1231:. At night, plants will respire and even lose biomass. Over a longer period (weeks to months), RGR will generally decrease because of several reasons. First, the newly formed leaves at the top of the plant will begin to shade lower leaves, and therefore, average photosynthesis per unit area will go down, and so will ULR. Second, non-photosynthetic biomass, especially stems, will increase with plant size. The RGR of trees in particular decreases with increasing size due in part to the large allocation to structural material in the trunk required to hold the leaves up in the canopy. Overall, respiration scales with total biomass, but photosynthesis only scales with photosynthetically active leaf area and as a result growth rate slows down as total biomass increases and LAR decreases. And thirdly, depending on the growth conditions applied, shoot and/or root space may become confined with plant age, or water and/or nutrient supply do not keep pace with plant size and become more and more limiting. One way to 'correct' for these differences is by plotting RGR and their growth components directly against plant size. If RGR specifically is of interest, another approach is to separate size effects from intrinsic growth differences mathematically.
1250:(exponents greater than 1). It has been demonstrated that traditional RGR lacks several of the critical traits influencing growth and the allometric dependency of leaf mass and also showed how to incorporate alloemtric dependencies into RGR growth equations. This has been used to derive a generalized trait-based model of plant growth (see also
461:
ln-transformed size data, and calculating the derivative with respect to time. For plants RGR values are typically (much) smaller than 1 g.g.day. Therefore, values are often reported in mg.g.day, with normal ranges for young, herbaceous species between 50–350 mg.g.day, and values for tree seedlings of 10–100 mg.g.day.
605:). This variable indicates the rate of biomass increase per unit leaf area, with typical values ranging from 5-15 g.m.day for herbaceous species and 1-5 g.m.day for woody seedlings. Although the ULR is not equal to the rate of photosynthesis per unit leaf area, both values are often well correlated.
460:
In the case of more harvests, a linear equation can be fitted through the ln-transformed size data. The slope of this line gives an estimate of the average RGR for the period under investigation, with units of g.g.day. A time-course of RGR can be estimated by fitting a non-linear equation through the
28:
In comparing different treatments, genotypes or species, the simplest type of growth analysis is to evaluate size of plants after a certain period of growth, typically from the time of germination. In plant biology, size is often measured as dry mass of whole plants (M), or the above-ground part of
156:
AGR is not constant, especially not in the first phases of plant growth. When there are enough resources available (light, nutrients, water), the increase of biomass after germination will be more or less proportional to the mass of the plant already present: small right after germination, larger
1501:
and then divided by the time difference between the two harvests. By not ln-transforming the data, no compounding is assumed within this time period and RGR values will be incorrect. Another mistake is to ln-transform the mean plant mass per harvest, rather than taking the mean of the individual
1270:
Agronomic studies often focus on the above-ground part of plant biomass, and consider crop growth rates rather than individual plant growth rates. Nonetheless there is a strong corollary between the two approaches. More specifically, the ULR as discussed above shows up in crop growth analysis as
1266:
Plant growth analysis is often applied at the individual level to young well-spaced plants grown individually in pots. However, plant growth is also highly relevant in agronomy, where plants are generally grown at high density and to seed maturity. After canopy closure, plant growth is not
1486:
Statistical testing of RGR assessed by following individual plants non-destructively over time can be done in an ANOVA with a repeated measurements design. When plants are harvested destructively, RGR can be analysed as the
Species x Time or Treatment x Time interaction in an ANOVA with
19:
refers to a set of concepts and equations by which changes in size of plants over time can be summarised and dissected in component variables. It is often applied in the analysis of growth of individual plants, but can also be used in a situation where crop growth is followed over time.
1453:
1226:
Although the increase in plant size is more or less proportional to plant mass already present, plants do not grow strictly exponentially. In a period of several days, plant growth rate will vary because of diurnal changes in light intensity, and day-to-day differences in the
1210:
794:
954:), the concentration of that element in the plant and the specific uptake rate of roots for the element of interest. Under the condition that the concentration of the element of interest remains constant (i.e. dE/dM = E/M), RGR can be also written as:
456:
813:
As much as RGR can be seen from the perspective of C-economy, by calculating leaf area and photosynthesis, it could equally well be approached from the perspective of organic N concentration, and the rate of biomass increase per unit organic N:
589:
931:
597:) and indicates how much leaf area there is per unit total plant mass. For young plants, values are often in the range of 1–20 m kg, for tree seedlings they are generally less. The second component is the 'Unit Leaf Rate' (
136:
1720:
Poorter, H; Van der Werf, A (1998). "Is inherent variation in RGR determined by LAR at low irradiance and by NAR at high irradiance? A review of herbaceous species". In
Lambers, H; Poorter, H.; Van Vuuren, MMI (eds.).
804:
Thus, by sequentially harvesting leaf, stem, and root biomass as well as determining leaf area, deeper insight can be achieved in the various components of a plant and how they together determine whole plant growth.
1276:
1483:
The degree to which the various components of RGR contribute to the observed differences in RGR between plants of different species or different treatments can be assessed with Growth
Response Coefficients.
1267:
proportional to size anymore, but changes to linear, with in the end saturation to a maximum value when crops mature. Equations used to describe plant size over time are then often expolinear or sigmoidal.
1035:
1941:
Philipson, C.D.; Saner, P.; Marthews, T.R.; Nilus, R.; Reynolds, G.; Turnbull, L.A.; Hector, A. (2012). "Light-based
Regeneration Niches: Evidence from 21 Dipterocarp Species using Size-specific RGRs".
29:
it. In high-throughput phenotyping platforms, the amount of green pixels as derived from photographs taken from plants from various directions is often the variable that is used to estimate plant size.
1025:
324:
628:
946:
Another way to break down RGR is to consider biomass increase from the perspective of a nutrient (element) and its uptake rate by the roots. RGR can then be rewritten as a function of the
237:
333:
1480:
A simple introduction into the techniques of growth analysis can be found in Hunt (1978). Further insights and discussion of underlying assumptions are given by Evans (1972).
1218:
is the mass of the roots, SAR the specific uptake rate of the roots (moles of E taken up per unit root mass and per time), and the concentration of element E in the plant.
623:). SLA is the leaf area of a plant (or a given leaf) divided by leaf mass. LMF characterizes the fraction of total plant biomass that is allocated to leaves. In formula:
37:
In the case that plant size was determined at more than one occasion, the increase in size over a given time period can be determined. The
Absolute Growth Rate (AGR) is
157:
when plants become bigger. Blackman (1919) was the first to recognize that this was similar to money accumulating in a bank account, with the increase determined by
474:
819:
50:
1258:) to show how plant size and the allometric scaling of key functional traits interact to regulate variation in whole-plant relative growth rate.
142:
Absolute size at the end of an experiment then depends on seed mass, germination time, and the integration of AGR over all time steps measured.
1448:{\displaystyle CGR\ =\ {\frac {1}{A_{g}}}\ .\ {\frac {dM}{dt}}\ =\ {\frac {A}{A_{g}}}\ .\ {\frac {1}{A}}{\frac {dM}{dt}}\ =\ LAI\ .\ ULR}
1205:{\displaystyle RGR\ =\ {\frac {M_{R}}{M}}\ .\ {\frac {M}{E}}\ .\ {\frac {1}{M_{R}}}{\frac {dE}{dt}}\ =\ RMF\ .\ {\frac {1}{}}\ .\ SAR}
1985:
Enquist, B.; et al. (2007). "A general integrative model for scaling plant growth, carbon flux, and functional trait spectra".
1738:"The effect of irradiance on the carbon balance and tissue characteristics of five herbaceous species differing in shade-tolerance"
959:
2178:
2084:
1527:
789:{\displaystyle RGR\ =\ {\frac {A}{M_{L}}}\ .\ {\frac {M_{L}}{M}}\ .\ {\frac {1}{A}}{\frac {dM}{dt}}\ =\ SLA\ .\ LMF\ .\ ULR}
264:
2260:
Poorter, H.; Lewis, C. (1986). "Testing differences in relative growth rate: A method avoiding curve fitting and pairing".
2203:
1255:
2411:
173:
1251:
451:{\displaystyle RGR\ =\ {\operatorname {\ln(M_{2})\ -\ \ln(M_{1})} \over \operatorname {t_{2}\ -\ t_{1}} \!}}
1242:). As a result RGR analyses assume that size effects are isometric (scaling exponents are 1.0) instead of
1902:"Growth and carbon economy of a fast-growing and a slow-growing grass species as dependent on ontogeny"
1994:
1517:
1228:
151:
1247:
469:
Soon after its inception, the RGR concept was expanded by a simple extension of the RGR equation:
2242:
2018:
1967:
1522:
1512:
947:
616:
608:
165:
607:
The LAR can be further subdivided into two other variables that are relevant for plant biology:
593:
where A is the total leaf area of a plant. The first component is called the 'Leaf Area Ratio' (
2387:
2336:
2318:
2277:
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2226:
2184:
2174:
2147:
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2010:
1959:
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1490:
For experimental designs with two harvest times, software is available to analyse growth data.
158:
2204:"Partitioning the components of Relative Growth Rate: How important is plant size variation?"
2038:"A Mathematical Function for Crop Growth Based on Light Interception and Leaf Area Expansion"
1690:
Briggs, G.E.; Kidd, F.; West, C. (1920). "A quantitative analysis of plant growth. Part II".
1465:
the ground area occupied by a crop, A the total amount of leaf area on that ground area, and
2377:
2367:
2326:
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2002:
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1804:
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1749:
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1238:) and assumes, incorrectly, that plant growth is directly proportional to total plant size (
2202:
Rees, M.; Osborne, C.P.; Woodward, F.I.; Hulme, S.P.; Turnbull, L.A.; Taylor, S.H. (2010).
1830:
Garnier, E (1991). "Resource capture, biomass allocation and growth in herbaceous plants".
1560:
1466:
584:{\displaystyle RGR\ =\ {\frac {A}{M}}\ .\ {\frac {1}{A}}{\frac {dM}{dt}}\ =\ LAR\ .\ ULR}
1998:
1723:
Inherent
Variation in Plant Growth: Physiological Mechanisms and Ecological Consequences
926:{\displaystyle RGR\ =\ {\frac {N}{M}}\ .\ {\frac {1}{N}}{\frac {dM}{dt}}\ =\ PNC\ .\ NP}
2382:
2355:
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2296:
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2167:
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1955:
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38:
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1971:
2022:
1234:
Decomposing the RGR ignores the dependency of plant growth rate on plant size (or
943:, the nitrogen productivity, the increase in biomass per unit organic N present.
2037:
1493:
Another potential mistake in the calculation of RGR is that plant mass at time t
1461:
is the Crop Growth Rate, the increase in (shoot) biomass per unit ground area, A
131:{\displaystyle AGR=\lim _{\Delta t\to 0}{\Delta M \over \Delta t}={dM \over dt}}
1243:
2322:
2281:
2230:
2133:
2061:
1963:
1927:
1851:
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1676:
161:. He applied the same mathematical formula to describe plant size over time.
2108:
Yin, X.; Goudriaan, J.; Lantinga, E.A.; Vos, J; Spiertz, H.J. (2003-02-01).
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2014:
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1650:
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1547:
Fiorani, F.; Schurr, U. (2013). "Future scenarios for plant phenotyping".
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2313:
2125:
1239:
2006:
140:
where M is the change in mass of the plant during time t, respectively.
1583:
2222:
1651:"Regression Smoothers for Estimating Parameters of Growth Analyses"
1471:
the Leaf Area Index, the amount of leaf area per unit ground area.
168:
mass growth rate in plant growth analysis is often expressed as:
42:
328:
In the case of two harvests, RGR can be simply calculated as
1795:
Ingestad, T. (1979). "Nitrogen stress in birch seedlings".
2295:
Hunt, R.; Causton, D.R.; Shipley, B.; Askew, A.P. (2002).
1873:
Hunt, R.; Lloyd, P.S. (1987). "Growth and partitioning".
1487:
ln-transformed dry mass values as the dependent variable.
1020:{\displaystyle RGR\ =\ =\ {\frac {1}{E}}{\frac {dE}{dt}}}
2356:"Avoiding bias in calculations of relative growth rate"
319:{\displaystyle RGR\ =\ {\frac {1}{M}}{\frac {dM}{dt}}}
1279:
1038:
962:
822:
631:
477:
336:
267:
176:
53:
2297:"A modern tool for classical plant growth analysis"
2110:"A Flexible Sigmoid Function of Determinate Growth"
2166:
1447:
1204:
1019:
925:
788:
583:
450:
318:
231:
130:
939:is the plant organic nitrogen concentration, and
601:), which is also termed 'Net Assimilation Rate' (
444:
1725:. Leiden: Backhuys Publishers. pp. 309–336.
245:M(t) is the final mass of the plant at time (t).
67:
1497:is simply subtracted from plant mass at time t
8:
1584:"The compound interest law and plant growth"
232:{\displaystyle M(t)=M_{0}\exp(RGR\cdot t)}
2381:
2371:
2330:
2312:
2141:
1917:
1771:
1753:
1666:
1618:The Quantitative Analysis of Plant Growth
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987:
961:
935:where N is total plant organic Nitrogen,
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2079:. Venus, Jill C. London: Edward Arnold.
1539:
2036:Goudriaan, J.; Monteith, J.L. (1990).
1561:10.1146/annurev-arplant-050312-120137
7:
2354:Hoffmann, W.A.; Poorter, H. (2002).
1715:
1713:
1629:
1627:
1611:
1609:
2274:10.1111/j.1399-3054.1986.tb02447.x
2054:10.1093/oxfordjournals.aob.a088084
1919:10.1111/j.1469-8137.1992.tb01069.x
1900:Poorter, H.; Pothmann, P. (1992).
1887:10.1111/j.1469-8137.1987.tb04692.x
1809:10.1111/j.1399-3054.1979.tb01679.x
1704:10.1111/j.1744-7348.1920.tb05308.x
1600:10.1093/oxfordjournals.aob.a089727
434:
415:
399:
368:
96:
88:
71:
14:
1832:Trends in Ecology & Evolution
809:Alternative ways to decompose RGR
252:is the initial mass of the plant.
1956:10.1111/j.1744-7429.2011.00833.x
1736:Pons, T.L.; Poorter, H. (2014).
255:RGR is the relative growth rate.
1649:Hunt, R.; Shipley, B. (1996).
1549:Annual Review of Plant Biology
1528:Theoretical production ecology
1178:
1172:
408:
395:
377:
364:
226:
208:
186:
180:
77:
1:
2077:The biometry of plant growth
1844:10.1016/0169-5347(91)90091-B
1502:ln-transformed plant masses.
1246:(exponents less than 1) or
465:RGR components (LAR and ULR)
259:RGR can then be written as:
1262:Growth analysis in agronomy
1256:Metabolic Theory of Ecology
2428:
2075:Causton, David R. (1981).
1742:Frontiers in Plant Science
1030:which can be expanded to:
802:is the mass of the leaves.
149:
146:Relative growth rate (RGR)
33:Absolute growth rate (AGR)
1692:Annals of Applied Biology
1638:. London: Edward Arnold.
1620:. London: Edward Arnold.
1252:Metabolic Scaling Theory
2211:The American Naturalist
1755:10.3389/fpls.2014.00012
1582:Blackman, V.H. (1919).
1668:10.1006/anbo.1996.0162
1449:
1222:Size-dependence of RGR
1206:
1021:
927:
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585:
452:
320:
233:
132:
2262:Physiologia Plantarum
2173:. London: E. Arnold.
2169:Plant Growth Analysis
1797:Physiologia Plantarum
1450:
1207:
1022:
928:
791:
586:
453:
321:
234:
133:
17:Plant growth analysis
1616:Evans, G.C. (1972).
1518:Relative growth rate
1277:
1229:daily light integral
1036:
960:
820:
629:
475:
334:
265:
174:
159:compounding interest
152:Relative growth rate
51:
2007:10.1038/nature06061
1999:2007Natur.449..218E
1636:Plant Growth Curves
41:of change of size (
2373:10.1093/aob/mcf140
2314:10.1093/aob/mcf214
2126:10.1093/aob/mcg029
1523:Specific leaf area
1513:Biomass allocation
1445:
1202:
1017:
948:Root Mass Fraction
923:
786:
617:Leaf Mass Fraction
609:Specific leaf area
581:
448:
316:
229:
128:
84:
1993:(7159): 218–222.
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164:The equation for
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2412:Plant physiology
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2360:Annals of Botany
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2301:Annals of Botany
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2217:(6): E152–E161.
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2165:Hunt, R (1978).
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2156:
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2114:Annals of Botany
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2042:Annals of Botany
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1698:(2–3): 202–223.
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1655:Annals of Botany
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1640:
1639:
1634:Hunt, R (1982).
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1588:Annals of Botany
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1906:New Phytologist
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1875:New Phytologist
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1475:Further reading
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154:
148:
141:
118:
110:
95:
87:
49:
48:
35:
26:
12:
11:
5:
2425:
2423:
2415:
2414:
2404:
2403:
2398:
2397:
2346:
2307:(4): 485–488.
2287:
2268:(2): 223–226.
2252:
2223:10.1086/657037
2194:
2179:
2157:
2120:(3): 361–371.
2100:
2085:
2067:
2048:(6): 695–701.
2028:
1977:
1950:(5): 627–636.
1933:
1912:(1): 159–166.
1892:
1865:
1838:(4): 126–131.
1822:
1803:(1): 149–157.
1787:
1728:
1709:
1682:
1661:(5): 569–576.
1641:
1623:
1605:
1594:(3): 353–360.
1574:
1538:
1537:
1535:
1532:
1531:
1530:
1525:
1520:
1515:
1508:
1505:
1504:
1503:
1498:
1494:
1491:
1488:
1484:
1481:
1476:
1473:
1462:
1444:
1441:
1438:
1432:
1426:
1423:
1420:
1414:
1405:
1402:
1397:
1394:
1386:
1383:
1375:
1365:
1361:
1357:
1349:
1340:
1337:
1332:
1329:
1320:
1310:
1306:
1302:
1294:
1288:
1285:
1282:
1263:
1260:
1248:hypoallometric
1223:
1220:
1215:
1201:
1198:
1195:
1189:
1180:
1177:
1174:
1170:
1162:
1156:
1153:
1150:
1144:
1135:
1132:
1127:
1124:
1114:
1110:
1106:
1098:
1090:
1087:
1079:
1071:
1066:
1062:
1053:
1047:
1044:
1041:
1013:
1010:
1005:
1002:
994:
991:
983:
977:
971:
968:
965:
922:
919:
913:
907:
904:
901:
895:
886:
883:
878:
875:
867:
864:
856:
848:
845:
837:
831:
828:
825:
810:
807:
799:
785:
782:
779:
773:
767:
764:
761:
755:
749:
746:
743:
737:
728:
725:
720:
717:
709:
706:
698:
690:
685:
681:
672:
662:
658:
654:
646:
640:
637:
634:
580:
577:
574:
568:
562:
559:
556:
550:
541:
538:
533:
530:
522:
519:
511:
503:
500:
492:
486:
483:
480:
466:
463:
440:
436:
421:
417:
410:
405:
401:
397:
394:
391:
379:
374:
370:
366:
363:
360:
351:
345:
342:
339:
312:
309:
304:
301:
293:
290:
282:
276:
273:
270:
257:
256:
253:
249:
246:
228:
225:
222:
219:
216:
213:
210:
207:
204:
199:
195:
191:
188:
185:
182:
179:
150:Main article:
147:
144:
124:
121:
116:
113:
107:
101:
98:
93:
90:
82:
79:
76:
73:
69:
65:
62:
59:
56:
34:
31:
25:
22:
13:
10:
9:
6:
4:
3:
2:
2424:
2413:
2410:
2409:
2407:
2393:
2389:
2384:
2379:
2374:
2369:
2365:
2361:
2357:
2350:
2347:
2342:
2338:
2333:
2328:
2324:
2320:
2315:
2310:
2306:
2302:
2298:
2291:
2288:
2283:
2279:
2275:
2271:
2267:
2263:
2256:
2253:
2248:
2244:
2240:
2236:
2232:
2228:
2224:
2220:
2216:
2212:
2205:
2198:
2195:
2190:
2186:
2182:
2176:
2171:
2170:
2161:
2158:
2153:
2149:
2144:
2139:
2135:
2131:
2127:
2123:
2119:
2115:
2111:
2104:
2101:
2096:
2092:
2088:
2082:
2078:
2071:
2068:
2063:
2059:
2055:
2051:
2047:
2043:
2039:
2032:
2029:
2024:
2020:
2016:
2012:
2008:
2004:
2000:
1996:
1992:
1988:
1981:
1978:
1973:
1969:
1965:
1961:
1957:
1953:
1949:
1945:
1937:
1934:
1929:
1925:
1920:
1915:
1911:
1907:
1903:
1896:
1893:
1888:
1884:
1880:
1876:
1869:
1866:
1861:
1857:
1853:
1849:
1845:
1841:
1837:
1833:
1826:
1823:
1818:
1814:
1810:
1806:
1802:
1798:
1791:
1788:
1783:
1779:
1774:
1769:
1765:
1761:
1756:
1751:
1747:
1743:
1739:
1732:
1729:
1724:
1716:
1714:
1710:
1705:
1701:
1697:
1693:
1686:
1683:
1678:
1674:
1669:
1664:
1660:
1656:
1652:
1645:
1642:
1637:
1630:
1628:
1624:
1619:
1612:
1610:
1606:
1601:
1597:
1593:
1589:
1585:
1578:
1575:
1570:
1566:
1562:
1558:
1554:
1550:
1543:
1540:
1533:
1529:
1526:
1524:
1521:
1519:
1516:
1514:
1511:
1510:
1506:
1492:
1489:
1485:
1482:
1479:
1478:
1474:
1472:
1470:
1469:
1460:
1455:
1442:
1439:
1436:
1430:
1424:
1421:
1418:
1412:
1403:
1400:
1395:
1392:
1384:
1381:
1373:
1363:
1359:
1355:
1347:
1338:
1335:
1330:
1327:
1318:
1308:
1304:
1300:
1292:
1286:
1283:
1280:
1272:
1268:
1261:
1259:
1257:
1253:
1249:
1245:
1241:
1237:
1232:
1230:
1221:
1219:
1212:
1199:
1196:
1193:
1187:
1175:
1168:
1160:
1154:
1151:
1148:
1142:
1133:
1130:
1125:
1122:
1112:
1108:
1104:
1096:
1088:
1085:
1077:
1069:
1064:
1060:
1051:
1045:
1042:
1039:
1031:
1028:
1011:
1008:
1003:
1000:
992:
989:
981:
975:
969:
966:
963:
955:
953:
949:
944:
942:
938:
933:
920:
917:
911:
905:
902:
899:
893:
884:
881:
876:
873:
865:
862:
854:
846:
843:
835:
829:
826:
823:
815:
808:
806:
796:
783:
780:
777:
771:
765:
762:
759:
753:
747:
744:
741:
735:
726:
723:
718:
715:
707:
704:
696:
688:
683:
679:
670:
660:
656:
652:
644:
638:
635:
632:
624:
622:
618:
614:
610:
604:
600:
596:
591:
578:
575:
572:
566:
560:
557:
554:
548:
539:
536:
531:
528:
520:
517:
509:
501:
498:
490:
484:
481:
478:
470:
464:
462:
458:
438:
419:
403:
392:
389:
372:
361:
358:
349:
343:
340:
337:
329:
326:
310:
307:
302:
299:
291:
288:
280:
274:
271:
268:
260:
254:
247:
244:
243:
242:
239:
223:
220:
217:
214:
211:
205:
202:
197:
193:
189:
183:
177:
169:
167:
162:
160:
153:
145:
143:
138:
122:
119:
114:
111:
105:
99:
91:
80:
74:
63:
60:
57:
54:
46:
44:
40:
39:temporal rate
32:
30:
24:Absolute size
23:
21:
18:
2366:(1): 37–42.
2363:
2359:
2349:
2304:
2300:
2290:
2265:
2261:
2255:
2214:
2210:
2197:
2168:
2160:
2117:
2113:
2103:
2076:
2070:
2045:
2041:
2031:
1990:
1986:
1980:
1947:
1943:
1936:
1909:
1905:
1895:
1878:
1874:
1868:
1835:
1831:
1825:
1800:
1796:
1790:
1745:
1741:
1731:
1722:
1695:
1691:
1685:
1658:
1654:
1644:
1635:
1617:
1591:
1587:
1577:
1552:
1548:
1542:
1467:
1458:
1456:
1273:
1269:
1265:
1233:
1225:
1213:
1032:
1029:
956:
951:
945:
940:
936:
934:
816:
812:
797:
625:
620:
612:
602:
598:
594:
592:
471:
468:
459:
330:
327:
261:
258:
240:
170:
163:
155:
139:
47:
36:
27:
16:
15:
1881:: 235–249.
1555:: 267–291.
166:exponential
2180:0713126957
2086:0713128127
1944:Biotropica
1534:References
1271:well, as:
1244:allometric
2323:0305-7364
2282:1399-3054
2231:0003-0147
2134:0305-7364
2062:0305-7364
1964:1744-7429
1928:1469-8137
1852:0169-5347
1817:1399-3054
1764:1664-462X
1677:0305-7364
1236:allometry
393:
362:
221:⋅
206:
97:Δ
89:Δ
78:→
72:Δ
2406:Category
2392:12125771
2341:12324272
2247:36532822
2239:20950150
2152:12547689
2015:17851525
1972:86837456
1860:21232441
1782:24550922
1569:23451789
1507:See also
1240:isometry
2383:4233846
2332:4240380
2189:4408604
2143:4244967
2095:8154990
2023:4411354
1995:Bibcode
1773:3912841
1214:where M
798:where M
241:Where:
2390:
2380:
2339:
2329:
2321:
2280:
2245:
2237:
2229:
2187:
2177:
2150:
2140:
2132:
2093:
2083:
2060:
2021:
2013:
1987:Nature
1970:
1962:
1926:
1858:
1850:
1815:
1780:
1770:
1762:
1748:: 12.
1675:
1567:
1457:where
1434:
1428:
1416:
1410:
1377:
1371:
1351:
1345:
1322:
1316:
1296:
1290:
1191:
1185:
1164:
1158:
1146:
1140:
1100:
1094:
1081:
1075:
1055:
1049:
985:
979:
973:
915:
909:
897:
891:
858:
852:
839:
833:
775:
769:
757:
751:
739:
733:
700:
694:
674:
668:
648:
642:
615:) and
570:
564:
552:
546:
513:
507:
494:
488:
431:
425:
387:
381:
353:
347:
284:
278:
2243:S2CID
2207:(PDF)
2019:S2CID
1968:S2CID
2388:PMID
2337:PMID
2319:ISSN
2278:ISSN
2235:PMID
2227:ISSN
2185:OCLC
2175:ISBN
2148:PMID
2130:ISSN
2091:OCLC
2081:ISBN
2058:ISSN
2011:PMID
1960:ISSN
1924:ISSN
1856:PMID
1848:ISSN
1813:ISSN
1778:PMID
1760:ISSN
1673:ISSN
1565:PMID
1254:and
43:mass
2378:PMC
2368:doi
2327:PMC
2309:doi
2270:doi
2219:doi
2215:176
2138:PMC
2122:doi
2050:doi
2003:doi
1991:449
1952:doi
1914:doi
1910:120
1883:doi
1879:106
1840:doi
1805:doi
1768:PMC
1750:doi
1700:doi
1663:doi
1596:doi
1557:doi
1468:LAI
1459:CGR
952:RMF
937:PNC
621:LMF
613:SLA
603:NAR
599:ULR
595:LAR
203:exp
68:lim
45:).
2408::
2386:.
2376:.
2364:90
2362:.
2358:.
2335:.
2325:.
2317:.
2305:90
2303:.
2299:.
2276:.
2266:67
2264:.
2241:.
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2225:.
2213:.
2209:.
2183:.
2146:.
2136:.
2128:.
2118:91
2116:.
2112:.
2089:.
2056:.
2046:66
2044:.
2040:.
2017:.
2009:.
2001:.
1989:.
1966:.
1958:.
1948:44
1946:.
1922:.
1908:.
1904:.
1877:.
1854:.
1846:.
1834:.
1811:.
1801:45
1799:.
1776:.
1766:.
1758:.
1744:.
1740:.
1712:^
1694:.
1671:.
1659:78
1657:.
1653:.
1626:^
1608:^
1592:33
1590:.
1586:.
1563:.
1553:64
1551:.
1027:,
941:NP
390:ln
359:ln
2394:.
2370::
2343:.
2311::
2284:.
2272::
2249:.
2221::
2191:.
2154:.
2124::
2097:.
2064:.
2052::
2025:.
2005::
1997::
1974:.
1954::
1930:.
1916::
1889:.
1885::
1862:.
1842::
1836:6
1819:.
1807::
1784:.
1752::
1746:5
1706:.
1702::
1696:7
1679:.
1665::
1602:.
1598::
1571:.
1559::
1499:2
1495:1
1463:g
1443:R
1440:L
1437:U
1431:.
1425:I
1422:A
1419:L
1413:=
1404:t
1401:d
1396:M
1393:d
1385:A
1382:1
1374:.
1364:g
1360:A
1356:A
1348:=
1339:t
1336:d
1331:M
1328:d
1319:.
1309:g
1305:A
1301:1
1293:=
1287:R
1284:G
1281:C
1216:R
1200:R
1197:A
1194:S
1188:.
1179:]
1176:E
1173:[
1169:1
1161:.
1155:F
1152:M
1149:R
1143:=
1134:t
1131:d
1126:E
1123:d
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1109:M
1105:1
1097:.
1089:E
1086:M
1078:.
1070:M
1065:R
1061:M
1052:=
1046:R
1043:G
1040:R
1012:t
1009:d
1004:E
1001:d
993:E
990:1
982:=
976:=
970:R
967:G
964:R
950:(
921:P
918:N
912:.
906:C
903:N
900:P
894:=
885:t
882:d
877:M
874:d
866:N
863:1
855:.
847:M
844:N
836:=
830:R
827:G
824:R
800:L
784:R
781:L
778:U
772:.
766:F
763:M
760:L
754:.
748:A
745:L
742:S
736:=
727:t
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719:M
716:d
708:A
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697:.
689:M
684:L
680:M
671:.
661:L
657:M
653:A
645:=
639:R
636:G
633:R
619:(
611:(
579:R
576:L
573:U
567:.
561:R
558:A
555:L
549:=
540:t
537:d
532:M
529:d
521:A
518:1
510:.
502:M
499:A
491:=
485:R
482:G
479:R
439:1
435:t
428:-
420:2
416:t
409:)
404:1
400:M
396:(
384:-
378:)
373:2
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365:(
350:=
344:R
341:G
338:R
311:t
308:d
303:M
300:d
292:M
289:1
281:=
275:R
272:G
269:R
250:0
248:M
227:)
224:t
218:R
215:G
212:R
209:(
198:0
194:M
190:=
187:)
184:t
181:(
178:M
123:t
120:d
115:M
112:d
106:=
100:t
92:M
81:0
75:t
64:=
61:R
58:G
55:A
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