Altitudinal variation in phase response curves for the Himalayan strains of Drosophila helvetica

In previous research, it was determined that the altitude of origin altered the parameters of photic entrainment and free-running rhythmicity of adult locomotor activity of the high-altitude Himalayan (haH) strain (Hemkund-Sahib, 4121 m above sea level) of Drosophila helvetica compared to the low-altitude Himalayan (laH) strain (Birahi, 1132 m above sea level) of the same species. The present study investigated whether the altitude of origin also affects the parameters of the light pulse phase response curve (PRC) of the adult locomotor activity rhythm of the haH strain. Light pulse PRCs were determined for both strains against the background of constant darkness. Although both were "weak" or type 1 PRCs, the PRC for the haH strain differed from that of the laH strain in three basic parameters. The PRC for the haH strain was of low amplitude, had a protracted dead zone, and showed a ratio of the advance to delay region (A/D>1), while the PRC of the laH strain was characterized by high amplitude, absence of dead zone, and a A/D ratio<1. The asymmetric PRCs of these strains might explain the process of photic entrainment to 24 h light-dark cycles, as the long period of the free-running rhythm (tau) of the haH strain is complemented with a larger advance portion of its PRC (A/D>1), whereas the short tau of the laH strain is matched with a larger delay portion of its PRC (A/D<1). Prolonged dead zone and low amplitude in the PRC of the haH strain imply that the photic sensitivity of this strain has been drastically diminished as an adaptation to environmental conditions at the altitude of its origin. While adults of this strain begin activity in very bright light in the forenoon due to non-permissible low temperature in the morning, the converse is true for the laH strain.     

Phase and Period Responses of the Two-Peak Circadian Rhythm of Trigonoscelis gigas Reitter (Coleoptera: Tenebrionidae) for 6-hr Light Pulses

Circadian rhythm of locomotor activity of the desert beetle T.gigas usually has two narrow peaks: morning (M) and evening (E). While entrained with diurnal (T_z = 24 hr) full or skeleton photoperiods, the M peak is precedes light, while the E peak coincides with light. In a variety of natural and laboratory conditions both peaks tend to maintain a stable mutual phase relationship, about 12 hr apart. The phase responses of the M and E peaks were studied using 6-hr, 30 lx green LED-light pulses applied around ct3, ?t12 and ct18. The PRC for the E peak, plotted versus ct0 (extrapolated moment of light-on) as abscissa, had the same position, as the PRC for the M peak. Both PRCs were asymmetric, but in an opposite way: for the M peak the area of phase advances was bigger, than the area of phase delays, while for the E peak, vice versa. The transient PRCs on day 1, 2 etc. did not differ from the steady state PRC, i.e, the phase response was accomplished virtually in one cycle. Period changes were almost all positive (period became longer after a light pulse). The only "dead zone" in the period response curve (decrease of Dt down to zero) was around subjective evening - early night. Here again, the M peak appeared more "eager" to phase advances than the E peak. Our data support the hypothesis that M and E peaks are controlled by putative separate oscillators. These oscillators seem to have different properties, tend to phase shift to a different extent, and are extremely strongly mutually coupled with phases locked at approximately 180°. The asymmetry of properties of the M and E oscillators has a clear adaptive significance.     

Altitudinal Variation In Phase Response Curves For The Himalayan Strains Of Drosophila Helvetica

In previous research, it was determined that the altitude of origin altered the parameters of photic entrainment and free‐running rhythmicity of adult locomotor activity of the high‐altitude Himalayan (haH) strain (Hemkund‐Sahib, 4121 m above sea level) of Drosophila helvetica compared to the low‐altitude Himalayan (laH) strain (Birahi, 1132 m above sea level) of the same species. The present study investigated whether the altitude of origin also affects the parameters of the light pulse phase response curve (PRC) of the adult locomotor activity rhythm of the haH strain. Light pulse PRCs were determined for both strains against the background of constant darkness. Although both were “weak” or type 1 PRCs, the PRC for the haH strain differed from that of the laH strain in three basic parameters. The PRC for the haH strain was of low amplitude, had a protracted dead zone, and showed a ratio of the advance to delay region (A/D>1), while the PRC of the laH strain was characterized by high amplitude, absence of dead zone, and a A/D ratio<1. The asymmetric PRCs of these strains might explain the process of photic entrainment to 24 h light‐dark cycles, as the long period of the free‐running rhythm (τ) of the haH strain is complemented with a larger advance portion of its PRC (A/D>1), whereas the short τ of the laH strain is matched with a larger delay portion of its PRC (A/D<1). Prolonged dead zone and low amplitude in the PRC of the haH strain imply that the photic sensitivity of this strain has been drastically diminished as an adaptation to environmental conditions at the altitude of its origin. While adults of this strain begin activity in very bright light in the forenoon due to non‐permissible low temperature in the morning, the converse is true for the laH strain.     

The action of skeleton photoperiods on flowering in Lemna perpusilla

The effects of 24 hr cycle skeleton photoperiodic schedulesinvolving two short light pulses on flowering in Lemna perpusillahave been studied. Simulation of complete photoperiods by correspondingskeletal ones is nearly perfect for all photoperiods up to 8hr and is unstable for periods of 9 to 13 hr. A jump in theresponse phase appears when skeleton photoperiods ranging from12 to 13hr are given. For all skeleton photoperiods longer than14 hr the phase is entrained so that it agrees with that givenby skeleton photoperiods of complemental lengths. That is, askeleton photoperiod of 18 hr is equivalent to that of 6 (=24–18) hr. Simulation is largely related to whether thesecond pulse is locked on to "dawn" or to "sunset" dependingon when it falls during the dark period following the firstpulse. The inductive action of skeleton photoperiods that gives unstableentrainment depends on the length of a preliminary dark periodgiven before the plant receives the first pulse, since in theseskeleton schedules the sensitive zone to the second pulse shiftswith the length of the preliminary darkness. Thus, we tentatively conclude that the circadian oscillationin L. perpusilla involves an entrainment mechanism and thatphotoperiodic induction is contingent on the coincidence oflight and a specific inductive phase in oscillation. (Received September 18, 1968; )     

Non-parametric photic entrainment of Djungarian hamsters with different rhythmic phenotypes

To investigate the role of non-parametric light effects in entrainment, Djungarian hamsters of two different circadian phenotypes were exposed to skeleton photoperiods, or to light pulses at different circadian times, to compile phase response curves (PRCs). Wild-type (WT) hamsters show daily rhythms of locomotor activity in accord with the ambient light/dark conditions, with activity onset and offset strongly coupled to light-off and light-on, respectively. Hamsters of the delayed activity onset (DAO) phenotype, in contrast, progressively delay their activity onset, whereas activity offset remains coupled to light-on. The present study was performed to better understand the underlying mechanisms of this phenomenon. Hamsters of DAO and WT phenotypes were kept first under standard housing conditions with a 14:10 h light–dark cycle, and then exposed to skeleton photoperiods (one or two 15-min light pulses of 100 lx at the times of the former light–dark and/or dark–light transitions). In a second experiment, hamsters of both phenotypes were transferred to constant darkness and allowed to free-run until the lengths of the active (α) and resting (ρ) periods were equal (α:ρ = 1). At this point, animals were then exposed to light pulses (100 lx, 15 min) at different circadian times (CTs). Phase and period changes were estimated separately for activity onset and offset. When exposed to skeleton-photoperiods with one or two light pulses, the daily activity patterns of DAO and WT hamsters were similar to those obtained under conditions of a complete 14:10 h light–dark cycle. However, in the case of giving only one light pulse at the time of the former light–dark transition, animals temporarily free-ran until activity offset coincided with the light pulse. These results show that photic entrainment of the circadian activity rhythm is attained primarily via non-parametric mechanisms, with the “morning” light pulse being the essential cue. In the second experiment, typical photic PRCs were obtained with phase delays in the first half of the subjective night, phase advances in the second half, and a dead zone during the subjective day. ANOVA indicated no significant differences between WT and DAO animals despite a significantly longer free-running period (tau) in DAO hamsters. Considering the phase shifts induced around CT0 and the different period lengths, it was possible to model the entrainment patterns of both phenotypes. It was shown that light-induced phase shifts of activity offset were sufficient to compensate for the long tau in WT and DAO hamsters, thus enabling a stable entrainment of their activity offsets to be achieved. With respect to activity onsets, phase shifts were sufficient only in WT animals; in DAO hamsters, activity onset showed increasing delays. The results of the present paper clearly demonstrate that, under laboratory conditions, the non-parametric component of light and dark leads to circadian entrainment in Djungarian hamsters. However, a stable entrainment of activity onset can be achieved only if the free-running period does not exceed a certain value. With longer tau values, hamsters reveal a DAO phenotype. Under field conditions, therefore, non-photic cues/zeitgebers must obviously be involved to enable a proper circadian entrainment.     

Period-Dependent Oscillatory Free-Run in the Locomotor Activity Rhythm of the Field Mouse Mus booduga Under Skeleton Photoperiodic Regimes

The entrainment behaviour of the circadian rhythm of locomotor activity in the field mouse Mus booduga was studied in order to evaluate the role of the animals' free-running period (τ) and the duration of skeleton photoperiods in determining entrainment of animals with τ values beyond and close to the “limits of entrainment”. We predicted that animals with τ lesser than the lower “limit of entrainment” would entrain only to short skeleton photoperiods (≤ 6 h) and not to longer skeleton photoperiods. Experimental animals (n = 25) were entrained to light/dark (LD) 12:12 h schedule, and then subjected to various skeleton photoperiods in which the duration of one of the two intervals of darkness was successively reduced while holding the zeitgeber period (T) constant. Some animals (n = 9) entrained to long as well as short photoperiods, whereas others (n = 5) entrained only to extremely short skeleton photoperiods of 6 h or less. The mean τ of the animals entraining to all photoperiods (23.78 ± 0.22 h) was significantly greater than that of the animals that entrained only to very short skeleton photoperiods (22.43 ± 0.41 h) (t _{df 12} = 5.3, p < 0.001). We also selected a few animals (n = 11) with average τ value of 23.13 ± 0.38 h and studied them under several skeleton photoperiods. To our surprise the animals which were subjected to restricted dark intervals invariably underwent “phase-jump” assuming the longer dark interval as “subjective night”. We suggest that the observed variation in entrainment behaviour might be due to the variation seen among individual animals in τ and the shape of their PRC. These results support the view that the duration of the skeleton photoperiod and the τ of an individual animal interact to determine its entrainment, and underscore the relevance of inter-individual variation in circadian organisation to studies of circadian rhythms.     

A phase response curve for circannual rhythm in the varied carpet beetle <Emphasis Type="Italic">Anthrenus verbasci</Emphasis>

We know that entrainment, a stable phase relationship with an environmental cycle, must be established for a biological clock to function properly. Phase response curves (PRCs), which are plots of phase shifts that result as a function of the phase of a stimulus, have been created to examine the mode of entrainment. In circadian rhythms, single-light pulse PRCs have been obtained by giving a light pulse to various phases of a free-running rhythm under continuous darkness. This successfully explains the entrainment to light-dark cycles. Some organisms show circannual rhythms. In some of these, changes in photoperiod entrain the circannual rhythms. However, no single-pulse PRCs have been created. Here we show the PRC to a long-day pulse superimposed for 4 weeks over constant short days in the circannual pupation rhythm in the varied carpet beetle Anthrenus verbasci. Because the shape of that PRC closely resembles that of the Type 0 PRC with large phase shifts in circadian rhythms, we suggest that an oscillator having a common feature in the phase response with the circadian clock, produces a circannual rhythm.     

Early- and late-emerging Drosophila melanogaster fruit flies differ in their sensitivity to light during morning and evening

The authors derived early and late populations of fruit flies showing increased incidence of emergence during morning or evening hours by imposing selection for timing of emergence under 12:12 h light/dark (LD) cycles. From previous studies, it was clear that the increased incidence of adult emergence during morning and evening hours in early and late populations was a result of evolution of divergent and characteristic emergence waveforms in these populations. Such characteristic waveforms are henceforth referred to as "evolved emergence waveforms" (EEWs). The early and late populations also evolved different circadian clocks, which is evident from the divergence in their clock period (τ) and photic phase response curve (PRC). Although correlation between emergence waveforms and clock properties suggests functional significance of circadian clocks, τ and PRCs do not satisfactorily explain the early and late emergence phenotypes. In order to understand the functional significance of the PRC for early and late emergence phenotypes, the authors investigated whether circadian clocks of these flies exhibit any difference in photosensitivity under entrained conditions. Such differences would suggest that the light requirement for circadian entrainment of the emergence rhythm in early and late populations is different. To test this, they examined if early and late flies differ in their light utilization behavior, first by assaying their emergence rhythm under complete photoperiod and then in three different skeleton photoperiods. The results showed that early and late populations require different durations of light during the morning and evening to achieve their EEWs, suggesting that for the circadian entrainment of the emergence rhythm, early and late flies utilize light from different parts of the day.     

Phase and period responses of the circadian system of mice (Mus musculus) to light stimuli of different duration

To understand entrainment of circadian systems to different photoperiods in nature, it is important to know the effects of single light pulses of different durations on the free-running system. The authors studied the phase and period responses of laboratory mice (C57BL6J//OlaHsd) to single light pulses of 7 different durations (1, 3, 4, 6, 9, 12, and 18 h) given once per 11 days in otherwise constant darkness. Light-pulse duration affected both amplitude and shape of the phase response curve. Nine-hour light pulses yielded the maximal amplitude PRC. As in other systems, the circadian period slightly lengthened following delays and shortened following advances. The authors aimed to understand how different parts of the light signal contribute to the eventual phase shift. When PRCs were plotted using the onset, midpoint, and end of the pulse as a phase reference, they corresponded best with each other when using the mid-pulse. Using a simple phase-only model, the authors explored the possibility that light affects oscillator velocity strongly in the 1st hour and at reduced strength in later hours of the pulse due to photoreceptor adaptation. They fitted models based on the 1-h PRC to the data for all light pulses. The best overall correspondence between PRCs was obtained when the effect of light during all hours after the first was reduced by a factor of 0.22 relative to the 1st hour. For the predicted PRCs, the light action centered on average at 38% of the light pulse. This is close to the reference phase yielding best correspondence at 36% of the pulses. The result is thus compatible with an initial major contribution of the onset of the light pulse followed by a reduced effect of light responsible for the differences between PRCs for different duration pulses. The authors suggest that the mid-pulse is a better phase reference than lights-on to plot and compare PRCs of different light-pulse durations.     

Latitudinal clines in the properties of a circadian pacemaker

The circadian rhythm of eclosion activity and its pacemaker were analyzed in a series of latitudinal races of Drosophila auraria ranging from 34.2 degrees to 42.9 degrees N in Japan. The phase of the rhythm (psi EL) to the daily photoperiod (PP) changes as daylength is increased, and the slope of psi EL (PP) changes with latitude. Is is sufficiently greater in the north to cause a phase reversal of northern and southern races on long versus short photoperiods. This reversal is found in assays of the pacemaker's phase (psi PL) as well as that of the rhythm (psi EL). Assay of the pacemaker shows that its period (tau) is longer in northern than in southern races, and that the amplitude of its phase response curve (PRC) is lower in the north. The period of the rhythm in all latitudinal races is longer than 24 hr in short photoperiods (LD 1:23), but is probably less than 24 hr (as an aftereffect of photoperiod) in longer days such as LD 14:10. The observed north-south differences in the phase relation of both pacemaker and rhythm to the light cycle are explained by the latitudinal clines in pacemaker properties and a postulated aftereffect of photoperiod on tau. It is suggested that the latitudinal cline in PRC amplitude has functional significance in conserving the amplitude of the pacemaker's signal to the rest of the system it times. Computer simulation shows that without such a reduction in the perceived light intensity, pacemaker amplitude will be lowered by the increase in duration of the daily light at higher latitudes.     

Entrainment of the Two-Peak Circadian Rhythm of Trigonoscelis gigas Reitter (Coleoptera: Tenebrionidae) with non-24-hr Zeitgebers

Circadian rhythms of locomotor activity of the desert beetles T.gigas were entrained with skeleton photoperiods (2x2 hr per circadian cycle 30 lx green LED light pulses). The Zeitgeber period was stepwise reduced by 1 hr down to 22 hr or increased up to 26 hr. Within the range of entrainment, the phase angle Ψ of a circadian rhythm with respect to light depends upon the period of Zeitgeber differently for the morning (M) and evening (E) peak: M is easier to advance, while E is easier to delay. Beyond the range of entrainment both peaks became free-running with some relative coordination. Masking (direct stimulation of activity by light) occurred only during the subjective night, and never in subjective day. In few cases one of two peaks became free-running while its counterpart remained entrained, suggesting that each of the two peaks has its own visual input and can be entrained by light. These results are in agreement with the difference in the PRC shape for the M and E peaks, and support the hypothesis that M and E peaks are controlled by two functionally separate oscillators that have polar different properties, and are extremely strongly mutually coupled with phases locked at about 180°.     

Circadian Rhythms,Monoamines and Behavior: Introduction and Overview

Predictions for the phase angle differences (ψ) between the activity rhythm and the zeitgeber for different skeleton photoperiods based on the phase response curve (PRC) and the free-running period (τ) of the field mouse Mus booduga were made. These predictions were based on two assumptions: (i) The PRC for light pulses of 1 h duration and ca 45 lx intensity should resemble the PRC for pulses of 15 min duration and 1000 lx intensity. (ii) One of the two light pulses (LP) constituting the skeleton photoperiod should always impinge upon that zone of the PRC which has a slope of < ?2. Experiments were performed to compare ψ under skeleton and complete photoperiods and also to test the assumptions made in predicting ψ. The results show that the basic oscillation underlying the activity rhythm of the field mouse Mus booduga undergoes a “phase-jump” when two brief light pulses (of 1 h duration) were used to mimic a photoperiod of 20 h. The ψ values obtained for skeleton photoperiods closely match the predicted values. Under complete photoperiods, the experimentally obtained values match the predictions only up to 16 h. We conclude therefore that beyond this photoperiod, two discrete light pulses may not be sufficient to simulate the effect of a complete photoperiod.     

Altitudinal variation in the circadian rhythm of oviposition in Drosophila ananassae

The effect of altitude on four basic properties of the pacemaker controlling the circadian rhythm of oviposition in two strains of Drosophila ananassae was determined. The high altitude (HA) strain from Badrinath (5123 m above sea level) had a low amplitude peak in the forenoon while the low altitude (LA) strain from Firozpur (179 m a.s.l.) had a high amplitude peak after the lights-off of LD 12:12 cycles. Free running periods in continuous darkness were about 22.6 and 27.4 h in the HA and LA strains, respectively. The light pulse phase response curve (PRC) for the HA strain showed a low amplitude and a dead zone of 8h; the ratio for the advance to delay region (A/D) was less than 1, while the PRC for the LA strain had a high amplitude, which was devoid of a dead zone and showed a ratio of A/D > 1. The magnitude of the delay phase shifts at CT 18 evoked by light pulses of 1 h duration, but varying light intensity was significantly different in the HA and LA strain, which suggests that the photic sensitivity of the clock photoreceptors mediating the phase shifts had been affected by the altitude.     

Effects of photoperiod and aging on locomotor activity rhythms in the onion fly,Delia antiqua

At photoperiods longer than 8h per 24h, adults of the day-active onion fly Delia antiqua showed a major peak of locomotor activity in the late photophase and also bursts of activity induced by lights-on or lights-off. At shorter photoperiods the activity peaks fused. After transfer from long photoperiods to constant darkness (DD), the rhythm free-ran, but only the major peak persisted. This suggests that only the major peak is controlled by the circadian pacemaker. At long photoperiods, the daily phase of the major peak occurred progressively later with age. As a result, the activity at short photoperiods often shifted from photophase to scotophase in old flies. The free-running period (tau) also changed with age; tau was shorter than 24h until 14-20 days after eclosion and thereafter became longer, but a few individuals repeated changes in tau. The phase delay of locomotor activity with age in D. antiqua would be attributable to the increase in tau.     

Analysis of entrainment of circadian oscillators by skeleton photoperiods using phase transition curves

A skeleton photoperiod consists of two short pulses which are applied on the circadian oscillator at times corresponding to the beginning and to the end of a continuous light stimulus. To study several problems in entrainment of circadian rhythms by skeleton photoperiods, we develop a simple diagrammatic solution of the steady state entrainment making use of phase transition curves which are directly gotten from phase response curves. The graphical method is simple and systematic to study entrainment by light cycles with various day lengths. As the method is also intuitive, we can easily examine three problems. (1) In Drosophila the phase relation (ψ) between rhythm and light cycle is a continuous function of day length of skeleton photoperiods up to about 12 h, but a marked discontinuity (ψ-jump) sets in between 13 and 14h. By the diagrammatic method we find that ψ-jump is mathematically a bifurcation phenomenon. (2) The action of photoperiods up to about 12 h is fully simulated by two 15-min skeleton pulses. Do 3-min skeleton pulses imitate the complete photoperiods? We find that pulse width is arbitrary to some extent. (3) Why skeleton photoperiods up to about 12 h are good models of complete photoperiods? The reason is the small amplitude and the nearly symmetrical form of phase response curves in the subjective day.     

Photic resetting and entrainment in CLOCK-deficient mice

Mice lacking the CLOCK protein have a relatively subtle circadian phenotype, including a slightly shorter period in constant darkness, differences in phase resetting after 4-hour light pulses in the early and late night, and a variably advanced phase angle of entrainment in a light-dark (LD) cycle. The present series of experiments was conducted to more fully characterize the circadian phenotype of Clock(-/-) mice under various lighting conditions. A phase-response curve (PRC) to 4-hour light pulses in free-running mice was conducted; the results confirm that Clock(-/-) mice exhibit very large phase advances after 4-hour light pulses in the late subjective night but have relatively normal responses to light at other phases. The abnormal shape of the PRC to light may explain the tendency of CLOCK-deficient mice to begin activity before lights-out when housed in a 12-hour light:12-hour dark lighting schedule. To assess this relationship further, Clock(-/-) and wild-type control mice were entrained to skeleton lighting cycles (1L:23D and 1L:10D:1L:12D). Comparing entrainment under the 2 types of skeleton photoperiods revealed that exposure to 1-hour light in the morning leads to a phase advance of activity onset (expressed the following afternoon) in Clock(-/-) mice but not in the controls. Constant light typically causes an intensity-dependent increase in circadian period in mice, but this did not occur in CLOCK-deficient mice. The failure of Clock(-/-) mice to respond to the period-lengthening effect of constant light likely results from the increased functional impact of light falling in the phase advance zone of the PRC. Collectively, these experiments reveal that alterations in the response of CLOCK-deficient mice to light in several paradigms are likely due to an imbalance in the shape of the PRC to light.     

External coincidence and photoperiodic time measurement in the spider mite Tetranychus urticae

The incidence of diapause in the spider mite Tetranychus urticae was predicted for various photoperiodic regimes, according to the external coincidence model of photoperiodic time measurement. A phase response curve was constructed for the hypothetical photoperiodic oscillator in these mites: entrainment of this photoperiodic oscillator to a variety of ‘complete’ and ‘skeleton’ photoperiods was calculated using a transformation method for circadian rhythms. The external coincidence model proved adequate to describe experimental results with T. urticae in ‘complete’ photoperiods (T = 24 hr), symmetrical ‘skeleton’ photoperiods (T = 24 hr), asymmetrical ‘skeleton’ photoperiods (T = 24 hr) (night-interruption experiments), and ‘resonance’ experiments, in which the light component of a light/dark cycle was held constant at 8 hr and the dark component was varied over a wide range in successive experiments, providing cycles with period lengths up to 92 hr. The external coincidence model proved inadequate to explain results obtained in a ‘T-experiment’ with T. urticae comprising 1 hr pulses of light in a cycle of LD1:17.5 (T = 18.5 hr) with the first pulse of the train starting at different circadian phases. The validity and limitations of the external coincidence model as an explanation of photoperiodic time measurement in T. urticae are discussed in view of the above results.     

PHOTIC ENTRAINMENT OF CIRCADIAN ACTIVITY PATTERNS IN THE TROPICAL LABRID FISH HALICHOERES CHRYSUS

Yellow wrasses (Halichoeres chrysus) show clear daily activity patterns. The fish hide in the substrate at (subjective) night, during the distinct rest phase. Initial entrainment in a 12h:12h light-dark (12:12 LD) cycle (mean period 24.02h, SD 0.27h, n = 16 was followed by a free run (mean period 24.42h, SD 1.33h) after transition into constant dim light conditions. Light pulses of a comparable intensity as used in the light part of the LD cycles did not result in significant phase shifts of the free-running rhythm in constant darkness. Application of much brighter 3h light pulses resulted in a phase-response curve (PRC) for a fish species, with pronounced phase advances during late subjective night. The PRCs differed from those mainly obtained in other vertebrate taxa by the absence of significant phase delays in the early subjective night. At that circadian phase, significant tonic effects of the light pulses caused a shortening of the circadian period length. Entrainment to skeleton photoperiods of 1:11 LD was observed in five of six wrasses exposed, also after a 3h phase advance of this LD cycle. Subsequently, a 1:11.25 LD cycle resulted in entrainment in four of the six fish. It is suggested that the expression of the circadian system in fish can be interpreted as a functional response to a weak natural zeitgeber, as present in the marine environment. This response allows photic entrainment as described here in the yellow wrasse. (Chronobiology International, 17(5), 613–622, 2000)     

Fault tolerance in the cardiac ganglion of the lobster

Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes of phase-locked entrainment of an N-oscillator ring network. We extend this work by developing a mathematical criterion to determine the local stability of such a mode based on the PRCs. Our method does not assume symmetry; neither the oscillators nor their connections need be identical. To use these techniques for predicting modes and determining their stability, one need only determine the PRC of each oscillator in the ring either experimentally or from a computational model. We show that network stability cannot be determined by simply testing the ability of each oscillator to entrain the next. Stability depends on the number of neurons in the ring, the type of mode, and the slope of each PRC at the point of entrainment of the respective neuron. We also describe simple criteria which are either necessary or sufficient for stability and examine the implications of these results. Received: 2 April 1998 / Accepted in revised form: 2 July 1998