Introduction 1983 2007 m a m b a b m 1983 1978 1989 1989 1995 2001 2001 2002 2005 2005 2005 1997 1999 r  K 1967 1970 1992 1997 2005 Materials and methods Regression collection and treatment 1983 1983 1999 1991 2 3 3 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. b b n b n Model development 2007 k p P B −1 −1 m 1 \documentclass[12pt]{minimal}
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$$ k_{{\text{p}}} = q_{{\text{T}}} \cdot \gamma _{{\text{p}}} \cdot m^{{ - \kappa }} . $$\end{document} κ 1983 1999 2007 γ p −4  κ −1 2007 q T 2001 k p q T 2007 k p k pr p rp k p 2 \documentclass[12pt]{minimal}
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$$ \begin{aligned}{} k_{{{\text{pr}}}} = & p_{{{\text{rp}}}} \cdot k_{{\text{p}}} \\ = & p_{{{\text{rp}}}} \cdot q_{{\text{T}}} \cdot \gamma _{{\text{p}}} \cdot m^{{ - \kappa }} . \\ \end{aligned} $$\end{document} 2002 p rp 1 p rp  m 1 Table 1 Main factors used in the equations Symbol Description Unit a γ p Scaling coefficients for production κ −1 −4 2007 k p k pr Rate constants for production and reproduction −1 1 κ Scaling exponent – p,c,w w 2007 m Adult mass kg Variable m r Total reproductive mass in a batch kg 5 m e Seed, egg or neonate mass kg m e −10 i −10 p,acv −7 tcv −3 r p rl Fraction inter-reproductive period of average life time – 0.2 p rp Fraction of production directed to reproduction – p 2002 i,v R 0 Fecundity, number of offspring released in a reproductive event −1 6 q T Temperature quotient – p,c w 2007 τ r Inter-reproductive period day 4 a  p  c  w  i , v , a , t Fig. 1 k pr −1 −1 m thick lines with letter thin lines A green dotted B yellow dashed-dotted C blue dashed D red solid 2 −1 −1  m r τ r 3 \documentclass[12pt]{minimal}
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$$ m_{{\text{r}}} = p_{{{\text{rp}}}} \cdot k_{{\text{p}}} \cdot m \cdot \tau _{{\text{r}}} . $$\end{document} τ r τ r m κ 1983 1999 1983 τ r τ l τ r p rl τ l τ l p rl τ l τ l 2007 τ r τ l m τ l k p 1983 τ r 4 \documentclass[12pt]{minimal}
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$$ \tau _{{\text{r}}} = p_{{{\text{rl}}}} \cdot \tau _{{\text{l}}} = \frac{{p_{{{\text{rl}}}} }} {{k_{{\text{p}}} }}. $$\end{document} τ l −4 −1/4 1/4 0.23 r 2 n 2007 4 3 m r m 2 5 \documentclass[12pt]{minimal}
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$$ m_{{\text{r}}} = p_{{{\text{rp}}}} \cdot p_{{{\text{rl}}}} \cdot m. $$\end{document} Fig. 2 m r m 1 3  5 r R 0 m e m e −15 −11 1998 2001 2005 2003 m e 1 1978 2003 m e m e m r p rp p rl m m e m e R 0 6 \documentclass[12pt]{minimal}
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$$ \begin{aligned}{} R_{0} = & \frac{{m_{r} }} {{{\text{min(}}m_{e} {\text{)}} \ldots {\text{max(}}m_{e} {\text{)}}}} \\ = & \frac{{m_{r} }} {{{\text{min(}}m_{e} {\text{)}} \ldots m_{r} /3}} \\ = & \frac{{p_{{rp}} \cdot p_{{rl}} }} {{{\text{min(}}m_{e} {\text{)}}}} \cdot m \ldots 3 \\ \end{aligned} $$\end{document} R 0 m  K r p rp p rl m e p rp p rl m e  m e m e m 1 m e m 0 m 1/2 3 4 Fig. 3 m e  m 1 E dashed-dotted m e 1/2 m e 3  Fig. 4 R 0 m 1 E dashed-dotted R 0 1/2 R 0 3  4 6 τ r τ r τ r 3 7 \documentclass[12pt]{minimal}
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$$ m_{{\text{r}}} = p_{{{\text{rp}}}} \cdot k_{{\text{p}}} \cdot m \cdot 365 = p_{{{\text{rp}}}} \cdot q_{{\text{T}}} \cdot \gamma _{{\text{p}}} \cdot m^{{1 - \kappa }} \cdot 365 $$\end{document} m r m κ τ r 1 4 m 8 \documentclass[12pt]{minimal}
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$$ m = {\left( {p_{{{\text{rl}}}} \cdot \frac{1} {{\tau _{{\text{r}}} \cdot q_{{\text{T}}} \cdot \gamma _{{\text{p}}} }}} \right)}^{{(1/ - \kappa )}} $$\end{document} 1 τ r m Results Reproduction rate constant k pr P 2 4 1 2003 2003 2001 2001 1968 1978 2 1982 2007 Table 2 k pr − 1 − 1 m y am b 1 No Taxon a b n r 2 P Source 1 Spermatophyta −4 −0.16 279 0.75 <0.0001 2003 2 Spermatophyta −4 −0.33 418 0.75 <0.0001 2003 11 Copepoda −4 −0.25 3081 0.06 <0.001 2003 12 Copepoda 0 0.17 452 0.05 <0.001 2003 13 Copepoda −3 −0.26 35 0.32 0.002 1995 14 Copepoda −3 −0.26 10 0.72 0.002 1995 21 Osteichthyes −4 −0.19 139 0.74 <0.0001 2001 31 Mammalia −4 −0.33 192 0.89 <0.0001 2001 32 Mammalia −3 −0.43 92 0.65 <0.0001 1978 33 Mammalia −3 −0.40 30 0.90 <0.0001 1968 34 Primates −4 −0.44 15 0.93 <0.0001 1968 k pr −1 −1 k p 2 κ 4 2004 2007 2 p rp γ p −4 −1 −1 1 2007 k p k p 2 Total offspring mass in a reproductive batch k p 2 P 3 2 4 3 2003 4 2 3 2005 k pr Table 3 m r m e R 0 m y am b  italics n.a. n.s. 1 2 No. Taxon e m r m e R 0 Source a b n r 2 P a b n r 2 p a b n r 2 P 1 a o −1 0.67 418 0.75 <0.0001           2003 2 a o −1 1.02 15 0.87 <0.0001 5.8 × 10 −6 0.23 15 0.08 0.30 5 1.01 15 0.49 0.004 2001 3 Spermatophyta o −2 1.08 13 0.94 <0.0001 1.0 × 10 −5 0.60 13 0.26 0.07 6.3 × 10 2 0.43 13 0.20 0.13 1994 4 Angiospermae o 5.5 −2 0.95 57 0.68 <0.0001      1.4 × 10 3 0.56 220 0.38 <0.0001 1992 5 Spermatophyta o      −5 0.47 224 0.43 <0.001      2005b 6 Spermatophyta o      −6 0.60 226 0.25 <0.0001      2005 11 Rotifera –      −5 0.60 43 0.55 0.001      1995 12 Copepoda –      −3 0.93 21 0.87 <0.001      1995 13 Copepoda –      −5 0.62 41 0.75 <0.001      1995 14 Crustacea e −2 1.16 23 0.99 <0.0001 −8 0.24 22 0.82 <0.0001 2.5 × 10 4 0.59 23 0.59 <0.0001 1978 15 a o −1 1.00 48 0.75 <0.05 −6 0.31 48 0.19 <0.05 5 0.62 48 0.19 <0.05 1991 16 a o −1 0.96 31 0.80 <0.05 −3 0.89 31 0.75 <0.05 1 0.07 31 0.02 n.s. 1991 17 a o −2 0.79 56 0.82 <0.05 −3 0.69 56 0.72 <0.05 1 0.10 56 0.05 n.s. 1991 18 Araneomorphae e 0 1.09 13 0.90 0.0001 −5 0.43 33 0.62 0.0001 4 0.66 39 0.70 0.0001 1994 19 Aphidae e           1.2 × 10 3 0.16 137 0.35 <0.0001 1953 20 Cephalopoda –      2.2 × 10 −5 0.26 18 0.08 0.25      2000 21 Osteichthyes o −2 1.04 20 0.85 <0.001           2005 22 Osteichthyes-Reptilia oe 1.1 −1 0.92 85 0.86 <0.0001 −5 0.43 63 0.82 0.0007 1.2 × 10 4 0.55 121 0.56 <0.0001 1978 23 Osteichthyes o −1 1.08 9 0.91 <0.0001           1997 24 Osteichthyes o −2 0.86 20 0.91 <0.0001           1997 25 Osteichthyes e           4 0.79 108 0.62 <0.0001 1992 26 Osteichthyes e           5 0.78 108 0.35 <0.0001 1992 27 Salamandrae e −2 0.64 74 0.89 <0.01 2.0 × 10 −5 0.25 25 0.19 0.02 7.1 × 10 2 0.31 25 0.25 0.01 1979 28 Salamandrae –      1.8 × 10 −4 0.37 25 0.58 <0.0001      1979 29 Salamandrae –      7.2 × 10 −4 0.49 21 0.55 0.0001      1979 30 Reptilia e −1 0.88 35 0.96 n.a. −3 0.42 35 0.70 <0.0001 1 0.48 54 0.78 <0.0001 1978 31 Aves e −1 0.64 114 0.69 <0.001 −2 0.67 76 0.88 <0.001 0 −0.08 114 0.10 <0.001 1982 32 Aves e −1 0.74 220 0.85 <0.0001 −2 0.77 160 0.83 <0.0001 0 ≈0 100 0 n.a. 1978 33 Aves e −1 0.72 350 0.79 n.a. −2 0.77 230 0.93 n.a.      1982 34 Mammalia e −1 0.84 76 0.93 <0.001 −2 0.94 114 0.94 <0.001      1982 35 Mammalia e −1 0.82 110 0.97 <0.0001 −2 0.92 200 0.94 <0.0001 0 ≈0 100 0 n.a. 1978 36 Mammalia e −1 0.79 92 0.95 n.a. −2 0.94 91 0.94 <0.0001 0 −0.14 91 0.74 <0.0001 1982 1974 37 Mammalia e      −2 0.71 95 0.88 <0.01 0 0.00 100 0 n.s. 1977 38 Mammalia e           0 −0.16 29 0.54 <0.001 1983 39 Mammalia e      2 0.95 4 0.98 <0.0001 0 −0.12 63 0.32 <0.0001 1995 40 Primates e      −2 0.85 100 0.93 <0.0001      1998 Table 4 2 3 1 4 italics  b 1 2 Parameter Reproduction rate Batch mass Offspring mass Offspring number Symbol p ap k p m r m e R 0 m r m e Unit −1 kg kg Number of individuals Empirical average Plants −0.33, −0.16 0.93 (0.65–1.22) 0.48 (0.20–0.75) 0.66 (−0.10 to 1.43) 0.45   0.78  0.65–0.91 0.53  0.45–0.60 0.58  0.38–0.78 0.25 Invertebrates −0.15 (−0.49 to 0.19) – – 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 0.39 Cold-blooded vertebrates −0.19 – – 0.58 (0.26–0.91) 0.51   0.85  0.78–0.91 0.40  0.27–0.53 0.67  0.54–0.81 0.45 Birds  – – −0.04 (−0.55 to 0.47) −0.04 Mammals −0.39 (−0.53 to −0.25) – 0.88 (0.77–1.00) −0.08 (−0.28 to 0.11) −0.06 Model value Cold-blooded −1/4 1 1/2 1/2  Warm-blooded −1/4 to −1/3 (3/4)–1 (3/4)–1 0  5 p rl p rp 5 7 Seed, egg and neonate mass P 3 P 3 3 3 1991 1995 m e 3 3 3 1978 1979 R 0 m e 3 6 3 m e m 0 m e m 1 K m e m r m e −10 1 m e −7 −3 −10 Seed, egg and neonate number 4 4 R 0 3 1992 1994 2001 3 1953 1978 1991 1994 3 1978 R 0 m r m e 4 m b P b P 1 Discussion Data variability 1993 1983 1991 1991 1999 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 5 k pr −1 −1 2 p rp k p  P B k pr k p 2 2 p rp 2002 Fig. 5 lines dotted area m r m e R 0 m  Slopes on the trade-off between offspring number and mass m r 3 2 5 p rp 5 R 0 m e r R 0 m 1 m e m 0 K m e m 1 R 0 m 0 R 0 m e r K 3 m e R 0 3 K 3 5 m e −7 m 1989 2005 2005 1983 1999 2006 m e m r 7 r K Intercepts on the trade-off between aquatic and terrestrial habitats 2001 2002 4 1978 1979 1991 1992 1997 2000 1989 3 1979 1978 1991 1994 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 5 r 5 5 5 5 r K r  K 1997 2001 2005 2004