The Arrangement 2
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In this study, to quantify the similarity or dissimilarity between stem-level phyllotaxis and leaf-level venation patterns, we investigated the arrangement of lateral veins along the midvein. Specifically, we asked the following questions: 1 does the arrangement of secondary veins reflect a species-specific, genetically determined pattern that is analogous to either an alternate or opposite phyllotaxis? Hereafter, the names of the species are abbreviated by their genus names. Each species was from a different family, except for two species Fraxinus and Ligustrum that both belonged to the family Oleaceae.
Among the woody species, three Aucuba , Lonicera , and Rhododendron were evergreens, and the rest were deciduous species. The plants were sampled from seven locations in Japan: 1 the Forest of Obihiro Obihironomori , a plantation forest that included a mixture of planted and regenerated trees. The sampling locations included the roadsides inside and around the forest; 2 the campus of the Obihiro University of Agriculture and Veterinary Medicine, including an experimental garden at the Field Center of Animal Science and Agriculture; 3 a roadside near the Obihiro station; 4 the riparian zone of the Urikari River; 5 Tokachi Ecology Park, which is located in the riparian zone of the Tokachi River; 6 the riparian zone of the Kikankono River; and 7 a roadside near the Taguri River.
The mean annual temperature and precipitation at the weather station during — were 7. The site 7 was located in Sakura City in Chiba prefecture in a warm-temperate region in Japan. This site was ca. The mean annual temperature and precipitation at the observatory during — were The weather data were taken from the Japan Meteorological Agency homepage, viewed 2 March For each species, 15 leaves three individuals and five leaves or leaflets per individual were measured, except for seven species Amphicarpaea , Chenopodium , Justicia , Lonicera , Paederia , Scutellaria , and Solanum that had relatively few lateral veins on each lamina.
For two clonal species, Cynanchum and Paederia , each individual ramet was sampled from separate places to ensure that it was sampled from a different genet. For other clonal species, Cayratia and Scutellaria , the ramets were sampled from two places for each species because of time constraints.
For the other clonal species, Fallopia , each ramet was sampled from different stands that were located in the same riparian zone of the Urikari River. For Cayratia , Scutellaria , and Fallopia , the total numbers of genets were therefore unknown. Living shoots of trees, or for herbaceous species usually entire ramets, were sampled at the study site with pruning scissors or a long-reach pruner.
Immediately after sampling, shoots or ramets were stored in closed plastic bags with wet paper towels to prevent desiccation and then transported to our laboratory or to a dormitory. The scanning was usually conducted on the same day as the sampling. Because of time constraints, in some cases samples in closed plastic bags were stored in a refrigerator, and the leaves were scanned within two days of the sampling day.
For simple leaves, we followed the definition of primary and secondary veins articulated by the Leaf Architecture Working Group 30 , which is an updated version of the standard definition by Hickey 47 , but with a few modifications. Similarly, for Cynanchum , thick basal lateral veins were not recognized as lateral veins. For leaves that had more than one primary vein, only the midveins were measured.
Intersecondary veins 30 that were considerably thinner than other lateral veins and did not reach the leaf margin were not considered to be lateral veins in the present analysis. If a single lateral vein bifurcated into two or more lateral veins on the way toward the leaf margin, it was still considered as a single lateral vein, and the point from which that lateral vein originated from the midvein central vein was measured. For compound leaves, following the model by Runions et al.
Nonetheless, because a lateral vein of a leaflet may not be equivalent to the lateral vein of a simple leaf, we performed the following preliminary analysis to determine whether we could regard a leaflet as equivalent to a leaf, at least for purposes of this study. We used leaflets of Amphicarpaea hog-peanut , which had ternate leaves, and we separately analyzed the terminal leaflets and compared them to the leaflets from all positions including the terminal, the left-positioned, and the right-positioned leaflets; we followed the left-right terminology by Martinez et al.
We considered the lateral veins of a terminal leaflet to be equivalent to those of a simple leaf. As shown in the Results section, we obtained similar results when we analyzed only the terminal leaflets and when we analyzed leaflets from all positions.
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The same procedure described above was therefore performed to determine the midvein and the lateral veins for each leaflet. The digital images were analyzed by using ImageJ ver 1. For each of those points, two sets of distances d opposite and d same were calculated from the coordinates.
For each vein, the ratio r between those two distances was calculated as follows:. If the lateral veins were arranged in the same way as the alternate phyllotaxis, the distribution of r should be unimodal, with a single mode at an r of 0. As shown in the Results, the shapes of the r distributions among the species investigated varied continuously between those two extremes. For each species, we therefore determined the degree of departure from unimodality as an index of departure from the alternate-like vein arrangement. We followed the argument by Freeman and Dale 57 that the p -value of the dip test can be used as a measure of departure from unimodality; a small p -value indicates a deviation from a unimodal distribution, and in the present context, was considered to indicate a departure from an alternate-like vein arrangement.
We therefore tested whether the p -values differed between species with different stem-level phyllotaxes alternate vs. Arrangement of lateral secondary veins along the midvein.
Leaves of Ulmus are shown as examples. In the panel a , d opposite is the distance between the first lateral vein 1 and the next lateral vein 2 on the opposite side of the central vein, and d same is the distance between the first lateral vein 1 and the next lateral vein 3 on the same side of the central vein. For each lateral vein, the ratio r is calculated as d opposite divided by d same. Photographs by Kohei Koyama. We occasionally observed cases in which two successive lateral veins were on the same side of a leaf lamina Fig. We hypothesized that if those irregular cases were generated by a systematic rule, they should appear at approximately the same positions on each pair of left- and right-positioned leaflets of ternately compound leaves of Amphicarpaea i.
For each of the species investigated, the arrangement of the secondary veins was therefore a mixture of symmetrically arranged opposite-like and asymmetrically arranged alternate-like pairs. The degree of unimodality differed among the species. The arrangements of the secondary veins of those species were therefore relatively close to opposite phyllotaxis, irrespective of their stem-level phyllotaxes alternate: Cayratia and Betula , opposite: Acer , and Euonymus. The arrangements of the lateral veins of those species were therefore closer to alternate phyllotaxis, irrespective of their stem-level phyllotaxes alternate: Magnolia , opposite: Bidens and Ligustrum.
The remainder of the species had r distributions that were intermediate patterns between those two extreme cases. Lateral vein arrangements were related neither to stem-level leaf phyllotaxis alternate vs. For Amphicarpaea , which has ternately compound leaves, we separately analyzed only the terminal leaflets. We obtained results similar to those we obtained when we analyzed leaflets from all positions; mixtures of alternate-like Fig.
The indication was that analyzing a leaflet as if it were equivalent to a leaf did not affect the results. Distributions of the relative position of lateral veins r. For each species, each value of r for a lateral vein is shown as a filled circle, which is arranged so as not to overlap others i.
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Species are arranged in alphabetical order, and data for the first fifteen species Ame—Hyp are shown see Fig. Distributions of the relative position of lateral veins r see Fig. Data for the last fifteen species Jms—Udj are shown. All the values of r are shown. An outlier extremely large value of r was observed when two successive lateral veins on the same side of the leaf were very close to each other. The value of each species is shown as an open circle, each of which is arranged so as not to overlap others i.
The p -value of the Brunner—Munzel test is shown above each panel; no significant difference was found between groups for each panel. Comparison of the results obtained from analysis of the leaflets from different positions T: terminal, L: left, R: right, and ALL: all positions pooled together for Amphicarpaea , which had ternate leaves an example of the scanned image is shown in the panel a. For Amphicarpaea , we found a total of 17 irregular cases on 12 leaflets among the 60 leaflets investigated.
We investigated whether these irregular cases appeared on both the left- and right-positioned leaflets of the same compound leaf at approximately mirror-image positions. However, except for one case Fig. Comparison of left- and right-positioned leaflets for Amphicarpaea , which has ternate leaves. Each panel b—l shows the result of a comparison of the left- L and the right- R positioned leaflets of the same compound leaf.
If those irregular cases had appeared as mirror images on each pair of leaflets, they should appear so on each panel. However, except for only one case panel e , they did not appear as mirror images panels b—d and f—l. The indication is that almost all cases were not generated by systematic rules. For some species, those patterns were closer to an alternate phyllotaxis i. For pairs of right- and left-positioned leaflets of Amphicarpaea , those irregular patterns did not appear as regular mirror images; instead, they appeared as irregular or random events Fig.
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These results are generally consistent with canalization models 41 , 42 , According to those models, locations of secondary veins are not strictly specified prior to leaf formation, and the leaf venation pattern is subject to considerable noise experienced during leaf development The canalization hypothesis has been further developed by Fujita and Mochizuki 43 , 44 , who conducted numerical simulations based on a model of the canalization hypothesis.
The venations produced by their simulations were neither strictly alternate-like nor opposite-like patterns, but instead were a mixture of symmetric and asymmetric arrangements of lateral veins, a pattern that was observed in the present results. Furthermore, their simulations also produced the irregular pattern, in which two or more successive lateral veins ran into the same side of the leaf lamina Fig.
The canalization hypothesis could therefore explain the observed large variations in the positions of lateral veins. Studies by Chitwood et al. Those studies have suggested that the position and the asymmetry of a leaf are determined prior to the development of each leaf. Results from those studies may imply that the arrangements of lateral veins along the midvein could also be determined systematically. Nonetheless, we found that the irregular cases usually appeared on only one leaflet of each pair Fig. Hence, the irregular cases usually did not appear as mirror images, at least in the present dataset.
The indication from these results that the irregular cases may have been extreme examples of noise supports the numerical simulations of the canalization model by Fujita and Mochizuki 43 , In the canalization models 35 , 43 , 44 , 45 , the positions of lateral veins on the lamina are determined not only by the initial distribution of auxin sinks, but also by the interactions between auxin sinks and developing leaf lamina.
These interactions are subject to considerable noise Our results showed that the arrangement of lateral veins along the midvein was a mixture of symmetric and asymmetric patterns. The indication seems to be that the mechanism underlying spacing of secondary veins around the midveins may differ from the mechanism underlying spacing of leaves, in agreement with previous studies 15 , 34 , 35 , 45 see Introduction.
Actual venation patterns may be a consequence of both pre-determined spacing of midveins associated with asymmetry in auxin concentrations and post-determined spacing of auxin canals within each leaf lamina. Further studies are needed to clarify the extent to which auxin flow within a single leaf is determined prior to leaf development.
Correlated growth between lobes and major veins has long been recognized by developmental studies 15 , 63 and is consistent with canalization models 40 , 43 , Those models have revealed that the locations of major veins are determined partially by the locations of lobes, the centers of which often become major veins. Those major veins follow a canal of auxin flow from the tip of the lobe toward the base of a leaf. The termination of some of the lateral veins of Acer , which has lobed leaves, at the lobe apexes is consistent with this scenario.
When leaf laminae were symmetric, the symmetrically arranged lobes in some cases corresponded to symmetrically arranged lateral veins Fig. Similar patterns were observed for the serrated leaves of Betula Fig.