2.1. Field observations
Field observations were conducted from 1995 to 1999 in two adjacent cattle ranches in the eastern Argentinean Pampas, in the Province of Buenos Aires, Argentina (36°25′S, 56°56′W). These are open grasslands (<10 m elevation), with homogeneous short pastures grazed mainly by cattle, and with scattered marshes and small patches of woodlands (Soriano et al. ). The ranches cover an area of approximately 4300 ha, and support a Rhea population of roughly 400 individuals. There were no natural predators of adult rheas present (i.e., cougar, Felis concolor) but rheas may be occasionally hunted by feral dogs (Canis lupus familiaris) and humans (Fernández and Reboreda ).
The activity of individuals in the study area was video-recorded (Sony Hi8 Camcorder, Sony Corp., New York, USA), at distances of 100–200 m between hours 07:30 to 19:30, from a vehicle. Observations involved focal groups of 1 to 12 individuals. Video-recording began 15–20 minutes after arriving where birds were found, allowing the animals to become accustomed to the presence of the vehicle. Recording was done at different sites each day to avoid sampling the same group, though birds were not marked and could move freely within the study area. Hence, repeated observations of the same birds from day-to-day may have occurred occasionally. Recordings were made for up to 10 minutes or until the focal animal moved out of sight or until any bird in the group showed signs of being disturbed. For the activity analysis, recordings shorter than 3 minutes were excluded. The mean length of recordings was 430 seconds (SD 151, range 187–635 s, n= 173 recordings). Video-tapes were analyzed with Etholog 2.5.2 (Ottoni ). From each video-tape we arbitrarily chose one or two individuals and analyzed the time spent in different behavioral activities (see below). The percentage of time spent in each activity, its frequency of occurrence, and the mean duration were thus estimated. During censuses and observations of individuals, every courtship and aggressive display was also recorded, and the sex (or age) of individuals involved in the aggression noted. Observations of different individuals within the same group were avoided, except in groups of more than four birds in order to reduce the possibility of pseudoreplication.
Seven behavioral categories were defined: feeding or foraging, vigilance, walking, resting, preening, courtship, and aggression. These categories follow those described by Raikow [1968, 1969], Bruning  and Codenotti and Alvarez . Feeding and walking are not exclusive behaviors, as rheas move continuously as they forage. We thus considered birds to be “walking” only when they were moving with their heads leveled with or higher than the body. Birds were considered vigilant when an individual stood with its head up, with its neck either stretched or forming an S above its body. An animal was considered resting when the behavior involved crouching and resting postures (Raikow ). A bird was considered preening when standing and inserting its bill among the feathers of wings or body, or pecking at its own neck or legs. Aggression involved threat displays, pecking, chases, and fights (Raikow , Bruning ).
2.2. The model
The energy that an individual can accumulate over 1 day depends, on the one hand, on the assimilated energy and, on the other hand, on the spent energy. Moreover, the energy that an individual assimilates depends on food type, rate of consumption, and its capacity to assimilate the different components or nutrients. The adult individual's daily energetic cost (field metabolic rate, FMR, measured in kJ/d) includes the costs of maintenance (basal metabolic rate, BMR), and the costs of locomotion, feeding, reproduction as well as other less intensive activities. BMR represents the minimum energy that an individual needs for supporting the basic functions (breathing, circulation, etc.) within the thermoneutral range. Growth is not considered in our computations because only adult individuals breed. Changes in weight reflect accumulation or consumption of fat reserves.
Alternatively, FMR can be estimated using the time that one individual assigns to each activity, and the energetic cost that this activity has. Here we construct a model considering the time that one bird assigns to the different activities, the photoperiod of the days of the observations, and also the range of weights that adults exhibit during the different seasons. Due to the fact that the individuals exhibit distinct behavioral patterns during each segment of the cycle (Carro and Fernández ), the year was split into three seasons: postreproductive (January–March), nonreproductive (April–August) and reproductive (September–December) (Figure 1 and Table 1).
Figure 1. Duration of the three seasons in which was divided the year (postreproductive, nonreproductive and reproductive) and the incubation period. The 38-day period can be located anywhere inside the reproductive season, however with different probability.
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Table 1. Portion of the day that non reproductive male and female individuals dedicate to the various activities during different seasons.
|Sex||Season||Mean portion of the day assigned to each activity|
|Foraging||Preening, aggression and vigilance||Locomotion||Rest during the day|
| Female || Post reproductive ||0.780||0.103||0.115||0|
| || Non reproductive ||0.807||0.093||0.098||0|
| || Reproductive ||0.728||0.082||0.2||0|
| Male || Post reproductive ||0.783||0.115||0.102||0|
| || Non reproductive ||0.792||0.099||0.109||0|
| || Reproductive ||0.615||0.179||0.158||0.031|
The field observations were used for estimating the time that an individual dedicated to each activity over a day. In the model, each observation represents the behavior of one individual along 1 day. In the simulations, one observation made during the corresponding season was randomly assigned to each individual each day.
The daily energetic investment or FMR was estimated, using the field observations, as the sum of the product between the time that the individual assigns to each activity and its energetic cost which also included maintenance costs (Simoy ). This can be written as the vector product of two vectors, B and C, where B is the vector associated with behavior, and C is the vector of the costs of each activity. Each component of B, ti, is the portion of day assigned to activity i ([h/d]) and each component of C, ci, is the energetic cost of activity i ([kJ/h]). The cost of reproduction is added as RC, and takes the null value during non reproductive and post reproductive season. RC will be defined further on. The following equation expresses FMR for 1 day
For modeling purposes, the activities were grouped into five categories: (1) preening, aggression and vigilance, (2) rest during the day, (3) locomotion, (4) feeding or foraging, and (5) rest during the night. Vector B, in this case, has five components ti. It is clear that the first four activities require the light of the day, while the last one takes place in the dark, so that the photoperiod has to be taken into account. Thus, the first four components are obtained from the proportion of day assigned to activity i multiplied by the photoperiod while the last component is the length of the night, so 24 minus the photoperiod. Our observations allow inferring that the individual remains at rest when it is dark. Because of this, B will depend on Julian day d, so we have B(d).
The costs associated with each category (Table 2) were estimated using repose metabolic rate (RMR)-based equations obtained from a study carried out for ostriches (Williams et al. ). The locomotion cost and RMR for rheas was estimated from Taylor et al. . The night repose cost is assumed to be the RMR. Consequently, vector C has five positive components too, each ci being the energetic cost associated with activity i. Since RMR depends on the bird's weight (W), and the cost associated with feeding and locomotion depend on the velocity of displacement during foraging (vf) and locomotion (vl), vector C will depend on W, vf and vl. This means that the cost C depends both on the individual's activity pattern and on the Julian day (photoperiod) and, because costs are associated with the weight of the individual which is not constant, we have C(d, W, vf, vl). Since the cost of each activity depends on the bird's weight, as a first approximation a weight was assigned to each individual for each season, as explained below. The weights of reference were obtained from a rhea population in captivity (M.V. S, unpubl. data).
Table 2. Cost associated with each activity.
|Activity||Locomotion and feeding ([v]= km/h, [activity]= ml O2/g]||Preening, aggression and vigilance, ([activity]= kJ/kg h)||Rest during the day and the night, ([w]= kg, [activity]= kJ/d)|
|Cost|| || || |
The daily energetic costs are added over a full year for estimating the yearly accumulated energetic cost for each adult individual not engaged in reproduction (RC ≡ 0). Since BMR and FMR are given in terms of daily costs, this yearly accumulated energetic cost is then divided by the length of the year to obtain average daily energetic costs, using
where: B(d) and C(d, W, vf, vl) are the vectors B and C for Julian day d, respectively. It is important to keep track of the Julian day because the photoperiod changes from day-to-day and so does the time assigned to each activity since the behavior is assigned during a portion of the day.
As mentioned earlier, the reproductive costs for females and males were estimated separately since the cost associated with the reproduction is different for each sex. In the case of females, reproductive costs include the development of reproductive structures and the energetic content of the egg. For the males, they are associated with the seasonal testicular growth, the production of sperm, and the cost of the incubation and parental care posthatching.
The energetic content of the ovary and oviduct  is directly related to the body size of the female [W] (Walsberg ) according to the relationship
where [E0]= kJ and [W]= kg.
The average weight of a rhea egg is 0.618 kg (Fernández and Reboreda ). This is approximately 2.5% of the corporal weight of an adult female. Walsberg  suggests that the average energetic content of eggs of precocial birds is 7760 ± 1560 kJ/kg. Thus, the cost of producing an egg,Ce(W) is given by
where [W]= kg and [Ce(W)]= kJ.
Then, the total cost of reproduction for females RC(n, W) is given by
where n is the number of eggs and [RC(n, W)]= kJ/d. A female can mate with up to three males and she can lay between six and eight eggs per male (Coddenotti ), so, during a breeding season, an adult female may lay 24 eggs at the most.
Regarding the males, Walsberg  has suggested that daily energetic costs of the seasonal testicular growth in birds are smaller than 2% of BMR, and hence it has been considered negligible. Ricklefs  estimated that the necessary energy for the production of semen is 0.8% of BMR, hence it is also negligible. For an individual weight in the range from 30 to 35 kg the 3% of the bird's BMR falls within the range from 70 to 80 kJ/d.
The most important energetic costs are generated once the male has mated and begins incubating the eggs. The cost of incubation is given by the energy that the male must invest in maintaining the temperature of eggs. It was estimated using the Kendeigh equation (Kendeigh ) which calculates the energy needed to keep the temperature of the eggs within the normal range of incubation (34–36 °C). The equation is
where n is the number of eggs in the nest, w is the average weight of the egg (kg), c is the specific heat of the egg (kJ kg−1°C−1), b is the cooling rate of the egg (°C h−1°C −1), Te is the egg temperature (°C), Tna is the nest air temperature (°C), s is the proportion of the surface of the egg covered by the incubating bird, pc is the proportion of time that the bird remains at the nest and t is the time interval in hours (24 hour if energetic cost is estimated for a day).
The cost of the others activities, mainly feeding, that the male develops while he is away from the nest may be added to the cost associated with maintaining the heat of eggs. The portion of time that the bird is in the nest is not constant: it increases as the incubation advances. Based on Bruning (1974), Fernández and Reboreda , and Piera [1874 in Davis ] observations, we assumed that at the beginning of the incubation the bird leaves the nest up to four times in a day for as much as of 1 hour (observed maximum length) and that during the last part of the incubation (from day 30 to hatching) he remains all the day on the nest. We formulated the portion of the day that the bird is on the nest by
where d is the day of incubation.
Assuming that during the incubation the male leaves the nest only for feeding, the portion of the day when he feeds is given by: 1 −f (d). Then, the FMR for males incubating can be formulated by
where tf and cf are the time spent in feeding and its cost, respectively and RC is the cost associated with incubation.
The value of M was obtained daily considering that the average male incubates 26 eggs whose mean weight is 647 g (Fernández and Reboreda ). The proportion of the egg's surface covered by the bird during incubation was assumed to be 0.4, the specific heat of the egg is 0.78 cal/g °C, the temperature of the eggs incubating was 35 °C, temperature of the nest 20 °C, and cooling rate of the eggs 0.47 °C/°C hour (GJF, unpubl. data). The portion of the day that the male is on the nest changes daily, as was mentioned above.
Thus, the reproductive energetic cost is added to the other accumulated energetic costs,—differentiating between males and females—, for obtaining the yearly accumulated energetic cost for individuals that engage in reproduction. Note that while the reproductive female continues engaging into the usual pattern of activities, the incubating male's only activities are resting over the nest and spending short periods in the vicinity of the nest for feeding. The average daily energetic cost for reproductive individuals can be estimated by dividing this by 365 days.
Since the purpose of this work is to estimate energetic costs and not to calculate an energy balance, it is not necessary to daily update the individuals’ weight. However, it is reasonable to update weights at the beginning of each season.
It is assumed that individuals intend to reproduce and thus choose a strategy that will allow them to gain weight, but not to decrease it. At the beginning of the postreproductive season, the simulation assigns each individual a weight in the range from 21 to 30 kg. At the end of the postreproductive season and beginning of the nonreproductive, another weight is drawn at random and compared to the previous one. If the new weight is higher, it is assigned to the individual, but if it is lower, the individual maintains its weight. The procedure is repeated at the end of this season and beginning of the reproductive season.