1
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Supporting Information
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Unraveling the annual cycle in a migratory animal: Breeding-season
habitat loss drives population declines of monarch butterflies
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D. T. Tyler Flockhart, Jean-Baptiste Pichancourt, D. Ryan Norris, Tara G. Martin
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correspondence to: dflockha@uoguelph.ca
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Appendix S1. Detailed description of methodology
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14
Our population model required parameter estimates of survival, fecundity and migration
15
throughout the annual cycle. We considered one overwintering and three breeding regions to
16
parameterize a stochastic, density-dependent periodic projection matrix model for monarch
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butterflies. Below we present details on the population model, the methods used to derive each
18
vital rate, and the results of four novel analyses relevant to understanding monarch population
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dynamics: (i) migration rates (transition) of reproductive butterflies between regions throughout
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the annual cycle, (ii) survival of butterflies during migration derived from an expert elicitation
21
exercise, (iii) a model to estimate milkweed abundance amongst the three breeding regions in
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eastern North America, and (iv) a model to estimate the effects of climate change and
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deforestation on the probability and intensity of mass mortality on the wintering grounds over
24
time.
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1
26
1. Matrix population Model
27
1.1. Transition Matrix
28
The global transition matrix Ap at a given month t of the year is used to project the population
29
vector from n(t) to n(t+1), such that:
30


n (t  1)  A t n (t )
eqn 1
31
Within each time step t, At included both migration amongst and demography within the four
32
geographic regions (k = 4) for the five life-stages (l = 5) using the block-diagonal formulation
33
and vec-permutation approach (Hunter & Caswell 2005):
At  PDt PT M t .
eqn 2
34
Here, P is the vec-permutation matrix with dimensions lk x lk, PT is the transpose of P, Dt is the
35
block-diagonal demography matrix, and Mt is the block-diagonal migration matrix between
36
regions at a given month t. In this arrangement, butterflies move between regions first before
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demographic events, such as reproduction, occur (Hunter & Caswell 2005), in order to reflect the
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rapid re-colonization of eastern North America over successive generations (Malcolm, Cockrell
39
& Brower 1993, Flockhart et al. 2013). The process is repeated for each of the p time steps.
40
Table S1 includes a list and description of all variables used in the model.
41
The block-diagonal matrix,
Dt

 diag Dt1, Dt2 , Dt3 , Dt4

eqn 3
42
organizes the demographic processes within regions, where Dti is an l x l demographic projection
43
matrix for region i:
2
f bi1 1  d i ei
0
i
s ow
2 1  ei 
0
sbi 1ei

0
0

0
 sL di
i

i
Dt 
0
s ow
1 1  ei 

 s L 1  d i 
0

0
0

i
f bi1
0
0
0
sbi 1
f bi2 

0 
0 
0 

sbi 2 
eqn 4
i
44
i
where s L is survival of immature, s ow1 and s ow2 is overwinter survival for butterflies in their first
45
and second month of diapause, and s b1 and s b 2 is first and second month survival of breeding
46
adults. The terms d i and ei are dummies [0,1] representing reproductive diapause before
47
autumn migration to the overwintering colonies, and emergence from diapauses at the end of the
48
winter, respectively. By doing so, the demographic matrix allows us to follow the two cohorts of
49
butterflies simultaneously, breeding butterflies and butterflies in a reproductive diapause. The
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top row is fecundity of breeding butterflies in their first ( f b1 ) and second ( f b 2 ) months (Table
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S1).
i
i
i
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53
i
The migration process was structured with the block-diagonal dispersal matrix that
accounts for migration between regions,
Mt

 diag I , M tow1, M tow2 , M tb1, M tb 2

eqn 5
54
where I is a k x k identity matrix representing the absence of migration between regions for
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larvae, and 𝑀𝑡𝑜𝑤𝑖 and 𝑀𝑡𝑏𝑖 are k x k dispersal projection matrices for overwintering stage ow or
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breeding stage b, respectively, such that at each month we have for σ  [ow,b]:
M
i
t
i
 Tt  S
i
t
 t Mt , M
 t
t
  St , M
 t C ,M
tt
 N ,M
t Mt , S
t Mt ,C
t St , S
t St ,C
t Ct , S
t Ct ,C
t
N ,S
t
N ,C
t
t
t Mt , N   s Mt , M
 
t St , N   s St , M

t Ct , N   sCt , M
t Nt , N   s Nt , M
s Mt , S
s Mt ,C
s St , S
s St ,C
s St ,C
sCt ,C
t
S ,N
t
N ,C
s
s
s Mt , N 

s St , N 

sCt , N 
s Nt , N 
eqn 6
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tit, j is the transition rate between regions i and j based on stable isotope values (Flockhart
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where
58
et al. 2013), ∘ is the Hadamard or element-by-element product, and s i , j is survival during
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migration between these same regions (Table S1).
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t
We analyzed the population model by using the population size observed in 1994
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(Rendón-Salinas & Tavera-Alonso 2014) to assess the model fit from the first 19 years of the
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simulation (1995 to 2013) and then projected the population for 100 years and calculated the
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stochastic population growth rate (log λs) and 95% confidence interval from 1000 simulations.
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Model fit was assessed by testing the standard deviates of the population growth rates from
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observed and projected population sizes (McCarthy et al. 2001). Standard deviates were
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calculated by subtracting the observed population growth rate (Rendón-Salinas & Tavera-Alonso
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2014) from the mean projected population growth rate and dividing by the standard deviation of
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the projected growth rate. Using population growth rate accounts for autocorrelation in the data
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and allows the standard deviates to be independent (McCarthy et al. 2001).
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The mean of the deviates were compared to an expected mean of zero with a t-test to test
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the null hypothesis that the predicted population growth rate, derived from the projected
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population estimates of the model, does not differ from the observed population growth rate. If
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the mean is >0 then the model over-predicts population size whereas if the mean is <0 then the
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model under-predicts population size (McCarthy et al. 2001). The mean of the standard deviates
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was -0.053, which failed to reject the null hypothesis (95% CI: [-0.283, 0.176], t = -0.4889,
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df=18, P=0.63) indicating that our model outputs accurately predict monarch population size.
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The variance of the deviates is compared to an expected variance of one with a chi-
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squared test to test the null hypothesis that variance in the predicted population growth rate does
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not differ from the observed population growth rate (McCarthy et al. 2001). If the variance is >1
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then the variance of population size predicted by the model are less than those observed in the
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population whereas if the variance is <1 then the variance of population size predicted by the
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model tend to be greater than those observed in the population. The result of this test suggested
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that the predicted population size from our model tended to be more variable than those of the
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observed population (mean = 0.227, 95% CI: [0.129, 0.496], χ2 = 4.08, df=18, P < 0.001)
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however this statistical test assumes that there is no measurement error in the population counts
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or errors are normally distributed. Monarch population size is measured as the forest area (ha)
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covered by clusters of butterflies in Mexico (Brower et al. 2012, Rendón-Salinas & Tavera-
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Alonso 2014) and while the methodology to estimate the forest area is standardized and robust
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(Rendón-Salinas & Tavera-Alonso 2014), the monarch density (butterflies/ha) within these
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clusters is measured with a high degree of uncertainty (Brower et al. 2004, Calvert 2004).
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Therefore, the statistical test above should not be considered a definitive test of the validity of
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the variance in population size from our model but rather suggests that reducing variation in vital
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rate estimates would improve the precision of projected population size.
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For every month, we estimated the transient elasticities of the total species abundance to
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perturbation of the migration and demographic vital rates (Caswell 2007). To understand long-
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term sensitivities of monarch population growth rate, we summed the transition elasticity values
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between life-stages (immature, adults), life history events (breeding, non-breeding), regions
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(Mexico, South, Central, North) or months. The sensitivity matrices were arranged as (Hunter &
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Caswell 2005):
SDt  PT SAt MtT P
eqn 7
SMt  PDtT PT SAt
eqn 8
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where SAt is the sensitivity matrix of the transition matrix A (Caswell 2007). We then estimated
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the elasticities matrices as:
EDt 

sr
1
E t 

sr
1
1
D t  SDt

n (t )
eqn 9
1
 t  S t .

n (t )
eqn 10
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Each element within E represents the proportional monthly impact on monarch butterfly
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abundance of small, proportional disturbances on the demographic parameters within regions and
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on migration parameters between regions, separately. This separation allows for distinction
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between the different cohorts in the model to determine the sensitivity to population growth of
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all life history stages throughout the annual cycle.
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1.2. Fecundity rates
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There are no field-derived estimates of adult lifetime fecundity but lab experiments have
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shown that daily egg output is curvilinear with respect to age (Oberhauser 1997). As butterflies
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were provided with food and not exposed to predators, the mean lifetime fecundity estimates
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likely represent maximum values (range = 290 - 1179 eggs; Oberhauser 1997). We estimated
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fecundity of first month adults and second month to older adults (Table S1: f b1 , f b 2 ) using a
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log-normal distribution (Morris & Doak 2002) derived from the mean (715 eggs) and variance
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(std. dev. = 232) of lifetime egg output presented in Oberhauser (1997). We scaled fecundity
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such that butterflies in their first month laid 75% of their lifetime egg output and 25% in the
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second month. There is no evidence that females will lay fewer eggs with increasing adult
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intraspecific competition for host plants (Flockhart, Martin & Norris 2012), so lifetime fecundity
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was assumed density independent. Sex ratio of offspring was assumed to be 50:50.
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1.3. Migration rates
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Migration is the transition probability of adults flying between different regions at each time
tit, j ). Following the two-cohort structure of the model (eqn 4), we differentiate
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step (Table S1;
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rates between non-reproductive butterflies that are on fall migration to Mexico and
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reproductively active butterflies that move between breeding regions. We differentiate these two
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stages because we predict there to be both different mortality rates and different contributions to
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population dynamics between the cohorts (Herman & Tatar 2001).
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1) Butterflies in reproductive diapause (non-reproductive)
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The timing of migration of butterflies in reproductive diapause migrating to Mexico follows
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a relatively predictable pattern by latitude, where peak migration occurs in mid-September in the
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north, late September - early October in the central and mid-October in the south (Taylor 2013).
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We incorporated these temporal migration patterns in our model by assuming that butterflies
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depart to Mexico from the north during the September time-step, from the central during the
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October time-step and from the south during the November time-step. Collectively, these
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butterflies arrived at the overwintering colonies in December where they remained until April, at
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which time they transition, ei , into being reproductively active (Brower 1995).
t
138
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2) Breeding butterflies (reproductive)
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Reproductive monarch butterflies colonize the breeding grounds over successive generations
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(Cockrell, Malcolm & Brower 1993, Malcolm, Cockrell & Brower 1993, Brower 1995, Miller et
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al. 2011, 2012, Flockhart et al. 2013). We assumed the main cohort of butterflies colonized the
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south in April, the central in May and the north in June (Cockrell, Malcolm & Brower 1993). We
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assumed the last breeding generation would occur in August in the north and September in the
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central and the south regions (Brower 1995, Calvert 1999, Prysby & Oberhauser 2004, Baum &
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Sharber 2012, Flockhart et al. 2013), which implies the induction of diapause among eclosing
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adults, d i , the following month (e.g. adults eclosing in the North in September are assumed in
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diapause).
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t
We calculated migration rates of breeding butterflies based on published information in
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Flockhart et al. (2013) who used stable-hydrogen and -carbon isotopes to assign a geographic
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natal origin of butterflies captured across the breeding range and throughout the breeding season.
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To achieve a smooth temporal transition gradient throughout the breeding period, we categorized
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butterflies into 30-day bins to ensure that we had samples of butterflies for each month and
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region following the colonization dynamics stated above. For example, butterflies that were
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captured between March 20 and April 19 were used to estimate transition probabilities in April
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(Table S2). We reasoned that, since our model structure had butterflies migrating between
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regions before reproduction (Hunter & Caswell 2005), this adjustment would more closely
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represent migration and resulting egg laying dynamics during the breeding season and minimize
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bias in migration estimates that could arise with low sample size (Table S2). We omitted 25
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butterflies captured in the north region from Flockhart et al. (2013) that were caught after our
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September cutoff date of August 19 and pooled butterflies captured in the south region in
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September and October to increase the sample size of butterflies to improve estimates of
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migration in the south in late summer (Calvert 1999, Prysby & Oberhauser 2004, Baum &
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Sharber 2012).
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Results in Flockhart et al. (2013) presented cumulative spatial surface grids for multiple
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butterflies captured during each month of the breeding season but we are interested in the
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transition probabilities between our pre-defined regions (Mexico, South, Central, North).
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Therefore, for each butterfly we summed the number of cells in the grid consistent with an
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individual’s natal origin in each region and calculated the relative proportion of those cells
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among the three regions. The region with the highest relative proportion was assigned as the
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natal region; simulations of the probability of assignment regions using stable isotopes are robust
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(Miller et al. 2011). Here, the assigned natal region was considered the region of origin except
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for overwintered butterflies that were identified by their wing wear score that were assigned as
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originating in Mexico (see Flockhart et al. 2013). In all cases, the region in which the butterfly
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was sampled was considered the destination.
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For each month during the breeding season, we cross-tabulated origin and destination
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regions to produce a contingency table of relative frequencies by dividing the number assigned to
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each origin region by the marginal total of the destination regions. This marginal total assumes
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butterflies migrating between regions had an equal mortality risk so we corrected for the effects
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of differential survival (see Mortality during migration below) on transition probabilities by
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dividing the relative frequencies in each cell by the mean probability of survival during
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migration for that cell. Transition probabilities therefore reflect transition in the absence of
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mortality during migration and therefore assume that butterflies had equal detection and capture
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probabilities across regions in Flockhart et al. (2013). Using this approach, we calculated
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deterministic migration rates between the four regions (origin region included Mexico for
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overwintered butterflies) within a 4 × 4 matrix ( Tt ;Table S1) for each month during the
i
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breeding season. Samples from Flockhart et al. (2013) were collected in one year so migration
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rates in the population model were assumed constant over the study.
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Migration of reproductively active butterflies continued throughout the breeding season
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(Table S3). In April, about 88% of the butterflies captured in the South were overwintered
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butterflies from Mexico while the remaining were first generation monarchs born in the South. In
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May, 96% of the butterflies in the South were either born (26%) or had remained there since re-
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migrating from Mexico in April (70%). Butterflies in the Central region in May came from
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locally produced butterflies (52%), first generation butterflies from the South (13%) or
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overwintered butterflies that had migrated from the South (35%). In June, approximately 2/3 of
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butterflies captured in the Central were born in that region (65%) while the remaining were
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butterflies born in the South. Most (67%) butterflies colonizing the North in June were from the
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Central while the rest were from the South (33%). Butterflies captured in July came primarily
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from the Central region (Central: 80%, North: 74%) while the fewest came from the North
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(Central: 2%, North: 9%). Individuals captured in August in the North found 55% were produced
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locally while 44% had migrated north from the Central region. In contrast, the vast majority of
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butterflies captured in the Central were produced there (74%). In September, most butterflies
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breeding in the Central had stayed there to breed (83%). The last breeding generation in October
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that occupied the South was comprised of butterflies from all regions (Table S3).
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1.4. Survival rates
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We estimated survival for adults and larvae during the breeding season and for adults during
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the overwinter season and on migration. Estimates were based on published research, modeling
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simulation, and elicitation of expert judgment.
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1. Breeding grounds
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Adults
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Adult female survival (Table S1; sb1 , s b 2 ) came from estimated longevity measures of
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captured wild female butterflies that were kept in envelopes until they died (Herman & Tatar
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2001). Males and females had different survival rates, but our matrix model only considered the
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vital rates of females. Using the median life expectancy of 25.5 days from an accelerated failure
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hazard model resulted in the survivorship function S(t) = e(-t/25.5),where t is days, we calculated
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survival to mid-point of the first month (day 15) and second month (day 45). These rates
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represent adult sedentary survival in the absence of migration and, as these rates come from
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captive butterflies, it assumes negligible mortality from predators. Survival to mid-point of the
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first month was 0.56 whereas for the second month was 0.17.
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Immature
Immature survival ( s Li  p p  pl 
pd d
pmax
) was considered as the cumulative survival from
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egg to eclosion as an adult butterfly. Survival was the product of a density-dependent survival
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relationship based on larval competition for host plants (
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2012), larval survival ( p l ; Oberhauser et al. 2001), and pupal survival ( p p ; Oberhauser 2012).
pdd
pmax ;
Flockhart, Martin & Norris
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a) Pupal Survival
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Tachinid flies parasitize monarch larvae that result in mortality realized during the pupa
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stage (Oberhauser 2012). Mean and standard deviation of pupal survival from pupation to
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eclosion, ( p p ),based on 11 years of data , was assumed as one minus the marginal parasitism
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rate of fifth instars (mean = 0.849, SD = 0.0778; Oberhauser 2012). These values assumed that
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mortality during the pupal stage result solely from tachinid fly parasitism, all parasitized pupae
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will die, and the parasitism rate of late fifth-instar caterpillars was negligible. Mean and standard
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deviation of the pupal survival rates were fit to a beta distribution (Morris & Doak 2002) to be
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included in the population model.
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b) Larval Survival
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We calculated larval survival from egg to pupation, p l , by digitizing the values from fig
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3 in Oberhauser et al. (2001) who presented counts of 5th instar larvae relative to eggs from
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count data made in non-agricultural areas, agricultural fields and field margins in four
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geographic regions that spanned the breeding range. The mean larval survival probability ranged
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from 0 to 0.122 with a mean of 0.049 and standard deviation of 0.044 and these estimates were
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used in a stretch beta distribution to represent larval survival, p l , in the matrix model (Morris &
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Doak 2002).
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c) Density-dependent larval survival
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A decline in milkweed could influence vital rates through density dependent competition
245
amongst larvae for food resources (Flockhart, Martin & Norris 2012). We applied the model of
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Flockhart, Martin & Norris (2012) who found larval survival probability declined as the average
247
number of eggs per milkweed stem, d, increased.
pdd 
248
1
1 1
1.0175( 0.1972d )
e
.
eqn 11
To account for uncertainty in the strength of density dependence, we randomly selected a
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parameter estimate for both the slope (std. error = 0.0736) and intercept (std. error = 0.2863)
250
from normal distributions. The intercept term in the linear model (eqn 11; Flockhart, Martin &
251
Norris 2012) was speculated to be the density-independent mortality caused from feeding upon
252
toxic host plants or mouthparts being imbibed in latex (Zalucki, Brower & Alonso-M 2001). As
253
this source of mortality is already accounted for in our density independent survival estimate (pl,
12
254
see above), we removed this effect by dividing pdd by pmax, where pmax was the density dependent
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survival relationship with d set to zero. To apply this relationship in the population model
256
requires that we estimate milkweed abundance within each breeding region and account for the
257
change in milkweed abundance over time (see A model of milkweed abundance in eastern North
258
America).
259
260
2. Mortality during migration
261
Evidence for Lepidoptera suggests mortality during migration to be low relative to the
262
stationary portions of the annual cycle (Chapman et al. 2012) whereas the opposite pattern has
263
been found for vertebrates (Muir et al. 2001, Sillett & Holmes 2002). Few data exist to estimate
264
these mortality rates directly and there is currently no published information for monarch
265
butterflies. In the absence of empirical estimates, the opinions of experts can provide valuable
266
information to understand population processes (Martin et al. 2012). We used an expert
267
elicitation exercise to estimate the survival of monarch butterflies during both fall and spring
268
migration. We elicited nine experts that had extensive knowledge of monarch butterfly migration
269
and six experts participated in the expert elicitation exercise. The exercise consisted of
270
independent elicitation of survival estimates, an anonymous review of the group results, and a
271
second round of elicitations where experts were allowed to modify their original responses after
272
having seen the group results (Martin et al. 2012).
273
Each expert was provided a questionnaire with a map that outlined the four study regions
274
and asked to provide a worst-case, average-case, and best-case estimate of the probability of
275
survival for: (i) butterflies in reproductive diapause that migrate from each of the three breeding
276
regions to the overwintering colonies during autumn migration, (ii) overwintered adult monarch
13
277
butterflies that migrate from the overwintering colonies to the Southern region, and (iii) first or
278
second generation breeding adult butterflies that migrate from the South region to the Central
279
region and first or second generation breeding adult butterflies that migrate from the Central
280
region to the North region.
281
Using the values provided by experts as data, we calculated the mean and standard
282
deviation for the average-case values provided by experts and found that the modeled variation
283
of survival implemented into the matrix model contained both the mean worst-case and best-case
284
estimates provided by experts suggesting that the estimates of survival during migration
285
generated during simulations of the model captured a range of expected survival rates. To
286
calculate survival when breeding individuals traversed multiple regions to reach their destination
287
we multiplied the survival estimate between successive regions. However, we needed to modify
288
this approach for overwintered individuals that were captured in the Central region given that
289
they were up to 6 months of age and had been breeding for the previous month. To discount this
290
reduced survival, we multiplied the mortality of overwintered butterflies to reach the South
291
(0.517) by the combined product of survival to the south and the survival of fresh butterflies to
292
reach the central region (0.517 × 0.734).
293
Survival of butterflies on fall migration is provided above the diagonal in Table S4.
294
Experts thought that migratory distance would influence survival probability to reach Mexico.
295
Butterflies departing the South were predicted to be 1.38 times more likely than butterflies
296
departing the North to arrive in Mexico. Similarly, butterflies departing the South were expected
297
to be 1.22 times more likely than butterflies departing the Central to arrive in Mexico. Butterflies
298
departing the Central were predicted to be 1.13 times more likely than butterflies departing the
299
North to arrive in Mexico. Survival during migration was estimated to be higher for butterflies
14
300
on fall migration compared to reproductively active butterflies that were recolonizing the
301
breeding grounds (Table S4).
302
Survival of butterflies during the recolonization of the breeding grounds is provided
303
below the diagonal in Table S4. Survival of first or second generation butterflies moving to an
304
adjacent breeding region had similar survival estimates regardless of whether they originated in
305
the South (0.733) or Central region (0.742). Experts thought that survival would be lowest for
306
butterflies that depart the overwintering to reach breeding grounds in the South (0.517), however,
307
estimates provided by experts ranged from 0.25 to 0.9 which resulted in the largest variance
308
(Table S4). For butterflies that moved over multiple regions to breed, first or second generation
309
butterflies were more than 2 times more likely to survive moving from the South to the North
310
(Table S4).
311
To test the sensitivity of the survival estimates applied in the model, we ran model
312
simulations using best-case and worse-case scenarios provided by experts and 1) determined the
313
population response and time to extinction and 2) how well the resulting population predictions
314
matched the observed population decline (McCarthy et al. 2001). Using the best-case survival
315
estimates provided by the experts resulted in an increasing population growth rate (r = 0.0018),
316
which is contrary to observed population decline, but model-predicted population size fit the
317
observed population data (t = -0.3848, P = 0.7049) suggesting estimates of survival during
318
migration that are higher than the values we used in the model are consistent with monarch
319
population dynamics. In contrast, using the worst-case survival during migration estimates
320
resulted in a population crash in less than 10 years and is therefore inconsistent with monarch
321
population dynamics. These results suggests that the survival during migration estimates we
322
applied in the matrix model (average-case scenario, noted above) are robust to observed
15
323
population declines and are reasonable for monarch life history. It also suggests that true values
324
of survival during migration may be equal or slightly higher than those applied in the population
325
model.
326
3. Overwintering grounds
327
The probability of survival for overwintering adult butterflies (sow = sc×sm) is a product of
328
two processes: baseline survival in the presence of predators (sc; Brower & Calvert 1985,
329
Glendinning, Alonso Mejia & Brower 1988) and catastrophic mortality events caused by
330
extreme weather phenomena (sm; Brower et al. 2004).
331
332
Adult sedentary survival
Mortality from predators (sc) was estimated as the product of avian (Calvert, Hedrick &
333
Brower 1979, Brower & Calvert 1985) and mammalian predation rate (Brower et al. 1985,
334
Glendinning, Alonso Mejia & Brower 1988). Birds were estimated to kill 9% of all butterflies in
335
colonies (Brower & Calvert 1985), whereas mice were estimated to kill approximately 4% of the
336
population (Glendinning, Alonso Mejia & Brower 1988). These estimates assumed butterfly
337
density within the colonies was 10 million/ha, but subsequent analysis have indicated densities
338
are probably higher (Brower et al. 2004, Calvert 2004) which implies these values overestimate
339
mortality. Therefore, we estimated mortality from both birds and mice by dividing the number of
340
depredated butterflies from Brower et al. (1985) and Glendinning, Alonso Mejia & Brower
341
(1988) by the product of the observed colony sizes and a randomly selected density
342
(butterflies/ha) from a log-normal distribution based on the mean and 95% CI estimates from the
343
Jolly-Seber estimates in Calvert (2004). Subtracting the proportion of the colony killed by birds
344
and mice from one provides the predicted survival rate and, assuming that predation by birds and
345
mice are independent, multiplying the product of these two survival estimates yielded the
16
346
overwinter survival. We ran 1000 simulations, calculated the mean and standard deviation of
347
survival and fit these terms to a beta distribution to represent baseline overwinter survival.
348
Using adjusted estimates of butterfly density in the overwinter colonies (Calvert 2004)
349
resulted in overwinter survival rate of 0.959 (SD = 0.0173) over the 4 months that was higher
350
than original estimates (0.858 - 0.873; Brower & Calvert 1985, Brower et al. 1985). The monthly
351
survival rate was therefore estimated as 0.9896 for overwintering adult butterflies.
352
353
a) Catastrophic mortality
Stochastic mass mortality events in the overwintering colonies can kill significant numbers of
354
the entire eastern population during a single storm (Brower et al. 2004) and therefore directly
355
influence population viability. The magnitude of each mortality event is the interplay between
356
ambient temperature, precipitation and exposure that directly determines body temperature of
357
monarch butterflies (Anderson & Brower 1996). Given that temperature and precipitation
358
patterns are predicted to change (Oberhauser & Peterson 2003, Sáenz-Romero et al. 2010) and
359
forest habitat loss will continue (Brower et al. 2002, Ramírez, Azcárate & Luna 2003, López-
360
García & Alcántara-Ayala 2012, Sáenz-Romero et al. 2012, Vidal, López-García & Rendón-
361
Salinas 2014 ), we built a stochastic function to predict mass mortality events in Mexico that we
362
incorporated into the matrix model (see, A stochastic model of overwinter mass-mortality events
363
in Mexico).
364
365
366
2. A model of milkweed abundance in eastern North America
Milkweed (Asclepias spp) is the obligate host plant of monarch butterflies, and the
367
abundance of milkweed is thought to be declining across the breeding range from land cover
368
alterations (Brower et al. 2012, Pleasants & Oberhauser 2013) and the adoption of genetically
17
369
modified agricultural crops (Oberhauser et al. 2001, Hartzler 2010, Pleasants & Oberhauser
370
2013). Higher egg densities and hence stronger density-dependent intraspecific larval
371
competition mortality could arise from a larger number of adults laying eggs on a set number of
372
milkweed or by a steady number of females laying eggs on fewer milkweed plants.
373
The model to estimate milkweed abundance at time t, MWt, combined four pieces of
374
information. First, we estimated land area amongst land cover categories (Ai) using a Geographic
375
Information System (e.g. Taylor & Shields 2000). Second, for each land cover type we
376
multiplied land area by the empirical estimates of the area infested by milkweed (Hartzler &
377
Buhler 2000, Taylor & Shields 2000, Hartzler 2010) to derive the total area infested with
378
milkweed (Ri). Third, we multiplied the area infested with milkweed by the mean density of
379
milkweed stems (m) from more than 2000 samples of milkweed density following a standardized
380
protocol.
MWt   Ai ,t Ri m
eqn 12
381
Finally, to estimate milkweed change over time (Pleasants & Oberhauser 2013), we applied
382
annual rates of land cover conversion using data (U.S. Department of Agriculture 2009) between
383
1982 and 2007, and the expected adoption rate of genetically modified, herbicide resistant corn
384
and soybean crops (U.S. Department of Agriculture 2012).
385
386
Land cover area using a Geographic Information System
387
Different land cover types provide different suitability for milkweed and, by association,
388
monarch butterfly habitat (Taylor & Shields 2000, Oberhauser et al. 2001, Pleasants &
389
Oberhauser 2013). For each breeding region, we produced land cover classification maps by
390
merging several data sets using a Geographic Information System (Table S5). We assumed our
18
391
data sets were representative of conditions in 2009. Our southern spatial extent was limited to the
392
USA/Mexico border because roads and right-of-way areas were not available for Mexico (see
393
Roads and Right-of-ways below). We conducted overlay analysis using ArcMap 10.1 and, using
394
the Albers Equal Area projection, summed the area in each land cover category within each
395
breeding region (Ai).
396
We reclassified the 2009 GlobCover dataset (Arino et al. 2008) to 8 land cover types
397
(Table S6) that had estimates of the area infested by milkweed (Hartzler & Buhler 2000, Hartzler
398
2010). We also calculated the area covered by roads and associated right-of-ways from detailed
399
line features data sets of roads compiled for Canada and the United States (Haklay & Weber
400
2008). To quantify these important habitats (Taylor & Shields 2000, Pleasants & Obserhauser
401
2013) we used stratified subsets of random locations of these line features to estimate road and
402
right-of-way widths using aerial photographs; see Roads and Right-of-ways below. A detailed
403
layer of urban extent for Canada and the United States (Schneider, Friedl & Potere 2009) was
404
used to exclude dense road and right-of-ways networks that would have biased estimates of these
405
habitats and to account for small settlements that, if ignored, result in biased urban area
406
estimates. Finally, a terrestrial protected areas data set (Commission for Environmental
407
Cooperation 2010) outlined lands held in biological reserve programs that may be less prone to
408
landscape changes and hold higher amounts of natural vegetation including milkweed (Hartzler
409
& Buhler 2000). We assumed lands within protected areas held the same amount of milkweed as
410
non-protected counterparts but that they would not transition to a different land cover and that
411
agricultural lands within reserve areas represented land in the Conservation Reserve Program
412
(CRP; see Table S7) which are important habitats for monarch in agricultural landscapes
413
(Pleasants & Oberhauser 2013).
19
414
Road and Right-of-ways
415
Our objective here was to estimate the area of land encompassed in roads and the
416
vegetated right-of-ways (i.e. ditches) as these are an increasingly important habitat for monarch
417
butterflies (Hartzler & Buhler 2000, Taylor & Shields 2000, Oberhauser et al. 2001, Hartzler
418
2010, Pleasants & Oberhauser 2013). The data were line features (Haklay & Weber 2008) and
419
therefore provide no information to estimate land area. We used four steps to derive land cover
420
polygons of roads and associated right-of-ways that could be used to estimate the area of these
421
features across the breeding range (Taylor & Shields 2000). First, we reclassified the
422
descriptions provided for each line feature into nine road types (motorways, primary highways,
423
secondary highways, tertiary highways, residential roads, service roads, tracks, bike/walk paths,
424
and unclassified) and clipped roads covered by the urban extent layer.
425
Second, for each state or province, we randomly chose a sampling location from 5
426
randomly selected roads of each type (five locations from nine road types equals 45 observations
427
per state/province). For the derived sampling locations we used the measurement tool in Google
428
Earth to measure the width of the road surface and the mean of the two right-of-ways for each
429
road (n = 1772). Roads that could not be positively located after cross-referencing between our
430
geospatial layers and Google Earth were omitted (n = 163; 75% of which were walk/bike). Roads
431
that did not have road margins (e.g. private rural driveways) or were surrounded by continuous
432
habitat for greater than 50m on each side of the road (e.g. roads in pasture fields) were
433
considered to have no right-of-way. The majority of motorways (52%) were divided and in these
434
cases we measured to the middle of the median divider for one of the right-of-ways. While the
435
width of right-of-ways is likely to change based on local and regional factors over time, we
436
assumed that right-of-way widths were fixed over our study period.
20
437
Third, we used generalized linear models in two analyses using road width and mean
438
one-sided right-of-way width as the response variable to test for variation in road and right-of
439
way width due to the road type (classification), geography (state/province, country, breeding
440
region), or additive models of both factors. We used Gaussian error distributions for both models
441
but because right-of-way values were continuous-positive greater than zero, we used a log-link
442
function for the dependent right-of-way value (Crawley 2007, p.514). For each analysis, we
443
compared models using Akaike Information Criterion (AIC) values, selecting the model with the
444
lowest AIC as the most parsimonious explanation of the data.
445
Last, we applied the model results to draw two buffers on each line segment; one that
446
included the combined road and the right-of-way widths (right-of-way layer) from which we
447
erased the second layer which was the width of the road only (road layer). Since we measured
448
two right-of-ways for each road but used the mean value of the two measurements in the
449
analysis, we used the predicted one-sided estimate to represent right-of-way width on each side
450
of the road. This analysis encompassed a study area greater than 4 million km2 and the detailed
451
road and right-of-way layers included more than 5 million line segments.
452
Road classification best explained road width and was more than twice as likely as a
453
model that suggested differences in road width between countries and almost five times more
454
likely than a model indicating differences between breeding regions (Table S8). Results from the
455
top model found road widths that ranged from 3.8 m for walk/bike trails to 23.8 m for
456
motorways (Table S9).
457
Road classification and state/province held all support to explain variation in right-of-
458
way width (Table S8). Motorways (31.7 m, one-sided) had the largest right-of-ways and tracks
459
(1.1 m) had the smallest (Table S10). Differences among states showed North Dakota (motorway
21
460
= 40.0 m) to have the widest right-of-ways and Rhode Island (motorway = 8.0 m) to have the
461
narrowest (Table S10).
462
463
Assignment of infested area of milkweed in land cover types
464
Results in Hartzler & Buhler (2000) and Hartzler (2010) sampled for common milkweed
465
across a variety of habitat types and presented the proportion of their samples that contained
466
milkweed (i.e. occupied) and, of occupied sites, the mean area (m2) covered in milkweed plants.
467
Combining these two metrics produces an estimate of the “infested area” of milkweed per
468
hectare of land (m2/ha) for a given habitat type (Ri; see Table S7). Other land cover classes were
469
deemed as unsuitable habitat by Taylor & Shields (2000) and given an infested areas estimate of
470
zero (Table S7). This simple calculation does not account for the shifts in agricultural practices
471
hypothesized to cause rapid declines in milkweed abundance through the adoption of genetically-
472
modified crops (Brower et al. 2010). We consider this land cover type in more detail below (see
473
Effects of genetically modified, herbicide resistant crops on milkweed abundance).
474
The infested area of milkweed described above is an area of milkweed occurring in an area of
475
land (m2/ha) but we are interested in a count of milkweed stems given an area of land (stems/ha).
476
Thus, we multiplied the infested area of milkweed by an estimate of the density of milkweed
477
stems in infested areas to arrive at the number of milkweed plants per land cover type within a
478
region. The number of stems of milkweed within infested areas was estimated from 1 m2 samples
479
(n = 2200) made at 16 sites in Illinois and 6 sites in Ontario during June and July, 2012,
480
following the protocol of the Monarch Larvae Monitoring Project (Prysby & Oberhauser 2004;
481
see http://www.mlmp.org/Monitoring/ Overview.aspx). Here, infested areas are represented by
482
those samples (n = 482) that contained 1 ≥ common milkweed (Aslepias syraica) stems. The
22
483
mean number of milkweed stems in infested areas, m, was 1.948 stems/m2 (SD = 1.609/m2). Our
484
estimate of milkweed stem density was assumed constant over time.
485
486
487
Rates of land-use change
Summaries of land cover area over time were used to calculate land cover transition
488
matrices. These transition matrices accounted for milkweed loss that is concomitant with habitat
489
changes from land cover that supports milkweed (e.g. pasture) to those that support none (e.g.
490
urban areas). We estimated annual land cover change for cropland, pastureland, rangeland,
491
forest, and developed land using data of cumulative land cover change (U.S. Department of
492
Agriculture 2009) between 1982 and 2007.
493
Using habitat transitions over a long time interval (25 years) avoids potential issues of
494
habitat alterations that may be variable over short time spans. The analysis in U.S. Department of
495
Agriculture (2009) provides land area estimates for: cropland, CRP, pastureland, rangeland,
496
forest, developed land, other rural areas and federal lands including waterbodies. We ignored
497
these last two categories from the analysis (but see below for waterbodies). We also excluded
498
CRP lands since change in this habitat type was dramatic (the program was initiated in 1985),
499
and instead we considered agricultural habitat in protected areas as representative of these areas
500
and, hence, constant (see Table S7). Developed land was described as those lands removed from
501
the rural land base (including urban areas, built up land, and transportation and associated right-
502
of-ways), and was considered as representative of urban areas.
503
To calculate annual transitions of land between different classifications between 1982
504
and 2007 (see table 10 in U.S. Department of Agriculture 2009), we needed to adapt the data to
505
eliminate new classifications (CRP lands) and remove unnecessary classifications (other rural
23
506
and federal land and water bodies) from the analysis. Since we were calculating transition rates,
507
we removed categories but maintained the proportional values of the land base. For example, we
508
first added the land area that had been designated as 2007 CRP lands back to the category that
509
they had been classified to in 1982 (since the program did not yet exist). Next we did the
510
opposite for 2007 lands classified as rural land and federal land and waterbodies back to their
511
original state in 1982. For the land area that had remained as these land cover classifications
512
between the start and end of the study, we eliminated the land area sum from the total land area,
513
thereby keeping the proportions of all land cover consistent between the two time periods.
514
Finally, since the change between classifications occurred over a 25 year interval, we took the
515
25th root of the cumulative change to derive the annual rate of change (Table S11). Values for all
516
other land cover types were assumed constant and resulted in no net change which is reasonable
517
for water bodies and, to a certain degree, for long-term infrastructure such as roads and right-of-
518
ways. We assumed that these rates of change would continue into the future.
519
Effects of genetically modified, herbicide resistant crops on milkweed abundance
520
Rapid adoption of genetically modified and herbicide resistant corn and soybean crops
521
has been implicated as one factor influencing milkweed abundance in agricultural landscapes55
522
and the abundance of monarch butterflies (Oberhauser et al. 2001, Brower et al. 2012, Pleasants
523
& Oberhauser 2013). However, the ecological effects of these agricultural land changes are
524
expected to influence monarch populations by (i) the spatial arrangement of crops (corn and
525
soybean) that have genetically modified strains that negatively influence milkweed abundance,
526
(ii) the adoption rate of genetically-modified crops, and (iii) the functional relationship between
527
genetically-modified crops and milkweed abundance. For each region, we estimated total
528
milkweed abundance in cropland in region i at time t, MWc, as:
24
soy
other
MWci,t  Ac m( K icorn
,t  K i ,t  K i ,t )
eqn 13
529
where Ac is the area of cropland in region i, m is the density of milkweed stems of infested areas
530
(1.948 stems/m2; see Milkweed Density in Infested Areas above), and Ki,t is the weighted area
531
infested with milkweed in corn, soybean and other agricultural crops. The variable K allows us
532
to partition milkweed abundance between different crop types, where Kother
K iother
 R other (1  ( picorn  pisoybean ))
,t
corn
other
K icorn
 picorn ( Ricorn
(1  g icorn
,t
,t g i ,t  R
,t ))
eqn 14
eqn 15
533
considers the abundance of milkweed in crops after removing the proportion of corn ( picorn ) and
534
soybean crops ( p isoybean ), while Kcorn (and similarly for Ksoybean) partitions milkweed abundance
535
by those grown with traditional (Rother) or genetically modified strains (Rcorn) as
gicorn
,t
Ricorn
 R other  0.0151
,t
eqn 16
a
g
corn
i ,t
 c ( 2000 x )
 1  be
.
100
eqn 17
536
The proportion of crops grown as corn ( picorn ), soybean ( p isoybean ), and other crops sum to 1 (see
537
Proportion of corn and soybean crops on the landscape, below). The term Ri,t is the area (m2/ha)
538
infested with milkweed within agricultural fields where R other is a constant applicable to all crop
539
types except genetically-modified strains of corn and soybean (26.52; Table S7) and Rcorn
540
(similarly for Rsoybean) represents the response of milkweed abundance with proportions changes
541
of genetically modified corn strain use (see Relationship between genetically modified crops and
542
milkweed abundance, below). The term gi,t is the proportion of the corn or soybean crop planted
543
with genetically-modified strains and subtracting this term from one gives the proportion of
544
traditional corn or soybean planted in fields. The term gi,t was modeled using 3-term non-linear
25
545
regression (eqn 17) and represents the expected proportion of genetically-modified strains of
546
corn and soybean on the landscape for year x (see Adoption rate of genetically modified crops,
547
below).
548
549
i) Proportion of corn and soybean crops on the landscape
The spatial correlation between highly productive breeding habitats and agriculturally
550
intensive areas of the Midwest Corn Belt means that our model must account for the spatial
551
arrangement of corn and soybean crops (Oberhauser et al. 2001, Brower et al. 2012, Pleasants &
552
Oberhauser 2013). Our land cover layer estimated cropland which was predominately comprised
553
of row crops (U.S. Department of Agriculture 2009), but corn and soybean only make up a
554
portion of all row crops in eastern North America. We calculated the proportion of corn (pcorn)
555
and soybean (psoybean) of all row crops for each state and province within our study area.
556
We obtained estimates of planted areas from 2009 in Canada
557
(http://cansim2.statcan.gc.ca) and U.S.A. (http://www.nass.usda.gov) and compared total row
558
crop area to corn and soybean area to derive proportions. For Canada, total row crops considered
559
all wheat estimates, summed corn for grain and fodder but we excluded tame hay from the sum
560
of all crops. For U.S.A., we subtracted winter wheat from total wheat, and included double-
561
cropped soybeans in the soybean total. To estimate row crop totals, we subtracted hay (alfalfa)
562
from the field crop total. We divided the area of corn and soybean crops by total row crops to
563
derive the proportion of crops that could potentially be influenced by changes in the use of
564
genetically-modified corn and soybean. We assumed the proportion of these two crops relative to
565
total crops to remain consistent over time on the presumption that the proportion of corn and
566
soybean would remain the same between the three breeding regions.
26
567
The area planted with corn and soybean crops was different between regions (Table S12).
568
Combined, the proportion of corn and soybean crops was lowest in the South (20.8%) and
569
approximately equal proportions in the Central (36.5%) and North region (36.6%). The
570
proportion of total crops grown as soybeans comprised more than 17% of all row crops grown in
571
the Central region and almost 14% in the North. In contrast, proportion of corn was higher in the
572
North (22.6%) compared to the Central (19%). The lowest proportions occurred in the South
573
where slightly greater than 10% of total crops were grown as of corn and soybean (Table S12).
574
575
ii) Adoption rate of genetically modified crops
Adoption of genetically modified crops has increased since they were introduced in 1996
576
(Dill, CaJacob & Padgette 2008). Adoption rates differ for corn and soybean but standardized
577
data on the proportion of corn and soybean crops planted as genetically modified stains was not
578
collected until 2000 (U.S. Department of Agriculture 2012). We used the annual national average
579
of the percent corn (herbicide tolerant and herbicide-Bt stacked varieties) and soybean crop
580
planted as herbicide tolerant forms between 2000 and 2012 (U.S. Department of Agriculture
581
2012) to fit a three-term non-linear regression model to predict the proportion of the corn and
582
soybean crop that is planted as genetically modified, herbicide resistance strains (gi). The
583
proportion of the corn and soybean corn planted as genetically-modified strains in Canada is
584
unavailable so we assumed equal adoption rates as those from the USA. Parameter estimates for
585
the logistic equations are presented in Table S13.
586
iii) Relationship between genetically modified crops and milkweed abundance
587
The functional relationship between milkweed abundance and genetically modified crops
588
use has not been identified so we used three pieces of information to justify a model of expected
589
declines in milkweed abundance. First, an extensive study in Europe found that the use of
27
590
genetically modified crops reduced overall weed abundance from 60-80% over baseline levels
591
(Heard et al. 2003). Second, Hartzler (2010) documented a 90% reduction in milkweed plants in
592
corn and soybean fields in Iowa between 1999 and 2009 in conjunction with a rapid adoption of
593
genetically modified crops in that state. Third, Pleasants & Oberhauser (2013) modeled
594
exponential declines in milkweed abundance in both agricultural fields and pastures over a 10-
595
year period (they did not speculate the mechanism underlying the trend in pastures).
596
We calculated the infested area of milkweed by combining the occupied area and
597
proportion of sites occupied data (Hatzler 2010) from 1999 (assuming 0% genetically modified
598
crop results in an infested area of 26.52m2/ha of milkweed) and from 2009 (assuming 100%
599
genetically modified crop results in an infested area of 0.4m2/ha of milkweed). Using these two
600
points, we modeled the negative effect of genetically modified crops as the exponential decay
601
function: 26.52  0.0151 i where gi is the proportion of the corn or soybean crop that is planted
602
as genetically modified, herbicide resistance strains (as above). We assumed this functional
603
relationship, but not the proportion of each crop planted as genetically modified strains (see
604
above), was the same for both crop types.
g
605
606
3. A stochastic model of overwinter mass-mortality events in Mexico
607
Our objective was to incorporate environmental conditions (temperature, precipitation and
608
exposure) that butterflies experience in the overwintering colonies into a stochastic function to
609
predict mass mortality events in simulations of the matrix model. We did this in four steps: (i)
610
derive a functional form of mass mortality with respect to environmental variables (temperature,
611
precipitation, and tree cover), (ii) develop a stochastic model to represent specific weather
28
612
variables experienced within the overwintering colonies, (iii) predict temperature and
613
precipitation changes over time, and (iv) derive a rate of forest cover degradation.
614
615
Functional form of mass-mortality events
616
We estimated the daily proportion of the total overwintering population that would die from
617
extreme weather, following a logistic function as:
if B  0
 0

sm   B n
if B  0
 n
B  Kn
eqn 18
618
where K and n are fitted constants using the cumulative survival probability function
619
reconstructed from fig. 2 in Anderson & Brower (1996) using open-source SciDAVis software
620
(http://scidavis.sourceforge.net/), for wet (n = 9.32, SE = 0.0067; K = 4.3, SE = 0.004) and dry (n
621
= 5.5, SE = 0.0067; K = 7.66, SE = 0.002) butterflies, and B represents the body temperature.
622
Body temperature used to predict the probability of mortality given ambient temperatures (t c )
623
and the percent exposure (ec ), which we considered as the proportion of tree cover, came from
624
Anderson & Brower (1996). We modified the equation in Anderson & Brower (1996) by
625
multiplying by -1, to ensure B was non-negative which was required for the logistic function
626
above, giving
B  11.078tc  0.034ec  0.089.
eqn 19
627
This equation can accommodate the effects of increasing mean minimum winter temperature
628
from climate change and decreasing tree cover from deforestation. The addition of an exposure
629
parameter incorporates the blanket effects offered by high quality forest habitat that reduces
630
mortality due to freezing (Anderson & Brower 1996). The sum of these daily estimates
631
represented the population-level stochastic mortality rate, sm, of each year of the model. We note
29
632
that we considered only the effects of cold weather on mass mortality events (Anderson &
633
Brower 1996, Brower et al. 2004) and not the influence of warm weather on lipid depletion
634
(Masters, Malcolm & Brower 1988).
635
636
A stochastic model of weather conditions at the overwintering colonies
637
Our objective was to form a model of weather experienced by butterflies at the overwintering
638
colonies to estimate stochastic mortality events that could be applied in population model
639
simulations. For each day of the overwintering season between December 1 and March 30, the
640
model randomly selected (i) a minimum temperature (to designate tc ~ N(μ,σ) in eqn 19) based
641
on a month-specific mean and standard deviation of minimum temperature and (ii) if a large rain
642
event (>10 mm) occurred (to designate n and K in eqn 18, above) based on the month-specific
643
probability of these events (eqn 18).
644
Temperature
645
To fulfill these requirements, it was necessary to obtain daily minimum temperatures and
646
precipitation events for each month between December and March. However, there are no long-
647
term data available for daily weather conditions at the overwintering colonies. Instead, we
648
obtained daily minimum temperatures and precipitation data for December to March from 5
649
federal weather stations in Mexico (federal weather station identification numbers: 15070,
650
15310, 15334, 15206, and 15267). On average, these stations were 274 m below (range: 575 m
651
below to 167 m above) and 42 km (range 2.9 – 93.2 km) away from previously occupied
652
butterfly overwintering colonies (García-Serrano, Lobato Reyes & Mora Alvarez 2004).
653
654
Given the narrow physiological niche that support butterflies (Anderson & Brower 1996,
Brower et al. 2008), having a high level of confidence in our estimated temperatures was
30
655
important to avoid biased inference. To do so, we compared the current monthly mean minimum
656
temperature value from Sáenz-Romero et al. (2010) with the observed data derived from the
657
weather stations. The models presented in Sáenz-Romero et al. (2010) were spline models that
658
incorporate both a spatial location and altitude to calculate a precise estimate of the temperatures
659
experienced by butterflies at the overwintering colonies (see Projected climate change). The
660
concordance between predicted and observed mean minimum temperatures at of the five stations
661
supported our assumption that the weather conditions at the stations could be used to represent
662
conditions experienced by butterflies within the overwintering colonies (Fig. S2). Therefore, for
663
each month we calculated the standard deviation of the daily minimum temperature (σ) to apply
664
to eqn 19. Below (see Projected climate change), we incorporate this model into a linear form to
665
account for projected temperature change at the overwintering colonies into the future (Sáenz-
666
Romero et al. 2010).
667
Precipitation
668
We assumed that daily rain events greater than 10 mm would result in butterflies being
669
wet and therefore at higher risk of cryogentic mortality (Anderson & Brower 1996). For each
670
month, we used the weather station data and divided the number of observed days that had
671
rainfall greater than 10 mm by the number of observations to calculate a probability of a large
672
rain event (Table S14) which were applied in eqn 18.
673
Projected climate change
674
Temperatures and rainfall patterns are predicted to change over the next 100 years in Mexico
675
(Sáenz-Romero et al. 2010, 2012) and these changes are predicted to influence monarch mass
676
mortality events (Oberhauser & Peterson 2003). Using the spatial locations and altitudes of the
677
monarch overwintering colonies listed in García-Serrano, Lobato Reyes & Mora Alvarez (2004),
31
678
we constructed a linear regression for each month of the predicted mean minimum temperature
679
by using data from the years 2000 (current), 2030, 2060, and 2090 under the A2 scenario of the
680
Canadian Center for Climate Modelling and Analysis using the CGCM3 (T62 resolution) model
681
(Intergovernmental Panel on Climate Change 2000). While the A2 scenario model assumes high
682
greenhouse gas emissions and a growing human population with heterogeneous global economic
683
and technological change (Intergovernmental Panel on Climate Change 2000), increasing
684
temperatures may reduce the frequency of catastrophic mortality events at the overwintering
685
grounds. The linear model of the predicted mean minimum temperature (μ) for each month is
686
presented in Table S15. Variation in daily minimum temperatures over time was considered to
687
remain the same as current conditions (Table S14).
688
We assumed that the monthly probability would remain consistent over time as monthly
689
precipitation totals near the breeding colonies were not predicted to change dramatically (Sáenz-
690
Romero et al. 2012).
691
692
Rates of deforestation
693
Monarchs occupy closed or semi-closed forest habitats in Mexico (Williams, Stow & Brower
694
2007) and forest loss and degradation has been implicated as important to monarch persistence
695
on the wintering grounds (Brower et al. 2012, Vidal, López-García & Rendón-Salinas 2014).
696
Rates of change (Brower et al. 2002, Ramírez, Azcárate & Luna 2003, López-García &
697
Alcántara-Ayala 2012, Vidal, López-García & Rendón-Salinas 2014) show annual variation in
698
rates of forest degradation (Table S16). We assumed a conservative annual rate of degradation of
699
forest of 1.3% per year (to designate ec in eqn 19) from initial conditions of a fully closed forest.
700
We assumed that degraded forest was permanent and cumulative throughout the study.
32
701
33
702
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863
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867
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41
869
Williams, J.J., Stow, D.A & Brower, L.P. (2007) The influence of forest fragmentation on the
870
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871
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872
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873
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874
feeding on the sandhill milkweed Asclepias humistrata. Ecological Entomology, 26, 212-224.
875
876
877
878
42
879
880
881
Figure S1. The annual probability of a mass-mortality event (>1% mortality of total population)
882
under different proportions of habitat forest cover on the wintering grounds over time. The
883
degradation of forest cover has little influence on the annual probability of a mass mortality
884
event relative to the positive effects of warming temperatures from climate change.
885
43
886
887
888
Figure S2. Daily minimum temperature used to describe temperature patterns at the
889
overwintering colonies in Mexico between December and March. The mean (dot) and error bars
890
indicate the mean minimum temperature ± 95% CI from each of 5 weather stations (station
891
identification numbers are listed). The dashed line is the mean and the grey shading the 95% CI
892
of the combined data from the 5 weather stations. The solid line is the point estimate of the
893
current mean minimum temperature at the overwintering colonies from Sáenz-Romero et al.
894
2010. The correspondence between the temperature means (solid and dashed lines) and variance
895
(error bars and grey shading) supported using data from the weather stations to model monthly
896
stochastic minimum temperatures experienced by monarch butterflies at overwintering colonies
897
in Mexico.
898
44
Table S1. Key to notation used in the spatial periodic matrix model for migratory monarch
butterflies (Danaus plexippus) in eastern North America. Demographic vital rates occur within
region i at time t, while transition vital rates occur among a pair of regions i,j at time t. Also
included is the section in the Supporting Information that explains how parameters were
estimated.
Symbol
Definition
f bi1,t , f bi2,t The fecundity of breeding butterflies in their first and second
Matrix
Section
Dti
1.2
Dti
1.3
Dti
1.3
Dti
1.4
Dti
1.4
Dti
1.4
M ti
1.4
M ti
1.3
month in region i at time t
d it
Rate of butterflies entering a reproductive diapauses in region i
at time t
eit
Rate of overwintered butterflies emerging from a reproductive
diapauses in region i at time t
s Li ,t
Immature survival rate. The product of density dependent
survival, density independent survival from predation, and
density independent pupal survival in region i at time t
i ,t
i ,t
Probability of survival of overwintering butterflies in their first
s ow
1 , s ow 2
and second month in region i at time t
sbi ,1t , s bi ,2t
Probability of survival of breeding butterflies in their first and
second month in region i at time t
sit, j
Probability of survival during migration from region i to j in
the migration matrix (Mi) at time t
tit, j
Probability of moving between region i and j in the transition
matrix (Ti) at time t
899
900
45
901
Table S2. Sample sizes of monarch butterflies captured in each region for assigning migratory
connectivity (Flockhart et al. 2013). Note that butterflies captured in the South in September
and October were pooled.
Month
Capture dates
South
Central
North
Total
April
March 20 – April 19
24
0
0
24
May
April 20 – May 19
76
69
0
145
June
May 20 – June 18
0
76
48
124
July
June 19 – July 18
0
60
65
125
August
July 19 – August 17
0
239
128
367
September
August 18 – September 16
6
12
0
18
October
September 17 – October 16
10
0
0
10
902
903
46
Table S3. Monthly transition of monarch butterflies between destination region where they were
captured and their region of origin based on stable isotopes. Butterflies (number of individuals
in parentheses), captured in April and May with high wing wear scores, were assumed to be
overwintered individuals (Flockhart et al. 2013) and therefore were considered to originate in
Mexico. No butterflies were collected in the South between June and August because monarchs
occur at very low densities here at this time (Calvert 1999, Prysby & Oberhauser 2004). Rows
whose proportions do not sum to unity arise from rounding error.
Region of origin
Month
Destination
Mexico
South
Central
North
region
April
South
0.875 (21)
0.125 (3)
May
South
0.697 (53)
0.263 (20)
0.039 (3)
Central
0.348 (24)
0.13 (9)
0.52 (36)
Central
0.355 (27)
0.645 (49)
North
0.333 (16)
0.667 (32)
Central
0.183 (11)
0.80 (48)
0.017 (1)
North
0.169 (11)
0.738 (48)
0.092 (6)
Central
0.18 (43)
0.736 (176)
0.084 (20)
North
0.016 (2)
0.438 (56)
0.547 (70)
0.833 (10)
0.167 (2)
0.563 (9)
0.125 (2)
June
July
August
September
Central
South
0.313 (5)
904
905
47
906
Table S4. Survival of monarch butterflies during migration. Survival of monarch butterflies
during migration between different geographic regions in eastern North America as estimated
using expert opinion. Presented are the means and standard deviations where values below the
diagonal are for breeding butterflies moving between April and September and values above the
diagonal are for butterflies in reproductive diapause on migration to Mexico. Diagonal survival
values are 1 and represent the assumption that there is no mortality associated with remaining in
the same region between time steps.
Parameter
Region
Mexico
Mean
Mexico
1
0.69
South
0.517a
1
Central
0.196
0.733
1
0.544
0.742
North
Central
0.567
North
0.5
1
0.159687b
Standard
Mexico
Deviation
South
0.273252
Central
0.210636
North
a
South
0.128239b
0.190489b
0.136626
0.182836
0.135708
estimated with a stretch beta distribution using the minimum (0.25) and maximum (0.9)
estimates of survival provided by experts.
b
survival of individuals to Mexico was modeled by successive regions using these estimates of
standard deviation at each step.
907
48
908
Table S5. Data used in the Geographic Information System used to calculate milkweed
abundance in eastern North America.
Layer
Description
Study area
Probability >50% of monarch occurrence as a function of geographic,
climatic, and vegetation characteristics22
Land cover
Global 2009 land cover map at a 300m resolution. The 22 land cover
classes are based upon United Nations Land Cover Classification System60
Roads
Line features of roads classified into 9 categories61
Urban
Urban areas of Canada and the USA62
Protected Areas
Terrestrial protected areas in North America classified by management
objectives based on IUCN criteria63
909
910
49
911
Table S6. Land cover classification. Re-classification table of original categories from the Global
land cover and the reduced land cover categories used to estimate milkweed abundance in North
America.
Reclassified
Description [Global land cover index value]
Crop
Cultivated and managed areas/Rainfed cropland [11]
Crop
Post-flooding or irrigated croplands [14]
Crop
Mosaic cropland (50-70%)/vegetation (glassland/shrubland/forest) 20-50% [20]
Crop
Mosaic vegetation (grassland/shrubland/forest) (50-70%)/cropland (20-50%) [30]
Forest
Closed to open (>15%) broadleaved evergreen and/or semi-deciduous forest
(>5m) [40]
Forest
Closed (>40%) broadleaved deciduous forest (>5m) [50]
Pasture
Open (15-40%) broadleaved deciduous forest/woodland (>5m) [60]
Forest
Closed (>40%) needle-leaved evergreen forest (>5m) [70]
Forest
Open (15-40%) needle-leaved deciduous or evergreen forest (>5m) [90]
Forest
Closed to open (>15%) mixed broadleaved and needleaved forest [100]
Rangeland
Mosaic forest or shrubland (50-70%) and grassland (20-50%) [110]
Rangeland
Mosaic grassland (50-70%) and forest or shrubland (20-50%) [120]
Rangeland
Closed to open (>15%) shrubland (<5m) [130]
Pasture
Closed to open (>15%) grassland [140]
Rangeland
Sparse (<15%) vegetation [150]
Wetland
Closed (>40%) broadleaved forest regularly flooded, fresh water [160]
Wetland
Closed (>40%) broadleaved semi-deciduous and/or evergreen forest regularly
flooded, saline water [170]
Wetland
Closed to open (>15%) grassland or shrubland or woody vegetation on regularly
flooded or waterlogged soil, fresh, brakish or saline water [180]
Urban
Artificial surfaces and associated areas (Urban areas>50%) [190]
Bare
Bare areas [200]
Water
Waterbodies [210]
Bare
Permanent snow and ice [220]
No Data
No Data [NoData]
50
912
Table S7. Milkweed density (m2/ha) for different land cover types in eastern North America.
The occupied area was multiplied by the proportion of sites occupied to arrive at the area
infested with milkweed (Ri). Estimates from Hartzler (2010) used the measurements from 1999.
Land cover
Occupied Area
Proportion occupied
(m2/ha)
Infested Area
(m2/ha): Ri
Bare56
N/A
N/A
0
Crop55
52
0.51
26.52a
Crop (protected) CRP57
212
0.67
142.04
Pasture57
14
0.28
3.92
Rangeland b
14
0.28
3.92
Forest56
N/A
N/A
0
Urban56
N/A
N/A
0
Water56
N/A
N/A
0
Wetland57
169
0.46
77.74
Right-of-ways55
102
0.71
72.42
Roads56
N/A
N/A
0
a
the values applied to all crop types except genetically modified corn and soybean which had a
milkweed infested area of 26.52 × 0.0151gi,t , where gi,t is the proportion of the corn or soybean
crop planted with genetically-modified strains, see Adoption of genetically modified, herbicide
resistant crops for details.
b
Assumed same as pasture
913
51
914
Table S8. Results of models used to explain road and right-of-way widths in eastern North
America. The model that best explain variation in road width included road classification
whereas the model that best explain variation in right-of-way width included both the road
classification and state/province. Presented for each model is the Akaike Information Criterion
(AIC), difference in AIC from the model with the lowest AIC (ΔAIC), likelihood (li), weight (wi),
number of parameters (K) and the fit statistic (Deviance).
AIC
ΔAIC
li
wi
K
Deviance
Road classification
11692.7
0
1
0.607
9
75303.4
Road classification + Country
11694.3
1.6
0.438
0.266
10
75288.5
Road classification + Breeding region
11695.8
3.1
0.208
0.126
11
75266.8
Road classification + State/Province
11726.5
33.9
0
0
51
73201.8
Constant
12779.6
1087
0
0
1
140326.1
Country
12781.6
1088.9 0
0
2
140322.8
Breeding region
12783.5
1090.8 0
0
3
140311.5
State/Province
12835.4
1142.7 0
0
43
138102.3
Road classification + State/Province
12490.5
0
1
1
51
112655.6
Road classification + Country
12687.1
196.6
0
0
10
161835.6
Road classification + Breeding region
12694.0
203.6
0
0
11
132205.1
Road classification
12696.8
206.3
0
0
9
132710.7
State/Province
13478.8
988.4
0
0
43
198565.8
Country
13493.2
1002.8 0
0
2
209668.0
Constant
13493.4
1003.0 0
0
1
209931.2
Breeding region
13495.3
1004.9 0
0
3
209680.0
Model
Road width
Right-of-way width
915
916
917
52
Table S9. The width of roads in eastern North America. Parameter estimates from a generalized
linear model to explain road width based on the road classification (top model in Table S8). Note
the intercept value represents the predicted width of motorways.
Parameter
Estimate
SE
t
P-value
Intercept
23.7941
0.4386
54.25
<0.001
Road: primary
-9.7655
0.6169
-15.83
<0.001
Road: residential
-17.8008
0.6414
-27.75
<0.001
Road: track
-19.636
0.6586
-29.82
<0.001
Road: secondary
-13.2227
0.6089
-21.36
<0.001
Road: service
-18.3977
0.6397
-28.76
<0.001
Road: tertiary
-15.2311
0.6203
-24.55
<0.001
Road: unclassified
-10.4053
0.6246
-16.66
<0.001
Road: walk/bike
-20.0322
0.8104
-24.72
<0.001
918
919
920
53
921
922
Table S10. The width of road right-of-ways in eastern North America. Parameter estimates from
a generalized linear model (of the form y = e(ax+b) ) to explain right-of-way widths based on the
road classification and state/province (top model in Table S8). Note the intercept value
represents the predicted width of motorways in the state of Alabama.
Parameter
Estimate
SE
t
P-value
Intercept
3.4565
0.09193
37.599
<0.001
primary
-0.87603
0.06068
-14.437
<0.001
residential
-2.31504
0.25043
-9.244
<0.001
track
-3.39672
0.77341
-4.392
<0.001
secondary
-1.08278
0.07148
-15.149
<0.001
service
-2.73301
0.38089
-7.175
<0.001
tertiary
-1.37064
0.09247
-14.823
<0.001
unclassified
-0.77589
0.05591
-13.878
<0.001
walk/bike
-3.30929
0.8442
-3.92
<0.001
Arkansas
-0.21961
0.14001
-1.568
0.116952
Connecticut
-1.0411
0.27288
-3.815
<0.001
Delaware
-0.34933
0.15762
-2.216
0.026802
Florida
-0.20437
0.14479
-1.411
0.15829
Georgia
-0.42976
0.16654
-2.581
0.009947
Iowa
0.02941
0.12017
0.245
0.806668
Illinois
-0.6465
0.11286
-0.573
0.566831
Indiana
-0.26721
0.14942
-1.788
0.073907
Kansas
0.1955
0.10904
1.793
0.073155
Kentucky
-0.65157
0.1932
-3.372
0.000762
Louisiana
-0.2801
0.15089
-1.856
0.063575
Massachusetts
-1.17586
0.31688
-3.711
0.000213
Manitoba
-0.32351
0.20489
-1.579
0.114543
Road:
State:
54
Maryland
-0.70844
0.20556
-3.446
0.000582
Maine
-0.93395
0.24827
-3.762
0.00174
Michigan
-0.19998
0.1431
-1.397
0.162467
Minnesota
-0.02522
0.13007
-0.194
0.846292
Missouri
-0.30986
0.13622
-2.275
0.023048
Mississippi
-0.18346
0.14259
-1.287
0.198395
New Brunswick
-0.54312
0.19408
-2.798
0.005193
North Carolina
-0.5419
0.1902
-2.849
0.004436
North Dakota
0.20655
0.11708
1.764
0.07787
Nebraska
0.03351
0.12634
0.265
0.790837
New Hampshire
-0.72377
0.20942
-3.456
0.000561
New Jersey
-1.10087
0.27384
-4.02
<0.001
New Mexico
-0.40887
0.16433
-0.488
0.012937
Nova Scotia
-1.1526
0.40636
-2.836
0.004616
New York
-0.79893
0.224
-3.567
0.000372
Ohio
-0.28007
0.14535
-1.927
0.054159
Oklahoma
-0.03509
0.1308
-0.268
0.788526
Ontario
-0.70749
0.21094
-3.354
0.000814
Pennsylvania
-0.53985
0.18222
-2.963
0.003093
Quebec
-0.56099
0.19557
-2.869
0.004174
Rhode Island
-1.38093
0.40642
-3.398
0.000695
South Carolina
-0.52982
0.17915
-2.957
0.003145
South Dakota
-0.12583
0.13845
-0.909
0.36354
Tennessee
-0.47362
0.16557
-2.861
0.00428
Texas
-0.31985
0.14359
-2.228
0.026038
Virginia
-0.59126
0.18445
-3.205
0.001373
Vermont
-0.48434
0.17323
-2.796
0.005232
Wisconsin
-0.26346
0.14688
-1.794
0.073026
West Virginia
-0.76623
0.21775
-3.519
0.000445
923
924
925
55
926
927
Table S11. Transition matrix of annual land-cover change based on data between 1982 and
2007. For all other land cover types in Table S7, including CRP lands, it was assumed there were
no changes.
Crop
Pasture
Rangeland
Forest
Urban
Crop
0.994539
0.005661
0.000711
0.00021
0.000149
Pasture
0.002893
0.985265
0.000322
0.000481
0.0000923
Rangeland
0.000657
0.001554
0.998145
0.000216
0.0000995
Forest
0.000851
0.005427
0.000323
0.997399
0.000249
Urban
0.00106
0.002092
0.000498
0.001694
0.99941
928
929
930
56
931
Table S12. The proportion of total row crops grown as corn and soybean among the three
breeding regions in eastern North America.
Crop
South
Central
North
Corn
0.1033125
0.1899692
0.2265820
Soybean
0.1049510
0.1746945
0.1393207
Total
0.2082635
0.3646637
0.3659026
932
933
934
57
935
Table S13. Parameter estimates used in a logistic regression to predict changes in the adoption
rates of genetically modified corn and soybean crops over time.
Crop
Parameter
Estimate
Std. Error
t-value
P-value
Corn
a
0.77998
0.03014
25.875
<0.001
b
23.39976
5.69792
4.107
<0.001
c
0.53485
0.05147
10.391
<0.001
a
0.92779
0.00528
175.70
<0.001
b
0.67319
0.02809
23.96
<0.001
c
0.50995
0.03074
16.59
<0.001
Soybean
936
937
938
939
58
940
Table S14. Monthly weather in monarch butterfly overwintering colonies in Mexico. Monthly
precipitation and temperature statistics compiled from 5 weather stations that have similar
weather profiles to the monarch overwintering colonies. We assumed daily rain events >10mm,
which are rare events during the winter months, resulted in wet butterflies for our simulations.
Precipitation
Month
Daily probability of
Monthly mean
event (>10mm)
(mm)
Temperature
Mean minimum
Std. Deviation
December 0.0129
12.1
3.57
2.27
January
0.0187
17.1
2.90
2.07
February
0.0155
15.7
3.40
2.09
March
0.0082
8.7
4.91
2.41
941
942
59
943
Table S15. Future monthly mean minimum temperatures in monarch butterfly overwintering
colonies in Mexico. The current (1961-1990) and predicted future mean minimum monthly
temperatures from December to March experienced by monarch butterflies. Future temperatures
are linear models derived from current, 2030, 2060 and 2090 temperatures (Sáenz-Romero et al.
2010) using previously occupied overwintering locations and elevations (García-Serrano, Lobato
Reyes & Mora Alvarez 2004). The current temperature estimates can be compared to those of
weather station data presented in Table S14.
Month
Current
Future
December
3.80
0.038935×year – 73.683188
January
2.88
0.034369×year – 65.638522
February
3.34
0.037929×year – 72.566895
March
4.60
0.045230×year – 85.75124
944
945
60
946
Table S16. Annual rates of winter habitat degradation between 1971 and 2012 in Oyamel firpine forest ecosystems, Mexico.
Time period
Annual rate of degradation
1971-1984
1.70%8
1984-1999
2.41%8
1994-2010
1.30-1.43%a,53,54
2001-2012
1.38%18
a
Rate of loss within the Anganaueo basin within the Monarch Butterfly Biosphere Reserve
947
948
949
61