpr (kg kg−1 day−1) decrease with size, as expected from the model. According to Eq. 2, reproduction is considered to be a fraction (prp) of the production kp, representing the P/B of a population. Reproduction kpr by homeotherms has steeper slopes and larger intercepts in comparison with heterotherms, as earlier noted for production kp (Fig. 2, Table 2). It indicates that the trade-off between somatic and gonadic growth is rather invariant to size and metabolism. The fraction of the production directed to reproduction (prp) was found to be 28% for plants after conversion to seedling wet weight, indeed independent of the species weight (Niklas and Enquist 2002). The similarity between slopes for reproduction and overall population production indicates that such a relationship also exists for animals. However, the derivation of such a fraction is yet impeded by large variability among intercepts, by a lack of information on many heterothermic species and by the focus on adult animals instead of whole populations.
Fig. 5Theoretical (lines) and empirical (dotted area) trends of seed, egg or neonate mass (mr, me) (kg) and number (R0) versus m (kg) for several species groups
Slopes on the trade-off between offspring number and mass
The meta-analysis in the present paper shows that the mass released in a single reproductive event (mr) (kg) is a constant fraction of the parents’ weight for a remarkable variety of plant and animal species (Table 3, Fig. 2). Over the whole range of species studied, the slope is close to 1 but exponents for specific groups, such as homeotherms and possibly plants, are smaller. Ignoring differences in slopes and intercepts, about 20% of the adult mass is released in a sowing, clutch or litter (Eq. 5). This supports, though not necessarily implies, the existence of a size-independent prp.
In addition to the trade-off between somatic and gonadic growth, organisms may divert their reproductive mass over many small or a few large offspring (Fig. 5). In other words, the R0 is inverse proportional to seed, egg or neonate mass (me). As elaborated in the Model development section, one may distinguish between species with r-tactics that maximize the number of offspring with increasing adult mass (R0~m1, me~m0) and K-strategists that amplify seed, egg or neonate weight (me~m1, R0~m0). Slopes of regressions on R0 and me of the offspring generally vary around the intermediate value of 1/2, expected if species with an r- and K-strategy are equally distributed (Table 3). However, regressions on egg-carrying copepods, wasps, birds and mammals have exponents close to 1 for egg and neonate size (me) and near 0 for R0 (Table 3). These species groups thus largely consist of K-strategists.
Graphically, seed, egg and neonate mass are confined to a triangular envelope that contains small species with small offspring and large species with small or large offspring (Figs. 3–5). Such a pattern has been previously recognized in original data on plants and fish. The triangle was found to be right-angled for fish, with a minimum egg size [min(me)] of 10−7 kg independent of the m (e.g., Duarte and Alearaz 1989). In plants, the envelope was reported to be obtuse-angled, where the 5%-tile and the 95%-tile of seed size scaled to total plant mass with exponents in the range of 0.21–0.32 and 0.38–0.68, respectively (Grubb et al. 2005; Moles et al. 2005b). The slopes for the lower boundary encompass the value of 1/4, known for scaling of biological time variables (Peters 1983; Hendriks 1999). Although the period to adulthood has been suggested to limit egg and seed size, such a relationship may be more complex than a 1/4 power scaling to size (see, e.g., Kiflawi 2006). In addition, some proof for the underlying mechanisms, including an explanation for its absence and presence in different species, as well as taxon-specific slope values, is yet lacking.
Similar considerations apply to the upper boundary. The egg and neonate mass (me) in warm-blooded species is proportional to the weight of their parents. Each of the slopes is steeper than observed for clutch or litter mass (mr). However, confidence intervals for the averages indicate that 3/4 may be the appropriate exponent in addition to 1, at least within small size ranges such as noted for birds. Slopes of 3/4 can be understood from inter-reproductive periods that synchronize to annual cycles rather than to adult mass (Eq. 7). Yet, the difference between cold-blooded (≈1/2) and warm-blooded [(3/4)–1] species indicate that metabolism-related mechanisms may be important too. Just as size of warm-blooded adults appears to be constrained by heat exchange, neonate mass may be also be determined by thermodynamic principles. However, the exploration and underpinning of other values for the slopes is beyond the scope of the present paper. For now, we assume that the lower and upper end of the range scale to between 0 and 1. Most species groups contain both an r- and K-strategists yielding an average of slope of about 1/2, whereas some animal taxa were shown to scale to 1. Future refinement by thermodynamic principles may lead to a smaller range between, e.g., 1/4 and 3/4, still yielding average slopes around 1/2.
Intercepts on the trade-off between aquatic and terrestrial habitats
Having described the possible values of the slopes, we will now take a look at the intercepts. The variability of the exponents excludes detection of subtle differences between coefficients. Yet, there is an evident increase in egg size from aquatic to terrestrial habitats, both among invertebrates and vertebrates. The difference has historically been attributed to oxygen limitations as its diffusion in air is 10,000 times faster than in water (Hendry et al. 2001). However, experiments within the same species do not confirm this explanation (Einum et al. 2002). We therefore suggest that an alternative, more universal, mechanism may be more important. A parent is more willing to invest in the size of a seed or egg when it can influence its fate. Organisms have little control of transport and development in large homogeneous compartments such as water and air. Consequently, clutches of aquatic animals consist of many small eggs (Fig. 4; Blueweiss et al. 1978; Kaplan and Salthe 1979; Berrigan 1991; Winemiller and Rose 1992; McCann and Shuter 1997; Wood and O’dor 2000). Even within fish, pelagic species reproduce by smaller and more eggs than demersal counterparts of equal size (Duarte and Alearaz 1989). The intercepts for the amphibians increase in the sequence of pond breeders that attach eggs to plants followed by stream and land breeders with nests (Table 3, 27 < 28 < 29; Kaplan and Salthe 1979). Within the heterogeneous terrestrial environment, land animals can direct their offspring to sites that provide shelter or food to avoid wasting reproductive mass in unfavorable patches (Blueweiss et al. 1978; Berrigan 1991; Marshall and Gittleman 1994). The small seed size of terrestrial plants in comparison to egg masses in reptiles can be understood from the extra dispersal function of propagules in the former case.
Obviously, other factors that covary with the water–land gradient may be responsible for the observed patterns. For instance, the dry–wet weight fraction of adults increases from aquatic to terrestrial habitats and a similar trend might exist in their offspring too. However, this explanation, and the related interpretation, is unlikely to cover the orders of magnitude of the noted differences.
Integration of theoretical and empirical evidence
Integrating these trends, we can now derive common patterns within the triangular envelope of offspring and adult mass (Fig. 5). In general, r-strategists are found amongst small adults (Fig. 5, left-hand side) with many small offspring in aquatic environments (Fig. 5, lower end). Large adults (Fig. 5, right-hand side) with a few large young live in terrestrial habitats (Fig. 5, upper end). Obviously, these patterns cannot cover all reproductive and non-reproductive characteristics associated with r−K gradients. For instance, ruderal plants typically reproduce as r-strategists, but more K-type species, especially in close canopies, may also regenerate via wind dispersal of small seeds (Grime et al. 1997; Grime 2001; Aarssen 2005). In addition, seed mass is known to be negatively correlated with the leaf size or the life span of 640 plant species (Díaz et al. 2004). Such results for plants strongly imply the existence of correlated traits in other taxa and demand further investigation.

reproduction
body size
macroecology
fecundity
allometric scaling


TeCK Database: A comprehensive collection of telomeric and centromeric sequences with their associated proteins

Telomeres and centromere are two essential features of all eukaryotic chromosomes. They provide function that is necessary for the stability of chromosomes. We developed a comprehensive database named TeCK, which covers a gamut of sequence and other related information about telomeric patterns, telomere repeat sequences, centromere sequences and centromeric patterns present in chromosomes. It also contains information about telomerase ribo-nucleoprotein complexes, centromere binding protein and centromere DNA-binding protein complexes. The database also includes a collection of all kinetochore-associated proteins including inner, outer and central kinetochore proteins. The database can be searched using a user-friendly web interface.
Background
Telomeres [1] are a series of repeated DNA sequences located at the end of chromosomes, with strand asymmetry in GC
content, resulting in one G-rich strand and one C-rich strand. They serve to assure that a chromosome is replicated properly during cell division. During this process some of the
telomeres are lost. Eventually little or no telomere remains, and the cell dies. [2] Telomerase is an enzyme that adds specific
DNA sequence repeats, (“TTAGGG” in all vertebrates) to the 3’ end of DNA strands, in the telomere regions at the ends of chromosomes, thus preventing it from getting shorter.
Centromeres [3] are DNA sequences contained in the heterochromatin, responsible for the segregation of each chromosome into
daughter cells during cell division. The kinetochore [4] assembled on the centromere links the chromosome to the mitotic
spindle during mitosis. As a cell tends to become cancerous [5], it divides more often, and its telomeres become very short,
causing death of cells, which can be prevented by activating the enzyme telomerase. By understanding these regions of chromosomes, cancer and aging can be treated effectively and
thus is a potential target of drug design approach. Hence, a database for analyzing and interpreting  chromosomal information is essential. So far there had been no attempts to
annotate and curate these parts of chromosomes.
Methodology
TECK is developed using MySQL [6] a relational database management system that serves as the backend for storing data.
IIS (Internet Information Server) is used as the web server and PHP5 (Hypertext preprocessor) [7] a widely used scripting
language driven by Zend engine is used as the web interface.
The nucleotide information is retrieved from NCBI, [8] a national resource repository for molecular biological information.
About 160 entries are obtained for both telomere and centromere. The information about the associated proteins is retrieved from SWISSPROT, [9]
a protein database. About 154 entries are obtained for telomerase, 162 entries are obtained for centromere binding proteins and 170 entries are obtained for kinetochore. Hyperlinks are
provided to the corresponding databases for each entry with their IDs displayed.
Each entry is given an unique ID called TeCK ID consisting of three parts, the first part indicating the class and the second depicting the organism and the last denoting the position of
that particular entry in the table. About 16 tables had been created all of which are linked using their unique TeCK ID. Each protein entry is described using twenty parameters such as protein name,
gene name, source, lineage, function, other interacting proteins etc. The nucleotide information is described using parameters such as chromosome number, keywords, lineage, the articles along with
the author details and references. BLAST [10] is a search tool for comparing biological sequences. A stand alone BLAST Program obtained from NCBI
has been installed for searching similar sequences.
Accessibility
TeCK database can be accessed via internet and the screen shot of the homepage is displayed [Figure 1A]. There are three ways by which the user can query the database. The first one is the keyword
search in home page that can be performed for five categories (Telomere, Centromere and its associated proteins along with Kinetochore proteins) by giving any text data related to organism name, protein name,
function etc. to retrieve the required data. The second one is the advanced search option for specific requirements [Figure 1B], where the user can fill the form by specifying the input parameters such as
SwissProt, Interpro, Pfam, BLOCKS, PDB, ModBase IDs or TeCk ID. Alternatively, the users can also browse the database [Figure 1C] by organisms and category. On selection of the required query, a result page
containing the number of hits and the list of all entries ID with a short description is displayed. Detailed information can be obtained by clicking each entry ID [Figure 1D]. The sequences are displayed in
FASTA format and the retrieval can be done using a separate ‘retrieve in FASTA format’ link. BLASTn can be done against TeCK database & NCBI and BLASTp against TeCK database, SwissProt & PDB.
Utility
As TeCK database includes name, function, sequence, subunits, and other literature information. The data for TeCK database were obtained from various curated databases and hence TeCK database helps end users
to study, compare, analyze and interpret them and finds utility in control of cancer and ageing.
Caveats
It should be noted that the consistency depends on the source of the original data.

telomere
centromere
chromosome
kinetochore proteins