APPLICABILITY OF THE MODELS
The suggested logistic model for describing the dependency of survival on time (equation 1) fitted the experimental data well, as indicated by the high χ2 values (33–168) from the maximum likelihood method. Equation
2 describing survival as a function of both time and temperature also fitted well, as shown by the χ2 and the squared correlation coefficient of the least squares method. Thus, these equations are valuable in the analysis of survival data in cryoscience when parametric description is needed.
There are also other equations/models that describe the sigmoid shape of the relationship which can be used in the three-dimensional description of survival dependence on both time and temperature. The Gompertz formula is based on the exponential increase of the hazard function over time, therefore there is a double exponential, e.g. in the form (modified after Batschelet 1973):
The Gompertz function has been used by actuaries and has been applied in entomology, e.g. to mortality rate in Blow Fly (Readshaw & van Gerven 1983); however, the analysis uses an incorrect least squares loss function. The problem is that the computing of parameters using maximum likelihood estimation of the equation is not available in most statistical packages. In practice, the least squares method is widely used and does not cause severe deviations. If visual observation shows that the resulting curve runs through the data points then the use of the least squares method is justified.
The Weibull model has been used a few times to compare survival after cold exposure (Worland, Block & Rotheery 1992; Han & Bauce 1995) and it seems a reasonable choice in two-dimensional modelling (survival as a function of either time or temperature, modified after Dent 1997):
The model becomes complicated (with four parameters) in three-dimensional modelling (survival as a function of both time and temperature), but it represents an advantage, since separated parameters (and hence ‘weights’) are given to the two independent variables.
The listed methods (logistic, Gompertz and Weibull) have advantages over others in plotting survival data. Salt (1961, 1963) used a semilogarithmic plot of survival with time on a linear scale, and the number of unfrozen individuals on a logarithmic scale. This type of transformation produces an almost linear decrease of survival with time over a wide range of time. Values may, however, deviate in margins (very short and very long exposures). Zero survival is necessarily excluded from the plot, although it has its meaning. The logit transformation used by Turnock (1993) excludes even initial total (unit or 100%) survival.
There can be low precision in parameter estimation of any model if the range of S is low, mainly if it does not contain the point of inflection, or the value 0·5. Turnock’s method is useful in integrating and accumulating the chill injury through a series of different temperatures and exposure periods. In the cases where the temperature fluctuates and rises to the zone of repair of cold injury, however, the partial exposures may not be additive and a different approach may be necessary.
The calculated ULCIZ in summer acclimated O. cincta (+1·4°C) might be a realistic estimate. However, temperatures slightly above zero induce acclimation (van der Woude & Verhoef 1986); thus, after about 2 weeks of exposure, the ‘summer’ animals will change to ‘winter’ animals.
The parameters of equation 2 were estimated for the published data on survival of Lacanobia atlantica (Table 1 in Turnock 1993) as follows: a = 1·23, b = 0·0106, c = – 15·6, χ2 = 1124, variance explained (using least squares loss function) R2 = 0·69. The lower correlation coefficient is probably caused by the few survival values in the data matrix that are near to 50%. Estimation of the ULCIZ (– 15·6 °C) corresponds with the raw data and also with Turnock’s hyperbola (Fig. 2 in Turnock 1993). His estimation of ULCIZ, based on nonzero slope of fitting polynomial, was between – 12·6 and – 15 °C.
Where ULCIZ lies much below zero and does not involve acclimation, there might be other objections in considering this estimation to be valid in long-term experiments (or for long storage purposes). Chill injury at moderate temperatures and during moderate exposure periods may be attributable to metabolic disorder or phase changes in membranes, while other types of injury, such as desiccation of the supercooled organism, become more important after long exposure (see Ring & Danks 1994). Thus the actual ULCIZ will tend to be much higher, mainly depending on what is considered an ecologically valid duration of exposure. In tropical and parasitic species, the instantaneous cause of injury and death at low (but still positive) temperatures might be due to starvation of the inactivated insect.
Although the estimation of ULCIZ may seem valid, the estimation of the lower lethal temperature in brief exposures, based on equation 2 and parameters obtained for longer periods of time, is erroneous. The value LT50(24 h) = – 12·2 °C for summer acclimated O. cincta is incorrect, as the SCP of the freeze-susceptible animals fluctuates between – 6 and – 9 °C in summer (van der Woude 1987), and previous studies estimated the absolute lower lethal temperature LT100(24 h) at – 6·5 °C (van der Woude & Verhoef 1986). In Lacanobia atlantica, there was 18% survival at – 22·4 °C (Turnock 1993) with a mean SCP of – 26·4 °C; while the value we have calculated from equation 4 LT18%(4 days) = – 274 °C, a temperature of no physical sense.
The above-mentioned contradictions are examples of different processes causing injury and death additional to the chill injury (metabolic disorder and membrane phase changes), i.e. freeze injury. Probability of freezing increases dramatically at lower temperatures and freezing prevails over chill injury, making equation 2 of little value. When describing mortality within the whole range of subzero temperatures, equation 2 should be combined with another equation for freezing probability. This may be a negative exponential, without a lag in the initial period. In the case of O. cincta, two such terms should be added to equation 2 as the distribution of SCPs in O. cincta is bimodal (van der Woude 1987).
IMPROVEMENT OF SURVIVAL
Survival of exposure at – 3 °C, a temperature that normally causes death in 50% of animals after 3 days and in most individuals after 4 days, was much higher when interruption procedures were applied. The warm interval resets the physiological state of the animals towards the initial values. The chill injury during subsequent cold exposure was almost the same as for the initial exposure. Therefore, chill injury did not accumulate from day to day; the effects of chilling were almost completely reversed or repaired by returning the insects to higher temperatures.
Chill injury was reversible for about 2 days, corresponding to the time lag after which survival started to decrease steeply. Following the reversible phase (after 3 days’ exposure), even living animals did not recover during the warm interval and died during the following cold exposure. This suggests a limit of interpreting results of survival experiments when survival is counted shortly after recovering from the cold exposure, as was the case in the present study. Observing survival for some substantial time after the end of the exposure or establishing viable progeny is highly recommended (Bale 1987; Baust & Rojas 1985).
The ability to recover without accumulating chill injury might be of ecological importance for many temperate invertebrates, since alternating cooling and warming periods during autumn and spring are more common (measured on the surface, not deeply in soil) than prolonged periods of constant cold. The temperatures that occur during the day time, alternating with freezing nights, will be lower than the 19 °C used in the present experiments. The improvement of survival acquired after 2 h at 5 °C was weak (similar to the effect of 19 °C lasting only 0·5 h). However, when considering the effect of the duration of the warm interval, a day at + 5 °C may ensure surviving a night with temperatures below zero.
The possibility of improving survival by the alternation of cold and warm intervals for a long period of time may have an application in long-term storage of insects. Recently, Gagne & Coderre (1996) studied survival in larvae of the Ladybeetle Coleomegilla maculata, at 4 and 8 °C, and their subsequent development and voracity. Survival was high after 2 weeks’ exposure but decreased dramatically after 3 weeks. Application of high-temperature intervals might extend the storage period.
Turnock & Bodnaryk (1991, 1993) reported on the importance of poststress temperature and its duration on the expression of chill injury in Mamestra configurata. In O. cincta, the non-lethal chill injury was repetitively reversed by a warm interval to provide a chance to survive subsequent cold exposure. Turnock et al. (1983) found that survival of M. configurata pupae given a continuous exposure to – 10 °C and an exposure interrupted by 28 days at 0 or – 5 °C did not differ, indicating that repair of cold injury does not occur at or below 0 °C. Survival was even slightly less in the butterfly Inachis io when the cold exposure (– 5 °C) was interrupted daily by high temperature (+ 10 °C) (Pullin & Bale 1989). Survival of the weevil Rhynchaenus fagi at temperatures cycling from + 2 to – 15 °C over 48 h was higher than survival at a constant – 15 °C, but survival at cycling + 10 to – 5 °C was less than in constant – 5 °C (Coulson & Bale 1996). Therefore a distinction should be made between temperatures which promote repair of injury and those that cause deacclimation.
Winter acclimated animals survived in high numbers at all combinations of time and temperature, either continuous or interrupted. Thus, it can be concluded that short warm intervals did not cause a higher mortality, i.e. did not deacclimate the winter animals to the summer level. The possibility that the summer animals exposed to repetitive cold and warm intervals do acclimate to low temperature cannot be excluded. This response occurs in diverse insect species at temperatures fluctuating around zero. It seems that the summer acclimated O. cincta were able to achieve a moderate cold hardiness in an interrupted exposure in these experiments. Since this epedaphic species does not show strong avoidance behaviour (as other collembolans do, see van der Woude & Verhoef 1986), a rapid cold hardening ability is quite important.
CAUSE OF DEATH
Mortality in summer acclimated O. cincta is not caused by freezing but by non-freezing cold injury (some metabolic disorder and failure, or membrane lipid changes). The positive effect of the interruption of cold exposure on survival might be explained as interrupting the period during which the chance (stochastic probability) of freezing (nucleation or inoculation) increased, subsequently starting again from zero time. In that case, no clear positive effects of the length of the warm interval and the temperature during the interruption would be expected. Instead, it would be likely that of the animals that survived 3 days at – 3 °C (50% of initial number), 50% of the remainder would survive the second 3-day period. This was, however, not the case. Therefore, it does not seem plausible to explain the positive effect of the interruptions on survival simply by diminishing the chance of freezing.
The injury could also be attributed to the desiccation that takes place in supercooled animals surrounded by ice (Zachariassen 1991). This may be important after a longer period of time, but this cannot explain the effect on survival of the duration and of the temperature of the interruption interval. Partial dehydration may be favourable in several ways in overwintering insects (Block 1996), either in freeze-susceptible species by depressing the SCP or in freeze-tolerant ones, but no survival improvement was described in chill (non-freeze) injury in insects.
The deleterious effect of artificial desiccation before cold treatment suggests that the natural desiccation during cold exposure can be dangerous when water loss is extreme (> 20%). However, among diverse collembolans, O. cincta is relatively strongly resistant to desiccation (Verhoef & Witteveen 1980). It tolerates fast dehydration and long dry periods, resulting in up to 47% water loss (Verhoef & Prast 1989). Haemolymph osmolality of about 450 mOsm kg–1 can be commonly found in the field during frost periods (van der Woude 1987). The expected depression of SCP related to desiccation was too small to improve survival even if mortality were caused by nucleated freezing. There was no death caused by inoculation by external ice as well, because survival was the same on the dry surface. Moreover, it was proven elsewhere (Lavy 1996) that gut evacuation during starvation in O. cincta, which should void efficient nucleators from the body, did not improve survival, although the SCP depression has been found to correlate with gut clearance in previous studies (van der Woude 1987, 1988).
Turnock & Bodnaryk (1991, 1993) ascribed the chill injury in insects to phase changes in membrane lipids. It is suggested here that the nature of the chill injury in summer acclimated O. cincta may be also a complex metabolic disorder. It may include a non-proportional decrease (imbalance, decoupling) in enzymatic reactions and transports, resulting in the accumulation of some harmful compounds (e.g. lactic acid, the nitrogenous waste substances) and lack of other, essential compounds. During the warm interval, a substantial part of the waste is metabolized or excreted, essentials are produced and distributed, some injuries are repaired. Rebuilding the order in an organism takes time, which explains the positive effect of the duration of the interruption. As temperature is important in many metabolic processes, a relatively high temperature during the interruption resulted in higher survival.
Prolonged chilling might cause disorder to such an extent that it is impossible to be repaired, or it may cause injury to the reparative mechanisms themselves (waste compounds reaching toxic concentrations). Death would then follow even in virtually healthy individuals (Bale 1991a), or developmental malformations and delays, and a decreased reproductive potential, will occur (see Sehnal 1991; Turnock et al. 1983). The potential of insects to recover from short exposures to temperatures that may become lethal in longer exposures complicates the issue of calculating a cumulative injury at fluctuating temperatures. Predictions of field mortality will have to include the effects of such warmer intervals during the entire exposure. Turnock & Bodnaryk (1993) also consider the importance of postexposure conditions in predicting field mortality.
The chill resistance of winter acclimated animals might be ascribed to the lower metabolic activity (hence a relationship between cold hardiness and diapause), to the rebuilt metabolic and transport systems (membrane lipid composition), and possibly also to changed neural and hormonal control of the organism.