Epidemic cycles and environmental pressure in colonial Quebec Tim - - PDF document

1 Epidemic cycles and environmental pressure in colonial Quebec Tim Bruckner1 Samantha Gailey1 Stacey Hallman2 Marilyn Gentil3 Lisa Dillon3 Alain Gagnon3

1University California Irvine, Program in Public Health and School of Social Ecology 2 Statistics Canada, Ottawa, Canada 3Département de démographie, Université de Montréal, Montréal, Québec, H3C 3J7 Canada

Correspondence to: tim.bruckner@uci.edu or alain.gagnon.4@umontreal.ca

2 Abstract Objectives: Research on historical populations in Europe finds that infectious disease epidemics appear to induce predictable cycles in age-specific mortality. We know little, however, on whether such cycles also occurred in less dense founder populations of North

• America. We used high-quality data on the Quebecois population from 1680-1798 to

examine the extent to which age-specific mortality showed predictable epidemic cycles. We further examined whether environmental pressures―temperature, lack of precipitation, or crop failure―may have set the stage for the emergence of epidemics. Methods: We applied autoregressive, integrated, moving average time series methods to annual counts of period mortality for the following age groups: <1 year, 1 to <5 years, 5 to <15 years, 15 to <50 years, and 50 years and above. These methods controlled for other patterns (e.g., trend) before empirically identifying cycles between two- and ten-year lags. Results: Results indicate a strong seven-year cycle in mortality among infants and children under seven years of age, likely due to smallpox. Warm temperatures (across Quebec

• verall) and relatively dry years (in Eastern Quebec) also predicted an increased risk of

mortality in infancy and childhood, although these environmental variables appear to act independently of the epidemic cycle pattern. Discussion: Findings indicate a strong seven-year epidemic cycle in historical Quebec which afflicted naïve birth cohorts not previously exposed to the prior epidemic. The seven- year cycle, moreover, occurred only in the latter half of the test period (post 1740) with increasing size of the colony and population concentration in urban areas.

3 Introduction In pre-industrial Europe, infectious diseases in both rural and urban settings predominated as leading causes of death (Bengtsson, Campbell, & Lee, 2004). Infectious disease mortality included both endemic and epidemic events. Research using historical data in Europe before the 20th century has characterized the mortality dynamics that arose from infectious disease epidemics. Although research indicates regional variation in the response to epidemics, the literature tends to converge on two findings. First, rural areas, small towns and large urban areas alike show epidemic “cycles” of high mortality ranging from a few to eight years (Bengtsson et al. 2004; Duncan, Scott, & Duncan, 1993; Mielke et al., 1984). Second, infants and children appear most susceptible to these epidemic cycles. Whether, and to what extent, epidemic cycles occurred in newly founded populations (e.g., English and French nascent colonies in North America) remains less clear. Patterns of mortality during epidemics may appear much less predictable, or “cyclical,” for frontier

• populations. Most individuals born in these isolated and sparsely populated areas did not

have previous experience with the virulent diseases that affected their European

• counterparts. Colonists, for instance, could live many years without ever contacting

smallpox or measles. Consequently, a larger proportion of frontier populations may have been susceptible to disease. Infectious diseases could surge following the arrival of a vessel

• r of a voyager along the fur trade routes and spread rapidly through the colonies, affecting

all ages. Such a circumstance, for instance, occurred during the smallpox outbreak of 1702- 1703 in New France (Desjardins, 1996). Newly founded populations, such as the well-documented colonial Quebecois in the 17th and 18th centuries, may also have withstood the joint exposures of environmental pressure

4 and epidemic risk differently given their nature of subsistence (Charbonneau et al., 1993). In England and Sweden, periodic variations in grain price – a proxy for food supply – often coincided with epidemic cycles (Duncan et al., 1993, Bengtsson, 1999). One hypothesis, which enjoys empirical support (Bengtsson, 1999), posits that cycles of malnutrition during low subsistence years may have weakened the immune system and thereby increased risk of mortality due to infectious diseases (Duncan et al., 1993; Duncan, Duncan, & Scott, 2001). Unlike most of the populations studied in Europe, however, the frontier population in Quebec supplemented their diet through fishing and hunting. In addition, in their study of 18th century Quebec mortality, Landry and Lessard (1996) find resilience to food shortages and extreme cold, and further report that epidemic diseases induced lower levels of mortality than in other places (e.g., Finland and Philadelphia). Short-run variations in food from arable land in Quebec, therefore, may not have impacted susceptibility to lethal infectious diseases. We contribute to the literature by investigating whether and to what extent mortality in the founder population of historical Quebec showed an epidemic “cycle.” We use periodicity in age-specific mortality from 1680 to 1798 to approximate epidemic cycles. In addition, we analyze the extent to which environmental pressure (e.g., temperature, lack of precipitation, or crop scarcity) accounted for a portion of any discovered epidemic cycle and/or affected mortality. Lastly, we assess whether epidemic cycles appeared only after the establishment of urban centers (e.g., Quebec City circa 1740).

5 METHODS Variables and Data We retrieved age-specific counts of death, from 1680 to 1798, from the Registre de la population du Québec ancien, compiled by the Programme de recherche en démographie historique (PRDH) at the University of Montreal. The database comprises vital rates for the first centuries of the settlement of the French-Canadian population (Desjardins, 1998, 2012; Dillon et al., 2017). Researchers at the PRDH reconstituted individual and familial biographies by linking individuals to their baptismal, marriage, and burial certificates. Given the ubiquity of the Catholic Church in historical Quebec, the PRDH data include the entire population base of the historical French-Canadian territory, covering 153 parishes by 1800. Demographic estimates of complete follow-up of life histories range from 81 to 91 percent for married individuals, which to our knowledge remains among the best follow-up of any population over this time period (Gagnon & Mazan, 2009). This circumstance avoids loss to follow-up problems observed in other historical datasets that could arise due to inter-regional or inter-parish migration following extremely harsh years. Over 200 publications use the high-quality PRDH data (Dillon et al., 2017). The PRDH data do not include cause of death information systematically recorded at the individual level. Only 2.2 % of death certificates issued between 1625 and 1799 cited a cause of death or described the circumstances in which death took place (Landry & Lessard, 1996, p. 50). Only 6% of cited causes of death specifically identified an infectious or parasitic disease, most often smallpox. Collecting information about causes of death, if known at all, was not mandatory. We also know of no dataset of Quebec that documents all

6 infectious disease epidemics for the 17th and 18th centuries. As a surrogate, we examined counts of age-specific mortality, by calendar year of death, to identify mortality cycles. Consistent with the literature on historical populations, we (as described below) infer an infectious disease epidemic cycle from the existence of mortality periodicity during this time period. When possible, we also used historical accounts of smallpox epidemics such as the correspondence between the colonial authorities and the French administration (see Amorevieta-Gentil, 2009; Goulet & Paradis, 1992; Lessard, 2012). We initially categorized mortality into age groups that cohere with the literature as well as with distinct life course stages of mortality risk. The age groups also provide a sufficient number of deaths in each age category to produce an annual time series that does not have “0” counts in any year. These age groups include infancy (0 to <1 year), childhood (1 to <5 years), adolescence (5 to <15 years), adulthood (15 to <50 years), and older age (50 years or greater). High or low temperatures, drought, and crop scarcity all may affect immune function and pathogen resistance. We retrieved annual data on these variables from several sources. We used two North American temperature reconstructions and calculated the mean of these temperature series to define annual temperature (Mann, Bradley, Hughes, 1999; Rutherford et al., 2005). Both reconstructions include annual measures, from land and marine locations for the North American continent, from 0-90°N. Both reconstructions also incorporate tree- ring and ice-core measurements from locations across North America. We retrieved precipitation data from the North American Drought Atlas PDSI Reconstructions (Cook et al., 1999), made available through the NOAA/NESDIS North American Drought Variability section of the NOAA Climatic Data Center

7 (https://www.ncdc.noaa.gov/data-access). We used data on wheat prices from Dechêne (1974) for the New France era and from Paquet and Wallot (2007) for the post-conquest period (i.e., after 1760). We examined wheat prices because previous research indicates that they correlate inversely with agricultural yield and inversely with infant and child mortality in some European settings (Lee, 1981; Bengtsson & Ohlsson, 1985), although infant mortality did not respond to food prices in Italy (Livi-Bacci, 1991). Analysis We used Autoregressive, Integrated, Moving Average (ARIMA) time series methods, developed by Box and Jenkins, to detect cyclical patterns in age-specific mortality (Box, Jenkins, & Reinsel, 1994). These methods enjoy wide application in demography and epidemiology (Scott & Duncan, 2005). The logic underlying ARIMA methods involves empirical identification of temporal patterns in a time series, which researchers refer to as

• autocorrelation. The ARIMA approach contrasts other time-series approaches in which the

researcher assumes a pattern a priori (e.g., spline, linear trend). Annual age-specific mortality in the late 18th and 19th century Europe, the earliest periods for which the needed historical demography data for Europe are usually available,

• ften exhibits downward trend as life expectancy improves over time. By contrast, infant

and child mortality in the frontier population of Quebec (in terms of rate and absolute counts) shows an upward trend as both population size and urbanization increased (Gagnon & Mazan, 2009; Amoreviata-Gentil, 2009). While vital event under-registration hinders similar assessments of U.S. death rates prior to the nineteenth century, the upward mortality trend seen in Quebec converges with findings for the United States, including New York

8 City and Boston, during the first half of the nineteenth century (Vinovskis 1972). This pattern complicates identification of cycles because the expected value of age-specific mortality in any year is not the mean of mortality in past years. We therefore removed this upward trend, if detected by ARIMA routines, in any of the age-specific mortality counts before inspecting the series for cyclical patterns. Based on prior literature on epidemics in historical Europe (Duncan, Scott, & Duncan, 1994; Duncan et al., 1993; Fridlizius & Ohlsson, 1984), we focused our detection of cycles between years 2 to 10 (i.e., high or low mortality that echoes from 2 to 10 years later with similar values). We defined an epidemic cycle of length n as any lag t+n of year t that time- series routines detect as having positive autocorrelation. This positive autocorrelation, which identifies memory of similarly high (or low) values of mortality in year t+n following high (or low) values of mortality in year t, must reach conventional levels of statistical significance (i.e., T-value > 1.96, p<.05) over the entire series in order for the routines to identify a cycle. For each age group, our analysis proceeded through the following steps. First, we plotted annual mortality counts over the test period. Second, we inspected the mortality series for trend and, if identified, removed trend. Third, we inspected the autocorrelation function of the mortality series for annual lags in which the lag coefficient was positive and exceeded 1.96 times the standard error (i.e., p<.05). We focused on autocorrelation between lags at year t+2 through year t+10 given prior literature which reports epidemic cycles ranging from two to ten years (Bengtsson et al. 2004; Duncan, Scott, & Duncan, 1993; Mielke et al., 1984; Scott & Duncan, 2005). Fourth, if any cycles were found, we included environmental variables of temperature, drought, and wheat prices in separate time-series

9 models to examine whether their inclusion attenuated the strength of the epidemic cycle. Fifth, we divided our time series into two halves and examined the first (i.e., 1680-1739) and second (i.e., 1740-1798) half of the time period separately. We divided the series into two series given that increasing urban concentration in Quebec City and Montreal― especially after 1740― may have induced epidemic cycles. Sixth, we explored the extent to which years with documented smallpox epidemics accounted for any discovered cycle. RESULTS Over the test period, parish records show 195,098 deaths. Figures 1a and 1b plot age- specific mortality counts for the first and second half of the study period. We plot these time periods separately given the dramatic difference in mortality counts over time as the Quebecois population grew. The rise in mean infant mortality counts over time reflects the growing population size, as well rising mortality rates. Before 1740, we observe some large peaks in mortality across all age groups. During the 1703 smallpox epidemic, for instance, all age groups appeared affected (Desjardins, 1996), while only those less than age 30 appeared to suffer increased mortality upon the return of smallpox in 1732-1733. This response appears consistent with acquired lifetime immunity for most generations born before 1703. Indeed, we know of no historical accounts of the presence of smallpox in the colony during the intervening years. After 1740, mortality for several younger ages appears to exhibit cycles, although in varying strength. The autocorrelation function showed that mortality counts in three of the five age groups exhibits trend: infants age <1 year, adolescents and adults ages 15 to <50 years, and adults ages 50 years and above. We, therefore, took the first differences of these series (i.e.,

10 values at t subtracted from t+1) to render them stationary in their mean. Although the children ages 1 to <5 years and juvenile ages 5 to <15 years categories did not trend sufficiently to warrant first differencing, they showed strong autoregressive memory at lag 1-year which is mathematically similar to trend. For these series, we included an autoregressive (AR) parameter at lag 1-year before inspecting cycles. Figure 2 plots the T-values of the autocorrelation function for mortality from lags t+2 through t+10 years. We shade the region of non-significant T-values in gray (i.e., absolute value <1.96). Infants, children, and juveniles show a mortality cycle of 7 years. The strongest cycle occurs for children ages 1 to <5 years (coef = 0.49, SE=.10, p<.0001), followed by infants age <1 year (coef = 0.49, SE=.15, p<.01), and then juveniles ages 5 to <15 years (coef = 0.27, SE=.10, p<.01). This cycle indicates that, for children ages 1 to <5 years, 49% of mortality counts in year t are remembered t+7 years later with similar mortality counts. We observe no other positive cycles at any other lags for any group, although the negative lag at year 2 for juveniles falls slightly below conventional levels of statistical significance. The discovered cycle only at young ages led us to disaggregate the juvenile category (5 to <15 years) to determine whether the 7-year cycle occurred only among immunologically naïve cohorts born after the previous epidemic. Figure 3 shows that the 7-year cycle in juvenile mortality disappears when we restrict that category to ages 7 to <15 years, which indicates that the epidemic cycle induces mortality only among the immunological naïve cohort under 7 years of age. Given the detection of cycles in ages under 7 years, we examined whether environmental variables accounted for a portion of epidemic cycles for deaths in this age

11

• group. Table 2 shows time-series regression results from nine separate models; we present

coefficients only for the cycle and the ecological variable of interest (ARIMA details available upon request). None of the variables—temperature, drought, or price of wheat— attenuate the coefficient for the 7-year epidemic cycle (Models 2, 4, 6, 8) as compared with the base model (Model 1) without ecological variables. Although the discovered cycle at lag 7 years appears to account for large increases in mortality, ecological perturbations may increase mortality in non-epidemic years. To assess this possibility, we applied outlier detection and correction routines to the dependent variable of mortality in ages under 7 years and re-estimated the ecological coefficients. This method iteratively adds binary variables for each year to find any year that, if added to the equation, would have coefficients with t-values greater than 3.5 (Chang, Tiao, & Chen, 1988). The method also adjusts the time-series parameters as outliers are added. Outlier routines detected several outliers in mortality. After their removal, warm annual temperatures coincided with more deaths in ages under 7 years (Model 3). In addition, precipitation in East and West Quebec showed an inverse relation with mortality in ages under 7 years (Models 5 and 7), which suggests heightened mortality during drought years. This drought coefficient exceeds conventional levels of statistical detection only in East

• Quebec. In addition, in outlier-adjusted analyses, wheat prices vary positively with

mortality in ages under 7 years (p=.07; see Model 9), which appears consistent with the notion that food scarcity may precede increased mortality. Based on results that identified epidemic cycles only in ages under 7 years, we focused

• n this group and repeated our analyses of cycles separately for the first (1680-1739) and

second (1740-1798) halves of the series. The positive cycle at lag 7 years occurred after

12 1740 (T-value for lag 7 = 3.78, p<.001) but not before (T-value for lag 7 = .43, p=.67). The coefficient for the cycle at lag 7 years from 1740-1798 is 0.53, which indicates that among ages under 7 years, over 50% of mortality in year t was “remembered” seven years later (time t+7). Discovered evidence of cyclical mortality at lag 7 years led us to explore the possibility that smallpox epidemics likely account for this cycle. Whereas we do not have complete data on smallpox epidemics over the test period, previous papers indicate the following years in Quebec in which smallpox outbreaks occurred: 1740, 1745, 1747, 1755-59, 1765, 1769-70, 1775-77, 1783-4 (Amorevieta-Gentil, 2009; Goulet & Paradis, 1992; Lessard, 2012). We, therefore, conducted two additional exploratory analyses that incorporated this

• information. First, for ages under 7 years age only, we specified a binary smallpox variable,

scored “1” for these years and “0” for other years, included the smallpox variable in the time-series equation for the period 1740-1798, and re-estimated the cycle coefficient. The smallpox coefficient varied positively with mortality (smallpox coefficient = 573.7 excess deaths <7 years, SE=162.6, p<.001). The coefficient for the lag 7-year cycle was 0.41 (T value=2.73, p<.01), which indicates a 22% attenuation relative to the cycle coefficient from the equation absent the smallpox variable. Second, we checked whether years with positive

• utliers in mortality, as detected by outlier routines (Alwan & Roberts, 1988), corresponded

to years identified as “smallpox epidemic” years, based on previous literature. We discovered four years with positive mortality outliers: 1765, 1777, 1784, and 1791. Three of these four years correspond with smallpox epidemic years. The last three outliers, moreover, show a 7-year interval between them.

13 DISCUSSION Although the literature documents predictable mortality cycles due to epidemics in historical Europe, we know of no research that rigorously examines this possibility in frontier populations in North America. Our time-series results in colonial Quebec indicate strong mortality cycles at an interval of seven years, particularly when population size

• increased. We attribute this pattern to smallpox. Many years with peak mortality within the

seven-year cycle that emerge in the last 50 years of the series reflect years in which smallpox epidemics appear in historical accounts. This cycle, however, affected only children less than seven years of age and began only after ~1740, with increasing population size and density. Taken together, the evidence indicates that smallpox cyclicity occurred following population concentration by families with susceptible children born after the previous epidemic. Strengths of our analyses include use of rigorous time-series methods which permit detection of mortality cycles over a wide range of time lags (i.e., two to ten years). Availability of environmental variables also enabled us to examine the relative contribution

• f ecological pressure to epidemic cycles. In addition, the PRDH data show excellent

population-based coverage and follow-up relative to many other regions examined from this era. We used spikes in mortality counts to approximate increases in mortality rates and the detection of epidemic cycles. We view this assumption as reasonable for two reasons. First, we know of no documented occurrence in colonial Quebec from 1740-1798 in which a sudden influx of settlers increased the population size by over 50% in one year, and then the

14 influx was “remembered” by similar immigration seven years thereafter. Second, our time- series methods identified and removed trend in the age-specific mortality series, which controls for rises in mortality counts due to gradual increases in population growth. Any cyclicity we observe is net of this trend. Careful study of archival documents such as official correspondence and diaries has yielded evidence that smallpox and measles caused many of the large epidemic events among the colonial Quebecois. We, however, had no – or very sparse – cause-of-death information in the parish records from which our data were collected (Amorevieta-Gentil, 2009). We, consistent with the literature, used detection of cycles in mortality to infer the presence of epidemic cycles. Smallpox cyclicity in rural parishes in Finland, moreover, showed a seven-year cycle (Mielke et al., 1984), while it showed up to four- and five-year cyclicity in Sweden and England (Bengtsson & Ohlsson, 1985; Duncan et al., 1993). In light

• f previous literature which documents smallpox epidemic years in this historical

population, we view the seven-year cycle as consistent with the periodicity of smallpox. Historical records on smallpox, however, remain incomplete. For example, 1791 and 1798 represent two years in which child mortality rose above expected levels. These years are spaced seven years apart, and 1791 also follows the last documented smallpox epidemic (i.e., 1784) by seven years. It remains possible that record-keepers habituated to these large cyclical rises in child mortality and therefore did not note them as “unusual” years affected by smallpox. We know of no other pathogen that appears as well-documented in colonial Quebec archival sources as was smallpox. For these reasons, the principle of parsimony leads us to attribute the 7- year cyclicity in child mortality to smallpox.

15 Inspection of the role of environmental variables indicates that temperature, drought, and grain prices did not affect the strength of the 7-year epidemic cycle. Some studies in Europe and Sweden find that smallpox mortality increased following years of poor harvest. It remains unclear whether the association in Europe arises from increased exposure to disease among farmers in search of work or increased susceptibility due to malnutrition (Duncan et al., 1993; Bengtsson, 1999). In Quebec, inhabitants may have been protected from poor harvests by relying on game and fish for sustenance and work. Once we removed the influence of cycles on mortality, warm temperatures, drought, and high food prices coincided with elevated child mortality in that same year. These results indicate that the dynamics of smallpox appeared to act separately from other ecological pressures. Infants and children in non-epidemic years responded to various environmental

• variables. Whereas a full exploration of these associations lies beyond the scope of this

paper, we offer a few interpretations post hoc. Relatively low precipitation indicates drought conditions, which could adversely affect agricultural yields and reduce nutritional intake among pregnant women and children. Similarly, high food price may signal lack of food availability, which may adversely affect infants and children. The discovered association between warm temperatures and elevated infant and child mortality appears counterintuitive. We offer two speculative explanations for this

• result. First, warm temperatures may have increased the spread of enteric pathogens via a

fecal-oral route and/or contaminated drinking water (Landry & Lessard, 1996). In a historical analysis of the Netherlands, Ekamper and colleagues report a positive association

• f heat waves and mortality, with the strongest associations observed among infants and

young children (Ekamper et al., 2010). Gastrointestinal diseases in babies developed mainly

16 due to the spoilage of nutritional substitutes, such as milk, porridge and even water, used to nourish infants in the absence of breastfeeding (Ekamper et al., 2010). Higher summer temperatures also encouraged the proliferation of animal and insect carriers of infectious disease (Landry & Lessard 1996; Ekamper et al., 2010). Second, to the extent that annual warm temperature values correlate with large temperature oscillations across season but within calendar year, results may arise from responses to oscillations rather than from changes in mean temperature. We encourage more research in this area and remind the reader that our explanations remain informed speculation at best. The cycle results align with ) Imhof (1976) and Mielke and colleagues’ (1984) discovered interval between smallpox epidemics in rural parishes in 18th century Sweden and Finland. Wrigley and Schofield (1981) likewise find evidence of a six to seven year interval between mortality crises in 16th and 17th century England (p. 650). The cyclicity in colonial Quebec, however, diverges from the two-year interval reported in London by Duncan and colleagues (1993). We suspect that colonial Quebec showed longer intervals

• wing to much lower population density and population size than London. Mathematical

models of infectious disease dynamics assume an accumulation of a sufficient number of naïve susceptibles before an epidemic can occur (Duncan et al., 2001). Colonial Quebec (post-1740) may have required seven years’ time to build up a sufficient pool of susceptible children who would sustain a smallpox epidemic. As the population size grew well into the 19th century, we expect that the intervals between smallpox epidemics would shorten in

• length. We await newly harmonized data on the colonial Quebecois from 1800 onward to

test this proposition.

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22 Figures 1a and 1b. Death counts by age in Quebec, 1680-1739 (top) and 1740-1798 (bottom). 500 1000 1500 2000 2500 1740 1760 1780 Death count Year <1 year 1 to 4 years 5 to 14 years 15 to 49 years >49 years 100 200 300 400 500 600 700 1680 1700 1720 Death count Year <1 year 1 to 4 years 5 to 14 years 15 to 49 years >49 years

23 Figure 2. T-value of autocorrelation function in age-specific death counts in Quebec (1680- 1798) for a lag of up to ten years. Absolute value of T-value less than 1.96 is shaded in gray.

• 3
• 2
• 1

1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 T-value Lag in Years <1 year 1 to 4 years 5 to 14 years 15 to 49 years >49 years

24 Figure 3. T-value of autocorrelation function in age-specific death counts for various youth age cutpoints in Quebec (1680-1798) for a lag of up to ten years.

• 3
• 2
• 1

1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 T-value Lag in Years <7 years 6 to 14 years 7 to 14 years

25 Table 1. Time series results for nine separate models predicting annual death counts from birth to 6.99 years of age as a function of environmental variables and autocorrelation1, historical Quebec. Models 1 through 9 include years 1680 to 1798. Models 3,5,7 and 9 control for outlier years in death counts. ________________________________________________________________________ Coefficient SE p-value ________________________________________________________________________ Model 1: No environmental variables autoregressive parameter, lag 7 years .53 .09 <.0001 Model 2: Temperature autoregressive parameter, lag 7 years .50 .08 <.0001 temperature (continuous) 97.20 204.39 .63 Model 3: Temperature, outlier control autoregressive parameter, lag 7 years .08 .11 .45 temperature (continuous) 377.51 57.31 <.0001 Model 4: Precipitation, East Quebec autoregressive parameter, lag 7 years .47 .08 <.0001 precipitation index .002 3.78 .99 Model 5: Precipitation, East Quebec, outlier control autoregressive parameter, lag 7 years .47 .09 <.0001 precipitation index

• 4.8

2.09 .02 Model 6: Precipitation, West Quebec autoregressive parameter, lag 7 years .51 .09 <.0001 precipitation index

• 3.25

13.17 .80 Model 7: Precipitation, West Quebec, outlier control autoregressive parameter, lag 7 years .54 .09 <.0001 precipitation index

• 8.61

5.67 .13 Model 8: Standardized Food Price autoregressive parameter, lag 7 years .50 .08 <.0001 food price (z-score)

• 7.14

27.40 .77 Model 9: Standardized Food Price, outlier control autoregressive parameter, lag 7 years .50 .09 <.0001 food price (z- score) 29.2 15.70 .07 ________________________________________________________________________

1 Full autocorrelation parameters from 9 ARIMA models not shown; available upon request.