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Matrix models for size-structured populations: unrealistic fast growth or simply diffusion?

Picard N, Liang J - PLoS ONE (2014)

Bottom Line: For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic.Moreover, λ could either increase or decrease when class width increased depending on the species.Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.

View Article: PubMed Central - PubMed

Affiliation: UPR Biens et services des écosystèmes forestiers tropicaux (BSEF), Centre de coopération internationale en recherche agronomique pour le développement (CIRAD), Montpellier, France.

ABSTRACT
Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate (λ) because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of λ to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class i to class i + 1, λ was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of λ to matrix dimension for a class width in the range 1-10 cm was small, much smaller than the sampling uncertainty on the value of λ. Moreover, λ could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.

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Variations of the population growth rate  of Celtis zenkeri with class width . is computed using a Usher matrix model. It increases with  (solid line), but this increase is negligible on the range from 1 to 10 cm as compared to the 95% confidence interval of the estimate of  (shown by the dot and whiskers). The horizontal dotted line corresponds to the value of  for  cm.
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pone-0098254-g002: Variations of the population growth rate of Celtis zenkeri with class width . is computed using a Usher matrix model. It increases with (solid line), but this increase is negligible on the range from 1 to 10 cm as compared to the 95% confidence interval of the estimate of (shown by the dot and whiskers). The horizontal dotted line corresponds to the value of for cm.

Mentions: The population growth rate of C. zenkeri increased from for a class width of 1 cm to 1.00457 for a class width of 10 cm. In comparison, the 95% confidence interval of the estimate of for cm was 1.00212–1.00709. Therefore, the amplitude of the 95% confidence interval of the estimate of for cm was 96 times greater than that of the variations of for varying from 1 to 10 cm (Figure 2), even though C. zenkeri was the species with the largest number of observations and the narrowest 95% confidence interval.


Matrix models for size-structured populations: unrealistic fast growth or simply diffusion?

Picard N, Liang J - PLoS ONE (2014)

Variations of the population growth rate  of Celtis zenkeri with class width . is computed using a Usher matrix model. It increases with  (solid line), but this increase is negligible on the range from 1 to 10 cm as compared to the 95% confidence interval of the estimate of  (shown by the dot and whiskers). The horizontal dotted line corresponds to the value of  for  cm.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4048208&req=5

pone-0098254-g002: Variations of the population growth rate of Celtis zenkeri with class width . is computed using a Usher matrix model. It increases with (solid line), but this increase is negligible on the range from 1 to 10 cm as compared to the 95% confidence interval of the estimate of (shown by the dot and whiskers). The horizontal dotted line corresponds to the value of for cm.
Mentions: The population growth rate of C. zenkeri increased from for a class width of 1 cm to 1.00457 for a class width of 10 cm. In comparison, the 95% confidence interval of the estimate of for cm was 1.00212–1.00709. Therefore, the amplitude of the 95% confidence interval of the estimate of for cm was 96 times greater than that of the variations of for varying from 1 to 10 cm (Figure 2), even though C. zenkeri was the species with the largest number of observations and the narrowest 95% confidence interval.

Bottom Line: For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic.Moreover, λ could either increase or decrease when class width increased depending on the species.Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.

View Article: PubMed Central - PubMed

Affiliation: UPR Biens et services des écosystèmes forestiers tropicaux (BSEF), Centre de coopération internationale en recherche agronomique pour le développement (CIRAD), Montpellier, France.

ABSTRACT
Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate (λ) because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of λ to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class i to class i + 1, λ was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of λ to matrix dimension for a class width in the range 1-10 cm was small, much smaller than the sampling uncertainty on the value of λ. Moreover, λ could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.

Show MeSH