circadian rhythms, as you cite, and endogenous and can be measured under constant conditions only.  The name circadian comes from Circa- about, and dien - day, and describes the fact that endogenous circadian rhythms have a period of about 24 hours.  Using the word circadian for describing activity or other patterns in the presence of other environmental cues is wrong and should be avoided.

Generally, Circadian Rhythms are thought of as something that is endogenously generated and has a period of ~24hrs. To definitively characterize a daily rhythm in an environment with an external cue (what chronobiologist call Zeitgebers) that is rhythmically present, you have to isolate the subject from that cue and see if the behavior free runs from the point that their pattern of activity was before removing the cue.

Basically, Circadian biologists want to know if a behavior is driven by an internal clock or the environment. They test this through isolation from environmental cues.

If you want to learn more about the definitions of rhythms, I would suggest you read the classic papers by Pittendrigh and Daan (1976).   

It is common to incorrectly refer to daily patterns of behavior and physiology in field studies with the term "circadian rhythm". However, this inference can only be confirmed experimentally by maintaining the organism under study in constant environmental conditions, such as constant darkness (DD) or very dim light, and constant temperature to discount the real possibility that the organism's rhythmic pattern is due to response to the rhythmic signal or Zeitgeber. If the rhythm persists in constant environmental conditions, it would be considered a circadian rhythm. Typically, these rhythms are expressed with a period of approximately (circa) 24 hrs, and the organism's internal circadian clock is then synchronized or entrained to the Zeitgeber (usually the light:dark cycle.). In the specific case of alligator circadian rhythms, I believe there is a 1976 paper in Science by Lang and a 1980 paper in J. Comp. Physiol. by Kavaliers and Ralph showing free-running circadian rhythms in juvenile alligators that entrain to LD cycles. Therefore, it is reasonable to infer that field studies of the phenology of alligator behavior has as one of its underpinnings a circadian clock.

I would like to add to Nogas answer, that in the strict sense you can use the term circadian rhythm only, if it is recorded in a constant environment, e.g. constant light or constant darkness and no other environmental timeteller. Thus, even in your example of an experimentally controlled light-dark cycle you would have to use the term "daily rhythm" since the animal is in an (artificial) environment with a temporal information, the light dark cycle.

Thank you all for clarifying the use of the term "circadian". I will hereby use "daily activity" for my work. 

That's right Ronny Steen.. according to what your questions using "daily activity" It's the right term to use in the study that you're doing.

Circadian rhythms are ubiquitous among living organisms at almost all levels of biological organization. This implies that the locomotor activity in juvenile Alligator must be under the control of a circadian clock. Therefore, using the term 'circadian rhythm' to describe its locomotor activity is not wrong. There are hundreds and thousands of variables in a single organism those exhibit rhythmic pattern. Let others test if they free run under constant conditions with a tau of nearly 24 hrs. It is really difficult to create constant conditions under laboratory set up. Many people think that LL or DD is enough, but unfortunately they ignore many other factors that are rhythmic in so called constant conditions. You can very well term daily variation in locomotor activity of Alligator as circadian rhythm. The chronobiologists are still in the Pittendrigh and Daan's era - rigid and rigid and rigid.  

Just to add that being alligators poikilotherms a third important characteristic of circadian rhythms, once again according to Pittendrigh, is temperature  compensation. That is to say that the endogenous period of the rhythm remains quite constant at very different temperatures which may have profound effects on may other physiological processes.

So to summarize, circadian rhythms has three main characteristics:

1) They are generated by physiological processes endogenous to the organism, thus they persist in an environment free of time cues, generally referred to as "constant" conditions. The rhythm is then considered to be "free running" from external time signals or zeitgebers and shows a period close to 24 h.

2) The free running rhythm is able to "entrain" or synchronize to environmental time cues related to the day/night cycle, such as the light-dark cycle, or temperature cycles. This property provides the adaptive relevance of circadian rhythms to the organism. As a consequence the endogenous period of rhythmicity becomes equal to the period of the day/night cycle.

3) The free running period is temperature compensated. It remains constant at very different temperatures, in spite that such range of temperatures may affect the rates of enzymatic processes involved in other physiological processes.

In case of poikilothermic animals, such as alligators, this last characteristic of circadian rhythms is quite relevant to provide the organism with"a clock for all seasons", to borrow Dann and Pittendrigh's words. 

All this characteristics can be studied at the behavioral level.

Ronny, I just checked the source from your querry, the exchange between Kanciruk and Lang. Is not only some workers who prefer to restrict the use of the term circadian to endogenous generated rhythms or "clock controlled" rhythms, as Lang states, but as early as 1960, during the Cold Spring Harbor Symposium on Chronobiology,  the scientific community dealing with this topic has already  "agreed" to restrict the use of the term circadian to endogenous generated rhythms. The use of the term diurnal for those whom origin has not been establishe as either endogenous or exogenous.

It is not clear to me from the letters exchange in Science whether the gradual pahse shift in movements between water and land demonstrated by Lang under different light cycles, is related to an adjustment in the phase of the behaviour to photoperiodic changes (increasing the daylength). But I´m not convinced that this may be enough to claim to be an endogenous rhythm. I REALLY WOULD LIKE TO READ OTHER OPINIONS ON THE MATTER OF PHOTOPERIODISM. 

Also, it seems that Vincent Cassone response to your question is making reference the same paper from Lang which generates the exchange between Kanciruk and Lang. 

I think it is time for some definitions, because there might be some confusion about them.

The word 'circadian' means about (circa) a day (dies). Therefore a circadian rhythm is a rhythm of about a day. You can measure these rhythms where ever you like. So you can measure circadian rhythms in free living animals in their natural environment. See for example Van Oort et al 2005.

Where it goes wrong here, is the distinction between Circadian Time (CT) and Zeitgeber Time (ZT) which has everything to do with entrainment. Circadian hours are different from Zeitgeber hours. Circadian Time is based on the endognous rhythm of an organism which is not entrained to a Zeitgeber. Zeitgeber Time is based on the rhythm of the Zeitgeber to which an animal is entrained. You can also talk about Internal and External Time as discussed by Daan & Merrow in 2002.

For a review about entrainment see Roenneberg, Daan & Merrow 2003

So, since you study animals in their natural environment, they are probably entrained to the 24 hours cycle of the sun. Therefore, you can measure their circadian rhythmicity expressed in Zeitgeber or External Time. However, you can not use the expressions Circadian or Internal Time, because your animals were probably not exposed to constant conditions.

http://www.ncbi.nlm.nih.gov/pubmed/16371996

http://www.ncbi.nlm.nih.gov/pubmed/12002157

http://www.ncbi.nlm.nih.gov/pubmed/12828276

To quote from The Concise Oxford Dictionary of Zoology: "circadian rhythm: The approximately 24-hourly pattern of various metabolic activities seen in most organisms.  The rhythm patterns may persist even when the organism is removed from exposure to 24-hour cycles of light and dark.  In a natural habitat the rhythm is 24-hourly: in constant conditions it becomes slightly longer or shorter than 24 hours."

It is derived from the Latin - circa = about; dies = day.

Excellent discussion!

In different words, when evaluating prominent daily variation that occur in endocrine, termoregulatory, cardiac, pulmonary, and other functions, it is important to distinguish between those passively evoked by periodic environmental and behavioural changes ( e.g., the increase in BP/heart rate due to upright posture) and those actively driven by an endogenious oscillatory process (SCN).

Kind regards,

Tatyana