## 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

*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:

*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).

Degree . | r^{2} adjusted
. | Residual sum of squares . | d.f. . | F
. | P(F)
. | t for the highest term
. | P(t)
. |
---|---|---|---|---|---|---|---|

1 | 0.394 | 2240 | 14 | 10.75 | 0.0055 | -3.28 | 0.005 |

2 | 0.349 | 2232 | 13 | 5.03 | 0.0240 | 0.20 | 0.843 |

3 | 0.634 | 1159 | 12 | 9.67 | 0.0016 | 3.34 | 0.006 |

4 | 0.602 | 1155 | 11 | 6.68 | 0.0056 | -0.19 | 0.853 |

5 | 0.708 | 770 | 10 | 8.28 | 0.0025 | -2.23 | 0.050 |

Degree . | r^{2} adjusted
. | Residual sum of squares . | d.f. . | F
. | P(F)
. | t for the highest term
. | P(t)
. |
---|---|---|---|---|---|---|---|

1 | 0.394 | 2240 | 14 | 10.75 | 0.0055 | -3.28 | 0.005 |

2 | 0.349 | 2232 | 13 | 5.03 | 0.0240 | 0.20 | 0.843 |

3 | 0.634 | 1159 | 12 | 9.67 | 0.0016 | 3.34 | 0.006 |

4 | 0.602 | 1155 | 11 | 6.68 | 0.0056 | -0.19 | 0.853 |

5 | 0.708 | 770 | 10 | 8.28 | 0.0025 | -2.23 | 0.050 |

Total sum of squares 3959, d.f. 15.

The table includes the following: the degree of polynomial regression(Degree); the adjusted coefficient of determination (*r*^{2});the sum of squares about the regression (Residual sum of squares) and degrees of freedom (d.f.); the variance ratio (*F*) and the probability value, *P(F)*, testing the significance of the decrease in residual mean square; Student's *t*-test (*t* for the highest term) and its *P(t)* value for the introduction of the last term in the regression equation.

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).

Curves . | Variance . | d.f. . | F
. | P(F)
. |
---|---|---|---|---|

c | 853 | 14 | — | — |

a | 5637 | 16 | 6.61 | 0.00048 |

b | 1408 | 16 | 1.65 | 0.176 |

d | 1789 | 16 | 2.10 | 0.085 |

e | 1891 | 16 | 2.22 | 0.070 |

Curves . | Variance . | d.f. . | F
. | P(F)
. |
---|---|---|---|---|

c | 853 | 14 | — | — |

a | 5637 | 16 | 6.61 | 0.00048 |

b | 1408 | 16 | 1.65 | 0.176 |

d | 1789 | 16 | 2.10 | 0.085 |

e | 1891 | 16 | 2.22 | 0.070 |

The Table includes the following: identifiers of the curves in Fig. 2C (a—e); mean squares about the regression (Variance) and degrees of freedom (d.f.); the variance ratio (*F*) and the probability value, *P*(*F*),for comparison of variability about each curve and polynomial regression.

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. 2Band 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.

## References

**Armitage, P., Berry, G. and Matthews J. N. S.**(

**Batschelet, E.**(

**Birukow, G.**(

*Velia currens*F.(Heteroptera) am Tage und zur Nachtzeit. I. Herbst-und Winterversuche.

**Dyer, F. C. and Dickinson, J. A.**(

**Ercolini, A. and Scapini, F.**(

*Paederus rubrothoracicus*Goeze e

*Stenus bipunctatus*Erichson).

**Lindauer, M.**(

**Lindauer, M.**(

**Marchionni, V.**(

*Talorchestia deshayesei*Aud. (Crustacea, Amphipoda).

**Neuss, M. and Wallraff, H. G.**(

**Papi, F.**(

*Talitrus saltator*(Montagu) (Crustacea, Amphipoda).

**Papi, F. and Pardi, L.**(

*Talitrus saltator*(Montagu) (Crustacea,Amphipoda). II. Sui fattori che regolano la variazione dell'angolo di orientamento nel corso del giorno. L'orientamento di notte. L'orientamento diurno di altre popolazioni.

**Pardi, L.**(

*Talitrus saltator*(Montagu) (Crustacea, Amphipoda): l'orientamento al sole degli individui a ritmo nictiemerale invertito, durante la `loro notte'.

**Pardi, L.**(

**Pardi, L.**(

*Phaleria provincialis*Fauv. (Coleoptera): il comportamento a luce artificiale durante l'intero ciclo di 24 ore.

**Pardi, L. and Ercolini, A.**(

**Pardi, L. and Grassi, M.**(

*Talitrus saltator*(Montagu) and

*Talorchestia deshayesei*(Aud.) (Crustacea, Amphipoda).

**Pardi, L. and Papi, F.**(

*Talitrus saltator*(Montagu).

**Pardi, L. and Papi, F.**(

*Talitrus saltator*(Montagu) (Crustacea,Amphipoda). I. L'orientamento durante il giorno in una popolazione del litorale tirrenico.

**Schmidt-Koenig, K., Ranvaud, R., Ganzhorn, J. U. and Gasparotto,O. C.**(

**Towne, W. F. and Kirchner, W. H.**(

**Ugolini, A.**(

**Ugolini, A.**(

**Ugolini, A. and Frittelli, F.**(

**Ugolini A. and Macchi, T.**(

*Talitrus saltator*Montagu(Amphipoda — Talitridae).

**Wehner, R. and Lanfranconi, B.**(

**Wehner, R. and Müller, M.**(

**Williams, J. A.**(

*Talitrus saltator*(Crustacea, Amphipoda).

**Wiltschko, R., Walker, M. and Wiltschko, W.**(