# Spatial changes in park visitation at the onset of the pandemic

Kelsey Linnell  Vermont Complex Systems Center, University of Vermont  Mikaela
Fudolig  Vermont Complex Systems Center, University of Vermont  Aaron Schwartz
Gund Institute for Environment, University of Vermont  Taylor H. Ricketts
Gund Institute for Environment, University of Vermont  Jarlath P. M. O’Neil-
Dunne  Spatial Analysis Laboratory, University of Vermont  Peter Sheridan
Dodds  Vermont Complex Systems Center, University of Vermont  Christopher M.
Danforth  Vermont Complex Systems Center, University of Vermont

###### Abstract

The COVID-19 pandemic disrupted the mobility patterns of a majority of
Americans beginning in March 2020. Despite the beneficial, socially distanced
activity offered by outdoor recreation, confusing and contradictory public
health messaging complicated access to natural spaces.

Working with a dataset comprising the locations of roughly 50 million distinct
mobile devices in 2019 and 2020, we analyze weekly visitation patterns for
8,135 parks across the United States.

Using Bayesian inference, we identify regions that experienced a substantial
change in visitation in the first few weeks of the pandemic.

We find that regions that did not exhibit a change were likely to have smaller
populations, and to have voted more republican than democrat in the 2020
elections. Our study contributes to a growing body of literature using passive
observations to explore who benefits from access to nature.

††preprint: APS/123-QED

##  I  Introduction

Parks are important public infrastructure that provide a venue for interaction
with nature, socialization, and exercise. Park access and use has been found
to offer both mental and physical health benefits [1, 2, 3, 4, 5, 6]. Among
the many benefits of exposure to nature are faster healing, decreased stress
and increased ability to manage life’s challenges [7, 8]. During the COVID–19
pandemic, access to parks may have been important for mitigating and managing
the secondary impacts of the virus. Recent publications indicate that access
to parks during the pandemic is important for a variety of reasons including
providing a venue for exercise, increasing happiness, and improving social
cohesion [9, 10, 11, 12].

While park visitation may have provided significant support to personal and
public health at the time, it is unclear whether park visitation changed, to
what extent, and for whom in the United States. In March of 2020, stay at home
orders were issued in most states, and many non-essential workplaces and
public spaces were closed. Following these events, overall mobility decreased
dramatically for most Americans, reaching a maximum reduction by 34 to 69%
depending on the state [13, 14]. While Americans were visiting fewer locations
in general, some research suggests that park visitation may not have been
subject to this decline. An early study of parks on the West Coast determined
changes in visitation at the onset of the pandemic to be primarily motivated
by seasonal change, while a study of parks in New Jersey found that early
pandemic visitation was higher than the baseline [15, 16]. Together these
results indicate that visits to parks may have differed from other points of
interest at the onset of the pandemic.

Preliminary examination of trends suggest that changes in park visitation were
not universal. In the United States, partisanship, even at the regional level,
is associated with behavioral differences. Researchers have found that
Thanksgiving dinners were 30 to 50 minutes shorter when the guests and hosts
resided in voting precincts that had been in opposition in 2016 [17]. Mobility
studies of Americans during the pandemic have found differences along partisan
lines as well. The American political system is largely dominated by two
political parties: Democrats, and Republicans. This divide in political
ideology has been found to be indicative of differing identities and
behaviors. This is particularly true of COVID-19 policy response and
preferences [18]. Republicans have been found to have lower vaccination rates,
have a smaller decrease in mobility during the pandemic, and to be less
compliant with non-pharmaceutical interventions [19, 13, 20, 21, 22, 23].
Counties with more Republicans also had less severe mobility restrictions, and
were less responsive to their governor’s recommendation to stay home [13, 24].
Given these partisan differences in general mobility, we seek to determine
whether changes in local park visitation at the onset of the pandemic also
differed by partisanship, or whether park visitation uniquely transcended
these differences.

Studies of park usage in March and April of 2020 have thus far relied on
survey data, or have been geographically limited, and neglected to establish a
baseline of seasonality of park usage [25, 16, 15, 26]. Here we utilize mobile
device data from across the United States to explore abrupt non-seasonal
changes in park visitation at the regional level. We use data from 2019 to
discern seasonal visitation patterns, and employ a change-point detection
algorithm to diagnose sudden changes in behavior at the onset of the pandemic.
By classifying regions by whether or not an abrupt change in park visitation
took place, we are able to discern whether or not these abrupt changes
occurred along partisan lines. We conduct further comparisons across
population, income, and share of employment by industry to provide insight
into other factors that may have influenced whether or not an abrupt change
occurred. In Section II we introduce the data used to classify regions, and
make these comparisons. Section III then gives a detailed explanation of the
data aggregation for each region, and the classification procedure and methods
of comparison applied to the aggregated data. The results of the comparisons
are described in Section IV, and are discussed in Section V.

##  II  Data

To determine whether a partisan effect is observed in park visitation we used
park visitation data from across the United States, and voting share data from
the 2020 Presidential Election. Differences in regions with and without abrupt
changes in visitation were further analyzed using population estimates, and
income and employment share data from the US Census and the Bureau of Economic
Affairs. Details for these data sources are provided below.

###  II.1 Park Visitation Data

Our park visitation dataset was acquired from UberMedia (now part of Near),
and consists of daily visitation counts for non-commercial parks for each day
of 2019 and 2020. There are 8,135 parks in the data set, including municipal,
neighborhood, and city parks. National and State Parks were specifically
excluded as predominantly travel destinations. Parks are located in each of
the 50 states, and Washington DC. A total of 1,033 counties, roughly a third
of all counties, contain at least one park from our dataset.

Daily visitation counts were determined using location data from mobile
devices. Each unique device appearing within a park’s bounds on a single day
was counted as a visit. A device’s location was reported when an individual
used one of over 400 apps utilizing a GPS Software Development Kit (SDK) in
partnership with UberMedia (90% of data by volume), or when a user interacted
with an advertisement through real time bidding on one of over 250,000 apps
(10% of data by volume). GPS location and an accompanying timestamp were
determined from the device’s operating system.

The number of devices reporting activity in at least one location in the US on
a given day is referred to as the Daily Active Users (DAUs). This number
refers to all locations, not simply parks. In 2019 and 2020 the monthly DAUs
varied between 38 and 60 million, and represented roughly 10% of the adult
population in the United States.

In mid December 2019 the set of SDK’s in partnership with UberMedia was
updated. This change in data collection corresponded to a large increase in
observations throughout the US, and was not spatially uniform. Thus, while the
raw 2019 and 2020 park visitation data are not directly comparable, we analyze
their relationship where possible.

###  II.2  Voting and Economic Data

Voting data at the state and county levels from the 2020 election was
retrieved from MIT Election Data and Science Lab, and is available at
https://electionlab.mit.edu/data.

The BEA publishes data on employment by industry (using the North American
Industry Classification System (NAICS)) for each county in table ”CAEMP25N”,
which can be found at https://apps.bea.gov/regional/downloadzip.cfm . In this
table “Farming” and “Forestry” are considered as separate, though they appear
as one sector in the NAICS classification. For this study they were considered
separately, as they appear in the table. County level population, income, and
economic data from the 2019 American Community Survey were obtained from US
census API.

##  III  Methods

Figure 1:  A heat map of the population of the contiguous United States in log
scale overlaid with the locations of the parks used in the study, with each
park demarcated with a black point. Observation of this map indicates that the
parks in this data set have an urban bias, and that the parks are roughly
distributed according to population distribution in the United States.
Population heat maps in the log scale are shown for Massachusetts (top) and
Oklahoma (bottom), overlaid with park locations in black. The color scale
chosen for each state represents the political party receiving the most votes
in the 2020 Presidential election (Democrats for Massachusetts, and
Republicans in Oklahoma). Normalized weekly park visitation for each state is
plotted to the right. Visitation for 2019 is plotted in blue, while visitation
for 2020 is plotted in orange. For Massachusetts there is a significant dip in
visitation bottoming out the week of March 25, 2020, and the visitation plots
for 2019 and 2020 diverge. For Oklahoma visitation does not drop off in March,
and does not diverge from 2019 visitation patterns.

###  III.1  Aggregation

Daily visits to a park were defined as the unique number of mobile devices
reporting GPS coordinates found inside the park polygon bound on a day. This
daily visit count was then normalized by the average Daily Active Users for
the month in which it was found, approximating the percentage of devices
observed in parks relative to all observed devices. The normalized visitation
was then summed over each week in order to minimize noise. Weekly visitation
was summed for parks contained in a county, or a state, and thus a time series
of weekly park visitation between 2019 and 2020 was created for each county
and state containing at least one park from our data set.

###  III.2 Change Point Detection

To determine whether a substantive change in visitation is observed in each
time series, we use the Bayesian Estimator of Abrupt Change, Seasonality, and
Trend (BEAST) [27]. This method decomposes a time series into a seasonal
(harmonic) component, and trend (linear) component, and uses Bayesian
Inference to fit a model which estimates the location of change points in
either of the components. BEAST was chosen because the underlying model
acknowledges the seasonal nature of most park visitation time series (more
visits in summer). By specifying a 52 week season length, we were able to
train the model to the annual cycle shape of the data.

Parametric methods applied without the seasonal decomposition are susceptible
to under estimating

change points in these particular time series because of the combination of
seasonality and the proximity in the series of the data collection change in
December 2019 to the onset of the pandemic in March 2020. The initial event
represents a sharp increase in visitation volume (roughly 150 pct), while the
second appears, for most regions, as a sharp decline. When fit with a single
model, these two features appear together as a change in variance, and a
parametric model can be nicely fit using a single change point in December
2019.

By decomposing the time series and forcing a decoupling of the two events by
specification of seasonal, length we make each event visible as a unique
discontinuity in the linear component.

The December 2019 discontinuity could then be accommodated with a trend change
point, which incorporates a discontinuity into the linear component. In this
way the model was fit while accounting for seasonality, and the abrupt change
in data volume.

Allowing a trend change point to be used as described above, the model was
effectively limited to selecting a single trend change point, which enabled it
to identify the most likely change point in the data. It is possible for the
algorithm to detect no change point, reducing concern that one would be
identified artificially.

Regions which had a change point occurring in between mid March and mid April
2020 were considered to have had an abrupt change in park visitation
coinciding with the onset of the pandemic and social distancing measures. If a
region was found not to have had a change point in this window, it can be
assumed that either no change point was found in the time series, or any
change occurring in the specified window was not as significant as a change at
another time.

Changes induced by seasonality are in most cases more gradual than those that
occur in the window of interest, and these changes are accounted for by the
harmonic component of the model. The harmonic component is fit using both 2019
and 2020 data, which informs the model of the expected seasonal shape. Since
these changes are accounted for in the model fitting, it is unlikely that
change points identified in the window of interest are due only to seasonal
variation. Because the length of the time series only included two seasons
(park visitation demonstrates a yearly cycle), it was not pertinent to search
for changes in the seasonal structure.

BEAST is less effective in identifying change points in time series with high
variance. The recorded park visits in some of the counties were low enough
that the behavior of only a few individuals could have large impacts on the
time series itself. To ensure that BEAST was only considering counties for
which there was enough data we used a mean normalized visitation threshold of
$10^{-5.5}$ (this corresponds to about 120 visits per week in the month with
the least DAUs) in 2020. A total of 322 counties did not meet this criteria
and were excluded from further analysis. The remaining 711 counties that
contain parks in our dataset met this criteria. The counties included in the
analysis are roughly 21% of all the counties in the United States, and span
all of the states. Details on the selection of the visitation threshold can be
found in the Supplementary Materials (See Fig S1).

###  III.3  Comparison

Regions were binned according to whether a change point in mid March 2020 was
identified or not, and comparisons of the populations of the regions in each
category were made. Using data from the 2020 election, states and counties
were assigned a percent of the population having voted either Republican
(Trump and Pence) or Democrat (Biden and Harris) in the 2020 election.
Counties were assigned personal incomes, and population counts using Census
estimates from 2019. Voting records and census data were combined to determine
the votes cast per capita for each county. Finally, a fraction of employment
(employment share) for each industry in the North American Industry
Classification System (NAICS) was assigned to each county in the study using
data from the BEA. Counties which had no available employment data for an
industry were exclcuded from the analysis of that particular industry.
Counties with and without detected change points were compared across vote
share, population, votes per capita, personal income, and industry employment
using Kolomogorov-Smirnov two sample tests. This test was chosen for its
ubiquity in the literature and ability to compare distributions with different
sample sizes. The means of the distributions are compared using Welch’s
t-test, which also accommodates different sample sizes.

##  IV  Results

###  IV.1 Partisanship in Abrupt Changes

With the parameters discussed in the Methods section, BEAST found a change
point in the window of interest for 21 states, while the remaining 29 states
did not exhibit an abrupt change in visitation. Comparison of the 2020
presidential election results for states where visitation did and did not
change abruptly is shown in the top row of Fig 2. The distributions across
vote share for the two sets of states were not significantly different for
either the Democratic or Republican parties (KS statistic=0.2, p=0.63 and KS
statistic=0.2, p=0.63 respectively). The distributions for each party are
neither similar, nor mirrored. The difference is accounted for by third party
votes, most notably Libertarian votes.

Comparison of the distributions across percent voting Libertarian (which
accounted for less than 3% of the vote in all states) indicates that the
distributions were significantly different (KS statistic=0.44, p=0.015), where
Libertarians had greater vote share in states without an abrupt change.
Supplementary Fig S2 demonstrates the relative proportion of Democrat,
Republican, and third party votes for each state and county. The state
appearing as an outlier in the distributions, where Democrats had the highest
vote share, and which did not have an abrupt change, is Washington DC, which
was treated as a state for this study. Exclusion of Washington DC does not
change the results.

Figure 2:  Top: Distributions of states where a pandemic response change point
was detected (pink), and not (green), across proportion of votes cast for the
Democratic (left) and Republican (right) parties in the 2020 Presidential
Election. The distributions are not significantly different across voting
proportion for either party. The apparent outlier in each figure is Washington
DC, which did not exhibit a change point, and for which more than 80% of the
votes cast were for the Democratic party. Exclusion of DC from the analysis
did not change the results. Bottom: Distributions of counties with (pink) and
without(green) detected change points across percent voting for the Democratic
(left) and Republican (right) parties in the 2020 Presidential Election.
Distributions across the percent of votes cast for the Democratic party were
determined to be significantly different by the Kolomogorov Smirnov 2 sample
test (KS statistic=0.33, p=4.23e-10). The distribution of counties with a
change point was shifted to the right of those without a change point,
indicating counties with change points had greater proportions of votes for
the Democratic party. The bulk of the mass of the two distributions lies on
either side of 0.5, meaning that the majority of counties with a change point
are majority Democrat counties. The distributions across percent voting for
the Republican party are likewise significantly different (KS statistic=0.33,
p=2.35e-10), and indicate counties without change points had greater
proportions of votes for the Republican party, and were more likely to be a
majority Republican county.

Partitioning the data by county led to significantly different distributions
across vote share (bottom row of Fig 2). When the BEAST classification
procedure was applied to county level aggregations of visitation data, 123 of
the 711 counties had abrupt visitation changes at the onset of the pandemic.
The distribution across Democratic vote share for counties with abrupt changes
is shifted to the right of the distribution for counties without- indicating
that Democrats were more likely to have greater vote share in counties with
abrupt changes. Kolomogorov Smirnov 2 sample results confirm that these
distributions are significantly different (KS statistic=0.33, p=4.23e-10).
Observation of the same distributions across Republican vote share reveals
that Republicans were more likely to have greater vote share in counties
without abrupt changes. KS 2 sample test results support that these
distributions are also significantly different (KS statistic=0.33,
p=2.35e-10).

Not only are the distributions significantly different, but across the vote
share for each party they are translated across the x=0.5 line (drawn in red).
This line represents the dividing point in the majority party support in a
county. This reveals that Democrats were not only more likely to have greater
vote share in counties with abrupt changes, they were more likely to hold a
majority in those counties. Likewise, Republicans were more likely to hold a
majority in counties without abrupt changes.

The distributions of the counties across vote share for the Democratic and
Republican parties are not mirrored on account of votes going to third
parties, meaning that ”not Democrat” is not the same as “Republican”. Both
distributions taken together support that there is a partisan divide between
counties with and without abrupt changes in park visitation at the onset of
the pandemic. This is further supported by no significant difference found in
the distributions of the counties over percent voting Libertarian (KS
statistic=0.13, p=0.087).

###  IV.2 Population, Income, and Employment

Figure 3:  Distributions of counties with and without change points across the
log base 10 of 2019 county population (left) and the votes cast per capita in
the 2020 Presidential Election (right). The distributions over population are
roughly log normal, and visibly and significantly different (KS
statistic=0.28, p=1.08e-07). The mean population of counties with change
points was 331,131 people, which is more than twice the mean population of
counties without change points, namely 144,544. The counties with the lowest
populations were exclusively without change points, while the counties with
the greatest populations were exclusively those with change points. The
distributions across votes per capita are also visibly and significantly
different (KS statistic=0.13, p=0.045) with the counties with change points
having fewer votes per capita than counties without.

Partitioning the data by county allowed further analysis using population,
employment, and income data. Differences in distribution across population
size, and votes cast per resident, for the counties with and without abrupt
changes, are displayed in Fig 3. Counties with an abrupt change had more than
twice the mean population of counties exhibiting no change, and fewer votes
per resident than counties that did not. The distributions across each of
these variables is significantly different (KS statistic=0.28, p=1.08e-07 for
log 10 scale population, and KS statistic=0.13, p=0.045 for votes cast per
resident).

The incomes of the counties were not significantly different (KS
statistic=0.10, p=0.23), as seen in the distributions in Fig 4.

Figure 4:  Distributions of counties with and without change points across the
log base 10 of 2019 personal income as reported by the census. The
distributions are visually similar, and not significantly different
(statistic=0.10, p-value = 0.23). There is not a statistically significant
difference between the incomes of counties where abrupt park visitation
changes occurred and those where it did not.

Counties were also compared on the basis of percent employment in each of the
20 NAICS sectors. The distributions of the counties with and without change
points across percent of employment were significantly different ($p<0.05$)
for 14 of the sectors. This includes both Farming Employment, and Forestry,
Fishing and Related Activities, which comprise a single sector in the NCAIS,
but are considered separately here. Of the 14 sectors with significantly
different distributions, Welch’s T-Tests found only 10 had significantly
different means. The distributions for these 10 sectors is shown for counties
with and without abrupt changes in Figure 5. For each sector, the box plot to
the left shows the distribution over the fraction of employment for counties
with an abrupt change (pink), and the box plot to the right represents the
same distribution for counties without an abrupt change (green).

For the 10 sectors with significantly different distributions and means, 5 had
higher mean employment share in counties with abrupt changes: Information,
Finance and insurance, Professional, scientific, and technical services,
Educational services, and Health care and social assistance. These sectors are
primarily comprised of white collar workers, and with the exception of Health
care and social assistance, require less onsite work. Farm employment, Mining,
quarrying, and oil and gas extraction, Construction, Manufacturing, and Retail
trade all had higher mean employment share in counties where abrupt changes in
park visitation did not occur.

##  V Discussion

At the state level, there was no significant difference in the partisanship of
regions where an abrupt change in park visitation took place, and those where
it had not. There was a significant difference in the vote share of
Libertarians, with Libertarians having smaller vote share in states with an
abrupt change. However, Libertarian voters account for less than 3 % of voters
in each state, and are unlikely to be themselves pivotal in deciding overall
park visitation behavior for a state. Thus, the practical significance of the
difference in Libertarian vote share is doubtful. However, at the county level
there is a clear divide in the partisanship of regions where park visitation
did and did not undergo abrupt change. Counties with an abrupt change were
more likely to be majority Democratic, while counties without a change point
were more likely to be Republican. Taken together with the urban bias of the
data set, it is possible that the state results are confounded by an over
representation of urban park visits.

If abrupt park visitation changes were more associated with Democrat behavior,
since urban areas have a Democratic bias, it is possible that the behavior of
the urban park goers (who are more likely to be Democrats) may have
overshadowed park going behavior in the rural parts of states. This
possibility is made further plausible by the observation that the counties
with a change point tend to be more populated. If park visitation changes are
more likely in areas of greater population, and these areas are also over
represented in the data, it stands to reason that aggregation to the state
level may obscure behavior of the rural residents in the park visitation data.

Of course there is a second implication of these observations which is that
whether or not park visitation exhibited an abrupt change is directly related
to population density. If true, this relationship would explain why there is a
disparity in population size for counties with and without abrupt changes, and
why the counties with the lowest populations did not have abrupt changes,
while the counties with the greatest populations did. In this case,
differences in party affiliation of the respective areas is possibly
unrelated, and only appears due to the confounding correlation between
population density and party affiliation [28]. Since there is a connection
between small populations and extreme partisanship as well, this would offer a
potential explanation for why the span of the distribution across vote share
for either party is greater for counties without abrupt changes.

Figure 5:  Box plots showing the distribution across employment share for
counties with and without change points in the sectors where the distributions
and their means were significantly different. Sectors in the plot to the left
were those where counties with a change point had significantly higher means
($p<0.05)$), sectors in the plot to the right had significantly greater mean
employment share in counties without change points. The distributions across
employment share for counties with change points are shown in pink, while the
distributions for counties without change points is shown in green. While the
differences in mean and distribution for all shown sectors are significant,
they are small.

Counties without abrupt changes in park visitation were more likely to have
higher proportions of employment in Manufacturing, Construction, Mining, and
Farming. Many of the workers in these sectors would have been considered
“essential,” and much of the work would be site specific. Meanwhile, counties
with abrupt changes were more likely to have greater proportions of jobs in
Information, Finance and insurance, Professional, scientific, and technical
services, and Educational services; sectors where remote work would have been
more widely adopted. It is curious that regions with greater proportions of
remote workers, who may have had greater time and opportunity to visit parks
at the time, were more likely to experience a drop-off in visits. The
difference is interesting and suggests it is possible that reductions in
employment related mobility impacted other mobility decisions, such as whether
or not to visit parks.

However, while there are differences in employment share by sector, they are
small, and their practical significance remains undetermined. The most
striking differences found in this study were in population, and partisanship.
Recent work [13, 19, 24] suggests that regions with higher Republican vote
share exhibited less social distancing at the onset of the pandemic, were
slower to adopt stay at home orders, and residents visited more points of
interest than residents of regions with higher Democratic vote share,
suggesting that overall mobility reduction was greater for Democratic counties
than Republican ones. Insight from these new studies suggests that the lack of
change in park visitation behavior among Republican regions simply reflects
this partisan difference in mobility, and indicates that parks were not
necessarily uniquely visited more or less relative to other points of
interest.

##  VI Limitations and Future Directions

This study did not account for differences in local COVID-19 response
policies. Incorporation of these differences would be necessary to understand
how local governance impacted park access, and how willing residents were to
defy local mobility restrictions for parks as opposed to other locations.

The spatial distribution of the parks in our data set roughly corresponds to
the spatial distribution of the population, creating a substantial urban bias
that we do not control for in this study. Weighing park visitation in such a
way to allow for aggregation to the state level without over representing the
urban parks would enable more revealing analysis at the state level, and
additional insight into the demographic differences between counties with and
without change points, with less influence from population density.

Augmenting the current data set with visitation data for more rural parks
could also aid in these goals. Greater representation of rural parks would
also allow a better investigation into population and park access as it
relates specifically to population density and general nature accessibility.

Due to a change in collection methodology at the end of 2019, which led to a
spatially non-uniform increase in total visitation counts, we were unable to
directly compare 2019 and 2020 data. While there are visibly dramatic dips in
behavior for some states and counties at the end of March 2020, it is not
possible to clearly quantify how these changes deviate from expected behavior,
nor how the magnitude of these changes compare across regions. Future work
could investigate other park visitation data, and attempt to use it to
normalize and perhaps compare visitation changes.

Comparison of visitation levels across years and regions, especially following
the initial pandemic reaction, would be extremely helpful in determining
whether or not there were differences in how park visitation was valued in
different regions. This could also be achieved by comparing dips in park
visitation to dips in visitation to other points of interest. In particular,
it would be useful to understand how different areas, and different
populations, weigh the benefits and risks of park usage in the pandemic, and
how park usage diverted visitation to other destinations. Studies indicating
which populations had access to parks, which may have been greatly beneficial
during 2020, could be used to address potential social inequality, and reduce
public health risk in the future.

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##  Appendix A Supplementary Material

Supplementary Figure S1:  Plots of the effect of the mean visitation threshold
on study results. Top: The mean percent having voted Democrat(left) and
Republican (right) in the 2020 Presidential election of the counties with and
without change points as the threshold is increased at the log 10 scale. When
the threshold is between -8 and -6 the gap in mean vote share between counties
with and without abrupt park visitation changes is stable. As the threshold
increases past -6 the gap begins to shrink, with the counties with abrupt
changes becoming slightly more democrat, and the counties without abrupt
changes becoming much more democrat, and both becoming less Republican. Bottom
Left: The p-value (blue) and statistic(black dashed) results of the KS 2
sample test on the partisan differences in counties with and without abrupt
changes as the threshold increases. The pvalue is stable until the threshold
is greater than -5, when it begins to increase, but never crosses the p=0.05
significance threshold (red dashed). The k statistic remains stable until the
threshold is increased past -6, when it decreases, but never falls below 0.2.
Bottom Right: The number of counties (black) which meet inclusion criteria as
the visitation threshold is increased. There is is rapid decline in counties
included in the study beginning at a threshold of -6. Past a threshold of -5
fewer than half of all counties in our data set meet inclusion criteria, and
at -4 there are almost none. The number of counties with an abrupt visitation
change (pink) remains constant in the study until a threshold greater than -5,
reflecting that these are among the counties with the greatest visitation. The
number of counties without a change (green) declines almost in parallel to the
total (black) counties, indicating that the threshold criteria eliminates
these counties almost exclusively.  Supplementary Figure S2:  Scatter plots
where each state and county is represented by a dot, the color of which
corresponds to whether or not an abrupt chagne took place. The location in the
x-y plane is determined by the percent of votes for the Republican(x) and
Democratic(y) candidates in the 2020 Presidential Election.