The death spiral: predicting death in Drosophila cohorts

Drosophila research has identified a new feature of aging that has been called the death spiral. The death spiral is a period prior to death during which there is a decline in life-history characters, such as fecundity, as well as physiological characters. First, we review the data from the Drosophila and medfly literature that suggest the existence of death spirals. Second, we re-analyze five cases with such data from four laboratories using a generalized statistical framework, a re-analysis that strengthens the case for the salience of the death spiral phenomenon. Third, we raise the issue whether death spirals need to be taken into account in the analysis of functional characters over age, in aging research with model species as well as human data.


Introduction
Research with humans, Drosophila, medflies, and other model organisms has revealed three distinct demographic phases (Greenwood and Irwin 1939;Beard 1959;Carey et al. 1992;Curtsinger et al. 1992;Vaupel et al. 1998;Mueller et al. 2003;Rose et al. 2006;Mueller et al. 2011).The first phase, which occurs prior to the start of reproduction, is the developmental period.Under protected conditions, at least after the perinatal period, this phase characteristically features low levels of mortality with no consistent trend relative to age.
The second phase, normally called ''aging,'' follows the onset of reproduction.During this phase, agespecific mortality rates almost always rise, even under protected conditions (Comfort 1979), with the singular exception of fissile species (e.g.Bell 1984;Martinez 1998).For fissile species it could be said that there is effectively no part of life history that follows the first act of reproduction.
In this paper we present a general case for the existence of a fourth feature of life cycles, which we call the ''death spiral'' (Rauser et al. 2005;Mueller et al. 2007Mueller et al. , 2011)).The death spiral is detectable across a wide range of adult ages, as we will show.An obvious interpretation is that it features a general and abrupt decline in physiological health prior to death.But more importantly for biogerontological analysis, death spirals create significant heterogeneity within cohorts, heterogeneity that raises problems for the analysis of age-dependent functional characters quite broadly.
Evidence for the existence of the death spiral from Mediterranean fruitflies Papadopoulos et al. (2002) noted that 97 % of male medflies (Ceratitis capitata) began showing a temporary upside-down orientation, or supine behavior, about 16 days before their death.Since these medflies have an average age at death of about 62 days, the 16-day onset of medfly supine behavior is roughly equivalent to the period of time that Drosophila exhibit death spiral phenomena (Mueller et al. 2007 and this paper).Mu ¨ller et al. (2001) studied lifetime fecundity in 531 medflies.They noted that, after reaching a peak in early life, fecundity declined in an approximately exponential fashion.The rate of decline in fecundity was measured by a parameter, b 1 , which showed wide variation among individual females.In particular, they noted that females that die early in life showed a rapid decline in fecundity with age (large b 1 ), while females that lived longer showed a slower decline in fecundity (small b 1 ).For instance, inspection of Fig. 1 in Mu ¨ller et al. (2001) shows that a female that died early in life (28 days) was predicted to lay only 18 eggs at age 25 days, while the average fecundity in the whole population at this age was 27 eggs.
The Mu ¨ller et al. data can be interpreted as capturing death-spiral phenomena in female fecundity.Females that die at young ages have steeper declines in age-specific fecundity, because their trajectories are based on fecundity observations that are part of the death spiral and thus decline faster than the fecundity of similarly aged females that are not about to die.Mu ¨ller et al. suggest that death is a consequence of females rapidly diminishing their reproductive reserves and that these reserves vary among individuals.
Evidence for the existence of the death spiral from Drosophila

Studies of individual female fecundity
Over the last decade, multiple Drosophila laboratories have independently discovered patterns of aging that suggest the existence of death spirals among laboratory cohorts handled as adults with sufficient care to minimize the possibility of artifactual effects, such as infectious disease.In each of the relevant studies, daily counts of female fecundity were made from very early in adult life until death.
In the course of analyzing adult female Drosophila melanogaster handled individually, Rauser et al. (2005) found that individual female fecundity steeply declines just prior to death.Further quantitative analysis of the Rauser data led us to develop a formal analysis of the death spiral (Mueller et al. 2007(Mueller et al. , 2011)).This analysis incorporated a two-phase adult female life-history, with both aging and late life, as well as a distinctive death spiral phase in which fecundity declines linearly, but at a more rapid pace than the decline that characterizes normal aging.Rogina et al. (2007) inferred the existence of a comparable death spiral phenomenon for Drosophila female fecundity, noting that females that were about to die the next day always laid zero eggs and that independently of their mating schedule showed fecundity declines for a week or more before death.The egg-laying of females on the day before that zerofecundity day averaged about 0.2 eggs.Their study used 386 females from a mutant balancer stock of D. melanogaster.Curtsinger (2015) proposed that the age at which a female first lays zero eggs is a significant indicator of impending death.In his analysis of several previously published databases, specifically those of Le Bourg et al. (1988), Rauser et al. (2005), Klepsatel et al. (2013) and Khazaeli and Curtsinger (2014), he shows that roughly 10 days before the first zero egg count day a standardized fecundity measure starts declining (Curtsinger 2015;Fig. 3b), which corresponds roughly to the start of the death spiral that had been previously inferred by Rauser et al.Death spirals in male virility data Shahrestani et al. (2012a) studied male fertility, often called virility, by counting the number of females, of eight total, that a male could fertilize in 24 h.They found that the virility of males that were within 7 days of death was significantly lower than that of similarly aged males that were not about to die.

Lifetime female fecundity
In the first re-analysis, we relied on lifetime fecundity records collected from the following four sets of cohorts: (Le Bourg et al. 1988;Rauser et al. 2005;Klepsatel et al. 2013;Khazaeli and Curtsinger 2014).We first review some important details of the biological Materials and methods used in the construction of each of these databases.
Le Bourg et al. (1988) collected lifetime fecundity records on 322 females.These samples came from three populations, two were selected for activity level and the third was a control population.Assays were conducted over seven generations of selection.These populations were started from a standard Oregon R stock and at each generation only ten pairs of flies were used to reconstitute the next generation.Over the course of this experiment, heterozygosity was reduced by about 17 %, and in all likelihood the original Oregon R stock was inbred to some degree.Vials consisted of a male-female pair and males were not replaced upon death.The flies were given standard food with live yeast.
Khazaeli and Curtsinger (2014) used two inbred lines, R17 and S9, to derive a total of 335 females.These inbred lines were created by 28 generations of full sib mating using two populations created by Luckinbill and Claire (1985).The R17 inbred line was derived from Luckinbill and Claire's LA line which was selected for late life fitness, while the S9 inbred line was derived from Luckinbill and Claire's LD1 control line.Females were assayed in vials with two males that were replaced as needed.Fresh food was supplied daily, although there did not appear to be any yeast supplementation.Klepsatel et al. (2013) collected lifetime fecundity records on 488 females derived from three populations collected from (i) Austria, (ii) South Africa, and (iii) Zambia.These populations were maintained in the laboratory for only 2-4 generations prior to these assays.The Austrian population was created from a sample of 200 flies, the South African population from 140 flies derived from 7 isofemale lines, and the Zambian population from 600 flies derived from 30 isofemale lines.An isofemale line would typically undergo at least one generation of full sib mating.Females were kept in vials with about 10 mg of live yeast supplement and 2 males.Dead males were replaced.Rauser et al. (2005) used adult flies that were aged 12 days from egg (not 12 days as adults as reported by Curtsinger 2015), which made the adults 1-2 days old at the start of the assays.Each female was housed in a vial with 2 males and these males were replaced as they died.Vials were supplemented with 5 mg live yeast.A single, large, lab-adapted population (called ''CO 1 '' created in the study of Rose et al. 1992) was used to derive three independent cohorts, yielding a total of sample size of 2828 females.

Lifetime male virility
We analyzed lifetime male virility from the data of Shahrestani et al. (2012a).Virility observations consist of counts of the number of females that a male fertilizes in 8 h.Like with the fecundity data, Shahrestani et al. tested large samples (712) of males once a week until their death.

Scaled age-specific fitness
The concept of the death spiral is a death process.Accordingly, we sought a means of examining this process independent of an individual's precise age.We chose to recast an individual's age as a series of target ages.We first describe the method used for female fecundity.At each target age we could classify a female as either alive or dead by the end of the target age.This would then create two groups of females and each female would have an associated history consisting of her record of eggs laid 0, 2,…, m days prior to the target age, e.g.days before death.To standardize an individual's fecundity phenotype, we scaled and centered the entire population's fecundity measurements at each age.Thus, if at age-t, the average fecundity of all live females and females that died at age-t were, f t , and the standard deviation, r t , then the fecundity of female-j at time-t, f tj , would be transformed to ftj ¼ f tj Àf t r t .If female-j is found dead on day-t there is a 24 h window on her exact time of death.Thus, the f tj values may reflect the eggs produced in a 24 h period (if the female died just before the census), or perhaps the eggs laid in just a few minutes of time (if she died immediately after being transferred to the fresh vial).
If at time-t there are n t , females at that age, either alive or those that died that day, we generate predictor vectors for female-j (j = 1,…, n t ) that look like, f j ¼ fm;j ; fmÀ1;j ; . ..; f0;j À Á , where we have now transformed the time scale so t = 0, t-1 = 1, and so on.Thus, fk;j , is the transformed fecundity for female-j, k days before the target age.This process is repeated for the next age, t ? 1, and n t ? 1 new records are created (Fig. 1).Obviously, females that did not die by age t ? 1 will have nearly the same fecundity records entered into the database at both target ages t and t ? 1.When creating these records, we omitted females that did not have complete fecundity records for the entire window of m ? 1 days.In addition, females that died at ages \m were not included in these records.These records were used to do regressions of scaled fecundity on days before the target age for the dead females and the live females.Since the database of live females included the same females multiple times, observations are correlated.Therefore, the analyses of the regression results must use methods that can take into account these correlations.
We did bootstrap resampling of our scaled fecundity dataset to determine the variances in scaled fecundity at various ages before the target age and to determine if the slope of the regression lines for the dead and live females differed.The total size, N, of the Rauser et al. dataset was large: 43,093 with a 15-day window (m = 14).At each bootstrap sample, we sampled with replacement N female fecundity records.From this we took a subsample of 1000 records of live females and 1000 records of dead females.We then computed the mean scaled-fecundity of each group and the regression of scaled fecundity versus days before target age.We did 100 bootstrap samples and from these computed empirical 95 % confidence intervals on the mean scaled-fecundity and confidence intervals on the slopes of each line.Some females will stop laying eggs sporadically or completely prior to death.Curtsinger (2015) has recently argued that the appearance of days with zero egg counts is an important indicator of the end of life, a phase he has called the retired stage.We followed up on his suggestion by examining how useful zero egg counts are for predicting death.To do this we took the records of lifetime female fecundity and changed each daily egg count to 0 if no eggs were laid and 1 if one or more eggs were laid.We then used the target age concept described previously to generate records for live and dead females.
The virility data at each age was scaled and centered in the same way we transformed female fecundity data.We also did bootstrap re-sampling to estimate the variance of the scaled virility values of males that were alive and dead on the target day.

Predicting death at the target age
Can we use scaled fecundity or zero egg counts at say up to m-days before the target age to predict which female will be dead at the target age?This is not as simple as one might think.Recall that a female that dies one day after the target age will be included in the ''live'' group and her fecundity record will be the same as when she actually dies, except for the inclusion of new information at day 1 and the removal of the day m observation.We used a statistical learning technique, boosted classification trees, to predict whether a female is dead or alive on the target age based on her fecundity record in the previous m days.Classification trees provide predictions on an individual's membership in a binary classification based on successive partitioning of the predictor space (Hastie et al. 2009, Chap. 9).Boosting is a technique for improving the prediction of methods such as classification trees, which employ the sequential building of trees in which each step creates additional tree branches that are constructed to improve the prediction of the residuals from the previous tree (Hastie et al. 2009, Chap. 9).
In order to avoid developing a classification tree that focused on the correct prediction of live females due simply to the much larger number of records for live flies, we created a data set with an equal number of records of live and dead flies from the Rauser et al. data.From this we used 80 % of all the data (training data) to train the boosted classification tree.The remaining 20 % of the observations (testing data) were used to predict whether each female was alive or dead at the target age.We determined how many days prior to the target age provided the best predictions based on 10-fold cross validation of the training data set.In addition, the same cross-validation statistics were used to determine (i) the number of trees that resulted in a minimum error, (ii) the best depth of the individual trees, and (iii) the optimal shrinkage parameter (for a discussion of these issues see Gareth et al. 2013, Chap. 8).
Predictions with the testing data gave rise to two sorts of errors.Females that were dead at the target age were incorrectly predicted to be alive (dead error rate), and females that were alive at the target age were incorrectly predicted to be dead (alive error rate).If we simply guessed female status the error rates would be 50 % since we had equal numbers of live and dead females in the testing data.

Destructive physiological measurements
If fitness components like fecundity and virility decline during the death-spiral, then we expect other physiological functions to change prior to death as well.One problem with testing this idea is that in Drosophila many physiological tests are destructive, and therefore we cannot use death as an indication of which flies are in the death-spiral.We have proposed as a solution to this problem to use female fecundity for several days prior to a destructive physiological assay (Mueller et al. 2009;Shahrestani et al. 2012b).One difficulty with any potential test by these techniques is that the physiological character may be correlated with fecundity, and thus by using fecundity to identify females in the death-spiral we may get a sample that looks different simply because of these correlations.Shahrestani et al. (2012b) developed a procedure that utilized principal components of physiological characters, such as desiccation resistance and time-inmotion, rather than the raw measurements.Thus, for each female the centered and scaled desiccation and time-in-motion observations were transformed to a vector, z i = (z 1i , z 2i ), i = 1,..,n, of the two principal components.Shahrestani et al. partitioned the n principal component vectors into a ''death-spiral'' group, with principal components Z s , and a ''non death-spiral'' group, with principal components Z ns , according to each female's fecundity.Using the mean, l, and covariance, R, of Z ns the Mahalanobis distance for every female was estimated as, The test statistic is then a simple t-statistic resulting from a comparison of the mean Mahalanobis distance among spiral females versus the mean among non-spiral females.This statistic has a nominal 5 % type-I error rate even when there are correlations between fecundity and these characters, but no difference in the mean value of these traits in the two groups (Shahrestani et al. 2012b).

Lifetime female fecundity
For the Rauser et al. data set, we see that the difference between the scaled fecundity of the dead and alive females becomes greater the closer the comparison is to the target age (Fig. 2a).The slopes of the regression are significantly different.Thus, we get an indication from these data that female fecundity starts declining well before death, perhaps as early as 2 weeks before.This is a strong indication that flies that are dying from intrinsic causes, not accidents or catastrophes, start to show physiological manifestations of this well before death.As we will see later, female fecundity is not the only trait that is adversely affected by the death process.
How robust are these results?We address this by creating scaled fecundity data for the three other published D. melanogaster data sets described previously.Each of these shows remarkable consistency with the Rauser et al. results (Fig. 2b), suggesting that the death spiral is common to this species, at least for female fecundity.
Although we have suggested that the death spiral is not a direct product of aging, its characteristics may be a function of age.To study this, we divided the females from Rauser et al. into quartiles according to their ages at death.Thus, the first quartile consisted of scaled fecundity records for females at target ages less than 24 days, then 24-30 days, 31-38 days, and greater than 38 days for the second, third and fourth quartile, respectively.When we examine the difference between the mean scaled fecundity for 4 days prior to the target day (Fig. 3), we see that age at death has a large effect on the difference between the live and dead groups at the target age, but that the differences between quartiles diminishes rapidly as we move further from the target age.Females that die at a young age will be more impacted by the death spiral than females that die at older ages, especially at ages very close to death.So while age at death has some impact on the magnitude of the death spiral effect, the number of days before death is a more substantial indicator of the impact of the death spiral effects.

Analysis of zero egg counts
Using the results from all four laboratories, we see that there is a distinct difference for the fraction of females laying zero eggs when we compare the females alive at the target age with those dead at the target age (Fig. 4).As mentioned previously, since some females may have only short periods to lay eggs on the day they died, the day zero observations are of limited utility.Just before death, all populations show a very high  Rogina et al. (2007).As with the scaled fecundities, the fraction of females with zero egg counts for females dead on the target day declines as we look further from the day the fly dies.It is similar to the values for live flies by about day 14 before death.
In this sense, the zero egg count days shows a death spiral decline that has a similar dynamic to the scaled fecundity decline.We used the large data set of Rauser et al. to examine if the fraction of females laying zero eggs differs depending on when a female died.We divided the Rauser et al. data into quartiles, as we did with the scaled fecundity.We see that the fraction of females with zero eggs is generally higher for females that die at older ages (Fig. 5).It also appears that as we examine days further removed from the day of death, fewer females are laying zero eggs and this is most pronounced with young females.
The best predictions utilized only 4 days of scaled fecundity records prior to the target day.For the Rauser et al. test data, the best predictions were for the dead females (Fig. 6a) and the average error rate was about 23 %.Using the boosted classification tree trained on the Rauser et al. scaled fecundity data, we also predicted the status of females in the three other data bases.While the predictions are slightly better for the Rauser et al. data, there were low prediction errors in all the other databases (Fig. 6a), and the predictions were certainly much better than simply guessing.
We next repeated the construction of boosted classification trees using the zero egg count data.Even though the classification tree was trained on the Rauser et al. data, the Le Bourg et al. and Klepsatel et al. data had a lower error rate for dead females than the Rauser et al. data (Fig. 6b).We can make sense out of these results if we examine the relative importance of the predictor variables.Each dependent variable can be assigned a relative weight in a classification tree based on the frequency it is used to bifurcate each branch of the tree.The day before the target age provides the most important predictor data when using either scaled fecundity or zero egg counts, although it is more so with zero egg counts (Fig. 7).The Klepsatel et al. and Le Bourg et al. data have a higher frequency of zero egg counts the day before death (Fig. 4) than the other two databases, accounting for the more accurate prediction of which females will die.Conversely, the Rauser et al. data show the lowest frequency of zero egg counts the day before the target age among live females (Fig. 4) and hence the most accurate prediction of which females are alive (Fig. 6b).
Are zero egg counts better at prediction than scaled fecundity?We can use the dead female error rates to do simple v 2 tests of dead error rates in each database comparing the predictions based on scaled fecundity records to zero egg count records.We used only the dead error rates, since these are constructed from independent female data, while the live error rates are not.Only the Rauser et al. data show a significantly different dead error rate.The scaled dead error rate (21 %) in the Rauser et al. database was significantly lower than the zero egg count rate (34 %, p \ 10 -5 ).Curtsinger (2015) has suggested that the days when flies lay zero eggs are especially important for identifying females that are characterized by low levels of oviposition and reduced prospective survival.Curtsinger uses the first zero-egg day as an indicator of the start of a life phase he calls retired.Females not in the retired stage are in the working stage.We have shown that the proportion of females that have zero egg days shows a pattern similar to average fecundity (Fig. 4).That is, prior to death there is, on average, about a two-week period during which the chance of a female with a zero egg day increases.We suggest that zero egg count days are simply a different scaling of fecundity and that the patterns of zero egg days can be explained by the death spiral.
We find the retired/working dichotomy less useful than the death spiral.Firstly, the retired/worker classification only works for females.But as we have shown, males undergo a similar decline in reproductive function prior to death.The death spiral includes multiple physiological traits, not simply reproductive traits.As a classification scheme, the retired/worker scheme is highly variable.In the Rauser et al. data, 20 % of females show no zero egg counts up to and including the day before they die.Among females showing a zero egg count day before death, the median first zero egg count day occurs seven days before a female's death.Thus, for females with zero egg count days, 50 % of them will have their first zero egg count day half way into the death spiral.Lastly, for predicting female death, zero counts work as well as scaled fecundity in 3 out of 4 databases, but in the Rauser et al. database scaled fecundity is significantly better than zero egg counts.It should be noted that the testing set of data used to predict the dead error rates in the Rauser et al. database had only about 500 samples, which was not substantially higher than the sample sizes used for predicting dead error rates in the other databases.Hence, the observed significance in the Rauser et al. database cannot be due to simply a difference in power.

Male virility
The slope of scaled male virility vs. weeks before target age (Fig. 8) for alive males is small (-0.01) and not significantly different from zero (95 % confidence interval, (-0.067, 0.046)).On the other hand, the males that were dead within a week of the target age showed a positive slope (0.12) that was significantly different from 0 (95 % confidence interval, (0.082, 0.16)).The pattern is very similar to that of fecundity, as displayed in Fig. 2, suggesting that the death spiral results in declining male virility as early as 2 weeks before death.

Desiccation resistance and time-in-motion
The distribution of distance values in the two groups (Fig. 9) shows that there is a higher frequency of small distance values in the non-spiral group and more frequent large distance values in the spiral group.The result of these differences in the distribution is that the two group means are significantly different (p = 0.00069).The p value reported in Shahrestani et al. (2012b) was for a two-tailed test, although in fact the correct alternative hypothesis is that the average distance in the spiral group is greater than the average distance in the non-spiral groups, which was in fact what was observed.Both mean time-in-motion and desiccation resistance were reduced in the death spiral group, indicating a decline in physiological function.
While the distributions (Fig. 9) look similar, the tests on the means used large samples to overcome the inevitable misclassification problem with data of this kind.Shahrestani et al. tested 3272 females for both desiccation resistance and time-in-motion.

Discussion
General lessons for the construction of demographic models One natural consequence of the death spiral is that population-level measurements of changes in phenotypes with age must allow for possible effects produced by the death spiral.In principle, a phenotype could stay constant in an individual until they enter the death spiral, at which point there would be a consistent and severe decline.At the population level, it would appear as if the average value of this phenotype declines with age, since an increasing fraction of the population would be expected to be in the death spiral as a cohort of individuals get older.In the case of fecundity and male virility, we know that such a pattern of non-aging is not the case, because after removing the individuals in the death spiral, we still see an age dependent decline in these phenotypes (Mueller et al. 2007;Shahrestani et al. 2012a).However, other phenotypes would have to be individually tested for the impact of death spirals.To model the dynamics of age-specific change in a phenotype like average fecundity, the number of females in the death spiral and the number that are not would need to be accounted for.Mueller et al. (2007) demonstrated how the death spiral can be incorporated into a model of age-specific fecundity.We should note that the population heterogeneity generated by the death spiral is fundamentally different from the heterogeneity in age-specific mortality that has been invoked as an explanation of mortality plateaus (Vaupel et al. 1979;Mueller et al. 2011, Chap. 8).There is no need to invoke heterogeneity in lifelong robustness to generate death spiral phenomena.
Mu ¨ller et al. ( 2001) argue that lifespan is tied to the rate at which fecundity declines and this rate is an indicator of frailty.They reason that females showing rapid fecundity declines early in life are frailer, and thus can be expected to die at an early chronological age.The death spiral, on the other hand, suggests the death process affects many physiological traits.With this interpretation, the rapid decline in female fecundity early in life is a symptom of dying rather than a cause of death.Traits affected by the death spiral may be related to important fitness characters, like fecundity and virility, or may be traits that are relatively unconnected with fitness, like supine behavior or timein-motion.Further research is required to sort through these alternative explanations of the death process.
A review of the literature suggests that many previously documented biomarkers of aging or death may in fact be part of the death spiral.We review some of these next.Wax and Goodrick (1978) have reported that old mice within 1 week of death display more random wheelrunning than old mice that are not within a week of death.Recently, Belsky et al. (2015) suggested that humans in midlife that are aging more rapidly also show (i) less physically ability, (ii) cognitive decline and brain aging, (iii) self-reported worse health, and (iv) looked older.Zhang and Pincus (2016) report that blood pressure and BMI are predictive of mortality in mid-life, while blood glucose is predictive at later ages.Rera et al. (2012) recently reported that adult D. melanogaster fed food laced with blue dye become blue colored sometime shortly before death.Rera et al. call these blue individuals ''Smurfs.''The fly's uptake of dye is related to the loss of intestinal barrier function.Smurfs also exhibit increased antimicrobial peptide expression, and impaired insulin/insulin-like growth factor signaling.It seems likely that the Smurf phenotype and its associated physiological syndromes are also part of the death spiral, although additional experiments would be needed to confirm this.
In longitudinal assays of individual D. melanogaster using real-time video tracking of GFP fluorescence, hsp22 and hsp70 transgenic reporters began to spike in expression *5-10 h before death (Grover et al. 2008(Grover et al. , 2009)).It has been suggested that hsp gene expression levels could possibly be used to predict remaining life span of individuals (Yang and Tower 2009).
The case of human disability Chronic disability among the U.S. population has been declining since 1982 (Cutler 2001;Manton and Gu 2001;Crimmins 2004;Manton et al. 2006).This decline has occurred despite the fact that the elderly have been increasing in numbers and living longer.Numerous reasons have been proposed for this decline, including improved human physiology from better diets and better medical care (Fogel and Costa 1997;Schoeni et al. 2008).Manton et al. (2006) estimate that these declines in disability rates saved Medicare around $26 billion in 1999 alone.The enormous costs of assisting the disabled make the study of the process of disability an important practical problem.
It has been suggested that, prior to becoming disabled, individuals go through a series of steps called the disablement process (Verbrugge and Jette 1994).The disablement process suggests that some pathology, like a disease or an injury, may lead to an impairment that is a dysfunction of a specific body system.Examples of such body systems include the musculoskeletal and cardiovascular systems.These impairments can lead to a specific limitation in activity or movement, which becomes a disability when it limits the individual's ability to carry out activities of daily life.This description of the disablement process has found support in the bio-medical literature (Fauth et al. 2008).The onset of disability may lead to a downward spiral of new pathologies and ultimately to death (Verbrugge and Jette 1994;Morley 2008).We suggest that this process in humans is the analog of the death spiral we have documented in fruit flies.

Fig. 4 Fig. 5
Fig. 4 The fraction of females laying zero eggs as a function of time before target ages in four different Drosophila databases.The bars on the Rauser et al. lines are 95 % confidence intervals computed from a standard binomial distribution

Fig. 6 Fig. 7
Fig. 6 Error rates from boosted classification trees in four different databases.The bars are 95 % confidence intervals.a Error rates for the scaled fecundity data.b Error rates for the zero egg count data.See the text for definitions of the error rates

Fig. 9
Fig.9The distribution of Mahalanobis distance values based on principal components of desiccation resistance and time-inmotion measurements in females identified as either in the death spiral or not in the death spiral based on their fecundity prior to assays The first quartile of data represents the youngest females while the fourth quartile represents the oldest females.The solid line is for the entire Rauser et al. data set fraction of females laying no eggs, although it is not 100 %, and the value varies substantially between lab populations.In the Rauser et al. and Khazaeli and Curtsinger cohorts, about 60 % of the females are not laying eggs the day before death, while in the Le Bourg et al. and Klepsatel cohorts, the number is closer to 80 % and as reported previously is 100 % for the flies studied by the line through the live female data is 0.0085, with a 95 % confidence interval of (0.004, 0.013) and the dead female slope is 0.062, with a 95 % confidence interval of (0.058, 0.066).bRegressionlinesfortheRauser et al. data in (a)and three other data sets as indicated Fig.3The differences between scaled fecundity in the live and dead females as a function of age-at-death (dashed lines).