## SUMMARY

Experiments on solar orientation were conducted with adult amphipods
(*Talitrus saltator*) subjected to a reduction and/or phase shift of
the hours of light (L) or dark (D) with respect to the natural photoperiod: 15
h:9 h L:D (controls), 15 h:9 h inverted (i.e. phase-shifted by 12 h and tested
with the sun during the subjective night), 4 h:20 h, 20 h:4 h inverted. The
sandhoppers were released in a confined environment, and individual
orientation angles were recorded. The results confirm the continuous
operation, through the entire 24-h period, of a chronometric mechanism of
compensation for apparent solar motion. They show excellent agreement with a
recently proposed model of compensation for the sun at constant (not
differential) speed and they demonstrate a dependence of the speed of the
chronometric mechanism on the L:D ratio in the 24-h period.

## Introduction

The ability of *Talitrus saltator* to use chronometrically
compensated astronomic references has been recognised for some time
(Pardi and Papi, 1952). The
sun and moon are the main compass orientation references, and the use of these
sources of information allows the sandhoppers to return to their preferred
zone (the band of wet sand) along the shortest path, i.e. the *y*-axis
(sea—land) of the beach (Papi and
Pardi, 1953; Pardi and Papi,
1953). This decreases the effect of numerous biological and
physical stress factors characteristic of the coastal ecotone (a boundary line
between two ecosystems; see Ugolini,
1996).

The sun compass mechanism in sandhoppers has been the subject of thorough investigations (Papi and Pardi, 1953; Pardi and Papi, 1953; Papi, 1955; Pardi and Grassi, 1955). These revealed the mechanism's chronometric basis, which results in compensation for the azimuthal variation of the sun. Experiments utilising photoperiod phase-shifting (Pardi and Grassi, 1955; Marchionni, 1958) and the `longitudinal jump' (i.e. Italian sandhoppers tested in Argentina; Papi, 1955) showed that the ability to compensate for apparent solar motion is not due to local orientation factors. On the basis of experimental observations made on freshly collected individuals, Pardi and Papi (1953) hypothesized that this mechanism compensates precisely for the azimuthal variation of the sun (= differential compensation). However, it should be remembered that the azimuthal speed of the sun varies during the day and the year depending on its height above the horizon. These variations could affect the accuracy of sandhopper orientation (for example, see Ugolini, 2001).

It has been hypothesised (Ugolini and Frittelli, 1998) that compensation for apparent solar motion does not vary during the day but is based on the mean speed of the sun (determined on the basis of the sun's daily azimuthal variation and the number of hours of light).

We have therefore carried out experiments to test the two hypotheses of sun
compensation in *T. saltator*. In particular, we tested whether the
light:dark (L:D) ratio affects the speed of compensation of the sun compass
chronometric mechanism.

## Materials and methods

This study used adult *Talitrus saltator* (Montagu) collected 10-15
days prior to experimental manipulation at a locality in southern Tuscany near
the mouth of the Albegna River. The direction of the *y*-axis
(sea—land) of the beach is 268° (sea) — 88° (land). The
individuals were transported to the laboratory and maintained in plastic
containers with wet sand and food until the tests. Groups of animals were
subjected to different artificial photoperiods, for 7-10 days as follows. (i)
A photoperiod corresponding to the natural photoperiod in duration and phase
(15 h:9 h L:D). (ii) A photoperiod corresponding to the natural photoperiod in
duration, but phase-shifted by a number of hours sufficient to cause a
day—night inversion. Thus, these individuals were tested under the sun
during their subjective night (see Pardi
and Grassi, 1955). (iii) A photoperiod with only 4 h of light and
20 h of dark (4 h:20 h L:D), maintaining the subjective noon coincident with
local noon. Unfortunately, in this case, it was impossible to carry out
experiments in the afternoon. (iv) A photoperiod with 4 h of dark and 20 h of
light (20 h:4 h L:D inverted). These individuals were tested under the natural
sun during the 4 h of their subjective night (subjective midnight corresponds
to local noon).

The experiments were conducted from August to October in 1998 and 1999 in Florence in conditions of natural sun and sky. The tests were performed every 15-30 min throughout the animals' subjective day or night.

The sandhoppers were released into an apparatus described previously (Ugolini and Macchi, 1988; Ugolini, 2001) composed of a transparent Plexiglas bowl (diameter 18 cm) set on a transparent Plexiglas plate placed horizontally on a tripod. A cylindrical white Plexiglas screen (3 cm high) around the bowl prevented the sandhoppers from viewing the surrounding landscape but allowed them to see the sun and sky. Groups of approximately five individuals were released into the bowl containing approximately 1 cm of seawater. Each individual was tested only once, and a single direction per individual was recorded 2 min after release by means of a video camera under the bowl.

Statistical analyses of the circular distributions deriving from each
release were performed using the procedure reported by Batschelet
(1981). For each distribution,
we calculated the mean resultant vector. Rao's test was applied to assess
whether the distribution differed from uniformity (*P*≤0.05). The
bimodality of each distribution was assessed by the possible increase in
length of the mean vector using the method of doubling angles
(Batschelet, 1981). In cases of
bimodality, only the landward resultant was considered. Uniform distributions
were excluded from further analysis. We chose the two-dimensional Cartesian
axes form rather than the circular form to represent the results because we
believed it would describe the results more effectively.

To test the time course of variation in compensation for apparent solar
motion, we used least-squares polynomial regression, testing the successive
powers of the independent variable (time) as separate predictor variables. The
fit of functions to the data was quantified both by adjusted
*r*^{2} (i.e. the adjusted coefficient of determination, the
percentage of the total variability explained by the particular function
taking account of the fact that the parameters are estimated from the data)
and by testing the highest term in the polynomial for significance by
Student's *t*-test. From the different polynomials tested for the same
values, the one with maximum *r*^{2} and the lowest *t*
probability was chosen.

To compare the fitting of the selected curves in
Fig. 2C, we chose the following
method. For each curve, we calculated the sum-of-squared differences between
the mean angle and the corresponding value on the curve; we then divided this
sum by the degrees of freedom to obtain a variance value quantifying the
variability about the regression. To compare these variabilities with the
variability about the polynomial regression, we calculated the variance ratio:
the variance about the regression for a single curve divided by the variance
about the regression for the polynomial regression; the result was compared
with the *F* table for *N*-1 and *N*-3 degrees of
freedom. The *F*-probability gives a measure of similarity between
curves, the highest probability indicating the greatest similarity (see
Armitage et al., 2002).

Tests of the slopes and intercepts and of whether the regression lines were
parallel were carried out with the usual Student's *t*-test
methods.

### Theoretical models of the sandhoppers' sun compass chronometric mechanism

The theoretical variation in the angle of orientation that individuals
should assume with respect to the sun to maintain a constant direction was
calculated according to the following criteria. For individuals tested when
their subjective day corresponds to the natural day, we considered the model
proposed by Ugolini and Frittelli
(1998), i.e. that the
mechanism of compensation for the movement of the sun has a constant speed
during the period of light (or dark) and that its speed is regulated by the
duration of the photoperiod of the previous day (or a few days) and the
azimuthal variation of the sun in that period of the year. Obviously, a
constant speed during the same time period will cause theoretically
predictable orientation `errors' by the animals, as a result of the
discrepancy between the speed of the internal chronometric mechanism and the
azimuthal speed of the sun (which is not constant during the day or year).
This can be represented by the following expression, given that the mean
direction of orientation of the sandhoppers and the solar azimuth at the time
of the release are parameters that derive from the experiment itself:
1
in which *Ey*_{L}(*t*) is the expected *y*-axis
landward direction, expressed in degrees from north, that the sandhoppers must
assume after *t* min from sunrise, *AZs*(*t*) is the
sun's azimuth at the time of the release. The angular speed of correction
*K* is:
2
where *AZs*_{S} and *AZs*_{R} are the azimuth of
the sun at sunset and sunrise, respectively, and *ML* indicates the
minutes of light from sunrise to sunset. Since the sun's azimuthal speed in
the period of the releases is not constant during the day,
*Ey*_{L} will assume a curvilinear form (not a horizontal line)
because of the discrepancy between the speed of the compensation mechanism and
the azimuthal speed of the sun.

To simplify interpretation of the experiments in which the tests occurred
during the sandhoppers' subjective night (inverted photoperiod), it should be
remembered that there are two models of compensation for apparent solar motion
at night: (i) the `*Apis mellifera* model' (Lindauer,
1954,
1957): at night, the sun passes
from west through north to its position in the east in the morning
(Fig. 1A); and (ii) the
`*Talitrus* model' proposed by Pardi
(1954) and not since tested in
amphipods, although confirmed in other riparian or littoral arthropods
(Birukow, 1957;
Ercolini and Scapini, 1976;
Pardi, 1958): compensation for
the sun in the nocturnal period of solar orientation occurs as if the sun,
once it has set in the west, retraces the path covered during the day, i.e.
passing from west to south to east at sunrise
(Fig. 1B). It should be
emphasised that, during the subjective night, the sandhoppers were tested
under the natural sun (which appears to move from east to west). Therefore,
the expected direction of orientation will necessarily be different from that
of the home beach (Fig.
1C).

## Results

The results of tests with individuals subjected to a photoperiod
corresponding to the natural photoperiod during the day
(Fig. 2A) were analysed using
the polynomial regression method described above
(Table 1). Introduction of the
cubic term into the regression equation produces a marked increase in adjusted
*r*^{2} and a significant decrease in the residual sum of
squares, marked by the highly significant *t* value for this
coefficient. This process, with the introduction of subsequent terms, could be
continued, but because of our sample size (*N*=16), it is doubtful
whether any useful purpose would be achieved. The effect of the fifth-degree
term is only marginally significant, and there are five terms in introducing
the polynomial regression and only 16 values. The final model chosen was the
third-degree polynomial (Table
1; Fig. 2A).

Tests with individuals kept under an artificial L:D cycle corresponding to
the natural photoperiod, during the subjective night
(Fig. 2B), gave the best fit to
the regression line (adjusted *r*^{2}=0.335). The slope, which
is positive and statistically significant (*P*=0.029), is significantly
different from that of the expected direction (*P*<0.0001). In fact,
there is a tendency for the animals to assume angles of orientation that are
constantly less than the expected ones.

Fig. 2C,D illustrates the results of experiments with sandhoppers subjected to 4h:20h L:D and 20h:4h L:D inverted (i.e. tested under the natural sun during the 4h of subjective night).

To determine the degree of the polynomial model for the regression of
Fig. 2C, we used the method
described above. The second-degree polynomial gave the best fit: adjusted
*r*^{2}=0.548; residual sum of squares=11940 (d.f.=14);
*F*=10.7; *P*(*F*)=0.0015; *t* for the highest
term=-2.61; *P*(*t*)=0.020. Comparisons of the fitting of the
curves to the second-degree polynomial are reported in
Table 2. The highest
*F*-probability indicates the highest similarity between the model and
the second-degree polynomial. The final model chosen (curve c) was the
second-degree polynomial (Fig.
2C).

For sandhoppers subjected to 20h:4h L:D inverted
(Fig. 2D), the fit to the
regression line is given by *r*^{2} adjusted=0.597; the slope,
which is positive and significant (*P*<0.0005), is not significantly
different from that of the expected direction (*P*=0.109).

The slopes of the regression lines in
Fig. 2B,D are significantly
different (*t*=4.18; d.f.=28; *P*=0.0003).

## Discussion

For nocturnal solar orientation (Fig. 2B,D), the data do not allow us to deduce the form of the curve of the sandhoppers' angular variation. However, for diurnal orientation (Fig. 2A), it appears to be a non-linear function (as it would be if it agreed with the model of differential compensation). Our results support those obtained in previous experiments carried out at a different time of year (June; Ugolini and Frittelli, 1998). Therefore, even though we cannot exclude other sources of error in orientation for sandhoppers, such as (modest) changes in the ephemerids between the date of capture and the date of testing, our model of sun compensation represents a valid alternative to that of differential compensation, at least in sandhoppers.

It is well documented that sunrise is an important *Zeitgeber* for
sandhoppers (Williams, 1980).
Therefore, it should be emphasised that in our experiments the imposed time of
sunrise does not cause a deviation in the mean directions of orientation
corresponding to the theoretically predicted deviation in the case of a
clock-shifting of 6 h and 17 min with respect to the natural sunrise, which
affects the subjective noon; in this case, the mean directions represented in
Fig. 2C should correspond to
lines d or e but not to line b.

Therefore, the relationship between the number of hours of light and the number of hours of dark influences the speed of the chronometric mechanism of compensation for apparent solar motion. However, this implies that the sandhoppers use information about the total azimuthal variation in the sun in that particular period of the year but not about the daily variation in the sun's azimuthal speed. In other words, the speed of the solar compensation mechanism is independent of the height of the sun above the horizon. Although experiments on this topic were not conducted in the present study, this hypothesis is supported by the results of previous experiments in which the solar azimuth was deflected with a mirror: the height of the reflected sun had no influence on the sandhoppers' choice of direction (see Pardi, 1957; Pardi and Ercolini, 1986).

We do not wish to enter the debate about the existence of an ephemerid's function in crustaceans, as demonstrated for insects and birds (see Wehner and Lanfranconi, 1981; Neuss and Wallraff, 1988; Schmidt-Koenig et al., 1991; Wehner and Müller, 1993; Dyer and Dickinson, 1994; Towne and Kirchner, 1998; Wiltschko et al., 2000). However, we would like to emphasize that sandhoppers are neither `homers' nor `central place foragers'; instead, they use a unidirectional, nonvectorial orientation in their zonal recovery (i.e. to return as quickly as possible to the belt of damp sand near the sea). Therefore, it would not be surprising if they used a chronometric system for sun compensation that differed somewhat from (i.e. was simpler than) that used by other animals with different spatio-temporal problems to solve.

Moreover, the present study shows that a single chronometric mechanism
provides for compensation for apparent solar motion both during the day and at
night. Concerning nocturnal compensation for the movement of the sun, our
results do not fully confirm the `*Talitrus* model' proposed by Pardi
(1954); a larger number of
releases is necessary to clarify the matter of sun compensation at night.
However, for the purposes of the present research, it is sufficient to note
the difference between Fig. 2B
and Fig. 2D: the slope of the
regression line in Fig. 2D is
significantly different from that in Fig.
2B, in agreement with the expected effect of a reduction in the
number of hours of dark.

## ACKNOWLEDGEMENTS

We wish to thank Professor Brian A. Hazlett (University of Michigan) for his stimulating discussion and critical reading of the manuscript. This research was financially supported by the Università di Firenze and by the MURST.

- © The Company of Biologists Limited 2002