Philippa Kaur

Study areaThere is a long history of diversified cropping patterns due to the climatic and topographic complexity in China4. Cropping intensity increases from north to south, and multiple cropping dominates in regions south of 400N4. For example, multiple cropping systems of double rice and winter wheat plus maize are popular in the Middle-lower Yangtze river plain and the Huang-Huai-Hai plain, respectively (Fig. 1)22. Three staple crops, maize, paddy rice, and wheat, are widely distributed across the country (Figure S1). These three major crops contributed to more than half (57.08%) of the total sown area in China in 2020 (http://www.stats.gov.cn/english/).Fig. 1The distribution map of cropping patterns in 2021, 9 agricultural regions and validation sites in China. Notes: A to I represented nine agricultural regions in China. (A) Middle-lower Yangtze River Plain; (B) Huang-Huai-Hai plain; (C) Northeast China; (D) Inner Mongolia and along the Great Wall; (E) Loess plateau; (F) Southwest China; (G) Southern China; (H) Gansu-Xinjiang region; (I) Qinghai-Tibet region.Full size imageMODIS images and pre-processingWe used the 500 m 8-day composite Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance products (MOD09A1) from 2015 to 2021. Three spectral indices were calculated: the 2-band Enhanced Vegetation Index (EVI2)23, LSWI16, and Normalized Multi-band Drought Index (NMDI)24 (Fig. 2). The functions of EVI2, LSWI, and NMDI are provided in Eqs. 1–3 as follows.$${rm{EVI2}}=2.5times left({rho }_{NIR}-{rho }_{{rm{Red}}}right)/left({rho }_{NIR}+2.4times {rho }_{{rm{Red}}}+1right)$$
(1)
$${rm{LSWI}}=left({rho }_{NIR}-{rho }_{SWIR6}right)/left({rho }_{NIR}+{rho }_{SWIR6}right)$$
(2)
$$NMDI=frac{{rho }_{NIR}-left({rho }_{SWIR6}-{rho }_{SWIR7}right)}{{rho }_{NIR}+left({rho }_{SWIR6}-{rho }_{SWIR7}right)}$$
(3)
where, ρNIR, ρRed, ρSWIR6 and ρSWIR7 represented the surface reflectance values from the red (620–670 nm), Near-infrared (841–875 nm), short wave infrared band centered at 1640 nm (1628–1652 nm) and 2130 nm (2105–2155 nm), respectively.Fig. 2The workflow of the methodology: Data preprocessing, deriving cropping intensity, mapping three staple crops and obtaining annual maps of cropping patterns in China.Full size imageFor each spectral index (EVI2, LSWI, and NMDI), a daily continuous time series was developed based on the cloud-free observations using the Whittaker Smoother (WS)25. The WS smoother performed well in multiple cropping regions and therefore was applied here26.Validation data and other datasetsThe validation data in this study included the ground truth reference data and agricultural census data. The ground truth reference data were collected in major agricultural regions with GPS receivers and digital cameras during the study period (2015–2021) (Fig. 1, Table S1). For each sampling site, the geographic location and crop types were recorded. The reliability of ground survey data was improved through visual confirmation based on high-resolution images in Google Earth. Some reference sites with small field sizes were removed to considering the mixed-pixel problems of MODIS images. Finally, we obtained a total of 18,379 ground samples collected during 2015–2021 (Table S1). All the ground truth reference data were used to validate the cropping pattern data in its corresponding year. Agricultural census data were obtained from the National Statistical Bureau of China (NSBC) (http://www.stats.gov.cn/english/), which was collected through sampling statistics. The crop calendar data from agro-meteorological stations recorded the sowing, seedling, tillering, heading, and harvesting dates of winter wheat (210 sites) or spring wheat (90 sites). The calendar data were applied to establish the trend surfaces of key phenological stages of winter wheat and spring wheat, respectively. The crop calendar data were provided by the National Meteorological Information Center, China Meteorological Administration.The cropland distribution data were derived from the 30 m GlobeLand30 global land cover data in 202027. The total accuracy of GlobeLand30 in 2020 is 85.72%, and the Kappa coefficient is 0.82 (www.globallandcover.com). To correspond to MODIS images, the 30 m cropland pixels from GlobeLand30 data were spatially aggregated to a 500 m cropland fraction map. For simplification, we classified pixel purity of MODIS pixels into three groups: cropland percentages of >90%, 50–90%, and More

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Effects of aqueous plant extracts on germination and early growth of B. bipinnata by in vitro bioassaysSeed germination and seedling growth of B. bipinnata were investigated after treatment with DT, RC, PT, and JG aqueous extracts to explore the allelopathic effects of these plant species. The pH of the aqueous extracts corresponded to 6.62 for DL, 5.59 for RC, 7.20 for PT, and 7.42 for JG, with no significant difference in pH values between DL and RC extracts or between PT and JG extracts; however, the pH of DL and RC extracts differed significantly (p  1000 cm−1 were attributed to the C − H out-of-plane bending vibration of aliphatic alkenes and aromatic benzene rings49,50.The range between 1800 and 600 cm−1 of the infrared spectra was selected for the PCA, as it is the most representative region of the differences present in the spectra. In the PC1 versus PC2 score plot (Fig. 6), representing 85.78% of the total variance, it is possible to observe the separation of the samples into three distinct groups. The samples of DL and RC extracts formed two distinct groups, since they showed a significant separation in the PC1 axis, with positive and negative scores for PC1, respectively. The samples of JG and PT extracts formed a single group, remaining superimposed and located close to the zero value of PC1, indicating intermediate spectral characteristics in relation to the DL and RC extracts. These results may be correlated with the allelopathic activity of these extracts, since the RC extract showed better performance, followed by the JG and PT extracts, with intermediate performance, and the DL extract showed lower activity compared to the others.Figure 6PCA score plot (PC1 × PC2) of D. lacunifera (DL), R. communis (RC), P. tuberculatum (PT), and J. gossypiifolia (JG) extracts.Full size imageThe PC1 loading plot (Fig. S1) has as main contributors the negative bands associated with signals at approximately 1732, 1595, 1404, 1200–1025, 1049, and 780–600 cm−1, which significantly contributed to the separation of RC extract samples that presented greater intensity than in DL extract samples. On the other hand, the positive bands in PC1 in the region of 780–970 cm−1 were more intense in DL extracts. When evaluating the negative region of the PC1 loading plot, it is possible to observe that the functional groups responsible for the discrimination are probably those present in flavonoids and phenolic acids, corroborating the data in the literature that demonstrate the identification of these compound classes in RC leaves, such as gallic acid, quercetin, gentisic acid, rutin, epicatechin, ellagic acid, etc.51,52,53.The presence of flavonoids can be observed due to the stretching of C=O at approximately 1732 cm−1, C=C of aromatics at 1600 cm−1, C–O at 1200–1000 cm−1, and O–H at 3284–3174 cm−1. Phenolic acids can be verified due to stretching of the O–H of carboxylic acid, C=O and aromatic ring, as well as the C − H out-of-plane bending vibration of aromatic benzene ring at  More

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A white truffle (Tuber magnatum Pico) in the laboratory of Robin Pépinières, a nursery in Saint Laurent-du-Cros, France.Philippe Desmazes/AFP via Getty Images

On 10 October 2019, a dog began pawing excitedly at the ground beneath a young oak tree in western France. Its owner eased it out of the way and pulled an Italian white truffle (Tuber magnatum Pico) from the earth. Knobbly, covered in soil and about the size of a hen’s egg, it was not much to look at, but the fungal discovery nonetheless generated ripples of excitement among researchers, chefs and truffle growers worldwide.That’s not just because T. magnatum is the most expensive truffle species, for which wealthy gastronomes are willing to pay up to US$11,000 per kilogram. Although more than 90% of the also highly sought-after black Périgord truffles (Tuber melanosporum) served in restaurants today are farmed, previous attempts to cultivate their more elusive white counterparts had failed.That changed three years ago, when the Lagotto Romagnolo, the Italian dog breed commonly used as a truffle hunter, unearthed the first Italian white truffle confirmed to have been cultivated outside its natural range. The dog made the find at its owner’s plantation in the Nouvelle Aquitaine region of France, but the precise location is being kept secret to deter thieves.Scientists at a laboratory run jointly by France’s National Research Institute for Agriculture, Food and the Environment (INRAE) and the University of Lorraine in Nancy reported1 that since that first T. magnatum truffle was unearthed, two more were found at the site in 2019 and four in 2020. In an article published last month in Le Trufficulteur, the magazine of the French Federation of Truffle Growers, the researchers report the cultivation of 26 truffles last year2.“I was very happy to hear these results,” says Alessandra Zambonelli, a mycologist at the University of Bologna, Italy, who has studied Italian white truffles for more than 40 years, and whose own attempts to cultivate them in the 1980s failed. “I was sure it was possible to cultivate T. magnatum, but only now do we have the scientific proof.”The INRAE project is helping growers to better understand the optimal conditions for cultivating Italian white truffles. Some scientists think the breakthrough could help to reverse falls in harvests of wild truffles that have been linked to climate change. Researchers also hope the work will help them to answer outstanding questions about the life cycle of the species and understand why it is so much harder to farm than are other truffles.Farming failureTuber magnatum’s natural range is more limited than those of other sought-after truffles, growing as it does in parts of Italy, southeastern France, the Balkans and Switzerland. It is highly prized for its intense, some say intoxicating, aroma and flavour, variously described as reminiscent of garlic, fermented cheese and methanethiol — the additive that gives domestic gas its smell. Prices fluctuate in line with supply, which varies according to climatic conditions. These hit an all-time high in 2021, when US prices were more than triple what they were in 2019.Most land plants form symbiotic relationships with fungi to access extra water and mineral nutrients. In return, the plants provide their fungal partners, which grow around and into their root tips, with carbon-rich nutrients. These associations are known as mycorrhizae. What most people call truffles are, in fact, just the spore-containing fruiting bodies of the fungus.In the 1970s, French scientists successfully induced Périgord truffles to form mycorrhizal associations with tree seedlings by inoculating the seedlings with their spores. The same technique was used at the time to produce trees with T. magnatum mycorrhizae. More than 500,000 of these were planted in Italy. But when researchers later began using the polymerase chain reaction (PCR) technique to accurately identify truffle mycorrhizae, fruiting bodies and the root-like mycelia, it became clear that this species’ physical characteristics had been poorly described, and that, as a result, many of the trees had in fact partnered with less sought-after truffle species.Some sites in Italy did produce T. magnatum truffles 15–20 years after planting, but only in areas where the species occurs naturally. “It is likely that those found so long after being planted came from chance colonization of host plants by native T. magnatum strains in the environment,” says Claudia Riccioni, a plant and fungal biologist at Italy’s Institute of Biosciences and BioResources in Perugia.After the Italian white and Périgord truffles, the next most sought-after species is the summer truffle (Tuber aestivum), which grows in many European countries and sells for much less than its more highly regarded cousins. Plantations of T. aestivum have been established in France, Italy, Scandinavia, Germany and elsewhere.Buried treasuresIn 1999, INRAE researchers joined forces with Robin Pépinières, a nursery based in Saint-Laurent-du-Cros, southern France. Genetic analysis confirmed that the nursery had produced trees that partnered with T. magnatum, leading, from 2008, to the establishment of plantations in France1. In 2018, the INRAE group selected five of these, all outside the part of southeastern France where T. magnatum grows naturally, to see whether it had become established and to record the conditions under which any truffle fruiting bodies were produced.PCR tests confirmed the fungus’s mycelia were present in soil samples taken from near the trees at four of the locations. The first three truffles, found in Nouvelle Aquitaine, were discovered four-and-a-half years after the inoculated trees had been planted. Further PCR tests confirmed they were T. magnatum. The 26 truffles found in 2021 were unearthed beneath 11 different trees, with 5 under one of them. The largest weighed 150g.Mycologists Claude Murat and Cyrille Bach, both members of the INRAE–University of Lorraine lab, were present when one of the four fruiting bodies produced in 2020 was discovered. Asked how sure he was that the truffle grew in the plantation and hadn’t originated elsewhere, Murat said: “I’m 100% sure. We could see the soil had not been disturbed and that grasses were growing there.”Mycorrhizal mysteryPrevious attempts to cultivate Italian white truffles failed in part because their life cycle remains poorly understood. Twenty years ago, it was widely assumed that truffles, including T. magnatum, were self-fertile. However, research then showed they have one of two ‘mating type’ genes, and that the mycelia of individuals of different mating types must meet for reproduction to occur3.A remaining unresolved puzzle is why researchers have found T. magnatum mycorrhizae much harder to locate than those of other truffles. Mycologist Paul Thomas works to establish joint ventures with truffle growers through Mycorrhizal Systems, his UK-based company. He inoculated host trees with T. magnatum, and generated mycorrhizae at the company’s greenhouses in Preston, but these did not last long, so the trials were abandoned.“When you find fruiting bodies, you quite often can’t find mycorrhizae,” says Thomas, “and sometimes you get mycorrhizae but no fruiting bodies. Perhaps, in the case of T. magnatum we’ve become too focused on linking truffle production to mycorrhizae.”When Zambonelli’s group analysed soil from four Italian white-truffle sites over three years, they found a correlation between production of fruiting bodies and a location’s concentration of DNA from T. magnatum mycelia4. Some researchers began to suspect that the host–fungus relationship might not be as important as previously thought, and that T. magnatum might be saprotrophic, meaning that it digests dead or decaying organic matter.However, a 2018 comparison5 of the genomes of truffle species with those of several saprotrophic fungi showed this to be unlikely. “T. magnatum has very few plant-wall-degrading enzymes, which does not support the saprotrophic hypothesis,” says Riccioni, one of the study’s authors. Other researchers have tried to explain the elusiveness of T. magnatum mycorrhizae by pointing out that other truffles can form endophytic relationships with plants in which they which live throughout them, not just at their roots.Murat wonders whether he and others have just been looking in the wrong place. “We look on the roots down to 20 centimetres, never looked at 50 centimetres, even though we know other mycorrhizae can be found at those depths,” he says. “Or perhaps they produce mycorrhizae just for a very short time; we just don’t know.”A growing body of research shows that microorganisms have important roles in truffle life cycles. A 2015 review found that bacteria in T. magnatum fruiting bodies help to create the truffles’ odours6. Zambonelli and her colleagues found that bacteria in T. magnatum fruiting bodies can fix nitrogen for nutritional purposes7. Another Italian team found that microbes commonly associated with white truffles are involved in fruiting-body maturation8. “Some bacteria could also help T. magnatum become established at tree roots and fruiting-body formation,” says Zambonelli.A changing climateGathering accurate statistics on truffle yields before cultivation is difficult, although it is widely accepted that these fell significantly during the twentieth century. One study reports that Périgord truffle harvests in France collapsed from 500–1,000 tonnes annually in the 1900s to 10–50 tonnes by the 2000s. Yields in Italy declined, too, but not by as much, and mostly in the first half of the twentieth century9.The reasons for falls in truffle harvests are complex and vary by location, but researchers have blamed depopulation, loss of knowledge about truffle hunting and deforestation. Some of the older men who featured in the highly rated 2020 documentary The Truffle Hunters, set in Piedmont, northern Italy, say they will take what they know about truffles to the grave rather than pass it on to younger generations because of the greed they see in the industry.

A canine forager and his owner who feature in the 2020 documentary The Truffle Hunters, set in northern Italy.BFA/Alamy

More recently, some researchers have highlighted climate change as another cause of declining yields. Truffle gastronomy and tourism are economically and culturally important in places where truffles occur naturally. That’s certainly true in parts of Croatia, where, from 2003 to 2013, reported annual harvests were 1–3 tonnes for Italian white truffles and 1–6 tonnes for Périgords, except for the years 2009, 2010 and 2013, when they fell to 0.1–0.5 tonnes.Field mycologist Željko Žgrablić at the Ruđer Bošković Institute in Zagreb says truffles have become harder to find on the Istria peninsula, where he grew up, in part because of increasingly frequent and severe droughts. Yields have also been affected by big increases in wild-boar populations as a result of warmer winters. The animals forage for the truffles and reduce human harvests, and, according to Žgrablić, also damage the fungus’s mycelia. “The climate has become unpredictable, with more extremes,” says Žgrablić. “It’s hard to prove it, but I think we have fewer white truffles as a result.”In a 2019 study, Thomas analysed annual Périgord truffle yields in the Mediterranean region over a 36-year period10. He concluded that decreased summer rain and increased summer temperatures significantly reduced subsequent winter harvests. He forecast declines of 78–100% in harvests between 2071 and 2100 as a result of further predicted warming. “White truffles need relatively moist soil, so in its natural range it might be okay in mountainous areas but particularly vulnerable in areas where falls in rainfall are predicted,” says Thomas.Future farmingBeyond producing the first confirmed cultivated white truffles, the INRAE project is also generating data on the optimal conditions for production. The soil temperature at the site that yielded the truffles was around 20 °C in the summer, and Murat says that the team’s tests suggest white truffles need more water than do Périgords.So could the increasing knowledge of how best to get Italian white truffles to grow be adopted more widely to help reverse declining yields? Fruiting bodies have been confirmed at only one site, so other growers are waiting to see whether this success will be repeated elsewhere. Murat is in the process of trying to confirm recent claims from two other owners that they, too, have cultivated T. magnatum truffles.Thomas is downbeat about the future of Italian white-truffle cultivation. “In parts of Spain, more and more orchards can no longer irrigate because of water shortages. Already, in France, it is hard to get permission to extract water from rivers for irrigation, and that’s only going to get worse.”Oak trees inoculated with Périgord- and summer-truffle spores are due to be planted later this year in Croatia as part of a collaboration run by the state-owned Croatian Forests. If successful, the group could try white truffles. Žgrablić, who is part of the project, is also advising an enthusiast who planted 650 seedlings inoculated with T. magnatum, also in Croatia, earlier this year. “We’re seeing increasing interest from private investors in cultivating Italian white truffles,” he says. “There is certainly a lot of potential, but what the results will be, I can’t tell.”Alongside his research work, Murat acts as a scientific consultant for WeTruf, a company he co-founded in Nancy that provides advice and monitoring services for truffle farmers. He is cautious about the potential for white-truffle cultivation, if optimistically so. “We are careful when people tell us they want to start big white-truffle plantations,” says Murat. “I tell them ‘we are only at the beginning, we don’t know if it will succeed or not’. But I think there will be more and more plantations, and, if they apply good management practices, I hope, more and more truffles.” More

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MaterialsData sourcesSupplementary Table S1 summarizes the definitions of all the variables and Supplementary Table S2 displays the descriptive statistics of the variables. A detailed description of our data sources is summarized in Supplementary Table S3.In summary, our mobile phone data, containing Jan 2018 to Apr 2021 visitation records to each national park and the visitors’ respective census block groups, are courtesy of SafeGraph Inc47. The geographical boundaries of national parks that are used to extract records only relevant to national parks are provided by the NPS Land Resources Division48. Finally, the racial and population demographics of each census block group are provided by the 2015-2019 American Community Survey (ACS)16.The utilization of each distinct dataset towards the extraction of our materials of interest are elaborated in the subsequent sections.Validation of SafeGraph’s mobile-phone datasetThe validation of SafeGraph’s mobile-phone dataset in its application to national parks has been previously validated by Yun et al17. Specifically, Yun et al’s17 work showed a close resemblance between the NPS visitor use survey and SafeGraph’s mobile-phone dataset in terms of visitation counts, temporal visitation patterns, racial demographics, and state-level residential origins of the visitors to Yellowstone National Park. However, SafeGraph’s POI classification of “National Parks” remains inconsistent with the NPS’s official definition of National Park. To circumvent this problem, we have utilized shapefiles courtesy of the NPS OpenData48 to extract the most visited POIs that fall within the shapefiles of each respective “National Park”. This process would be detailed in the subsequent sub-sections below.Selection of mainland US national parksWe adopted the official and formal definition of national parks as defined and listed by the NPS System49.We selected national parks within the 48 states encompassing the contiguous U.S. We chose to omit the parks that fall within the states of Alaska, Hawaii, Puerto Rico and other US minor Islands considering the fact that air travel is a necessity for out-of-state visitors to visit these select parks. These separate travel behavioral patterns could result in confounding variables towards our analysis, particularly since air travel faced major disruptions amidst the COVID-19 pandemic50.It is worth noting that New River George National Park was declared as a national park only following the COVID-19 pandemic51. Hence, it is excluded from our study.Finally, we lack the data availability for White Sands National Park and Dry Tortugas National Park. The former is due to its proximity to White Sands Missile Range and security concerns on mobile device data52. The latter’s lack of data availability could be attributed to the fact that the park is an island off the coast of Key West, FL53.Henceforth, we included a grand total of 48 national parks in our study.Extraction of POIsWe selected our points-of-interests (POIs) based on the dataset made available by SafeGraph47. While SafeGraph does provide its own classification of “national parks”, its classification methodology remains inconsistent with the NPS’s official definition and formal list of “national parks”17,49.Hence, we extracted POIs that fall within the encompassed polygon shapefiles of each respective national park. The polygon shapefiles are courtesy of the NPS OpenData48.We then selected the POI with the highest average monthly visitation records for each distinct national park.The choice to select the POI with the highest visitation record could be attributed to the fact that a brief analysis reveals that in many parks, the top 5 most populated POIs tends to fall within the same vicinity17. Specifically, the top 5 most populated POIs for many large national parks, like Cuyahoga National Park, Indiana Dunes National park, and Yellowstone National Park, typically encompass the areas surrounding the park entrances17. This remains rational since visitors would have to pass through park entrances to enter the parks and gain access other areas of the park. Hence, selecting only the POI with the highest visitation record for each park prevents us from making duplicate counts from separate POIs.Computing census block group-based racial demographicsThe aforementioned Safegraph47 data provides us with the census block group origins of the visitors to each distinct POI. The census block group origins are identified by its 12-digit Federal Information Processing Standard (FIPS) code. We are thus able to retrieve our racial demographics of interests (% of non-whites, % of African-, % Hispanics-, % of Asian-, and % Native Americans) pertaining to each visitors census block origins.Our study only considered all visitations across mainland U.S. As such, we have excluded visitors from Hawaii, Alaska, Puerto Rico and other minor US islands for their visitation patterns are expected to be abruptly disrupted following the pandemic due to restrictions put in place from air travel50. This decision would prevent the effects of confounding variables and avoid drastically skewing our data.Computing distance travelled by visitor to each national parkLikewise, we obtain the variables of distance through the utilization of the Haversine formula54 between the POIs coordinates and the centroids of the visitors census block group. We standardize the units of distance to kilometers in our analysis.Categorization of visitation records falling before and after COVID-19We categorize pre-COVID era as any time-period that occurs prior to the month of March 2020. Hence, we classify the COVID era as any time period from the month of March 2020 onward. We selected March 2020 for it was the month in which the UN declared COVID-19 a global pandemic55. This declaration was proceeded by numerous state and local lockdown measures which drastically impacted American commerce56 and the lifestyles of many Americans57.Methods and ModelOffsetting visitation counts with the census block group populationWe offset our dependent variable of visitation counts per census block population because racial demographics of the visitors’ census origins are measured at a census block level. This allows us to account for the fact that one would naturally expect higher visitation counts from more populated census block groups. Hence, the visitation counts per thousand population of the census block group would serve as a function of our independent variables (COVID-19 era, distance and racial demographics). This could be illustrated in Eq. (1) in the introduction section.Gravity ModelWe incorporated gravity models into our methodology. In the context of tourism, the gravity model explores the behavior and travel patterns over distances between two unique POIs.The gravity model was adopted from Newton’s law of universal gravitation in physics58. Newton’s law of universal gravitation states that distance and mass determine the gravitational forces between two objects. The gravity model has since been adapted by numerous disciplines in the social sciences. These topics include trade21, tourism19,20, and migration22. For instance, the gravity model is popular in studies involving bilateral trade21. This is because the gravity model allows economists to measure how specific economic indicators (such as GDP) could attract trade between two countries, given the distances between them21.We thus elected to use the gravity model because it best represents our research theme of seeking to analyze the changes in visitations to national parks amongst individual racial communities across the U.S. Henceforth, the gravity model allows us to best analyze the change in visitations from different racial communities to each specified national park given the required distance of travel. The selection of our variables, in seeking to optimally represent the gravity model, while preserving its assumptions, would be elaborated in the subsequent subsections below.Our application of the gravity model works as such: given (i{mathrm{th}}) census block group and (j{mathrm{th}}) national park where (alpha _k) symbolizes each respective coefficient towards the determined independent variable, the gravity model could be demonstrated as such:$$begin{aligned} frac{visitation_{ijt}}{left( frac{population_i}{1000}right) }propto frac{race_i^{alpha _1}*interaction_terms^{alpha _2}}{distance_{ij}^{alpha _3}} end{aligned}$$
(2)
which can be remodelled as:$$begin{aligned} visitation_{ijt}propto frac{race_i^{alpha _1}*(interaction~terms)^{alpha _2}*left( frac{population_i}{1000}right) ^{alpha _4}}{distance_{ij}^{alpha _3}} end{aligned}$$
(3)
using natural logarithms could be transformed to:$$begin{aligned} ln (visitation_{ijt})propto {alpha _1}ln (race_i)+{alpha _2}ln (interaction~terms)+alpha _3ln (distance_{ij})+ {alpha _4}ln left( frac{population_i}{1000}right) end{aligned}$$
(4)
Model SpecificationThe gravity model is incorporated using panel data with interaction terms19,21. Incorporating panel data allows us to control for unobservable individual effects19,21, such as time invariant monthly and seasonal fluctuations in park visitations, as best illustrated in the peaks and troughs witnessed in Fig. 1. The interaction terms allows us to measure the impact of COVID-19 towards our selected predictors. Specifically, the random-effects panel approach was selected in favor of the fixed-effects panel model and the pooled ordinary least squares (OLS) model as evident by the results of the F-tests, Hausman’s Chi-Squared, and the Breusch-Pagan (BP) Lagrange Multiplier59 tests displayed in Supplementary Table S4.This results in Eq. (5), given each (i{mathrm{th}}) census block group’s visitation to (j{mathrm{th}}) national parks during (t{mathrm{th}}) month over specified race (race_i).$$begin{aligned} begin{aligned} ln left( visitation_{ijt}right)&= beta _0+beta _1(COVID~era)+beta _2[ln (race_{i})] +beta _3[ln (distance_{ij})] +beta _4left[ ln left( frac{population_{i}}{1000}right) right] \ {}&quad +,beta _5[COVID~eratimes ln (race_{i})] +beta _6[(COVID~eratimes ln (distance_{ij})] +beta _7[ln (distance_{ij})times ln (race_i)] \ {}&quad +,beta _8[(COVID~eratimes ln (distance_{ij})times ln (race_i)]+V_{ijt} \ end{aligned} end{aligned}$$
(5)
The assumptions of log-linearity and multi-collinearity19,20,21 in our specified model, per Eq. (5), have been tested and could be referenced in Supplementary Table S5.Consideration of variables in our modelWe explored using the size area (in km(^2)) of each respective park, instead of distance travelled, as the denominator of our gravity model per Eq. (2). However, the substantially lower (R^2) values obtained when using a park’s size suggests that a park’s area is a poor factor in explaining visitation trends across socio-economic variables. These are detailed in Supplemental Table S6.We also initially considered fitting other socio-economic independent variables into the same analysis. We did so in the hopes of gaining further insights on COVID-19’s impact towards park visitation. Some other independent variables that were considered included median income and median age. However, fitting them into same analysis resulted in high multi-collinearity. These are detailed in Supplemental Table S6. Multi-collinearity occurs when an independent variable is highly correlated with another independent variable in an analysis involving multiple independent variables60. This could consequently “undermine the statistical significance of an independent variable”60.To mitigate concerns of multi-collinearity in our analysis involving different racial groups, we adopt the procedures outlined by Lewis-Beck and Lewis-Beck60. Lewis-Beck and Lewis-Beck recommends separating our analysis of each racial composition. This means that we would analyze the composition of non-whites, African-, Asian-, Hispanic-, and Native American with our other variables separately.Finally, we considered analyzing the variables of income and age separately. However, the variables of income and age still resulted in high multi-collinearity amongst the existing independent variables. Furthermore, the different characteristics displayed amongst our analysis involving variables like income and age (compared to race) meant that our suggested random-effects gravity model is not a one-size-fits-all model for other analysis involving separate variables. These are detailed in Supplemental Table S6. For this reason, we hope to study variables like age and income in some of our future studies, using a different model. More