Mass distribution in the fronds of macrocystis pyrifera ... - Springer Link

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'Department of Mathematics & Computer Science, Alma College, Alma, Michigan USA; ... Key words: Macrocystis, Mass distribution, California, New Zealand, ...
Hydrobiologia 260/261: 57-65, 1993. A. R. O. Chapman, M. T. Brown & M. Lahaye (eds), Fourteenth InternationalSeaweed Symposium. © 1993 Kluwer Academic Publishers. Printed in Belgium.

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Mass distribution in the fronds of macrocystis pyrifera from New Zealand and California Melvin A. Nyman 1, Murray T. Brown 2 , Michael Neushul 3 , Bruce W. W. Harger4 & Jonathan A. Keogh 2 'Department of Mathematics & Computer Science, Alma College, Alma, Michigan USA; 2 Department of Botany, University of Otago, Dunedin, New Zealand; 3 Department of Biological Sciences, University of California - Santa Barbara,Santa Barbara, California USA; 4Neushul Mariculture, Goleta, CA, USA

Key words: Macrocystis, Mass distribution, California, New Zealand, Mathematical models

Abstract The mass distribution along the fronds of Macrocystis is examined for plants collected from California and New Zealand. Analysis of fronds classified according to length and condition yields polynomial curves for cumulative mass as a function of distance above the holdfast. Models for this functional relationship are discussed. Similarities and differences between the deep-water California plant and the shallow-water New Zealand plant are highlighted.

Introduction The giant kelp Macrocystis pyrifera is one of the most morphologically complex seaweeds. It consists of two or more fronds which arise from basal meristems above the holdfast; each frond is differentiated into a narrow stipe and flattened blades. A growing frond produces new stipe and blade from the apical meristem and thus projects the frond upward through the water column. Its efficiency as a biological system and in particular the capacity for rapid growth is well documented. The species has a bipolar distribution with circum-Antarctic and northeast Pacific components (Chin etal., 1991). In California it is the dominant seaweed along much of the coastline while in New Zealand, although not as abundant, it can form extensive beds along the coast and in sheltered harbours of the cooler waters around central and southern parts of the country. Various mathematical models have been ap-

plied to several aspects of the species growth and production including effects of harvesting (North, 1968), seasonal variation in growth (Anderson, 1974), photosynthetic capacity (Jackson, 1987), whole plant growth (Nyman etal., 1990), and population growth (Burgman & Gerard, 1990). Several workers have also assessed morphological, developmental and physiological patterns within the plant (e.g. North, 1971; Lobban, 1978a, b). Mathematical relationships have been developed to describe patterns in frond morphology. Kain (1982) has provided a detailed description of the morphology of Macrocystis pyrifera plants from New Zealand and California with particular emphasis on the apical two meters of growing fronds which had already reached the sea surface. Jackson etal. (1985) have used a series of regression equations to describe the morphological relationships both within and between fronds. In our study we investigate the distribution

58 of mass within whole plants collected from sites in New Zealand and California. Mathematical relationships are developed for the pool of all fronds and for different classes of fronds within a plant. Because of the way in which Macrocystisfronds grow upward through the water column, the oldest blades are those nearest to the base of the frond. Consequently, the majority of the blade biomass, is concentrated in the upper portion of the frond. Our study results in models for the distribution of biomass along the fronds of Macrocystis plants. This information can be of value for comparing the biomass productivity of plants from various locations and for evaluating commercial harvest.

Materials and methods Macrocystispyriferaplants were collected in 1980 and in 1988. In June, 1980, a whole plant was collected intact from a depth of 9.4 m at the outer edge of bed number 27 off Goleta Point, California. The plant was taken to the Marine Sciences Laboratory at the University of California at Santa Barbara where it was dissected, measured, and weighed. Thirty-five fronds of various lengths and conditions (senescent, mature, and growing) were removed from the plant. Each of these was labelled with a numbered tag, as was the stump on the holdfast from which it was removed. Nine young fronds under 1 m in length and fourteen broken and dying fronds remained attached to the holdfast. Each of the fronds removed from the plant was cut into 1 m segments. Segments were numbered from the base and the wet weight of each segment and lengths of apical segments recorded. In July, 1988, a plant was harvested at Aquarium Point, Otago Harbour on the east coast of South Island, New Zealand. This is a sheltered site with holdfast depth 3 m below MLWS and is subjected to a strong tidal stream on both ebb and flood. Twenty-seven fronds of various lengths and conditions were removed from the plant and each labelled with identifying tags. Several frond ini-

tials and broken and dying fronds remained attached to the holdfast. Each frond was cut into 0.5 m segments starting at the base. Segments were numbered from the base, the wet weight of stipe and blade of each segment, and the lengths of apical segments were recorded. The plant was subsequently oven dried and dry weights recorded. The data were plotted and least squares fits of polynomials applied using JMPTM (SAS Institute, Cary, NC). The degrees of the polynomials were chosen to be the minimum that fit the major features of the data while minimizing the complexity of the model. Generally, quadratic (2nd degree) polynomials were used; increasing the degree to three (cubic) or higher gave little or no increase in the percentage variation explained. Both plants were selected as being representative of the beds from which they were taken. Because the plants were not selected at random, and the frond lengths and weights are not normally distributed, we have not applied significance tests to our models. Moreover, in the segmentby-segment analysis of fronds, there is a data point for each segment of each frond, and thus the data points are not independent observations. We cite r2, the percentage variability explained by each of the curves, as an indicator of the quality of the fit.

Results Segment dry weight to segment wet weight The ratio of dry weight to wet weight was calculated for each half-meter segment of the New Zealand plant. This ratio has an approximately normal distribution with mean 0.128 and standard deviation 0.027, indicating that the plant is about 12.8% dry matter. The relationship between dry and wet weights, segment by segment for the 146 segments, was found to be linear (r = 0.93, r 2 = 0.86). Thus in the remainder of the analyses, wet weight is used as the measure of biomass in both plants.

59 has slope 33.6 g m- and explains 98% of the variation (Table 1). In order to obtain a clearer picture of where the mass is located along the fronds, cumulative wet weight (in grams) as a function of distance from base of plant (in meters) was studied for each of the plants. Quadratic polynomial regression curves explain 88 % and 68 % of the variability in cumulative wet weight for the California and New Zealand plants, respectively (Table 1). In the New Zealand plant cumulative stipe wet weight as a

Distributionof mass along the frond For both plants frond wet weight exhibits considerable variation as a function of frond length, but is approximately linear (Figs la, lb). The regression lines have slope 260 g m- and 115 g m- 1 for the California and New Zealand plants, respectively (Table 1). For the New Zealand plan, removal of blade weight from the analysis sharpens the picture; total stipe weight as a function of frond length is linear (Fig. lc). The regression line a

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Fig. la. Total Frond Wet Weight as a function of Frond Length for thirty-five fronds of the California plant. Least squares regression line shown (Table 1). Fig. Ib. Total Frond Wet Weight as a function of Frond Length for twenty-seven fronds of the New Zealand plant. Least squares regression line shown (Table 1). Fig. Ic. Total Stipe Wet Weight as a function of Frond Length for twenty-seven fronds of the New Zealand plant. Least squares regression line shown (Table 1).

60 Table 1. Biomass distribution as a function of location along all fronds. As a measure of the goodness of fit, r2 values are included. Fig.

Plant

Fronds included

Y

X

Equation

r2

la

California

All

Total Frond Wet Weight

Total Frond Length

y= 379.5 + 259.6 x

0.87

lb

New Zealand

All

Total Frond Wet Weight

Total Frond Length

y = 33.5 + 115.4 x

0.75

lc

New Zealand

All

Total Stipe Wet Weight

Total Frond Length

y = 15.2 + 33.6 x

0.98

-

California

All

Cumulative Wet Weight

Distance From Base

y = 132.7 - 2.6 x + 14.3 x2

0.88

-

New Zealand

All

Cumulative Wet Weight

Distance From Base

y = 3.2 + 57.7 x + 11.7 x2

0.68

-

New Zealand

All

Cumulative

Distance

y = - 4.3 + 32.0 x

0.97

Stipe Wet Weight

From Base

2a

California

All

Fractional Wet Weight

Fractional Frond Length

y= 0.043 - 0.075 x + 1.045 x2

0.95

2b

New Zealand

All

Fractional Wet Weight

Fractional Frond Length

y = 0.11 - 0.47 x + 1.36 x2

0.95

2b

New Zealand

All

Fractional Stipe Wet Weight

Fractional Frond Length

y= 0.01 + 1.02 x

0.99

function of distance from base of plant was analyzed separately and found to be strongly linear; the regression line slope is 32.0 g m- ' (Table 1). Because of the difference in water depth between locations, the differences in the size of the two plants, and the differences in frond length within plants, both cumulative weight and distance from the base of the plant were normalized. Fractional wet weight and fractional frond length, respectively, were calculated at each segment of each frond by dividing the cumulative wet weight by the total frond wet weight and the distance from the base of the frond by the total frond length. Fractional frond weight as a function of fractional frond length was analyzed for the pool of all fronds for each plant (Figs 2a, 2b). In both cases quadratic curves fit the concave upward relationship well and explain 95% of the variability in fractional frond weight (Table 1). Similarly, fractional stipe weight was calculated for the New Zealand plant and analyzed as a function of frac-

tional frond length (Fig. 2b). Linear regression explains 99% of the variability in fractional stipe weight; the line has slope 1.02 and intercept near zero (Table 1). In addition to analyzing the distribution of biomass along all the fronds of both plants, separate analyses of those fronds classified as growing and mature were done for each plant (Figs 3a, 3b, & 4a, 4b) (Table 2). In every case the scatterplots for fractional weight versus fractional frond length display a generally nonlinear, concave upward relationship and are wellfitted by quadratic (second degree) polynomials. The scatterplots for fractional stipe weight as a function of fractional frond length are linear (Figs 3b & 4b).

Blade to stipe distribution Many of the lower frond segments had no blades while segments in the upper half of the frond had

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Fractional Frond Length Fig. 2a. Fractional Wet Weight as a function of Fractional Frond Length for thirty-five fronds of the California plant. Curve is a least squares 2nd degree polynomial fit to the data (Table 1). Fig. 2b. Fractional Frond Wet Weight (curve) and Fractional Stipe Wet Weight (line) as a function of Fractional Frond Length for twenty-seven fronds of the New Zealand plant. Curve is a least squares 2nd degree polynomial fit to Fractional Frond Weight (Table 1). Least squares regression line for Fractional Stipe Weight (Table 1).

blades attached. In order to better understand this aspect of mass distribution, blades were separated from the stipe, and the ratio of blade to

Wet 0.Stipe Weight (line) as a function of Fractional Frond

is a least squares 2nd degree polynomial fit (Table 2).

Frond Length for mature fronds of the New Zealandi plant. Curveis isa least squares 2nddegree polynomial fit (Table 2). Least

squares regression line for Fractional Stipe Weight (Table 2).

stipe weight was calculated for each frond segment of the New Zealand plant. The distribution of the ratio is skewed strongly to the right. Figures 5a & 5b display this ratio as a function of fractional frond length for the mature and crow-

62 Table 2. Biomass distribution as a function of location along mature and growing fronds. As a measure of the goodness of fit, r2 values are included. Fig.

Plant

Fronds included

Y

X

Equation

r2

3a

California

Mature

Fractional Wet Weight

Fractional Frond Length

y = 0.074 - 0.34 x + 1.27 x2

0.97

3b

New Zealand

Mature

Fractional Wet Weight

Fractional Frond Length

y = 0.14 - 0.52 x + 1.35 x2

0.93

3b

New Zealand

Mature

Fractional Stipe Wet Weight

Fractional Frond Length

y = 0.02 + 1.00 x

0.99

4a

California

Growing

Fractional Wet Weight

Fractional Frond Length

y = 0.025 - 0.064 x + 1.062 x2

0.96

4b

New Zealand

Growing

Fractional Wet Weight

Fractional Frond Length

y= 0.102 - 0.474 x+ 1.386 x2

0.96

4b

New Zealand

Growing

Fractional Stipe Wet Weight

Fractional Frond Length

y= 0.003 + 1.03 x

0.99

5a

New Zealand

Mature

Blade Stipe Weight

Fractional Frond Length

y= 3.75 - 20.31 x + 30.20 x2

0.54

5b

New Zealand

Growing

Polygonal line is given by

y= 1.10, if 0< x