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Food Shortages Julianna Brunini Natalia Paine Danny Wilson

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Context: population growth drives demand for food Production from Poultry and Pigs in China ( ) Eggs Pigs Poultry ← Nonlinear increase in meat consumption with increasing GDP World Population v. Time ( ) Constant fertility High Medium Low Images: Population Division of the UN, World Population Prospects: the 2012 Revision; Food and Agricultural Organization of the UN, Livestock and global food security, 2011 Over 7 billion humans now live on the planet, consuming more crops and meat than ever before Million tonnes

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Worldwide famine has not yet ensued, thanks to technological innovation The Green Revolution (1940s-1960s) spread fertilizers, pesticides, high-yield and dwarf cultivars throughout the developed and developing worlds. Images: 1. Robert S. Peabody Museum of Archaeology, Phillips Academy, Andover, Massachusetts. 2. environment/14borlaug.html?pagewanted=all&_r=0http://www.nytimes.com/2009/09/14/business/energy- environment Farmer selection increases maize ear size Norman Borlaug won the Nobel Peace Prize for his work on high- yield and dwarf cultivars

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Contemporary concern: maintaining food security as the climate changes Climatic factors that affect the food supply include precipitation, temperature and concentration of atmospheric gases Heat Waves Images: Dole et. al (2011); IPCC 2013; environment.nationalgeographic.com;environment.nationalgeographic.com IPCC ^ Temperature predictions under various emissions scenarios Desertification Storms and floods

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Today’s topic: how will increasing temperatures affect crop yields? Historical Temperature Exposure for US Corn ( ): Corn growth and Temperature 35 C 5 C ← Growth range limits → Temperatures outside the survival range injure crops. Images: Schlenker and Roberts (2009) Supplement;

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In particular, we focus on crop yields and temperature in the eastern US Images: USDA 1. Soy Production by County, 2008 [Scale: bushels/acre] 2. Cotton Production by County, 2012 [Scale: 0-50+pounds/acre] 3. Corn Production by County, 2010 [Scale: 1 million million bushels] Schklenker & Roberts, Butler & Huybers

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Bushels per Acre Background: yield and agricultural output Yield (or agricultural output): Quite simply: dry volume of crop produced per unit area of land cultivation In the US, it’s measured in bushels/acre Yield has a complex relationship with temperature Corn Yield in the US ( ) Green Revolution

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Before we begin: A “Bushel” and an “Acre” in Relatable Terms 1 acre is approximately ¾ the area of a football field Harvard Yard is about 10 acres

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Review: regression models Temp Purpose 1.To test the validity or falsity of a hypothesis Method: least-squares regression 1.Define “error” as the distance between the observation and the model prediction 2.Square the error terms to eliminate negative values 3.Minimize the sum of the squared errors Data point Linear regression model Error = observed(x) - predicted(x) The dependent variable is functionally related to the independent variable Yield

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Schlenker & Roberts aggregate corn, soy and cotton exposure to 1 degree C intervals from across 2,000 US counties USDA Yield Data pdf/CR-PL12-RGBChor.pdf Schlenker (2006),Nonlinear effects of weather on cornfields Home Weather Station Weather data manipulated to “fine-scale”

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Schlenker and Roberts use an additive model, assuming yields are cumulative and proportional to temperature exposure y it = log(yield) in county i, year t g(h) = yield growth h = heat φ it (h) = time distribution of heat z it = control factor (to account for technological change, precipitation) c i = fixed-county effect (to control for soil type, quality) Residual error lower temperature bound upper temperature bound

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Histogram of Temperature Data for an average Corn Growing Season Histogram combines spatial and temporal data: - 50 growing seasons and 2000 counties - Normalized to the length of one growing season - Plotted as a histogram (x-axis is Temperature; y-axis is average number of days exposed to that particular one degree). Threshold Temperature In the model, the temperature distribution = φ it (h)

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Corn Shows Nonlinear Relationship between Temperature and Yield For corn, yield increases up to a threshold temperature (29 degrees C) and then drops precipitously. Schlenker and Roberts (2009), Figure 1 Threshold temperature Note that the y-axis is logarithmic Anomaly of Log Yield (bushels) Temperature (Celsius) Exposure (days) Blue fit: step function Black fit: 8th-order polynomial Red fit: piecewise linear ← Growth range limits →

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Understanding the Y-Axis - Anomaly of Log Yield (Bushels) - Misleadingly labeled Log Yield (Bushels) - A change of.01 on the axis corresponds to a 1% change in yield - A.075 decrease along the axis corresponds to a 7.5% decrease in yield Corn Temperature (C) Anomaly of Log Yield (Bushels)

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Soy and Cotton Also Show Nonlinear Relationship between Temperature and Yield Schlenker and Roberts (2009), Figure 1 SoyCotton Temperature (Celsius) For soy and cotton, the threshold temperatures are 30 and 32 degrees C, respectively. Threshold temperature Anomaly of Log Yield (bushels)

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Schlenker and Roberts claim best out-of- sample predictions yet Compared to other models from the literature, Schlenker and Roberts’ reduces the root-mean-squared prediction error the most. Schlenker & Roberts models Other models Percent reduction in Root-Mean-Squared prediction error for various models Schlenker and Roberts (2009), Fig years of data → Randomly choose 48 years and generate model estimates → Use model estimates to predict yields for the 8 leftover years

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Schlenker and Roberts compare their model to three previous models Mendelsohn et al: Temperatures for January, April, July, October Schlenker et al: Thom’s relationship for daily temperature to monthly Deschenes et al: Daily mean temperatures to GDDs Previous predictions inferior because temperatures were averaged over time or space

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Combining their statistical model with temperature forecasts, Schlenker and Roberts predict yield declines for The authors predict % yield decreases under the slowest warming scenario; % decreases under the fastest warming scenario. Schlenker and Roberts (2009), Figure 2 Colors match Figure 1 Blue = step function Black = 8th-order polynomial Red = piecewise linear Impacts by (percent) Corn Soy Cotton Greater warming

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Conclusions Persist Within Subsets of the Data The authors further divide the corn data by: 1.Temperature a. Warmest, intermediate, and coldest regions 2.Time period a. ( ) and ( ) 3.Level of precipitation a. Quartiles of total rainfall during June and July 4.Alternative growing seasons For all subsets of the data, the authors observe a nonlinear trend between yield and temperature.

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Breaking the dataset into warm, medium and cool subsets still results in a nonlinear trend between Yield and Temperature The Northern subset shows a slightly higher threshold temperature and a steeper decline than the Southern subset. Images: Schlenker and Roberts (2009) Supplementary Material Corn—North Corn—South Anomaly of Log Yield (bushels)

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Breaking the data into an early period and a late period still results in a consistent, nonlinear trend between yield and temperature Average yields were greater between 1977 and 2008 than between 1950 and 1977, but the trend between yield and temperature is similar. Soybeans ( ) Soybeans ( ) Anomaly of Log Yield (bushels)

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Precipitation quartiles show the same nonlinear trend between temperature and yield shown by the full dataset For corn, greater precipitation results in a shallower decline after the threshold temperature. Corn: linear fitCorn: polynomial fit Corn: step function fit Anomaly of Log Yield (bushels)

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Choosing alternate growing seasons results in the same nonlinear relationship between yield and temperature Corn (April to August)Corn (March to September) Anomaly of Log Yield (bushels) Temperature (Celsius) Exposure (days) For both extended and shortened growing seasons the nonlinear trend persists.

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Schlenker & Roberts: Methods and Conclusions Method Statistical regression, holding current growing regions fixed Conclusions Non-linear trend: yields increase with temperature up to a threshold, above which they decline precipitously Total yields decrease rapidly by 2099 for each of the 4 climate scenarios Fig. 1: Nonlinear relation between temperature and corn yield

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Capacity for Agricultural Mobility within the United States and North America As temperatures rise, land suitable for growing will see a northward shift. S&R models hold current growing regions fixed.

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Multiple Linear Regression: A review Butler and Huybers use multiple linear regression to measure the effects of several factors on yield. Multiple linear regression helps us answer four types of question: 1.Is at least one of the predictors useful in predicting the response? 2.Are all predictors useful or just a subset? 3.How well does the model fit the data? 4.Given a set of predictors, what responses can we expect? Remember: adding additional variables can only increase R 2 → you want a theoretical basis to justify their inclusion Y = β 0 +β 1 X 1 +β 2 X 2 +···+β p X p + ε Least-squares regression still applies

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Killing Degree Days Days that are so hot that they hinder grain development KDD = sum of all all days with average temperatures greater than 29 degrees C (84 F) Growing Degree Days Warm days that enable grain development GDD = sum of all days with average temperatures greater than 8 degrees C (46 F) Background: agricultural terms

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Butler and Huybers (2013) look at maize across 1600 counties in the eastern US between 1981 and 2008 USDA Yield Data gives maize yield from 19 states 534 Weather Stations give daily minimum and maximum temperatures

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Butler and Huybers represent county yields using a linear combination of Growing Degree Days and Killing Degree Days Beta(0) = mean yield in county i ( ) Beta(1) = sensitivity to technological change Beta(2) = cultivar sensitivity to growing degree days in county i Beta(3) = sensitivity to killing degree days in county i Y = yield in county i t = technological change GDD = Growing Degree Days KDD = Killing Degree Days Epsilon = error

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Yield sensitivity to Growing Degree Days varies spatially GDDs are a positive force on growth – they indicate higher yields In cooler regions, sensitivity to GDDs is 0.15 bushels/acre of yield Black boxes indicate irrigated counties Yield Sensitivity to GDDs (Beta-2) Butler and Huybers (2013), Fig. 1a Latitude Yield per GDD ( ) Sensitivity to GDDs decreases in hotter regions

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Yield sensitivity to KDDs varies spatially, with lower sensitivity in hotter climates Remember that KDDs → decreased yield Maize is from the tropics: adaptation interventions have been made for cold weather maize The authors take the spatial variation in KDD sensitivity as evidence of farmer adaptation Yield Sensitivity to KDDs (Beta-3) Latitude Yield per KDD ( ) Butler and Huybers (2013), Fig. 1b

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Distinguishing sensitivity from adaptation Sensitivity Strength of response to a given forcing Adaptation Actively choosing to minimize sensitivity to a particular forcing Sensitivity is a property of the plant, while adaptation refers to farming decisions

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Representing adapation: Butler and Huybers find a logarithmic relation between KDD sensitivity and climatology in unirrigated crops Figure 2, Butler and Huybers (2013). Climatology (Mean KDD) Sensitivity (Bushels/ acre/KDD) Red: logarithmic fit Red dashes: 95% confidence intervals Grey: linear and inverse fits Cold counties are most susceptible to yield loss from heat stress.

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- Equation (1) describes county Yield as a function of GDDs and KDDs - NO ADAPTATION YET -Spatial variation in Beta-3 is taken as evidence of adaptation - Logarithmic relation between KDD sensitivity and climatology represents adaptation mathematically - The authors substitute (2) into (1) - Add 2 degrees C to all Ts - Fit Beta-3 for higher Ts - Calculate new yields using Beta-3 as a function of KDDs and higher temperatures Incorporating adaptation into the model Y = yield t = technological changes GDD = growing degree days KDD = killing degree days Beta-0: mean county yield Beta 1, 2, 3: sensitivity parameters Epsilon: residual error

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Model output for 2 degree C warming: predicted yield losses with (right) and without (left) adaptation Figure 3a, 3b Huybers and Butler (2013) Yield increases in colder counties due to GDDs When adaptation is included, predicted yield loss with 2 degree Celsius warming decreases from 14% to 6%. Yield decreases in hot counties due to KDDs Using equation 1 (no adaptation) Using equation 3 (with adaptation)

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Schlenker and Roberts: adaptation does not ease the predicted impact of rising temperatures Blue, Black, Red represent no adaptation; Teal, Grey, Pink represent all farmers choosing to grow Southern corn. Impacts by , (%)

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Butler’s response: Schlenker’s data is heavily weighted by Southern counties The overall transfer function used by S&R is heavily determined by the South, biasing the results to favor greater losses Yield losses occur in the South, while gains occur in the North Spatial → Variation in Yield Loss, generated by Butler using Schlenker and Robert’s modeling technique

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Schlenker: Butler’s approach to modeling adaptation is flawed Butler incorporates adaptation by making KDD sensitivity a function of climatology Schlenker argues that adaptation should alter all parameters, including the intercept and GDD sensitivity

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Butler: we did look at GDD sensitivity and found it to be less important than KDD sensitivity Butler & Huybers, Figure S7 Focus on GDD sensitivity… Even with GDD sensitivity included, losses within confidence interval

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The debate: Where does adaptation come from? Which is it?

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Butler cites previous work showing Southern resiliency Damage to Southern, Northern and Central Pioneer Hi-Bred Seeds Ristic (1996): “Southern hybrids displayed greater ability to withstand drought and heat stress conditions than central and northern hybrids.” → greater ability to synthesize heat stress proteins than northern hybrids Ristic et al (1996), Dehydration, damage to cellular membranes,and heat-shock proteins in maize hybrids from different climates

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APPENDIX 43. Malthus 44. GMOs 45. Simulation models v. regression models Regression example 51.Schlenker & Roberts paper flow 52.Linear v. Log scale 53.Agronomists v. economists 54.Climate models 55.Multiple linear regression example 56. Canada and farming migration northwards Butler: what’s left out of the model Stages of corn growth, most vulnerable stages of corn growth 64.Butler and Huybers v. Schlenker and Roberts

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Context: a familiar dilemma? Thomas Malthus in the 18th century Malthus was concerned that exponential population growth would outpace linear growth in food production Images: Image: cw/content/index.htmlhttp://www.lawbookexchange.com/images/44869.JPGhttp://wps.aw.com/aw_miller_econtoday_13/29/7556/1

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In the 1970s, techniques emerged to genetically modify organisms; this process is fundamentally different from selective breeding To create GMOs, engineers take a desirable gene from one species and place it in the genome of another species Examples: 1.Insect immunity (Bt corn) 2.Vitamin A production (golden rice) Image:

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Background: mathematical models and agriculture Simulation models A strength of simulation models is that they utilize plant-growth theory; weaknesses include their complexity and oversight of farmers’ decisions. Simulation model for maize → Simulated maize = green line Red dots = experimental data Regression models ← Scatterplot showing Grain Yield v. Total Above Ground Dry Matter Regression models are able to incorporate farmers’ decisions, but they are susceptible to omitted variable bias. Images:

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Regression primer: Boston dataset The Boston dataset examines housing values in suburbs of Boston. There are 14 variables examined, including crime rate per capita per town, tax rates, and distance to employment centers. There are 506 neighborhoods around Boston examined.

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Boston dataset: Single linear regression – the basics Take median value (medv) as response with lower status of the population (lstat) as predictor In a single linear regression, our aim is to construct an equation that looks like this: Y ≈ β0 + β1X

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Boston dataset: Single linear regression – key terms Here, we are regressing medv onto lstat. What does this mean? We must use the data we do have (training data) to estimate the coefficients. We use the least squares criterion to ensure that the line we generate is close to our data points When we run this in the statistical software R, we get: Intercept (B0) = 34.55lstat (B1) = -0.95

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Boston dataset: Single linear regression – the error term A more accurate representation of the linear regression equation is: Y = β0 + β1X + ε The additional term accounts for error. The model cannot account for everything: the relationship is probably not linear; variation in Y (or in this case, median value) is not controlled solely by X.

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Boston dataset: Least squares regression line Median value (thousands of $) Lower status of the population

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Schlenker and Roberts: Paper flow Construct fine- scale weather data Demonstrate superiority of fine- scale models Obtain climate scenario outputs Examine yields based on climate scenarios Examine yield changes based on temperature/yield regressions Ensure nonlinear relationship holds Takeaway: S&R go to great lengths to justify nonlinearity, and subsequently, deleterious effects of climate change

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Reminder: the important difference between a log and a linear axis Remember that an increment of 1 log(x) corresponds to an increment of 10x Images: Karen on Matlab—thank you!

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Schlenker and Roberts vs. agronomists and economists Widely cited Mendelsohn paper shows benefits under climate change Hedonic approach associates land values with land characteristics, thereby accounting for whole sector…...but there are cross-sectional in nature, thereby emitting key components

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Schlenker and Roberts combine their yield model with temperature predictions from the Hadley III climate model The Hadley Centered Coupled Model, Version III, is a general circulation climate model used to predict changes in temperature with time. A1fi: most rapid warming scenario A2: rapid warming scenario B2: moderate warming scenario B1: slowest warming scenario Image from: Emissions pathways, climate change, and impacts on California, pl/DC1

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Boston dataset: Multiple Linear Regression We can also run a multiple linear regression in R. Let’s choose lstat and age as our predictors Residual standard error = 6.17 on 503 degrees of freedom F-statistic: 309 on 503 degrees of freedom p-value: <2e-16

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Headlines Highlight Canada Washington Post Headline 4/15/2014 Businessweek Headline Nov Bloomberg Headline 4/15/2014

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Signs of Potential for Northward Expansion

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What’s left out? Benefits to warming Farmers may respond to warming in other ways: o Planting earlier o Expanding into new regions Higher annual average temperatures may have other benefits: o The growing season may be elongated https://wildgreenyonder.files.wordpress.com/2010/06/front-range-planting-calendar.png Global Distribution of Croplands (2000) Ramankutty et al. 2008

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What’s left out? Physiological trade- offs Example: maladaption to GDDs o Growing degree days are defined as days that allow for grain development But how positive the effects are may decrease with temperature That is, a 10 degree Celsius day may be more beneficial than a 25 degree Celsius day o The authors’ exploration shows that this is a minor contributor, does not change results T < T threshold Yield sensitivity Graphical representation of reduction of positive effects of GDDs with warming

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What’s left out? Water availability Irrigated counties show lower sensitivities to KDDs than non-irrigated counties (p < 0.01, one- sided t-test) When the authors included water availability in the model, it did not appreciably increase model skill Precipitation may be redundant, since T and precipitation covary Butler and Huybers (2013), Fig. 1b Yield Sensitivity to KDDs

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Physiological theory suggests that temperature is more significant during the flowering period (July) than at other times Log(Yield) vs. Temperature for July corn and remaining months ←Predicted long-term impact for corn under 4 warming scenarios (0 to -100%) The authors find statistical support for this theory, but including more temperature variables does not improve the model or change the climate change impact predictions. Temperature (Celsius)

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Stages of Crown Growth VE = Emergence V1 - V9 = Vegetative Stages VT = Tasseling R1 = Silk Emergence and Pollen Shed R6 = Maturity VE V1 V3 V6 V9 VT R1 R6 R2 R3 R4 R5 R6 Kernel Maturation

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When does heat have the largest effect? R1- Silk Emergence and Pollen Shed Emerged silks are viable and receptive to pollen up to 10 days. Each silk is connected to a potential kernel on the cob. Stress can cause kernels to not be fertilized, resulting in a poor yield. Image Purdue University R.L. Neilsen

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B&H reproduce S&R’s model with their data; B&H find no sensitivity / temperature trade-off S&R B&H

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Appendix? Fig S1, S2 Butler appendix F-test and validity of their 4-parameter model?

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