Abstract
The competition–density (C–D) effect for non-self-thinning Populus deltoides and Populus × euramericana plantations from 3 to 9 years was analyzed using the reciprocal equation of the C–D effect. The C–D effect was well described by the reciprocal equation, and with the progress of time the C–D curve, on logarithmic coordinates, of the P. × euramericana plantations shifted upward faster than that of the P. deltoides plantations. With increasing physical time t, the biological time τ, i.e. the integral from zero to t of the coefficient of growth λ(t) in the general logistic curve with respect to t, increased rapidly during early growth stages and the increases in τ gradually became slow during later growth stages. This trend was more evident in the P. deltoides plantations than in the P. × euramericana plantations. The coefficients A and B included in the reciprocal equation were calculated at each growth stage. With increasing τ, the coefficient A, the reciprocal of which means the asymptote of yield (=wρ) at a given growth stage, increased abruptly to a maximum value and then tended to decrease gradually to a constant level. On the other hand, the coefficient B, the reciprocal of which means the asymptote of mean stem volume at a given growth stage, decreased exponentially and tended to be close to zero with increasing τ. The λ(t) decreased with increasing stand age, whereas the final yield Y(t) defined as W(t) ρ, where W(t) is the asymptote of w in the general logistic growth curve, increased gradually with increasing stand age. The differences in coefficients A, B, and λ(t) between the two species were reported.
Abstract from the paper’s OpenAlex record, shown for indexing and research. Copyright remains with the authors or the publisher. Read at the source ↗
The text the model read, with the source record’s inline markup (italics, sub- and superscripts) rendered and its character entities decoded; quote offsets refer to the raw text.
Claims 17
Claim · model-written summary
The reciprocal equation described the competition-density effect in Populus deltoides plantations well.
- Taxon
- Populus deltoides
Populus deltoidest0 - Outcome
- C–D effecte0
- Qualifier
- well describede0
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The C–D effect was well described by the reciprocal equation”
t0“Populus deltoides”
Claim · model-written summary
The reciprocal equation described the competition-density effect in Populus × euramericana plantations well.
- Taxon
- Populus × euramericana
Populus ×canadensist0 - Outcome
- C–D effecte0
- Qualifier
- well describede0
Not reportedComparator
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The C–D effect was well described by the reciprocal equation”
t0“Populus × euramericana”
Claim · model-written summary
The competition-density curve shifted upward faster in P. × euramericana than in P. deltoides over time.
- Taxon
- P. × euramericanaPopulus ×canadensise0
- Outcome
- C–D curvee0
- Direction
- shifted upward fastere0
- Qualifier
- on logarithmic coordinatese0
- Comparator
- P. deltoidese0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“with the progress of time the C–D curve, on logarithmic coordinates, of the P. × euramericana plantations shifted upward faster than that of the P. deltoides plantations”
Claim · model-written summary
Biological time increased rapidly early and more slowly later in Populus deltoides plantations.
- Taxon
- Populus deltoidesPopulus deltoidest0
- Organ / stage
- early growth stagese0
- Outcome
- biological time τe0
- Direction
- increasede0
- Qualifier
- the increases in τ gradually became slow during later growth stagese0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“With increasing physical time t, the biological time τ, i.e. the integral from zero to t of the coefficient of growth λ(t) in the general logistic curve with respect to t, increased rapidly during early growth stages and the increases in τ gradually became slow during later growth stages”
t0“Populus deltoides”
Claim · model-written summary
Biological time increased rapidly early and more slowly later in Populus × euramericana plantations.
- Taxon
- Populus × euramericanaPopulus ×canadensist0
- Organ / stage
- early growth stagese0
- Outcome
- biological time τe0
- Direction
- increasede0
- Qualifier
- the increases in τ gradually became slow during later growth stagese0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“With increasing physical time t, the biological time τ, i.e. the integral from zero to t of the coefficient of growth λ(t) in the general logistic curve with respect to t, increased rapidly during early growth stages and the increases in τ gradually became slow during later growth stages”
t0“Populus × euramericana”
Claim · model-written summary
The biological-time trend was more evident in P. deltoides than P. × euramericana.
- Taxon
- P. deltoidesPopulus deltoidese0
- Outcome
- trende0
- Direction
- more evidente0
- Comparator
- P. × euramericanae0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“This trend was more evident in the P. deltoides plantations than in the P. × euramericana plantations”
Claim · model-written summary
Coefficient A increased abruptly to a maximum with biological time in Populus deltoides.
- Taxon
- Populus deltoidesPopulus deltoidest0
- Organ / stage
- growth stagee0
- Outcome
- coefficient Ae0
- Direction
- increased abruptlye0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“With increasing τ, the coefficient A, the reciprocal of which means the asymptote of yield (=wρ) at a given growth stage, increased abruptly to a maximum value and then tended to decrease gradually to a constant level”
t0“Populus deltoides”
Claim · model-written summary
Coefficient A subsequently tended to decrease to a constant level in Populus deltoides.
- Taxon
- Populus deltoidesPopulus deltoidest0
- Organ / stage
- growth stagee0
- Outcome
- coefficient Ae0
- Direction
- decrease graduallye0
- Qualifier
- tendede0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“With increasing τ, the coefficient A, the reciprocal of which means the asymptote of yield (=wρ) at a given growth stage, increased abruptly to a maximum value and then tended to decrease gradually to a constant level”
t0“Populus deltoides”
Claim · model-written summary
Coefficient A increased abruptly to a maximum with biological time in Populus × euramericana.
- Taxon
- Populus × euramericanaPopulus ×canadensist0
- Organ / stage
- growth stagee0
- Outcome
- coefficient Ae0
- Direction
- increased abruptlye0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“With increasing τ, the coefficient A, the reciprocal of which means the asymptote of yield (=wρ) at a given growth stage, increased abruptly to a maximum value and then tended to decrease gradually to a constant level”
t0“Populus × euramericana”
Claim · model-written summary
Coefficient A subsequently tended to decrease to a constant level in Populus × euramericana.
- Taxon
- Populus × euramericanaPopulus ×canadensist0
- Organ / stage
- growth stagee0
- Outcome
- coefficient Ae0
- Direction
- decrease graduallye0
- Qualifier
- tendede0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“With increasing τ, the coefficient A, the reciprocal of which means the asymptote of yield (=wρ) at a given growth stage, increased abruptly to a maximum value and then tended to decrease gradually to a constant level”
t0“Populus × euramericana”
Claim · model-written summary
Coefficient B decreased exponentially toward zero with biological time in Populus deltoides.
- Taxon
- Populus deltoidesPopulus deltoidest0
- Organ / stage
- growth stagee0
- Outcome
- coefficient Be0
- Direction
- decreased exponentiallye0
- Qualifier
- tended to be close to zeroe0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the coefficient B, the reciprocal of which means the asymptote of mean stem volume at a given growth stage, decreased exponentially and tended to be close to zero with increasing τ”
t0“Populus deltoides”
Claim · model-written summary
Coefficient B decreased exponentially toward zero with biological time in Populus × euramericana.
- Taxon
- Populus × euramericanaPopulus ×canadensist0
- Organ / stage
- growth stagee0
- Outcome
- coefficient Be0
- Direction
- decreased exponentiallye0
- Qualifier
- tended to be close to zeroe0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the coefficient B, the reciprocal of which means the asymptote of mean stem volume at a given growth stage, decreased exponentially and tended to be close to zero with increasing τ”
t0“Populus × euramericana”
Claim · model-written summary
Growth coefficient λ(t) decreased with stand age in Populus deltoides.
- Taxon
- Populus deltoidesPopulus deltoidest0
- Outcome
- λ(t)e0
- Direction
- decreasede0
- Setting
- stande0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The λ(t) decreased with increasing stand age”
t0“Populus deltoides”
Claim · model-written summary
Growth coefficient λ(t) decreased with stand age in Populus × euramericana.
- Taxon
- Populus × euramericanaPopulus ×canadensist0
- Outcome
- λ(t)e0
- Direction
- decreasede0
- Setting
- stande0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The λ(t) decreased with increasing stand age”
t0“Populus × euramericana”
Claim · model-written summary
Final yield increased gradually with stand age in Populus deltoides.
- Taxon
- Populus deltoidesPopulus deltoidest0
- Outcome
- final yield Y(t)e0
- Direction
- increased graduallye0
- Setting
- stande0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the final yield Y(t) defined as W(t) ρ, where W(t) is the asymptote of w in the general logistic growth curve, increased gradually with increasing stand age”
t0“Populus deltoides”
Claim · model-written summary
Final yield increased gradually with stand age in Populus × euramericana.
- Taxon
- Populus × euramericanaPopulus ×canadensist0
- Outcome
- final yield Y(t)e0
- Direction
- increased graduallye0
- Setting
- stande0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the final yield Y(t) defined as W(t) ρ, where W(t) is the asymptote of w in the general logistic growth curve, increased gradually with increasing stand age”
t0“Populus × euramericana”
Claim · model-written summary
Coefficients A, B and λ(t) differed between the two poplar species.
- Taxon
- Populus deltoidesPopulus deltoidest0
- Outcome
- coefficients A, B, and λ(t)e0
- Comparator
- Populus × euramericanat1
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The differences in coefficients A, B, and λ(t) between the two species were reported”
t0“Populus deltoides”
t1“Populus × euramericana”