NONLINEAR MIXED-EFFECT HEIGHT-DIAMETER MODEL FOR Pinus pinaster AIT. AND Pinus radiata D. DON

Tree height-diameter (H-D) relationships are important for routine forest assessment. Several H-D relationships have been developed for different species and more are still evolving. This study introduces new H-D model developed for Pinus pinaster and Pinus radiata in Spain, based on data from 184 and 96 permanent sample plots, respectively, collected in the northwest region of the country. Nonlinear mixed-effect modelling technique was used to fit the generalized H-D model. The mixed-effect H-D model was calibrated using the random effects predicted from one to three randomly selected trees per sample plot. Different indices including root mean square error (RMSE) and adjusted coefficient of determination () were used to assess the predictive performance of the model. The results showed that the new model had and RMSE of 0.906 and 1.156 m and 0.814 and 1.703 m for P. pinaster and P. radiata, respectively. The calibration response involved the selection of one tree per sample plot and resulted in a reduction of RMSE by 6.5% and 13.5% for pinaster and P. radiata, respectively.

Keywords:
Hossfeld IV; Fixed-effect; Model calibration; Maritime pine; Monterrey pine

Authorship

Friday Nwabueze Ogana ⁺ + ogana_fry@yahoo.com

University of Ibadan, NigeriaUniversity of IbadanNigeriaNigeria University of Ibadan, Nigeria

http://orcid.org/0000-0002-8388-204X

Sacramento Corral-Rivas ² 2 Sacramento Corral-Rivas: Instituto Tecnológico de El Salto, Durango, México Instituto Tecnológico de el Salto Sacramento Corral-Rivas: Instituto Tecnológico de El Salto Durango Mexico

Sacramento Corral-Rivas: Instituto Tecnológico de El Salto, Durango, MéxicoSacramento Corral-Rivas: Instituto Tecnológico de El SaltoMexicoDurango, Mexico Sacramento Corral-Rivas: Instituto Tecnológico de El Salto, Durango, México

http://orcid.org/0000-0001-7624-0623

Jose Javier Gorgoso-Varela ³ 3 José Javier Gorgoso-Varela: föra forest technologies, Soria, Spain José Javier Gorgoso-Varela: föra forest technologies Soria Spain

José Javier Gorgoso-Varela: föra forest technologies, Soria, Spain José Javier Gorgoso-Varela: föra forest technologiesSpainSoria, Spain José Javier Gorgoso-Varela: föra forest technologies, Soria, Spain

http://orcid.org/0000-0002-8278-7876

+ ogana_fry@yahoo.com

SCIMAGO INSTITUTIONS RANKINGS

University of Ibadan, NigeriaUniversity of IbadanNigeriaNigeria University of Ibadan, Nigeria

Figures | Tables | Formulas

Figures (5)
Tables (9)
Formulas (36)

Species	Variables	Fitting data (N trees = 10776)				Validation (N trees = 7184)
		Mean	SD	Min	Max	Mean	SD	Min	Max
P. pinaster (184 plots)	D (cm)	17.4	7.0	1.8	56.7	17.4	6.8	1.6	63.2
	H (m)	11.5	3.8	1.4	32.7	11.4	3.7	2.3	36.0
	G (m².ha^-1)	34.4	12.2	7.8	115.1	34.3	12.0	7.8	115.1
	dg (cm)	18.0	5.4	10.4	41.5	17.9	5.2	10.4	41.5
	Hm (m)	11.4	3.4	4.7	24.3	11.3	3.3	4.7	24.3
	Ho (m)	13.1	3.7	5.5	30.6	13.0	3.6	5.5	30.6
	t (years)	19.8	8.1	8.0	61.5	19.6	7.9	8.0	61.5
	N (trees.ha^-1)	1466	510	375	2480	1465	507	375	2480
	Do (m)	26.1	6.9	13.8	55.8	26.0	6.6	13.8	55.8
		Fitting data (N trees = 7737)			Validation (N trees = 5158)				55.8
P. radiata (96 plots)	D (cm)	16.3	6.1	1.3	45.5	16.4	6.2	1.8	47.1
	H (m)	14.6	3.9	2.6	31.7	14.7	4.0	2.8	31.5
	G (m².ha^-1)	30.7	7.1	14.3	46.6	30.7	7.1	14.3	46.6
	dg (cm)	17.1	2.7	11.9	27.1	17.2	2.8	11.9	27.1
	Hm (m)	14.5	2.4	9.7	22.6	14.5	2.4	9.7	22.6
	Ho (m)	17.8	3.0	12.9	28.7	17.9	3.1	12.9	28.7
	t (years)	17.1	3.8	12.0	32.0	17.1	3.6	12.0	32.0
	N (trees ha^-1)	1373	397	530	2610	1363	399	530	2610
	Do (m)	26.4	3.9	19.3	38.3	26.6	3.9	19.3	38.3

Model name	Form	Reference	Eq.
Bertalanffy	$H = 1.3 + a {(1 - e^{(- b D)})}^{3}$ (3)	Von Bertalanffy (1957)VON BERTALANFFY, L. Quantitative laws in metabolism and growth. Q. Rev. Biol. V. 32, n. 3, p. 217-231, 1957.	(3)
Curtis	$H = 1.3 + a {(D / (1 + D))}^{b}$ (4)	Curtis (1967)	(4)
Meyer	$H = 1.3 + a (1 - e^{- b D})$ (5)	Meyer (1940)MEYER, W. A mathematical expression for height curves. J. For., V. 38, p. 415-420, 1940.	(5)
Michailoff	$H = 1.3 + a e^{(- b D^{- 1})}$ (6)	MIchailoff (1943)MICHAILOFF, I. Zahlenmassiges verfahren fur die ausfuhrung der bestandeshohenkurven forstw. Forstwissenschaftliches Centralblatt und Tharandter Forstliches Jahrbuch, V. 6, p. 273-279, 1943.	(6)
Michaelis-Menten (MM)	$H = 1.3 + \frac{a D}{(b + D)}$ (7)	Michaeli and Menten (1913)MICHAELIS, L.; MENTEN, M.L. Die kinetik der invertinwirkung. Biochem Z, V. 49, p. 333-369, 1913.	(7)
Naslund	$H = 1.3 + \frac{D^{2}}{{(a + b D)}^{2}}$ (8)	Näslund (1936NÄSLUND, M. Skogsförsöksanstaltens gallringsförsök I tallskog (Forest research institute’s thinning experiments in Scots pine forests). Meddelanden frstatens skogsförsöksanstalt Häfte, V. 29, p. 1-169, 1936. [In Swedish].)	(8)
Power	$H = 1.3 + a D^{b}$ (9)	Stoffels and van Soest (1953STOFFELS, A.; VAN SOEST, J. The main problems in sample plots. Ned Boschb Tijdschr, V. 25, p. 190-199, 1953.)	(9)
Wykoff	$H = 1.3 + e^{a + b / (D + 1)}$ (10)	Wykoff et al. (1982WYKOFF, W.R.; CROOKSTON, N.L.; STAGE, A.R. User’s guide to the stand prognosis model. USDA For. Serv. Gen. Tech. Rep. INT-133, 1982.)	(10)
Chapman-Richards	$H = 1.3 + a {(1 - e^{- b D})}^{c}$ (ll)	Richards (1959RICHARDS, F.J. A flexible growth function for empirical use. Journal of Experimental Biology, V. 10, p. 290-300, 1959.)	(11)
Gompertz	$H = 1.3 + {a e}^{(- b e^{(- c D)})}$ (12)	Gompertz (1825GOMPERTZ, B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos. Trans. R. Soc. Lond. B Biol. Sci., V. 115, p. 513-585, 1825.), Huang et al. (1992HUANG, S.; TITUS, S.J.; WEINS D.P. Comparison of nonlinear height-diameter functions for major Alberta tree species. Can. J. For. Res. , V. 22, p. 1297-1304, 1992.)	(12)
Korf	$H = 1.3 + a (- e^{- b D^{- c}})$ (13)	Lundqvist (1957LUNDQVIST, B. On the height growth in cultivated stands for pine and spruce in Northern Sweden. Medd. Frstatens skogforsk, V. 133, 1957.)	(13)
Logistic	$H = 1.3 + \frac{a}{1 + b e^{- c D}}$ (14)	Pearl and Reed (1920PEARL, R.; REED, L.J. On the rate of growth of the population of the United States since 1970 and its mathematical representation. Proc. Natl. Acad. Sci. U.S.A. V. 6, p. 275-288, 1920.)	(14)
Prodan	$H = 1.3 + \frac{D^{2}}{a + b D + c D^{2}}$ (15)	Strand (1959STRAND, L. The accuracy of some methods for estimating volume and increment on sample plots. Medd. Norske Skogfors. V. 15, n. 4, p. 284-392, 1959. [in Norwegian].)	(15)
Ratkowsky	$H = 1.3 + a e^{- b / (D + c)}$ (16)	Ratkowsky (1990RATKOWSKY, D.A. Handbook of nonlinear regression. Marcel Dekker, Inc., New York. 1990.)	(16)
Weibull	$H = 1.3 + a (1 - e^{b D^{c}})$ (17)	Yang et al. (1978YANG, R.C.; KOZAK, A.; SMITH, J.H.G. The potential of Weibull-type functions as a flexible growth curves. Can. J. For. Res. , V. 8, p. 424-431, 1978.)	(17)

Model	Parameter estimates			Fitting data				Validation data
	a	b	c	RMSE		AIC	BIC	∑Rank	RMSE		AIC	BIC	∑Rank
Bertalanffy	16.45(0.095)	0.117(0.001)		2.649	0.513	51589	51611	6416	2.591	0.514	13685	13698	6416
Curtis	23.885(0.170)	14.306(0.131)		2.504	0.565	50370	50392	5614	2.450	0.566	12878	12892	5614
Meyer	34.36(0.814)	0.021(0.001)		2.335	0.622	48864	48886	328	2.287	0.621	11892	11906	328
Michailoff	23.262(0.163)	13.408(0.125)		2.521	0.559	50517	50539	6015	2.466	0.56	12974	12988	6015
MM	56.677(1.526)	78.169(2.667)		2.33	0.623	48822	48844	287	2.283	0.623	11864	11878	287
Naslund	2.229(0.019)	0.18(0.001)		2.409	0.597	49542	49563	4812	2.359	0.598	12333	12347	4812
Power	1.145(0.019)	0.768(0.005)		2.305	0.632	48580	48602	195	2.259	0.631	11714	11728	164
Wykoff	3.20(0.007)	-15.26(0.137)		2.487	0.571	50227	50248	5213	2.434	0.572	12784	12798	5213
Chapman-Richards	25.00(0.666)	0.04(0.002)	1.30(0.035)	2.396	0.602	49420	49449	4411	2.343	0.603	12240	12261	4411
Gompertz	36.087(1.306)	2.322(0.023)	0.03(0.001)	2.291	0.636	48453	48482	41	2.249	0.634	11649	11669	41
Korf	70.00(9.374)	6.00(0.088)	0.40(0.029)	2.375	0.609	49228	49257	4010	2.322	0.610	12110	12131	4010
Logistic	27.647(0.548)	5.869(0.094)	0.069(0.001)	2.291	0.636	48459	48489	73	2.250	0.634	11658	11679	93
Prodan	-3.455(0.074)	1.746(0.014)	0.009(0.001)	2.305	0.632	48587	48615	216	2.259	0.631	11716	11736	185
Ratkowsky	96.23(6.848)	116.69(8.033)	34.39(1.923)	2.291	0.636	48459	48488	62	2.249	0.634	11653	11673	62
Weibull	85.00(23.107)	0.01(0.002)	0.900(0.023)	2.337	0.621	48885	48914	369	2.295	0.619	11940	11960	369
*Hossfeld	1.134(0.019)	-3.555(0.773)	3.771(0.006)	2.304	0.632	48573	48602	164	2.261	0.630	11727	11748	246

	Pinus pinaster					Pinus radiata
Model	RMSE		AIC	BIC	∑Rank	Model	RMSE		AIC	BIC	∑Rank
Canadas	1.277	0.882	3511	3518	195	Canadas	1.881	0.780	6517	6524	287
Monness	1.287	0.880	3625	3632	246	Monness	1.885	0.779	6543	6550	4010
Gaffrey	1.780	0.771	8290	8304	4812	Gaffrey	2.893	0.479	10964	10977	4812
Sloboda	1.255	0.886	3271	3285	41	Sloboda	1.982	0.755	7059	7072	4411
Gen.MM	1.293	0.879	3703	3724	297	Gen.MM	1.877	0.781	6501	6521	216
Piennaar	1.302	0.877	3795	3815	4010	Piennaar	1.881	0.780	6523	6543	329
Mirkovich	1.312	0.876	3909	3937	4411	Mirkovich	1.881	0.780	6521	6541	308
S.A I	1.299	0.878	3771	3799	369	S.A I	1.853	0.786	6371	6397	133
Tome	1.268	0.884	3416	3443	82	Tome	1.879	0.789	6512	6538	195
Cox III	1.275	0.882	3504	3539	174	Cox III	1.870	0.782	6468	6501	174
S.A II	1.293	0.879	3701	3735	297	S.A II	1.846	0.788	6336	6369	92
*Hossfeld	1.271	0.883	3454	3489	123	*Hossfeld	1.841	0.789	6307	6340	41

Parameters	P. pinaster	P. radiata
	Fixed parameters
b0	34.759	57.021
b1	41.344	46.516
b2	3.367	3.441
b3	0.358	1.211
b4	-5.651	-7.199
	Variance components
σ²u	0.022	0.013
σ²	1.439	2.92
	Fit indices
RMSE	1.156	1.703
	0.906	0.814
AIC	56171	50329
BIC	56218	50373

Species	Calibration options	RMSE		AIC	BIC
P. pinaster	ONLS	1.282	0.884	59908	59954
	Mixed model	1.156	0.906	56171	56218
	One sample tree	1.199	0.899	57506	57553
	Two sample trees	1.229	0.894	58380	58426
	Three sample trees	1.227	0.894	58326	58373
P. radiata	ONLS	2.452	0.607	35843	35871
	Mixed	1.690	0.814	30081	30108
	One sample tree	2.122	0.706	33601	33629
	Two sample trees	2.468	0.602	35940	35968
	Three sample trees	2.273	0.663	34669	34696

Model name	Form	Reference	Eq.
Canadas IV	$H = 1.3 + {[b_{0} (\frac{1}{D} - \frac{1}{D_{o}}) + {(\frac{1}{H_{o} - 1.3})}^{\frac{1}{2}}]}^{- 2}$ (19)	Cañadas et al. (1999CAÑADAS, N.; GARCÍA, C.; MONTERO, G. Relación altura-diámetro para Pinus pinea L. en el Sistema Central, in: Actas del Congreso de Ordenación y Gestión Sostenible de Montes, 1999. [in Spanish].)	(19)
Mønness	$H = 1.3 + {[b_{0} (\frac{1}{D} - \frac{1}{D_{o}}) + {(\frac{1}{H_{o} - 1.3})}^{\frac{1}{3}}]}^{- 3}$ (20)	Mønness (1982MØNNESS, E.N. Diameter distributions and height curves in evenaged stands of Pinus sylvestris L. Medd. No. Inst. Skogforsk, V. 36, p. 1-43, 1982.)	(20)
Gaffrey	$H = 1.3 + (H_{o} - 1.3) e^{b_{0} (1 - \frac{d_{g}}{D}) + b_{1} (\frac{1}{d_{g}} - \frac{1}{D})}$ (2l)	Gaffrey (1988GAFFREY, D. Forstamts-und bestandesindividuelles Sortimentierungsprogramm als Mittel zur Planung, Aushaltung und Simulation. Diplomarbeit Forscliche Fakultät, Universität Göttingen, 1988.)	(21)
Sloboda	$H = 1.3 + (H_{o} - 1.3) e^{(b_{0} (1 - \frac{D}{d_{g}}))} e^{b_{1} (\frac{D}{d_{g}} - \frac{1}{D})}$ (22)	Sloboda et al. (1993SLOBODA, V.B.; GAFFREY, D.; MATSUMURA, N. Regionale und locale Systeme von Höhenkurven für gleichaltrige Waldbestände. Allg Forst. Jagdztg. V. 164, p. 225-228, 1993.)	(22)
Gen.MM	$H = 1.3 + \frac{b_{0} D}{(b_{1} + D)} e^{\frac{- b_{2}}{\sqrt{H_{o}}}}$ (23)	Ogana (2019bOGANA, F.N. Bivariate modelling of diameter and height distributions of Eucalyptus plantations in Afaka forest reserves, Nigeria. 2019b. 216p. PhD thesis, Univ. of Ibadan, Ibadan, Nigeria.)	(23)
Pienaar	$H = b_{0} H_{o} {(1 - e^{\frac{- b_{1} D}{d_{g}}})}^{b_{2}}$ (24)	Pienaar (1991PIENAAR, L.V. PMRC Yield Prediction System for Slash Pine Plantations in the Atlantic Coast Flatwoods, PMRC Technical Report, Athens. 1991.)	(24)
Mirkovich	$H = 1.3 + (b_{0} + b_{1} H_{o} - b_{2} d_{g}) e^{\frac{- b_{3}}{D}}$ (25)	Mirkovich (1958MIRKOVICH, J.L. Normale visinske krive za chrast kitnak i bukvu v NR Srbiji. Zagreb. Glasnik sumarskog fakulteta, V. 13., 1958.)	(25)
S.A I	$H = 1.3 + (b_{0} + b_{1} H_{o} - b_{2} d_{g}) e^{\frac{- b_{3}}{\sqrt{D}}}$ (26)	Schroder, Álvarez-González (2001SCHRÖDER, J.; ÁLVAREZ-GONZÁLEZ, J.G. Developing a generalized diameter-height model for maritime pine in Northwestern Spain. Forstwissenschaftliches Centralblatt, V. 120, p. 18-23, 2001.)	(26)
Tome	$H = H_{o} e^{(b_{0} + b_{1} H_{o} + b_{2} \frac{N}{1000} + b_{3} t) (\frac{1}{D} - \frac{1}{D_{o}})}$ (27)	Tomé (1989TOMÉ, M. Modelaçao do crescimento da árvore individual em povoamentos de Eucalyptus globulus Labill. (1ª rotaçao) na regiao centro de Portugal. 1989. PhD. Thesis, Instituto Superior de Agronomía, Lisboa, Portugal.)	(27)
Cox III	$H = H_{m} [b_{0} + b_{1} H_{m} + b_{2} \frac{H_{m}}{d_{g}} + b_{3} D + b_{4} \frac{N}{\frac{d_{g} (H_{m} d_{g})}{D}}]$ (28)	Cox (1994COX, F. Modelos parametrizados de altura, Informe de convenio de investigación interempresas. 1994.); López-Sánchez et al. (2003)	(28)
S.A II	$H = 1.3 + (b_{0} + b_{1} H_{o} - b_{2} d_{g} + b_{3} G) e^{\frac{- b_{4}}{\sqrt{D}}}$ (29)	Schröder, Álvarez-González (2001SCHRÖDER, J.; ÁLVAREZ-GONZÁLEZ, J.G. Developing a generalized diameter-height model for maritime pine in Northwestern Spain. Forstwissenschaftliches Centralblatt, V. 120, p. 18-23, 2001.)	(29)

Model	Parameter estimates			Fitting data				Validation data
	a	b	c	RMSE	R ²	AIC	BIC	∑Rank	RMSE	R²	AIC	BIC	∑Rank
Bertalanffy	17.105(0.070)	0.178(0.001)		2.704	0.523	37350	37371	6416	2.788	0.516	10582	10596	6416
Curtis	24.001(0.149)	8.96(0.102)		2.537	0.58	36368	36388	5213	2.623	0.575	9914	9927	5313
Meyer	22.748(0.244)	0.058(0.001)		2.484	0.597	36042	36063	369	2.552	0.595	9668	9681	369
Michailoff	23.434(0.142)	8.272(0.095)		2.55	0.575	36447	36468	5614	2.627	0.570	9969	9982	5614
MM	33.362(0.481)	23.117(0.587)		2.47	0.602	35952	35973	195	2.534	0.600	9603	9616	267
Naslund	1.218(0.014)	0.193(0.001)		2.500	0.592	36141	36162	4411	2.572	0.588	9748	9761	4411
Power	2.642(0.044)	0.587(0.006)		2.455	0.606	35860	35880	82	2.515	0.606	9518	9531	82
Wykoff	3.203(0.006)	-9.696(0.108)		2.525	0.584	36294	36315	4812	2.600	0.579	9863	9876	4812
Chapman-Richards	25.322(0.156)	0.040(0.007)	0.832(0.008)	2.468	0.602	35939	35960	164	2.534	0.600	9597	9610	246
Gompertz	24.911(0.573)	1.699(0.017)	0.063(0.003)	2.470	0.602	35953	35981	216	2.531	0.601	9585	9605	215
Korf	35.00(2.196)	5.00(0.195)	0.60(0.037)	2.496	0.593	36117	36145	4010	2.566	0.590	9727	9746	4010
Logistic	22.808(0.378)	3.318(0.056)	0.097(0.003)	2.478	0.599	36009	36037	328	2.539	0.599	9620	9639	328
Prodan	-1.243(0.019)	0.875(0.010)	0.024(0.001)	2.473	0.601	35974	36002	287	2.527	0.603	9567	9587	154
Ratkowsky	39.943(1.547)	31.196(2.221)	12.71(0.996)	2.462	0.604	35904	35931	123	2.524	0.603	9556	9575	123
Weibull	25.00(1.807)	0.110(0.004)	0.070(0.033)	2.553	0.574	36465	36493	6015	2.632	0.569	9990	10010	6015
*Hossfeld	2.819(0.065)	12.995(3.530)	3.566(0.008)	2.452	0.607	35843	35871	41	2.513	0.607	9510	9530	41

Model	Parameter estimates					Fitting data
	b0	b1	b2	b3	b4	RMSE		AIC	BIC	∑Rank
P. pinaster					b4	RMSE		AIC	BIC	∑Rank
Canadas	0.992(0.008)					1.292	0.884	36102	36117	164
Monness	0.982(0.007)					1.301	0.883	36255	36269	236
Gaffrey	0.278(0.019)	2.447(0.340)				1.797	0.776	43221	43243	4812
Sloboda	-0.411(0.005)	0.014(0.001)				1.271	0.888	35759	35781	41
Gen.MM	95.899(0.818)	9.976(0.177)	6.352(0.042)			1.309	0.881	36390	36419	369
Piennaar	1.109(0.012)	1.498(0.086)	0.805(0.036)			1.310	0.881	36407	36437	4010
Mirkovich	2.844(0.096)	1.145(0.011)	0.158(0.007)	6.273(0.007)		1.313	0.881	36456	36492	4411
S.A I	5.665(0.179)	1.741(0.021)	0.302(0.012)	3.346(0.037)		1.305	0.882	36328	36364	287
Tome	-2.508(0.254)	-0.277(0.163)	0.770(0.083)	-0.026(0.008)		1.284	0.886	35976	36013	82
Cox III	0.718(0.010)	-0.029(0.001)	0.559(0.014)	0.017(0.001)	-0.42(0.024)	1.305	0.882	36336	36380	308
SA II	5.654(0.178)	1.663(0.022)	0.311(0.012)	0.035(0.004)	3.349(0.037)	1.299	0.883	36238	36282	205
*Hossfeld	40.728(1.104)	34.663(3.674)	3.368(0.006)	0.573(0.035)	-5.988(0.043)	1.290	0.885	36076	36120	123
P. radiata
Canadas	0.972(0.007)				-5.988(0.043)	1.290	0.885	36076	36120	123	1.812	0.786	31158	31172	267
Monness	1.005(0.007)					1.817	0.784	31205	31219	349
Gaffrey	0.424(0.037)	0.579(0.638)				2.833	0.476	38078	38099	4812
Sloboda	-0.486(0.006)	0.028(0.002)				1.941	0.754	32227	32249	4411
Gen.MM	122.169(2.221)	14.567(0.264)	6.492(0.081)			1.817	0.784	31203	31231	338
Piennaar	1.121(0.012)	1.466(0.067)	0.964(0.033)			1.801	0.788	31069	31097	164
Mirkovich	6.502(0.241)	1.101(0.015)	0.255(0.016)	7.200(0.068)		1.811	0.787	31159	31193	256
S.A I	12.959(0.441)	1.825(0.029)	0.512(0.028)	3.956(0.035)		1.787	0.791	30948	30983	123
Tome	-4.676(0.377)	-0.154(0.016)	1.554(0.124)	-0.061(0.012)		1.807	0.787	31121	31156	205
Cox III	0.699(0.016)	-0.042(0.001)	0.659(0.017)	0.025(0.001)	-2.032(0.092)	1.827	0.782	31291	31333	4010
S.A II	12.175(0.447)	1.803(0.028)	0.565(0.029)	0.065(0.009)	3.949(0.035)	1.780	0.793	30895	30937	82
*Hossfeld	59.376(2.467)	49.397(3.976)	3.436(0.007)	1.413(0.068)	-7.197(0.089)	1.775	0.794	30848	30890	41