Annual reversible plasticity of feeding structures: cyclical changes of
jaw allometry in a sea urchin
Ebert, T. A., Hernández, J. C., & Clemente, S. (2014). Annual reversible plasticity
of feeding structures: cyclical changes of jaw allometry in a sea urchin.
Proceedings of the Royal Society B: Biological Sciences, 281(1779), 20132284.
doi:10.1098/rspb.2013.2284
10.1098/rspb.2013.2284
Royal Society
Accepted Manuscript
http://cdss.library.oregonstate.edu/sa-termsofuse
1 Annual reversible plasticity of feeding structures: cyclical changes of jaw allometry in a sea
2 urchin.
3 4 Thomas A. Ebert1,*, José Carlos Hernández2,3, Sabrina Clemente2,3
5 1Department
of Zoology, Oregon State University, Corvallis, Oregon, 97331 USA;
6 2Department
of Biology, Villanova University, Villanova, Pennsylvania, 19085 USA.
7 Current address: 3Departamento de Biología Animal (Ciencias Marinas), Universidad de La
8 Laguna, La Laguna, Tenerife, islas Canarias.
9 10 *Corresponding author. Email: ebertt@science.oregonstate.edu
11 Running head: Reversible plasticity in sea urchin jaws
12 13 A wide variety of organisms show morphologically plastic responses to environmental
14 stressors but in general these changes are not reversible. Though less common, reversible
15 morphological structures are shown by a range of species in response to changes in predators,
16 competitors, or food. Theoretical analysis indicates that reversible plasticity increases fitness
17 if organisms are long-lived relative to the frequency of changes in the stressor and
18 morphological changes are rapid. Many sea urchin species show differences in the sizes of
19 jaws (demi-pyramids) of the feeding apparatus, Aristotle's lantern, relative to over-all body
20 size, and these differences have been correlated with available food. The question addressed
21 here is whether reversible changes of relative jaw size occur in the field as available food
22 changes with season. Monthly samples of the North American Pacific coast sea urchin
23 Strongylocentrotus purpuratus were collected from Gregory Point on the Oregon (USA)
24 coast and showed an annual cycle of relative jaw size together with a linear trend from 2007
25 to 2009. Strongylocentrotus purpuratus is a long-lived species and under field conditions
26 individuals experience multiple episodes of changes in food resources both seasonally and
27 from year-to-year. Their rapid and reversible jaw plasticity fits well with theoretical
28 expectations.
29 30 Key-words: morphology; Strongylocentrotus purpuratus; Aristotle's lantern; fitness; reaction
31 norm; Oregon
32 33 34 1. Introduction
Developmental variation of organisms in response to environmental stresses is well
35 known and there are numerous examples of morphological, physiological, behavioral and
36 life-history changes [1– 6]. Plastic responses are a part of the norms of reaction of a species
37 and can be continuous or discontinuous and reversible or irreversible [7]. Most
38 morphological responses are not reversible and can occur in both short and long-lived species
39 such as rotifers [8] and trees [9]. Less common is reversible plasticity of morphological
40 structures.
41 Reversible plasticity shows increased fitness if stresses occur many times over the
42 lifespan of individuals. This relationship has been modeled in the context of the mode and
43 breadth of tolerance functions [10] and a plastic response to stress may shift the mode or the
44 variance (breadth) of a tolerance function. There are lags in the plastic response to changing
45 stress both from the non-stressed condition to the stressed and back again as stress is relieved
46 and the changes may show a hysteresis curve rather than just following a reverse path.
47 Ideally, the response times in both directions should be short to provide maximum fitness.
48 Examples of reversible morphology include both structures associated with food and
49 feeding as well as defense from predators. The development of a carnivore morph from an
50 omnivore morph in spadefoot toad tadpoles can be shifted back towards a more omnivore
51 morphology by changing diet [11]. Tree frog tadpoles show reversible morphological
52 changes in response to changes in presence of dragon fly nymphs [12]. Some snakes show a
53 rapid increase in intestinal mass following a meal [13] and this is followed by reduction as
54 the meal is digested. Morphological changes have been documented in perch (fish) following
55 shifts in habitat complexity and food type [14]. Galápagos marine iguanas resorb bone and
56 shrink during low food conditions associated with El Niño but recover bone and increase in
57 size when food availability improves [15]. In birds, gizzard size in Japanese quail has shown
58 reversible changes to dietary fiber with a hysteresis curve of gizzard length [16] and the bills
59 of marsh sparrows change in size on an annual cycle associated with growth of the
60 keratinized rhamphotheca [17]. The sea urchin Strongylocentrotus purpuratus has shown
61 changes in relative demi-pyramid (jaw) size in response to changes in available food and
62 jaws become relatively larger at a low feeding rate; the pattern can be reversed if food is
63 increased [18,19].
64 Differences in the relative size of jaws (demi-pyramids) of Aristotle's lantern or the
65 entire lantern have been reported for a large number of sea urchin species in field studies
66 including Strongylocentrotus purpuratus [20], Mesocentrotus (Strongylocentrotus)
67 franciscanus [21,22], S. droebachiensis [23,24], Echinometra mathaei [25,26], Diadema
68 setosum and D. antillarum [25,27], Sterechinus neumayeri [28], Evechinus chloroticus [29],
69 Arbacia punctulata [30], Centrostephanus rodgersii [31], and Heliocidaris erythrogramma
70 [32]. Changes in jaw and diameter allometry also have been induced under laboratory
71 conditions of food manipulations in S. purpuratus [18,33,34], S. droebachiensis [24,35], M.
72 franciscanus [36,37], Diadema antillarum [27], Paracentrotus lividus [38], and Lytechinus
73 variegatus [39].
74 Under laboratory conditions, the change in relative lantern or jaw size can be rapid as
75 reported for S. purpuratus [33] where well-fed sea urchins developed relatively smaller jaws
76 than the original field sample within a month. The time and shape of the reverse course,
77 however, have not been studied in detail [18,19].
78 Where food is scarce, jaws tend to be large relative to test diameter. Consequently, the
79 relationship between jaw length and test diameter should reflect food conditions in the field and be
80 correlated with growth rates as shown for M. franciscanus [22]. Available food changes seasonally
81 along the Pacific coast of North America [40] and given rapid responses of jaw allometry observed
82 in the laboratory, seasonal changes in relative jaw length would be expected under field conditions.
83 This is the hypothesis we explore for Strongylocentrotus purpuratus.
84 85 2. Materials and Methods
86 (a) Study species and site
87 The purple sea urchin Strongylocentrotus purpuratus has a reported geographic range from
88 Isla Cedros, Baja California (28° N) [41] to at least Torch Bay, Alaska (58.33° N) [42] and is a
89 common and abundant member of both intertidal and subtidal environments. Monthly collections
90 of 20 S. purpuratus were made in the intertidal at Gregory Point, Oregon (43° 20' 24" N; 124° 22'
91 30" W) from January 2007 to July 2009 as part of a study of gonad development related to latitude
92 and ocean conditions [40]. Gregory Point is 0.7 km northwest of Sunset Bay where S. purpuratus
93 has been studied for many years [43,44]. Measurements used for gonad analysis were test diameter
94 and height, total wet weight, and gonad weight. Following dissection, body walls and lanterns
95 were saved and bleached with sodium hypochlorite, soaked in tap water to remove residual bleach,
96 and dried. Specimens were saved and subsequently jaws (demi-pyramids) of Aristotle's lantern
97 were measured with digital calipers. Four of the saved samples were missing lantern parts and so
98 reduced the analysis to 615 individuals. Jaw measurements were from the oral tip of the jaw to the
99 distal shelf that articulates with the epiphysis as used in previous studies [44]. All data have been
100 archived and are available [45].
101 102 (b) Methods of analysis
103 The approach to analysis was to look for an annual cyclical pattern of jaw length, J, relative
104 to test diameter, D, or total wet weight, T. The starting point for analysis was the basic allometric
105 equation
106 107 110 (1)
lnJ = lnα + βlnD.
(2)
or:
108 109 J=αDβ
Analysis of the annual cyclic change in jaw size started with a modification of a
general model used to describe biocycles [46],
111 y! = ! + !cos 2π τ t ! + ! + !!
112 Two additional parameters were then added to permit β to vary seasonally. Also, year-to-year
113 variation in jaw allometry could occur. To model these additional complications, Eq. 3 was
114 modified [40]:
115 ln! = ! + !cos 2π τ t ! + ! + !ln! + !cos 2π τ t ! + ! ln! + !! t ! + !! .
116 lnD = ln-transformed test diameter, D,
117 A = the mean of lnα, which in Eq. 4 was seasonally adjusted by !"#$ 2! ! !! + ! ,
118 M = the amplitude of half the total predicted change of lnα,
119 τ = duration of one cycle, which was fixed at 1.0 year,
120 ti = time in years when samples were collected starting with 0 at 1 Jan. 2007,
121 φ = lag from reference time of the crest of the cycle,
122 β = mean of the allometric exponent adjusted seasonally by !cos 2π τ t ! + ! ,
(3)
(4)
123 C = the amplitude of one half predicted change in β; and so similar to M,
124 B1 = coefficient of linear change with time, ti.
125 !! = error.
126 The inclusion of a coefficient of linear change with time, B1, is appropriate in this study
127 but probably would have to be changed for other data sets. For example, a second-order term
128 has been included in analysis [40] but with data sets spanning many years, direct inclusion of
129 environmental data probably would be preferable to adding additional higher-order terms.
130 Parameter estimates were made by nonlinear regression [47] using all data, including
131 outliers. Analyses were done with and without the linear term, B1, and with and without an
132 annual cycle of allometric change. Comparison of these four models was made using
133 Akaike's Information Criterion [48] with small sample adjustment, AICc:
134 AIC=nln(σ2)+2K.
135 The number of parameters, K, includes SSE so, for example, in Eq. 4 with both cyclic and
136 linear change with time, K=7. AIC differences, ∆i, were computed and used to calculate
137 Akaike weight, wi, which is the weight of evidence of model i being the best model of the
138 group of models considered.
139 (5)
Measuring diameter and height of living sea urchins is not easy because spines and
140 associated tubercles can interfere with positioning caliper jaws. Sea urchins are not circular
141 around the ambitus but rather slightly pentagonal and so a measurement of maximum
142 diameter requires positioning calipers running from the center of an ambulacral area to the
143 center of the opposite interambulacral. There also are problems with positioning caliper jaws
144 perpendicular to the sea urchin test. All of these problems can lead to errors or biases in
145 measurement [49]. It is reasonable, however, to assume that unlike linear measurements,
146 weight measurements with a digital balance are mostly free of problems of investigator
147 technique although inconsistency in removing excess water can lead to errors. Comparison of
148 linear and weight measurements over time can address the problem of consistency. There
149 also is a problem that monthly collections might have been made at slightly different
150 microhabitats and so any trends may not indicate the performance of single site. We
151 approach this problem by asking whether sizes in collections changed and whether there was
152 a change in height vs. diameter.
153 154 155 3. Results
Monthly samples collected at Gregory Point always contained a range of sizes (Fig.
156 1). Diameter measurements for the 620 dissections had a range of 2.53–9.17 cm with a mean
157 of 6.15 (1.35 sd) cm. Total wet weight ranged from 8.26–297.7 g with a mean of 119.62
158 (62.66 sd) g. Jaw (demipyramid) measurements ranged from 0.53–1.64 cm with a mean of
159 1.12 (0.22 sd) cm (N=615).
160 Analysis of lnJ as a function of lnD and time (Table 1) showed that the model with
161 the most support, largest wi (99.6%), was the one with both a seasonal cycle and a linear
162 trend from 2007 to 2009. Analysis with a trend from 2007 to 2009 but no annual cycle had
163 little support as the best model (wi = 0.37%), which also was the case for an annual cycle but
164 no trend (wi =0.002%).
165 The ANCOVA with lnJ as the dependent variable, lnD as a covariate, and monthly
166 sample date, ti, as a fixed factor (Table 2) provides an estimate of lnJ for each sample
167 adjusted to an overall mean lnD of 1.78879 (mean D = 5.928 cm). The interaction term of
168 lnD × sample date, ti, was not significant (p=0.33). A plot of adjusted means of lnJ together
169 with the fitted line using the parameters in Table 1 both transformed back to J (elnJ = J)
170 shows both the seasonal and linear trends (Fig. 2). Jaws were relatively large early in a year
171 and then declined in relative size during the summer with a minimum in October or
172 November. The linear decline could indicate improving food conditions each year from 2007
173 to 2009. There are, however, other possibilities including problems with measurement or
174 with sampling sea urchins from different microsites during the study.
175 Wet weights of sea urchins in samples (Fig. 1) did not change during the study
176 (F1,618 = 1.747, p = 0.19) but shape might have changed if sea urchins were collected from
177 slightly different microsites. No shape change, however, was detected with the logarithm of
178 height, lnH, as a function of the logarithm of diameter, lnD, and time (Table 3). Both the
179 analysis of total weight and shape indicate that microsite changes during the study were not
180 major contributors to the observed change in jaw:diameter allometry.
181 Analysis of ln jaw length, lnJ, as a function of ln total wet weight, lnT, and time
182 (Table 4A) showed a significant linear trend with a negative slope indicating decreasing
183 relative jaw size during the period of study. An ANCOVA with lnJ as the dependent
184 variable, lnT, as a covariate, and sample time, ti, as a fixed factor provided a pattern of
185 monthly lnJ adjusted to a common wet weight, lnT (4.58381). This pattern does not differ in
186 any major way from the pattern shown by lnJ as a function of lnD (Fig. 3). There is a cyclical
187 pattern to jaw size relative to diameter or total wet weight together with a general downward
188 trend from January 2007 to July 2009.
189 190 4. Discussion
191 The suggested significance of relative jaw size related to food is that larger jaws
192 increase the ability to graze and this has been shown for Echinometra mathaei [26] at
193 Rottnest Island, Western Australia. Sea urchins with larger jaws grazed larger areas on rock
194 surfaces. The direct demonstration of increased grazing ability with increased jaw size has
195 not been done for other sea urchin species but the many studies presented in the introduction
196 confirm that there is a relationship between relative jaw size and available food. Our
197 interpretation of results for S. purpuratus at Gregory Point is that relative growth of the jaws
198 and test change during a year in response to changes in available food with relatively larger
199 jaws arising in response to decreases in food. The linear trend downward from 2007 to 2009
200 means that jaws became relatively smaller in addition to the cyclical pattern within a year
201 suggesting that food availability improved during this time, which is consistent with the
202 maximum annual gonad sizes that were observed from 2007 to 2008 at Gregory Point [40].
203 Gonads in November 2008 were larger than in November 2007 and the relative size of the
204 jaws was smaller, indicating better food conditions, in 2008 compared with 2007.
205 Strongylocentrotus purpuratus has shown variation in relative jaw size at a very local
206 scale in Sunset Bay, Oregon, [20] where samples collected approximately 50 m apart were
207 different. The sea urchins with the smallest relative jaw sizes also had the largest test
208 diameters, the largest gonads, and the fastest growth rates [43]. Differences in growth related
209 to relative jaw size also have been reported for Mesocentrotus (Strongylocentrotus)
210 francsicanus [22], S. droebachiensis [24], Evechinus chloroticus [30], Heliocidaris
211 erythrogramma [33], Anthocidaris crassispina [50], and Centrostephanus rodgersii [32].
212 213 The food environment changes around S. purpuratus at Gregory Point on an annual
basis [40]. Under laboratory conditions allometric changes in response to food availability
214 have a short response time and are obvious after only a few weeks [33]. Food changes in the
215 field are more complex because on any particular day an individual sea urchin in a tide pool
216 may or may not have a piece of algae to eat and may just rasp the substrate for small,
217 attached algal filaments. Given the patterns of change in relative jaw size seen in both the
218 laboratory and in the field, tracking of food availability is very good and morphological
219 response is rapid.
220 There is an interesting problem posed by the reversible plasticity presented here;
221 specifically, is the plasticity actually adaptive in the sense of having a positive effect on
222 survival? Annual survival rates for S. purpuratus in the field have been estimated to be as
223 high as 0.9 [44], which means that 5% of a population could be 30 years old or older.
224 Strongylocentrotus purpuratus has remarkable survival ability when faced with
225 starvation. Under laboratory conditions sea urchins were fed at different frequencies [18,19]:
226 ad lib, once per week, once every two weeks, once every four weeks and once every eight
227 weeks. Mortality began to increase in the once-in-eight-weeks treatment after 30 weeks.
228 During this time the sea urchins had been fed just three times all that could be eaten in 24
229 hours after which all uneaten food was removed. The last survivor was dead at 52 weeks. The
230 treatment of being fed once every 4 weeks showed a rapid decline in survivorship at 45
231 weeks but some individuals were still alive when the experiment was terminated at 64 weeks.
232 These severe levels of food shortage probably never occur in the field. The point is that food
233 reduction unless very severe does not cause increased mortality under laboratory conditions.
234 Additional physical and biological stresses in the field, however, may make starved
235 individuals more vulnerable than in the lab and hence small increases in food intake would
236 improve survival rates.
237 Resorption as well as deposition occurs in the endoskeleton. Possibly the earliest
238 demonstration of this was in spines of sea urchins in the Order Cidaroida [51]. Cellular
239 processes associated with resorption have been described in a variety of sea urchin ossicles
240 [52–55] but not in plates of the test or jaws (demi-pyramids) of Aristotle's lantern.
241 There are reports of shrinkage of the body wall in echinoids [27,56] but such body
242 changes may best be explained as problems of measurement [49] or tightening of sutures
243 between test plates [57,58] without resorption of skeletal elements although the very large
244 changes shown for Diadema antillarum in both field and laboratory experiments [59]
245 indicated resorption of test plates. No statistically significant decrease in test diameter,
246 however, was found in S. purpuratus fed only one day every 8 weeks in the laboratory
247 [18,19]. There always is some food in the field and so it is unlikely sea urchins would shrink
248 while those starved in the laboratory did not. In general, changes in jaw allometry are
249 probably best thought of as due to changes in resource allocation to body parts rather than
250 resorption and rebuilding and so would be to be energetically very inexpensive. In this
251 regard, jaw allometry differs from the changes in gut structures of snakes or birds [13,16] or
252 bones in iguanas [15], which require energy first to breakdown and then rebuild. Diadema
253 antillarum, however, may be an exception [59] and deserves additional study.
254 Allometric adjustments of jaws of sea urchins indicate changes in available food.
255 Adjustments are reversible and rapid and so fit well with the model presented by Gabriel [10]
256 but additional work is needed that focuses on how the reversible changes explicitly
257 contribute to fitness. If, as suggested, reversible plasticity is very inexpensive in terms both
258 of energy and materials, small changes in survival of large individuals of long-lived species
259 can be very important as shown for the long-lived sea urchin Meocentrotus franciscanus
260 [60]. Fitness measured as population growth rate was most sensitive to changes in survival of
261 large M. franciscanus and the same would be true for long-lived S purpuratus. Changes in
262 jaw allometry would have small benefits in improving survival but because of low cost
263 nevertheless would be adaptive.
264 There is growing interest in the genomics, transcriptomics, and proteomics in studies
265 of plasticity [61-66]. The genome of S. purpuratus has been sequenced [67] and so provides
266 the basis for understanding the design of gene regulatory networks involved in translating
267 environmental cues into changes in relative growth. Various aspects of biomineralization in
268 sea urchins have used molecular techniques [66–70] and regulatory systems would be
269 involved [71,72]. Details of linking the changes in stress associated with available food will
270 involve cell-signaling systems. The changes of relative jaw size we have shown for S.
271 purpuratus may provide a model system for exploring the details of regulatory networks
272 involved in reversible plasticity.
273 274 Acknowledgements
275 Monthly collections and dissections were done by Bruce Miller, Oregon Department of Fish
276 and Wildlife, Charleston, Oregon. Miller also froze body walls and lanterns and sent them to
277 Villanova University for further processing. Collection was done under a permit from the
278 Oregon Department of Fish and Wildlife. Portions of this work were supported by the Ocean
279 Sciences Division Biological Oceanography of the US National Science Foundation grant
280 OCE-0623934. We gratefully acknowledge all of this support.
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Tables and Figures.
Table 1. Analysis of monthly jaw length, J, and test diameter, D, measurements of Strongylocentrotus
purpuratus collected at Gregory Point, Oregon, from January 2007 to July 2009; data were first
transformed using natural logarithms; ln! = ! + !cos 2π τ t ! + ! + !ln! + !cos 2π τ t ! +
! ln! + !! t ! + !! ; definition of parameters given in text.
Table 2. Strongylocentrotus purpuratus at Gregory Point, Oregon, USA; ln Jaw length, J, as a
function of ln diameter, D, and sample (time) as a fixed factor; N = 615; r2 = 0.94.
Table 3. Strongylocentrotus purpuratus at Gregory Point, Oregon, USA; test height as a
function of diameter and time; 20 individuals dissected each month; N=620, r2 = 0.91.
Table 4. Strongylocentrotus purpuratus at Gregory Point, Oregon, USA; ln Jaw length, ln J, as a
function of ln total wet weight, ln T, and sample (time) as a fixed factor; N = 615; r2 = 0.94.
Fig. 1. Monthly samples of Strongylocentrotus purpuratus at Gregory Point, Oregon, showing
the distributions of diameter and wet weight measured on live sea urchins, and length of jaws
(demi-pyramids) measured on bleached specimens.
Fig. 2. Change in ln jaw length adjusted to a mean ln test diameter of 1.78879 (5.982 cm) of
Strongylocentrotus purpuratus at Gregory Point, Oregon, by ANCOVA; sample date was as
fixed factor; ln values back transformed for plotting; fitted line based on parameters in Table 1.
Fig. 3. Comparison of ln jaw length adjusted to a mean ln test diameter of 1.78879 (5.982 cm)
(open circles as in Fig.1) and ln total wet weight adjusted to a mean total wet weight of 4.58381
(97.886 g) (filled circles) showing similar patterns of a cycle and a downward trend; ln values
back transformed for plotting.
Table 1. Analysis of monthly jaw length, J, and test diameter, D, measurements of Strongylocentrotus
purpuratus collected at Gregory Point, Oregon, from January 2007 to July 2009; data were first
transformed using natural logarithms; ln! = ! + !cos 2π τ t ! + ! + !ln! + !cos 2π τ t ! +
! ln! + !! t ! + !! ; definition of parameters given in text.
Model
Cycle and trend
Trend but no cycle
Cycle but no trend
No cycle or trend
param
estimate
se
-95%
+95%
param #
SSE
AICc
wi %
A
-1.3212
0.0163
-1.3532
-1.2891
7
1.7783
-3581.10
99.632
M
0.0580
0.0233
0.0122
0.1037
φ
-1.4254
0.2365
-1.8898
-0.9610
β
0.8220
0.0090
0.8043
0.8397
C
-0.0260
0.0129
-0.0513
-0.0007
B1
-0.0144
0.0029
-0.0202
-0.0086
A
-1.3112
0.0161
-1.3428
-1.2795
4
1.8291
-3569.88
0.366
β
0.8178
0.0089
0.8003
0.8352
B1
-0.0152
0.0030
-0.0210
-0.0094
A
-1.3310
0.0165
-1.3633
-1.2987
6
1.8484
-3559.35
0.002
M
0.0600
0.0234
0.0140
0.1060
φ
-1.3197
0.2256
-1.7627
-0.8767
β
0.8172
0.0091
0.7993
0.8350
C
-0.0266
0.0129
-0.0520
-0.0012
A
-1.3215
0.0163
-1.3535
-1.2894
3
1.9084
-3545.79
0.000
β
0.8126
0.0090
0.7949
0.8303
Table 2. Strongylocentrotus purpuratus at Gregory Point, Oregon, USA; ANCOVA of
ln Jaw length, lnJ, as a function of ln diameter, lnD, with sample time, ti, as a fixed
factor; N = 615; r2 = 0.94.
Source
ss
df
lnD
24.8431 1
ms
p
24.8431 8460.2572 <0.0001
Sample, ti 0.1965
30
Error
583 0.0029
1.7120
F-ratio
0.0066
2.2305
0.0002
Table 3. Strongylocentrotus purpuratus at Gregory Point, Oregon, USA; the natural
logarithm of test height, lnH, as a function of the logarithm of diameter, lnD, and time in
years; 20 individuals dissected each month; N=620, r2 = 0.93.
Effect
Constant
Coefficient
se
t
p
-1.0626
0.0242
-43.9000
<0.001
ln diameter
1.2396
0.0133
92.9184
<0.001
Time (year)
-0.0046
0.0044
-1.0339
0.302
Table 4. Strongylocentrotus purpuratus at Gregory Point, Oregon, USA; N=615
A. ln Jaw as a function of ln wet weight and sample time ,ti; time =0 at 1 January 2007;
r2=0.94; interaction term p=0.09 and analysis redone without interaction.
Effect
Coefficient
SE
t
p
Constant
-1.1451
0.0134 -85.5000 <0.0001
lnT
0.2823
0.0029 98.6934
<0.0001
0.0028 -4.7352
<0.0001
Sample, ti -0.0131
B. ln Jaw length, ln J, as a function of ln total wet weight, ln T, and sample (time), ti, as
a fixed factor; r2 = 0.94; interaction term, ln T × ti, p = 0.74 and so not included in
analysis.
Source
ss
df
ln T
25.06936 1
ms
p
25.0694 9837.7712 <0.0001
Sample, ti 0.17304
30
Error
583 0.0026
1.48565
F-ratio
0.0058
2.2634
0.0002
10
Diameter (cm)
8
6
4
2
1.70
Jaw length (cm)
1.50
1.30
1.10
0.90
0.70
0.50
Total wet weight (g)
300
200
100
0
J M M J S
2007
N
2008
Year
2009
1.20
Jaw length (cm)
1.18
1.16
1.14
1.12
1.10
1.08
J M M J S
2007
N
2008
Year
2009
1.20
Jaw length (cm)
1.18
1.16
1.14
1.12
1.10
1.08
J M M J S
2007
N
2008
Year
2009