Abstract
Littorina planaxis, an intertidal snail, is abundant on a variety of substrata.
Iwo rocks, granite and basalt, were examined to determine if the rock type or
the roughness of the rock influenced the movement pattern or population
density of the snail. A diffusion model was used to quantify the spread of the
snail across the rock in rough, intermediate and smooth areas on each rock
type. Additionally, the fractal dimension of the rock was measured on each
site in an attempt to quantify the topography of the rock and to provide a less
subjective estimate of roughness or smoothness.
The roughness of the rock was not found to have an effect on the
diffusion of the snail. However, there was an almost significant difference
(p=.052) between the movements of the snails on the granite and the basalt,
with snails spreading faster on the granite. Neither the rock type nor the
roughness of the rock was found to influence the population density of the
snails. While the diffusion model provided interesting information about
the movement patterns of the snail, the fractal dimension analysis was not
found to be helpful because no differences could be found in the fractal
dimension of the rock.
Introduction
Littorina planaxis is a an intertidal snail found abundantly on the west
coast of North America from Charleston, Oregon to Baja California. It grazes
on the microalgae which grow upon the rocks, living high in the intertidal
zone (Morris, et al., 1980). The rocks upon which the snails live are highly
variable in topography and composition, providing a range of habitats. The
substrate is likely to play a large role in the ecology of many intertidal
animals. Cracks and indentations in the rock provide the snails with
protection from wave exposure and desiccation. The microalgae they eat may
grow differently from rock to rock. Smoother rock may allow the snail to
crawl farther in a given amount of time, rather than navigating the jagged
bumps in rocks with a more complex topography. Studies on other intertidal
animals have shown that the substrate may affect their population turnover.
density and movement patterns (Underwood and Chapman, 1985; Raffaelli
and Hughes, 1978).
In this study, two aspects of the substrate were examined for their
affects on Littorina planaxis. The topography of two types of rock, granite and
basalt, was examined to find whether the roughness of a rock played a role in
the snail’s movement patterns or population density.
In examining the movement of a population of animals, it can be
difficult to describe which factors play a role in the movement of the group
Measurements can be made of the speed, direction or distance of an
individual, but often cannot be extended to describe the more complex
movements of the population. In most cases, the movement pattern of the
population as a whole is more relevant than that of a given individual. For
example, genetic mixing of a population may be affected by the distance a
group of snails spread in a breeding period. In order to more closely examine
the behavior of a population, the pattern of movements of a group of animals
should be measured rather than those of single animals. A diffusion model
is one way to measure the movement of a population. Diffusion is usually
used to describe the random motion of gas molecules due to thermal energy
However, it can also be used to describe other systems (Berg, 1993). In this
case, à diffusion model is used by analogy to describe the random motion of a
group of snails across a rock face. Using this model, the spread of the snails
across a substrate over a given period of time can be measured. Finding the
rate of spread of the population can be relevant information in learning about
immigration, emigration, and the gene flow within or among populations in
a given area.
Quantifying the differences in the substrate is an obstacle to objectively
examining its effect on intertidal animals. It is easy to categorize different
rocks, but how can the topography of the rock be adequately described? Often
the best attempt when studying the effect of substrate on animals is simply to
use a subjective measure, such as rough or smooth. This is usually less than
ideal because one person's perception of the differences in a rock do not alloy
a comparison to other rocks on an absolute scale. Additionally, as humans
we cannot know how a rock is perceived by an animal on a totally different
size scale. In an attempt to circumvent this problem, the fractal dimension o
the rock was used to describe the complexity of the topography of the rock.
Fractal geometry provides a useful way to describe the irregularities of the
surfaces often found in nature because it takes into account not only the
complexity of the surface but also the scale of its measurement.
Materials and Methods
The experiment was conducted at a point in Carmel Bay where basalt
and granite can be found in close proximity. Three sites were chosen on each
rock type that were visually classified as having rough, intermediate and
smooth topography. The sites were chosen at equivalent tidal heights in the
mid-littorina zone for and checked for similar wave exposure at high tide in
order to control as much as possible for these factors. Three trials were then
run on each of the six sites. On day 0 of each trial, a 0.25m2 quadrat was
cleared of Littorina planaxis, and the number of snails recorded. Thirty of the
snails taken from the site were then chosen randomly, marked with a dot of
enamel paint and placed at a point in the center of the quadrat marked as the
origin. Each day for the following three days, the positions of the snails were
recorded to the closest centimeter as Cartesian coordinates from the origin. A
minimum of 20 snails were recovered at any time. Three replicate diffusion
trials were performed on each of the rock sites.
To find the diffusion of the snails, the spatial variance was calculated at
each time period as:
L(X-X)?
n-1
here X = mean position of the snails
x = position of one snail
n = total f of snails recovered.
Because the diffusion model assumes random movement of the snails, the
diffusion of the snails in both the x and y direction were calculated. Using the
Student's t-test, movement in both directions could not be shown to be
different. Therefore, the radial distance of the snails from the mean position
of the group was considered to be an acceptable measure of diffusion. Because
the day to day measurements of the spread of the snails was so variable, likely
due to changing environmental factors such as weather, temperature or tidal
height, diffusion was measured as the net spread of the snails over the entire
three day period. This tends to average the spread over the three days and
decreases the noise from environmental factors. The diffusion of the snails in
the six sites were then tested for the effect of rock type and roughness using a
nested ANOVA. Because the variances of among sites were heterogeneous
(Cochran’s test), data were log-transformed prior to analysis. A second
ANOVA was performed on the population counts taken from each of the
sites to test for differences in population density between rock types and
topographies. The population data were analyzed in their untransformed
state.
In an attempt to quantify the fractal dimension of the rock, a mold was
taken of each rock site using liquid latex in four cases and Instamold in two
cases. The molds were then cut lengthwise and the profile of the rock traced
so it could be digitized by a computer. A computer program was then used to
analyze the fractal dimension of the rock in the following way (Morse,
Lawton, Dodson and Williamson, 1985). A box was drawn around each
digitized rock profile. The box was then divided into four, and four into
sixteen, up to 1024 boxes. For each level of subdivision, the computer
counted the number of boxes in which the line was found. The slope of the
regression of the natural logarithm of the number of boxes in which the line
was found to the natural logarithm of the size box is an estimate of the fractal
dimension of the rock. Then the digitized line was rotated a random amount
and the same count done. The line was rotated four times, giving four
estimates of the fractal dimension of the rock, which were averaged. A
dimension of 1 indicates a perfectly smooth surface, with increasing values as
the complexity of the surface increases.
Results
The fractal dimensions of the rock profiles were found to lie between
1.08 and 1.12 for all the sites, and were not statistically different among sites.
The mean spatial variance after three days ranged from 246.5 cm'on
the rough basalt site to 777.3 cm’ in the intermediate granite site. In all three
granite sites, the means of diffusion were greater than the means of diffusion
on the three basalt sites. However, the standard error was large because of the
variance in the diffusion rates from day to day and trial to trial (fig. 1). The
pooled mean for the spatial variance of granite sites was 543.4 cm’ while the
pooled mean of the basalt sites was 286.1 cm?
The ANÖVA performed on the diffusion of the snails showed the
roughness of the rock not to have a statistically significant effect on the
diffusion of the snails. However, the diffusion on the granite was found to be
significantly different than the diffusion on the basalt to a level of P =,052
(table 1), with granite having the larger diffusion.
An ANOVA was also done to compare the population densities of the
snails on the six rock sites (table 2). Although a graph shows a trend of
decreasing population density with decreasing rugosity in both rock types, and
a higher mean density in the basalt than the granite, these trends were not
statistically significant (fig. 2).
Discussion
The ANOVA performed on the diffusion data showed no statistical
difference of the movement of Littorina planaxis within the rock types. This
would indicate that the roughness of the rock did not substantially affect the
diffusion of the snails. Similar studies on related intertidal snails, Littoring
unifasciata showed an increased distance traveled on less complex surfaces
related to directional snail movement (Underwood and Chapman, 1989).
However, by using diffusion as a model, the distance traveled by the snails in
this study was only indirectly measured. Rather, the spread of a group of
snails was calculated. Implicit in the calculation of diffusion is a correction
for a changing mean position of the group. The group of snails could travel a
great distance in the same direction, but if the spread of their positions
relative to each other was not great, a small diffusion coefficient would be
calculated. From this data no conclusions can be made about the absolute
distance traveled by the snail, or how it may or may not relate to the
roughness of the substrate.
The ANOVA of diffusion as a function of rock type, although not quite
statistically significant at p =.052, suggests that the diffusion of the snails on
granite may be higher than that on the basalt. Although this experiment does
not meet the traditionally accepted significance level of p-.05, it is close
enough to warrant a closer look at rock type as a factor in snail movement.
Repeated trials with an increased sample size are necessary before these
results can be considered conclusive.
Other rock types should also be examined for an influence on the
movement of the snails. If it were found that the effect of rock type is real.
interesting questions are raised. If it is not the roughness of the different rock
types that influences the movement of the snails, what other aspects of the
rock might? One possibility could be a difference in growth of microalgae on
the two rock types. BecauseLittorina planaxis grazes on the microalgae,
differential abundance or types which grow on the granite and the basalt
might be examined as a factor in the movement of the snails.
The population density of Littorina planaxis was not found to be
dependent on the complexity or type of the substratum, and data on related
species do not show a consistent correlation of topography and population
density. Crevices and pits have been shown to affect population density of
Littorina rudis (Emson and Faller-Fritsch, 1976; Raffaelli and Hughes, 1978)
while Littorina unifasciata did not show any relationship between
topography and population density (Underwood and Chapman, 1985).
Intuitively, it might seem that surface complexities would influence the
population density of snails. In rougher areas, the snails have more cracks
and depressions for protection from wave exposure. Without protection, the
littorines might be more easily washed from the rock, which would tend to
decrease the size of the population. Because all density counts were taken
between the months of April and June, these results reflect only the
springtime population densities. It may be interesting to repeat the
comparison of population densities during the winter months when storms
may impose greater wave forces.
Fractal dimension is a useful tool in describing some aspects of nature.
It has been used to describe the complexity of algae (Dau, 1995), the path of
clownfish while swimming (Coughling, Strickler and Sanderson, 1992), and
the shape of coral reefs (Bradbury and Reichelt, 1983; Mark, 1984). However.
In this study, fractal analysis did not prove to be useful in quantifying the
different complexities of specific sites on rock. Despite the perceived
differences in the complexity of the substrate, the fractal dimension was not
found to be significantly different from site to site.
Using the diffusion model to describe the movement of a population
across a substrate provided interesting information about the snails and
questions for further thought and study, such as the average spread of the
snails over a given period of time. A diffusion coefficient can be calculated
from the temporal rate of change in the variance (Berg, 1993):
05
D-2
9t
here D = diffusion coefficient
og- change in variance
ot = change in time.
With the diffusion coefficient, the spread of the snails over a given period of
time can be calculated.
r(15 - JADt
Here «r' (t)2 - rms distance, or average displacement of snails for a given
time period
diffusion coefficient
time
Using these equations, the average spread of the snails on the basalt and on
the granite can be calculated. The mean variance after three days on basalt
was 286 cm' while on granite the mean variance was 543.4 cm’. Plugging in
these values gives a diffusion coefficient of 47.5 cm’day" for basalt and 90.6
cm'day“ for granite. Using these diffusion coefficients in the second
equation, the average displacement for a snail in one day on basalt is 13.8 cm.
and on granite is 19.0 cm. However, according to the diffusion model the
displacement of the snails from the mean varies with the square root of time.
rather than with time. For one year, the average displacement of a snail from
the mean position on basalt would be 186 cm and on granite would be 257 cm.
If the snails do conform to the diffusion model, this would mean that the
average displacement of the snail in a day may be on the scale of tens of
centimeters, but over a year the average displacement is only on the scale of a
few meters! Of course, snails do not perfectly mimic the motion of
molecules. The diffusion model assumes random motion, with an equal
probability of the snail moving in any direction. In reality, the snails are
likely to be influenced by the cracks in the rock or by following the trail of
öther snails. It would be interesting to track snails over a longer period of
time to see if their movements do match the predicted values. Further
analysis should be conducted to find how diffusion may be related to the
ecology of animals.
References
1.Berg, H., 1983. Random Walks in Biology, Princeton University Press
2.Bradbury, R. & Reichelt, R., 1983. Fractal dimension of a coral reef at
ecological scales. Mar. Ecol. Prog. Ser. vol 10, pp 169-171
3.Coughlin, D., Strickler, J. & Sanderson, B., 1992. Swimming and search
behaviour in clownfish, Amphiprion perideraion, larvae. Anim. Behav, vol
44, pp 427 - 440
4. Dau, B., 1995. The relationship between the fractal dimension of the
intertidal alga mastocarpus papillatus and the abundance of grazing snails.
Unpublished report, Bio 175H. Hopkins Marine Station
5.Emson, R.H. & Faller - Fritsch, 1976. An experimental investigation into
the effect of crevice availability on abundance and size-structure in a
population of Littorina rudis. J. Exp. Mar. Biol. Ecol., vol 23 pp 285-297
6.Mark, D., 1984. Fractal dimension of a coral reef at ecological scales: a
discussion. Mar. Ecol. Prog. Ser. vol 14, pp 293 - 294
7.Morris, Abbot & Haderlie, 1980. Intertidal Invertebrates of California.
Stanford University Press
8.Morse, D.R., Lawton, J.H., Dodson M. & Williamson M., 1985. Fractal
dimension of vegetation and the distribution of arthropod body lengths.
Nature, vol. 314, pp731 -733
9.Petriatis, P., 1982. Occurrence of random and directional movements in the
periwinkle, Littorina Littorea.J. Exp. Mar. Biol. Ecol., vol 59, pp 207 -217
10.Raffaelli, D. & Hughes, R., 1978. The effects of crevice size and availability
on populations of Littorina Rudis and Littorina Neritoides. J. Animal Ecol.
vol. 47, pp71-83
11.Sugihara, G. & May, R., 1990. Applications of fractals in ecology. Trends in
Evol. & Ecology, vol. 5, pp 79 -86
12.Underwood, A. & Chapman, M., 1985. Multifactorial analyses of directions
of movements of animals. J. Exp. Mar. Biol. Ecol., vol 91, pp 17 - 43
13.Underwood, A.J. & Chapman M., 1989. Experimental analyses of the
influences of topography of the subtratum on the movements and density of
an intertidal snail, Littorina unifasciata. J. Exp. Mar. Biol. Ecol., vol 134, pp175
-196
Source
Sum of
F - Ratio
DE
Mean¬
quares
Square
Rock
1.261
1.261
—7.482
0.052
1
Site (Rock)
0.674
0.791
0.169
0.42
ErrOt
4.817
121 0.401
Table 1. Analysis of snail diffusion on granite and basalt. Data are for six sites: rough,
intermediate and smooth on each of the two rock types. (Data are log-transformed for
homogeneous variances.)
Sum-of
Mean-
F-Ratio
Source
Squares
Square
6.589
10706.722
Rock
0.062
10706.7
Site
6499.556
1642.889
1.896 0.176
12 857.111
10285.333
Error
Table 2. Analysis of snail density on granite and basalt. Data are for six sites: rough,
intermediate and smooth on each of the two rock types.
ig. 1. Mean snail variances on six sites: br = rough basalt, bi = intermediate
basalt, bs = smooth basalt, gr = rough granite, gi = intermediate granite, gs -
smooth granite. Error bars show standard errors.
Fig. 2. Mean snail densities on six sites: br = rough basalt, bi = intermediate
basalt, bs = smooth basalt, gr= rough granite, gi = intermediate granite, gs -
smooth granite. Error bars show standard errors.
Spatial Variance, sq.cm
+ snails /(.25 sq.m)
1 would like to thank Mark Denny and Jim Watanabe for their patient
guidance, Brian Gaylord for his countless hours of help, and Judy Thompson
for her understanding with my use of the Hopkins truck.