Ecology

Database utilizedThe database comprises information obtained with permission from the Catalogue of Endangered Languages that is hosted on the Endangered Languages Project platform (https://www.endangeredlanguages.com/). The Endangered Languages Project was first developed and launched by Google, and is currently overseen by First People’s Cultural Council and the Institute for Language Information and Technology at Eastern Michigan University. Information about the languages in this project is provided by the Catalogue, which is produced by the University of Hawai’i at Mānoa and Eastern Michigan University, with funding provided by the U.S. National Science Foundation (Grants #1058096 and #1057725) and the Luce Foundation. The project is supported by a team of global experts comprising its Governance Council and Advisory Committee.In general, the Catalogue aims to present all languages that communities and scholars have pointed out to be at some level of risk as well as languages that have become dormant. In addition to being the largest database of endangered languages globally, the Catalogue is updated periodically based on feedback gathered from language communities and scholars worldwide. The data therefore represents what was most accurately known about the state of each language’s vitality at its point of utilization. At the time of usage, there were 3423 languages represented in the Catalogue that were determined to be at various levels of risk. Assessment of each language’s risk level is carried out using the Language Endangerment Index, which was developed for the Catalogue’s purposes. The Index is used to assess the level of endangerment of any given language based on whether there is intergenerational transmission of the language (whether the language is being passed on to younger generations), its absolute number of speakers, speaker number trends (whether numbers are stable, increasing, or decreasing), and domains of language use (whether the language is used in a wide number of domains or limited ones). The levels of endangerment that the Index generates include ‘safe’, ‘vulnerable’, ‘threatened’, ‘endangered’, ‘severely endangered’, and ‘critically endangered’. Languages for which it remains unclear if the language has gone extinct or whose last fluent speaker is reported to have died in recent times are referred to as ‘dormant’. Given that the focus of the Catalogue is languages that are at some level of threat, safe languages are excluded in general. Where locality information is available, each language is also accompanied with its latitudinal and longitudinal coordinates.Steps taken to prepare the data for network analysisThe data obtained from the Catalogue was further organized and cleaned up for analysis.

1.

Identifier code
Where available, the ISO 639-3 code for each language was utilized as its unique identifier. Otherwise, its LINGUIST List local use code was utilized. These are temporary codes that are not in the current version of the ISO 639-3 Standard for languages. For languages with neither, unique 3-letter codes were constructed.

2.

Endangerment level
Each language’s endangerment level appeared together with a level of certainty score in the same cell in the original data file. Both pieces of information were split into separate columns and only endangerment levels were utilized.
For languages where different data were available in the Catalogue depending on resource utilized, the data was listed in additional columns. The endangerment level data points utilized in these cases were the ones with the most complete and updated information. If there was no data available regarding endangerment level, this information was also reflected.

3.

Coordinates
Where exact coordinates were not available, coordinates were approximated using Google maps based on the location description provided in the Catalogue source (e.g., the Tel Aviv district), attained from other sources such as Glottolog, UNESCO Atlas of the World’s Languages in Danger, or approximated from maps provided in other sources. ‘NA’ was indicated in the field for coordinates if none could be found.
Coordinates found to be inaccurate were rejected, for example in the instance that coordinates provided indicate a different location than the country the language is supposedly found in. The above steps were then taken to populate the coordinates field.
In instances where a language appears in more than one country, these are listed in separate rows as separate entries. Where there are two sets of coordinates for a country, the set that best corresponds with the written description in the Catalogue source, has greater detail, or is more recent is chosen. Where there are more than two sets of coordinates, a middle point is chosen as being representative of the language’s location, by plotting all coordinates on MapCustomizer (www.mapcustomizer.com).

4.

Language family
On the Catalogue, the information regarding language family may be multi-tiered. For example, Laghuu falls under the Lolo-Burmese branch of the Sino-Tibetan family. For this study, the broader family is utilized—in the case of Laghuu the label ‘Sino-Tibetan’ is used.
Mixed languages, pidgins, and creoles have all been categorized as ‘contact languages’.
Language isolates are listed as ‘isolates’.

5.

Region

The Catalogue groups ‘Mexico, Central America, Caribbean’ together under region. Central America and Caribbean are listed as separate regions in this study, with Mexico falling under Central America.Network constructionA spatial network of endangered languages was constructed from the database. Each node represented an endangered language, and edges or links depicted the distance between the locations of the languages as specified in the database. A distance matrix containing the distances between all endangered languages was computed by using functions from the ‘geosphere’ R package. Specifically, Haversine distances were computed for each pair of longitude and latitude points in the dataset. The radius of the earth used in the Haversine distance calculation is 6,378,137 m (for more details see: https://www.rdocumentation.org/packages/geosphere/versions/1.5-14/topics/distHaversine). Haversine distance refers to the shortest distance between two points on a spherical earth, also referred to as the “great-circle-distance”29.Sensitivity analyses of edge thresholdsThe distance matrix is a fully connected network with weighted, undirected links. We set out to capture the strongest or “closest” spatial relationships among the endangered languages, therefore an edge threshold was applied to the distance matrix such that only the edges in the xth lowest percentile were retained in the spatial network. Such an approach allows for the analysis of the most meaningful (i.e., the physically closest) spatial relations in the dataset and how they relate to language endangerment status. The edges were then transformed into unweighted connections to create a simple unweighted, undirected graph for analysis. In order to determine the value of x (i.e., the percentile at which the edge threshold is to be applied), we constructed 10 spatial networks that retained edges with distances below the 1st, 2nd, 3rd… 10th percentile (in increments of 1%) of all distances in the matrix. Additional information of the distances depicted by the edges in each of the 10 networks is provided in Supplementary Information.These 10 networks were then analyzed for their macro- and meso-scale network properties. A summary of macro and meso-scale network measures used in this analysis and their definitions is provided in Table 1, which depicts the 10 networks showing similar patterns in their network structures.Table 1 An overview of macro- and meso-level network measures of spatial networks with different thresholds.Full size tableResultsAs expected, network density and average degree of the networks, which serve as indicators of the number of edges relative to the number of nodes in the network, increased as the edge threshold used to connect nodes became more liberal. The relatively high values of C (i.e., high levels of local clustering among nodes) and low values of ASPL (i.e., relatively short paths despite large size of network) suggested the presence of small world structure30. The community detection analysis using the Louvain method31 indicated strong evidence of community structure in the networks—suggesting the presence of clusters of endangered languages.The point at which the vast majority of nodes was located within the largest connected component of the network occurred at the 5% edge threshold. Because the 5% network was not too fragmented, we report the analyses conducted on the largest connected component of the 5% network in the following subsections. Please see Supplementary Information for additional details behind the rationale for selecting the 5% network for further analyses. The smaller connected components were excluded. Note however that our results are robust across spatial networks of various edge thresholds (due to lack of space, please see Supplementary Information for a complete summary of all reported analyses conducted on all 10 spatial networks).Macro-level analysis: assortative mixing of endangerment statusesMethodTo investigate the macro-level structure of the spatial network of endangered languages, we computed the assortativity coefficient of the spatial network. Specifically, we wanted to know if the endangerment statuses of the languages tended to cluster at the global level of the entire network. If the assortativity coefficient is positive, the languages in the network would tend to be connected to languages of similar levels of endangerment. If the assortativity coefficient is negative, the languages in the network would tend to be connected to languages of dissimilar levels of endangerment.ResultsThere is a significant positive correlation (Spearman’s rank correlation) between the endangerment status of connected pairs of endangered languages in the network, r = 0.20, p  More

Model 1: Evolution of multiple mating and mate monopolisation under ancestral monogamyIn all models, I assume a large population with a 1:1 sex ratio. I begin with what is possibly the simplest model set-up for deriving Bateman functions in a scenario that is completely symmetrical aside from gamete number. Assume a monogamous, externally fertilising population where parents pair up and release their gametes into a nest. That is, every individual in the initial population participates in exactly one fertilisation event (the equivalent of a mating). Now consider a mutant individual that can attract multiple mates of the opposite type to release gametes into its nest, with no competition from other individuals of its own type. This simple set-up avoids asymmetries arising from internal fertilisation, and the complication of direct gamete competition for the multiply mating mutant individual (which is examined in Models 2–3), placing focus directly on the core of the problem: the asymmetry arising in fertilisation from imbalanced gamete numbers. All gametes are released in one burst by all individuals, but the focal individual may achieve ‘multiple matings’ simply by monopolising multiple mates at its nest. The reproductive success of the focal individual is then equivalent to the number of fertilisations that take place in that nest. Our aim is to understand how the reproductive success of an individual deviating from the monogamous population strategy and instead mating with (hat{m}) individuals of the opposite type is altered. A strong positive relationship between (hat{m}) and reproductive success then indicates a steep Bateman gradient. If Bateman’s assertion is correct, the resulting gradient should be steeper for the type that produces the larger number of gametes. Note that there is a game-theoretical25 flavour to this setting, where the focus is on the fitness of a rare mutant in a population with a fixed resident strategy.The two types are labelled with x and y, which could correspond to the two sexes, depending on what gamete numbers are assigned to them. The number of gametes produced by a single individual is labelled nx and ny, and the total number of gametes in a nest (or more generally, a fertilisation arena which could be internal or external) is labelled with Nx and Ny. To compute the number of fertilisations in a nest with a total of Nx and Ny gametes, I use a fertilisation function first derived by Togashi et al.24 purely from biophysical principles, treating the two gamete types symmetrically, with no pre-existing assumptions about differences between females and males or their gametes (for a broader context and comparison to other functions, see Table 1 and function F7 in19). Any sex-specific differences arise only retrospectively after different gamete numbers are assigned to x and y of which either one could be male or female. The fertilisation function is (fleft({N}_{x},{N}_{y}right)={N}_{x}{N}_{y}frac{{e}^{a{N}_{x}}-{e}^{a{N}_{y}}}{{{N}_{x}e}^{a{N}_{x}}-{N}_{y}{e}^{a{N}_{y}}}), where a is a parameter controlling fertilisation efficiency (for the special case Nx = Ny the function is defined as (fleft({N}_{x},{N}_{y}right)=frac{a{N}_{x}^{2}}{1+a{N}_{x}})19,24, which is also the limit of f when Ny → Nx).In a monogamous resident pair, we have simply Nx = nx and Ny = ny. But if a mutant individual of type x is able to attract (hat{m}) fertilisation partners of type y, then for that individual ({N}_{y}=hat{m}{n}_{y}), and the corresponding Bateman function is$${b}_{x}left(hat{m}right)=fleft({N}_{x},{N}_{y}right)=fleft({n}_{x},hat{m}{n}_{y}right)$$
(1)
where the fertilisation function f is as described above. Because of symmetry, the corresponding function for y is found simply by swapping x and y. This function can reproduce the characteristic Bateman gradient asymmetry as gamete numbers diverge (progressing from isogamy to anisogamy in Fig. 1), showing how Bateman’s assertion follows from biophysical effects that arise from unequal numbers of fusing particles: the fertilisation function f is derived solely from such biophysical effects, not from any sex-specific assumptions. Equation (1) makes no reference to sexes, and they only become specified when values are assigned to nx and ny. For example, if nx = 10 and ny = 10,000, the female Bateman function is ({b}_{x}left(hat{m}right)) and the male Bateman function ({b}_{y}left(hat{m}right)), where for the latter all xs in Eq. (1) are replaced with ys and vice versa. The labels x and y are truly just labels. While there are inevitably assumptions built into the equations, crucially we can be certain there are no sex-specific assumptions. Yet the typical shapes reminiscent of Bateman gradients arise from the model when different values are specified for nx and ny (Fig. 1).Fig. 1: The Bateman function of Eq. (1).This figure shows how the basic Bateman gradient asymmetry arises from simple biophysics and mathematics of fertilisation. The population is monogamous aside from a mutant individual, whose number of fertilisation partners (‘matings’) varies on the horizontal axes within panels. a–d show the effect of variation in sex-specific gamete numbers under efficient fertilisation, while e–h show the effect of variation in sex-specific gamete numbers under inefficient fertilisation. Parameter values used are shown in the figure. Females (gamete number nx) are indicated by blue crosses and connecting lines, while males (gamete number ny) are indicated by black dots and connecting lines. Under isogamy, females and males are undefined, and the two colours overlap. The typical sex-specific shapes of Bateman gradients arise from a single equation (which itself is not sex-specific) when a difference in gamete numbers is assigned to nx and ny, confirming Bateman’s intuition that the primary cause of the difference in selection is that females produce fewer gametes than males. The entire range of gamete number ratios presented in the figure is observed in nature, from equal gamete size in many unicellular organisms39 to vertebrates, where sperm count per ejaculate can commonly exceed 109 (see ref. 40 and Supplementary Information therein).Full size imageGamete limitation changes the results quantitatively so that under conditions of poor fertilisation efficiency a larger imbalance in gamete numbers is needed for Bateman gradients to diverge to a similar extent. However, even under inefficient fertilisation, the Bateman gradients do not reverse.Model 2: An external fertiliser model with population-level polygamy and gamete competitionModel 1 presented the simplest possible scenario, where all individuals except a rare mutant mate only once, and gamete competition (sperm competition26, but without assigning either gamete type to be sperm) was thus excluded for the focal mutant individual. Now I generalise from this to a situation that remains entirely symmetrical, but where the resident number of matings can take on any value, and then derive the Bateman function for a rare mutant that deviates from this population-level value. This set-up allows for gamete competition for the focal mutant individual, a crucial addition because of the empirical and theoretical importance of sperm competition26, as well as earlier theory suggesting that polyandry decreases the sex difference in Bateman gradients2.The biological set-up is such that there is a large population and a large number of patches (fertilisation arenas) where multiple individuals of both sexes can release their gametes for fertilisation. After all individuals have released their gametes, those in each patch mix freely and fertilisations take place randomly. Set up in this way, the model is again identical from the perspective of both sexes, and gamete number can be isolated as the sole possible causal factor in any subsequent differences that may arise, extending from the initially monogamous and gamete competition-free scenario of Model 1. All individuals of both sexes are assumed to initially have the same strategy: to divide their nx or ny gametes equally between m patches, and distribute themselves in such a way that gametes from m individuals of each type release gametes into each patch (the number of individuals of each sex per patch need not necessarily be strictly equal to m, but this is the simplest assumption to account for the fact that gamete competition tends to increase with multiple ‘matings’). Now, if a rare x mutant divides its gametes evenly into (hat{m}) randomly selected patches, its gamete number per patch and consequently competitiveness in each patch is altered. Therefore, gametes of a mutant of type x will gain, on average, a fraction ({c}_{x}=left({n}_{x}/hat{m}right)/{N}_{x}) of the fertilisations in that patch, where ({N}_{x}={n}_{x}/hat{m}+(m-1){n}_{x}/m). To compute the number of realised fertilisations in a patch, I use the same fertilisation function as in Model 1, where the mutant number of gametes in a patch is Nx as above and the number of gametes of the opposite type is ({N}_{y}=mfrac{{n}_{y}}{m}={n}_{y}). All the components are now in place to write down the Bateman function corresponding to this scenario, for a mutant of type x:$${b}_{x}left(hat{m},mright)=hat{m}{c}_{x}fleft({N}_{x},{N}_{y}right)$$
(2)
where cx, Nx and Ny are as defined above, and the fertilisation function f is as in Model 1. For completeness, define bx(0, m) = 0, which is necessarily true, but useful to define separately because division by 0 renders Eq. (2) formally undefined when (hat{m}=0).As in Model 1, Eq. (2) makes no reference to sexes, and they only become specified when values are assigned to nx and ny (Fig. 2).Fig. 2: The Bateman function of Eq. (2) for an externally fertilising population with potential for population-wide polygamy and gamete competition.Results are shown for two values of resident matings (m = 1 and m = 2). a–h show the effect of variation in sex-specific gamete numbers and in fertilisation efficiency with m = 1, while i–p show the same with m = 2. Parameter values used are shown in the figure. The value m = 2 is used here because it is comparable to the mean number of matings in Bateman’s1 work (see Fig. 3 for corresponding results with internal fertilisation, but note that the aim of the models is not to quantitatively reproduce Bateman’s results). Females (gamete number nx) are indicated by blue crosses and connecting lines, while males (gamete number ny) are indicated by black dots and connecting lines. Under isogamy, females and males are undefined, and the two colours overlap. Further variation in m is examined in Fig. 4.Full size imageModel 3: An internal fertiliser modelModels 1–2 were set up with the central aim of full symmetry and exclusion of any sex-specific assumptions. Internal fertilisation breaks this symmetry by introducing a sex-specific assumption other than gamete number. Bateman gradients are, however, most commonly applied to situations with internal fertilisation where females are gamete recipients and males are gamete donors27. I therefore construct a model accounting for internal fertilisation. Where Eqs. (1) and (2) allowed no sex differences aside from gamete number, here I additionally consider the fact that females receive gametes while males donate them.As in model 2, there is a very large population, and I assume that in the resident population, all females and males mate exactly m times. It is then considered how a rare mutant individual’s (of either sex) fitness depends on its number of matings (hat{m}).I use the same fertilisation function as in Models 1-2. Consider first the female perspective (labelled with x). A female produces nx gametes and retains them internally. Each female mates with m males, who also mate with m females, dividing their gametes evenly over these matings. Therefore a mutant female receives (hat{m}frac{{n}_{y}}{m}) male gametes, and her reproductive success is$${b}_{x}left(hat{m},mright)=fleft({n}_{x},hat{m}frac{{n}_{y}}{m}right)$$
(3)
A mutant male, on the other hand, mates with (hat{m}) females, each of which mates with m−1 additional males. Therefore, the mutant male’s mating partners will receive a total of ({{N}_{y}=n}_{y}/hat{m}+(m-1){n}_{y}/{m}) male gametes. Thus, the mutant male gains a fraction ({c}_{y}=left({n}_{y}/hat{m}right)/{N}_{y}) of the fertilisations with each female, while the total reproductive success per female is f(nx,Ny). The mutant male’s reproductive success is therefore$${b}_{y}left(hat{m},mright)=hat{m}{c}_{y}fleft({n}_{x},{N}_{y}right)$$
(4)
To avoid division by 0, we can again define by (0, m) = 0, analogous to Model 2. In contrast to Models 1–2, there are now separate equations for each sex because of the additional sex-specific assumption of internal fertilisation, but no further sex-specific assumptions are used in their derivation. Visually the Bateman functions (Fig. 3) are nevertheless very similar to Model 2, and again reproduce the sex-specific shapes first proposed by Bateman1 when fertilisation is efficient. However, an interesting exception arises when relatively weak asymmetry in gamete numbers is combined with inefficient fertilisation and gamete limitation. When these conditions are combined with internal fertilisation, Bateman gradients can theoretically be reversed.Fig. 3: The Bateman functions of Eqs. (3) and (4) for internal fertilisation.Where Figs. 1 and 2 show that the sex-specific shapes of Bateman functions are ultimately caused by differences in gamete number, Fig. 3 shows that internal fertilisation does not invalidate this outcome when fertilisation is efficient. As in Fig. 2, results are shown for two values of resident matings (1 and 2), and the value m = 2 is used because it is comparable to the mean number of matings in Bateman’s1 work. a–h show the effect of variation in sex-specific gamete numbers and in fertilisation efficiency with m = 1, while i–p show the same with m = 2. Parameter values used are shown in the figure. Inefficient fertilisation combined with relatively low asymmetry in gamete numbers and the added asymmetry of internal fertilisation can in principle reverse the Bateman gradients (second and fourth row). Females (gamete number nx) are indicated by blue crosses and connecting lines, while males (gamete number ny) are indicated by black dots and connecting lines.Full size image More

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Geography and climatology of study areaThe area of study, Ghana, is on the coastal edge of tropical West African, bounded in latitude 4.5° N and 11.5° N and longitude 3.5° W and 1.5° E, and characterized by a tropical monsoon climate system23,24. Figure 1 shows map of the study area indicating the selected twenty two (22) sunshine measurement stations distributed across the four main climatological zones and Table 1 summarizes the geographical positions of selected stations.Figure 1Adapted from Asilevi27.Map of the study area showing all twenty two (22) synoptic stations distributed in four main climatological zones countrywide.Full size imageTable 1 Geographical position and elevation for study sites.Full size tableAtmospheric clarity over the area is closely connected to cloud amount distribution and rainfall activities, largely determined by the oscillatory migration of the Inter-Tropical Discontinuity (ITD), accounting for the West African Monsoon (WAM)25,26.Owing to the highly variable spatiotemporal distribution of cloud amount vis-à-vis rainfall activities, resulting in contrasting climatic conditions in different parts of the region, the country is partitioned by the Ghana Meteorological Agency (GMet) into four main agro-ecological zones namely, the Savannah, Transition, Forest and Coastal zones as shown in Fig. 123. As a result, the region experiences an estimated Global solar radiation (GSR) intensity peaks in April–May and then in October–November, with the highest monthly average of 22 MJm−2 day−1 over the savannah climatic zone and the lowest monthly average of 13 MJm−2 day−1 over the forest climatic zone27.Research datasetsGround-based measurement dataDaily sunshine duration measurement datasets (n) spanning 1983–2018 where derived for estimating Global solar radiation (GSR). The measurements were taken by the Campbell-Stokes sunshine recorder, mounted at the 22 stations shown in Fig. 1, under unshaded conditions to ensure optimum sunlight exposure. The device concentrates sunlight onto a thin strip of sunshine card, which causes a burnt line representing the total period in hours during which sunshine intensity exceeds 120.0 Wm−2 according to World Meteorological Organization (WMO) recommendations27. The as-received daily records were quality control checked by ensuring 0 ≤ n ≤ N, where N is the astronomical day length representing the possible maximum duration of sunshine in hours determined by Eq. 1 from the latitude (ϕ) of the site of interest and the solar declination (δ) computed by Eq. 227:$$ {text{N}} = frac{2}{15}cos^{ – 1} left[ { – tan phi tan {updelta }} right] $$
(1)
$$ {updelta } = 23.45sin left[ {360^{{text{o}}} times frac{{284 + {text{J}}}}{365}} right] $$
(2)
where J represents the number for the Julian day of the year (first January is 1 and second January is 2).NASA-POWER Global solar radiation (GSR) reanalysis dataThe satellite-based Global solar radiation (GSR) dataset for specific longitudes and latitudes of all 22 stations, assessed in the study, were retrieved from the National Aeronautics and Space Administration-Prediction of Worldwide Energy Resources (NASA-POWER) reanalysis repository based on the Modern Era Retrospective-Analysis for Research and Applications (MERRA-2) assimilation model products, developed from Surface Radiation Budget, and spanning equal study period (1983–2018). The datasets are accessible on a daily and monthly temporal resolution scales at 0.5° × 0.5° spatial coverage via a user friendly web-based mapping portal: https://power.larc.nasa.gov/data-access-viewer/17. The advantage of the NASA-POWER reanalysis GSR, is the wide spatial coverage, and thus can be used to develop a high spatial resolution of solar radiation across the study area.The POWER Project analyzes, synthesizes and makes available surface radiation related parameters on a global scale, primarily from the World Climate Research Programme (WCRP), Global Energy and Water cycle Experiment (GEWEX), Surface Radiation Budget (SRB) project (Version 2.9), the Clouds and the Earth’s Radiant Energy System (CERES), FLASHFlux (Fast Longwave and Shortwave Radiative Fluxes from CERES and MODIS), and the Global Modeling and Assimilation Office (GMAO)17. Table 2 shows the source satellites and the corresponding temporal coverage used in the development of NASA-POWER GSR products.Table 2 Satellites providing the NASA-POWER GSR datasets20.Full size tableThe monthly average NASA-POWER all-sky shortwave surface radiation reanalysis products are statistically validated, showing reasonable biases of − 6.6–13%, against a global network of surface radiation measurement metadata in an integrated database from the Baseline Surface Radiation Network (BSRN) of the World Radiation Monitoring Center (WRMC)20,22. The datasets are widely used in renewable energy application16,22, agricultural modelling of crop yields28, crop simulation exercises29, and plant disease modelling30.Furthermore, in order to assess the suitability of the NASA-POWER surface solar radiation products for the study area, a synthetic sunshine duration based Global solar radiation (GSR) is developed from the Angstrom-Prescott sunshine duration model by Eq. 3 for comparisons27.$$ {text{GSR}} = left[ {{text{a}} + {text{b}}frac{{text{n}}}{{text{N}}}} right]{text{H}}_{{text{o}}} $$
(3)
were Ho (kWhm−2 day−1) is the daily extraterrestrial solar radiation on an horizontal surface, n is the daily sunshine duration measurements obtained from the Ghana Meteorological Agency (GMet), and N is the maximum possible daily sunshine duration or the day length in hours determined by Eq. 1. Generalized regression constants a = 0.25 and b = 0.5 for the study area were determined by Asilevi27 from experimental radiometric data based on correlation regression analysis between atmospheric clarity index (GSR/Ho) and atmospheric cloudlessness index (n/N), for estimating solar radiation over the study area, and compared with other satellite data retrieved from the National Renewable Energy Laboratory (NREL) and the German Aerospace Centre (DLR)27. Ho was calculated from astronomical parameters by Eq. 4:$$ {text{H}}_{0} = frac{{24{ } cdot { }60}}{pi } cdot {text{G}}_{{{text{sc}}}} cdot {text{d}}_{{text{r}}} left[ {omega_{{text{s}}} sin varphi sin delta + cos varphi cos delta sin omega_{{text{s}}} } right] $$
(4)
where Gsc is the Solar constant in MJm−2 min−1, dr is the relative Earth–Sun distance in meters (m), (omega_{s}) is the sunset hour angle (angular distance between the meridian of the observer and the meridian whose plane contains the sun), (delta) is the angle of declination in degrees (°) and (varphi) is the local latitude. A detailed presentation of the calculation was published in a previous work27.Statistical assessment analysisFor the purpose of assessing the NASA-POWER derived monthly mean GSR (GSRn) datasets in comparison with the estimated Global Solar Radiation (GSRe) datasets used in this paper, the following deviation and correlation methods in Eqs. 5–11, each showing a complimentary result were used: Standard deviation (({upsigma })), residual error (RE), Root mean square error (RMSE), Mean bias error (MBE), Mean percentage error (MPE), Pearson’s correlation coefficient (r), and Willmott index of agreement (d) for n observations31,32,33,34,35. GSRe, GSRn, and RE represent the estimated GSR, NASA-POWER GSR, and the residual error between GSRe and GSRn respectively. A positive RE indicates that sunshine-based estimated GSR is larger than the NASA-POWER reanalysis dataset, while a negative RE indicates that sunshine-based estimated GSR is smaller than the NASA-POWER reanalysis dataset. The arithmetic mean of any dataset is µ.The standard deviation (({upsigma })) was used to check the upper and lower limits of distribution around the mean deviations between GSRe and GSRn in order to ascertain violations between both datasets33. The RMSE is a standard statistical metric to quantify error margins in meteorology and climate research studies, and by definition is always positive, representing zero in the ideal case, plus a smaller value signifying a good marginal deviation31. The MBE is a good indicator for under-or overestimation in observations, with MBE values closest to zero being desirable. The MPE further indicates the percentage deviation between the GSRe and GSRn individual datasets35.$$ {upsigma } = sqrt {frac{1}{{{text{n}} – 1}}mathop sum limits_{{{text{i}} = 1}}^{{text{n}}} left( {{text{GSR}} – {upmu }} right)^{2} } $$
(5)
$$ {text{RE}} = {text{GSR}}_{{text{e}}} – {text{GSR}}_{{text{n}}} $$
(6)
$$ {text{RMSE}} = sqrt {frac{1}{{text{n}}}mathop sum limits_{{{text{i}} = 1}}^{{text{n}}} left( {{text{RE}}} right)^{2} } $$
(7)
$$ {text{MBE}} = frac{1}{{text{n}}}mathop sum limits_{{{text{i}} = 1}}^{{text{n}}} left( {{text{RE}}} right) $$
(8)
$$ {text{MPE}} = frac{1}{{text{n}}}mathop sum limits_{{{text{i}} = 1}}^{{text{n}}} left( {frac{{{text{RE}}}}{{{text{GSR}}_{{text{e}}} }} times 100{text{% }}} right) $$
(9)
$$ {text{r}} = frac{{mathop sum nolimits_{{{text{i}} = 1}}^{{text{n}}} left( {{text{GSR}}_{{text{e}}} – {upsigma }_{{text{e}}} } right)left( {{text{GSR}}_{{text{n}}} – {upsigma }_{{text{n}}} } right)}}{{left( {{text{n}} – 1} right){upsigma }_{{text{e}}} {upsigma }_{{text{n}}} }} $$
(10)
$$ {text{d}} = 1 – left[ {frac{{mathop sum nolimits_{{{text{i}} = 1}}^{{text{n}}} left( {{text{GSR}}_{{text{e}}} – {text{GSR}}_{{text{n}}} } right)^{2} }}{{mathop sum nolimits_{{{text{i}} = 1}}^{{text{n}}} left( {left| {{text{GSR}}_{{text{e}}} – {text{GSR}}_{{{text{nave}}}} left| + right|{text{GSR}}_{{text{n}}} – {text{GSR}}_{{{text{nave}}}} } right|} right)^{2} }}} right] $$
(11)
Further, as with other statistical studies in meteorology36, the Pearson’s correlation coefficient (r) was used to quantify the strength of correlation between GSRe and GSRn. Finally, the Willmott index of agreement (d) commonly used in meteorological literature computed from Eq. 7 is used to assess the degree of GSRe/GSRn agreement34. More

Soil sample collectionSoil samples were collected from three different crude oil reservoirs et al. Faisaliyyah, Al Sina’iyah, and Ghubairah located in Riyadh, Saudi Arabia. Briefly, 400 g of soil samples were collected at 0–10 cm depth, under aseptic conditions. Samples were sieved by 2.5 mm pore size sieves, homogenized, and stored at 4ºC until use.Sources of different hydrocarbonsDifferent samples of crude oil, kerosene, diesel, and used oil were collected in sterile flasks from the tankers of Saudi Aramco Company (Dammam, Saudi Arabia). Additionally, another flask was prepared by mixing 1% of each oil in MSM liquid media to make up the mixed oil. The oil samples were sterilized by Millex® Syringe Filters (Merck Millipore co., Burlington, MA, United States) and stored at 4 °C for further usage.Isolation and identification of fungal speciesThe fungal species in the soil contaminated by crude oil were identified using the dilution method. Briefly, 10% of each soil sample was dissolved in distilled water and vortexed thoroughly. Then, 0.2 ml of each sample was cultured on a sterile PDA plate incubated at 28 °C for three days until the growth of different fungal colonies. Carefully, each colony was isolated, re-cultured on new PDA McCartney bottles of PDA slant, and incubated at 28 °C for three days. The fungi were identified microscopically using standard taxonomic keys based on typical mycelia growth and morphological characteristics provided in the mycological keys54. Besides, the taxonomy of the isolated yeast strains was confirmed by the API 20 C AUX kit (Biomerieux Corp., Marcy-l’Étoile, France) (data not shown). The morphology of pure cultures was tested and identified under a light microscope as described before55.The incidence of each strain was calculated as follows:$$ Incidence ;(% ) = frac{{{text{Number }};{text{of }};{text{samples }};{text{showed }};{text{microbial }};{text{growth}}}}{{{text{Total }};{text{samples}}}} times 100 $$Hydrocarbon tolerance testThe growth rate of isolated strains was tested in a liquid medium of MSM mixed with 1% of either crude oil, used oil, diesel, kerosene, or mixed oil. Furthermore, a control sample of MSM liquid medium without any of the oils tested and all culture media were autoclaved at 121 °C for 30 min. After cooling, 1 ml of each isolate was inoculated with one of the above mixtures and incubated at 25 °C on an orbital shaker. The growth rate was measured every three days for a month for each treatment versus the control. All experiments were performed in triplicates.Scanning electron microscopy (SEM)The morphology of different strains of the isolated fungi was tested by SEM, as previously described56, with some modifications. Briefly, 1 ml of each growing strain, in the liquid media, was centrifuged at the maximum speed (14,000 rpm) for 1 min, followed by fixation with 2.5% glutaraldehyde, and overnight incubation at 5 °C. Later, the sample was pelleted, washed with distilled water, then dehydrated with different ascending concentrations of ethanol (30, 50, 70, 90, 100 (v/v)) for 15 min at room temperature. Finally, samples were examined in the Prince Naif Research Centre (King Saud University, Riyadh, Saudi Arabia) by the JEOL JEM-2100 microscope (JEOL, Peabody, MA, United States), according to the manufacturer instructions.Crude oil degradation assayA modified version of the DCPIP assay57 was employed to assess the oil-degrading ability of the fungal isolates. For each strain, 100 ml of the autoclaved MSM was mixed with 1% (V/V) of one of the hydrocarbons (crude oil, used oil, diesel, kerosene, or mixed oil), 0.1% (v/v) of Tween 80, and 0.6 mg/mL of the redox indicator (DCPIP). Then, 1–2 ml of different fungi growing in liquid media (24–48 h) add to the Crude Oil Degradation media, prepared previously, and incubated for two weeks in a shaking incubator at 25 °C. All flasks were covered and protected from light, aeration, or temperature exchanges to reduce the effects of oil weathering (evaporation, photooxidation). The surfactant Tween 80 was used for bio-stimulation and acceleration of the biosurfactant production by increasing metabolism58. A non-inoculated Crude Oil Degradation media was used as the negative control. Afterward, the colorimetric analysis for the change in DCPIP color was estimated, spectrophotometrically, at 420 nm. All experiments were performed in triplicates.Preparation of cell-free supernatant (CFS)To prepare the Cell-Free Supernatant (CFS), all isolates were grown in MSM broth medium with 1% of either crude oil, used oil, diesel, kerosene, or mixed oil for 30 days in a shaking incubator at 25 °C. After incubation, the cells were removed by centrifugation at 10,000 rpm for 30 min at 4 °C. The supernatant (CFS) was collected and filter-sterilized with a 0.45 μm pore size sterile membrane. CFS was screened for the production of different biosurfactants. All the experiments were carried out in triplicates, and the average values were calculated.Drop-Collapse assayThe Drop-Collapse assay was performed as previously described9, with some modifications. 100 µl of crude oil was applied on glass slides, then 10 µl of each CFS was added to the center of the slide surface and incubated for a minute at room temperature. The slides were imaged by a light microscope using the 10X objective lenses. The spreading on the soil surface was scored by either « + » to indicate the level of positive spreading, biosurfactant production, or «—» for negative spreading. Biosurfactant production was considered positive at the drop diameter ≥ 0.5 mm, compared to the negative control (treated with distilled water).Oil spreading assayAn amount of 20 ml of water was added to the Petri plate (size of 100 mm) and mixed with 20 µl of crude oil or mixed oil, which created a thin layer on the water surface. Then, 10 µl of CFS was delivered onto the surface of the oil, and the clear zone surrounding the CFS drop was observed. The results were compared to the negative control (without CFS) and positive control of 1% SDS41. We have measured the clear zones diameter from images and calculate the actual values in regards to the diameter of the Petri dish (10 cm). The assay was performed in triplicates.Emulsification activity assayThe emulsification activity of each isolate was assessed by mixing equal volumes of MSM broth medium of each isolate with different oils in separate tubes. The samples were homogenized by vortex at high speed for two minutes at room temperature (25 °C) and allowed to settle for 24 h. The tests were performed in duplicate. Then, the emulsification index was calculated as follows59:$$ Emulsification; activity; left( % right) = frac{{{text{Height }};{text{of }};{text{emulsion }};{text{layer}}}}{{{text{Total }};{text{height}}}} times 100 $$Recovery of biosurfactantsThe recovery of biosurfactants from CFS was tested through different assays:Acid precipitation assay3 ml of each CFS was adjusted by 6 N HCl to pH 2 and incubated for 24 h at 4 °C. Later, equal volumes of chloroform/methanol mixture (2:1 v/v) were added to each tube, vortexed, and incubated overnight at room temperature. Afterward, the samples were centrifuged for 30 min at 10,000 rpm (4 °C), the precipitate (Light brown colored paste) was air-dried in a fume hood, and weighed53.Solvent extraction assayThe CFS containing biosurfactant was treated with a mixture of extraction solvents (equal volumes of methanol, chloroform, and acetone). Then, the new mixture was incubated in a shaking incubator at 200 rpm, 30 °C for 5 h. The precipitate was separated into two layers, in which the lower layer (White) was isolated, dried, weighed, and stored60.Ammonium sulfate precipitation assayThe CFS containing biosurfactant was precipitated with 40% (w/v) ammonium sulfate and incubated overnight at 4 °C. The samples were centrifuged at 10,000 rpm for 30 min (4 °C). The precipitate was collected and extracted with an amount of acetone equal to the volume of the supernatant. After centrifugation, the precipitate (Creamy-white) was isolated, air-dried in a fume hood, and weighed53.Zinc sulfate precipitation methodSimilarly, 40% (w/v) zinc sulfate was mixed with the CFS containing biosurfactant. Then, the mixture was incubated at 4 °C, overnight. The precipitate (Light Brown) was collected by centrifugation at 10,000 rpm for 30 min (4 °C), air-dried in a fume hood, and weighed53.Statistical analysisAll experiments were performed in triplicate, and the results were expressed as the mean values ± standard deviation (SD). One-way ANOVA and Dunnett’s tests were used to estimate the significance levels at P  More

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Study speciesCane toads (Rhinella marina) are large (to  > 1 kg) bufonids (Fig. 1a). Although native to north-eastern South America, these toads have been translocated to many countries worldwide to control insect pests12. Adult cane toads forage at night for insect prey and retreat to moist shelter-sites per day13. Small body size (and thus, high desiccation rate) restricts young toads to the margins of natal ponds14, but adult toads can survive even in highly arid habitats if they have access to water13,15. Cane toads prefer open habitats for foraging12, and thus can thrive in post-fire landscapes16,17. Cane toads in post-fire landscapes tend to have lower parasite burdens, probably because free-living larvae of their lungworm parasites cannot survive either the fire or the more sun-exposed post-fire landscape18.Figure 1taken from study sites between Casino, Grafton, and surrounds, NSW, by S.W. Kaiser.The cane toad Rhinella marina (a), and unburned, (b) and burned (c) habitats in which toads were collected and radio-tracked. Photographs were Full size imageStudy areaEast of the Great Dividing Range, near-coastal Clarence Dry Sclerophyll Forests of north-eastern New South Wales (NSW) are dominated by Spotted gum (Corymbia variegata) and Pink bloodwood (Corymbia intermedia)19. Fires are common, but typically cover relatively small areas before they are extinguished. In the summer of 2019–2020, however, prolonged drought followed by an unusually hot summer resulted in massive fires across this region, burning almost 100,000 km2 of vegetation9. In the current study, the toads we measured and dissected came from several sites within 75 km of the city of Casino (for site locations, see Fig. 2, Table 1, and18). The impacts of fire on faunal abundance and attributes shift with time since fire; for example, the abundance of a particular species may be reduced by fire (due to mortality from flames) but then increase as individuals from surrounding areas migrate to the recently-burned site to exploit new ecological opportunities provided by that landscape8. We chose to study this system 1-year post-fire, to allow time for such longer-term effects to be manifested.Figure 2Sampling sites relative to fire history. Sample sites are burned (red circles), and unburned (green squares). See Table 1 for key to sites. The legend shows the extent of burn a year prior to our study. Map created in QGIS 3.22.3. Fire history available from https://datasets.seed.nsw.gov.au/dataset/fire-extent-and-severity-mapping-fesm CC BY 4.0.Full size imageTable 1 Sampling sites and sample sizes for dissected and radio-tracked cane toads (Rhinella marina) in New South Wales, Australia.Full size tableSurveys of toad abundanceTo quantify toad abundance in burned and unburned sites, one observer (MJG) walked 100-m transects along roads at night (N = 23 and 8 respectively), recording all toads and native frogs (both adult and juvenile). The smaller number of unburned sites reflects the massive spatial scale of the wildfires, which made it difficult to find unburned areas. The transect sites were not the same as those sampled by “toad-busters” (below). We sampled both burned and unburned sites on each night, to de-confound effects of weather conditions with fire treatment. We scored frogs as well as toads to provide an estimate of overall anuran abundance and activity, and so that we could examine toad abundance relative to frog abundance as well as absolute toad numbers.“Toad-buster” sampleBecause of their ecological impact on native fauna, cane toads are culled by community groups as well as by government authorities12,20. We asked “toad-buster” groups to record whether the sites at which they collected toads had been burned during the 2019–2020 fires, or had remained unburned (Table 1). The toads were humanely euthanized (cooled-then-pithed: see21). The euthanasia method is brief (a few hours in the refrigerator, followed by pithing) and thus should not have affected any of the traits that we measured. For all of these toads, we measured body length (snout-urostyle length = SUL) and mass, and determined sex based on external morphology (skin colour and rugosity, nuptial pads: see22). A subset of toads (chosen to provide relatively equal numbers of males and females, and with equal numbers from burned and unburned sites) was dissected to provide data on mass of internal organs (fat bodies, liver, ovaries), reproductive condition (state of ovarian follicle development) and diet (mass and identity of prey items). To select the subsample of toads for dissection, we took relatively equal numbers of male and female toads from each bag of toads that was provided to us by the “toad-busters”. For logistical reasons, we were unable to dissect all of the toads that had been collected. Overall, we obtained data on morphology, diets and other traits from 481 fully dissected and 1443 partially dissected cane toads.Radio-trackingTo explore habitat use and movement patterns, we radio-tracked 57 toads over the course of two fieldtrips (0900–1800 h from 20 Nov 2021 to 6 Dec 2021 and 25 Jan 2022 to 10 Feb 2022). We selected seven sites (4 burned, 3 unburned) within 28 km of Tabbimoble, NSW (see Table 1 for locations and sample sizes of tracked toads). We hand-captured toads found active at night. These were measured, and their sex determined by external morphology (see above) and behaviour (release calls, given only by males: see23). We then fitted the toads with radio-transmitters (PD-2; Holohil Systems, Ontario, Canada; weighing ≤ 3.8 g) on cotton waist-belts, and released them at the site of capture. Tracked toads were 88.2–160.9 mm SUL (mass 70.1–546.3 g); thus, transmitters weighed  20 mm thick) within the quadrat, and estimated exposure of the toad within its refuge (the percentage of the animal’s body exposed to the naked eye). We then selected a compass bearing at random and walked 20 m in that direction where we rescored all of the above habitat attributes, to quantify habitat features in the broader environment (i.e., not just in microhabitats used by toads). We used those “random” sites to quantify overall habitat attributes of burned and unburned sites. Temperature was recorded by directing a temperature gun (Digitech QM7221) on (or otherwise close-to) toads and at a random point on the ground for random replicates. In total, we gathered radio-tracking data on movements and habitat variables from 57 cane toads, each of which was tracked for 5 days. Recaptured toads were euthanized by cooling-then-pithing.Morphological traitsTo obtain an index of body condition of toads, we regressed ln mass against ln SUL, and used the residual scores from that general linear regression as our estimate of body condition. Negative residual scores show an individual that weighs less-than-expected based on its body length. Likewise, we regressed mass of the fat bodies, liver and stomach against body mass to obtain indices of energy stores and stomach-content volumes relative to body mass. We scored male secondary sexual characteristics using the system of Bowcock et al.22. In their system, three sexually dimorphic traits (nuptial pad size, skin roughness and skin colouration) are scored from 0 to 2, and the scores from those three traits are summed to create a final value (on a 6-point scale) for the degree of elaboration of male-specific secondary sexual characteristics. We scored reproductive condition in adult female toads based on whether or not egg masses were visible during dissection, based on dissected toads from both “toad-buster” and telemetry samples.Statistical methodsData were analysed in R version 4.2.025. We used Linear Mixed Models (LMMs), Generalised Linear Mixed Models (GLMMs) and logistic regressions for our analyses. The R packages ‘tidyverse’26, ‘lmerTest’27, and ‘performance’28 were used.Habitat dataWe compared habitat variables between burned and unburned sites, and attributes of toads in burned versus unburned sites, using GLMMs (with negative binomial distribution) for count data (models were checked for overdispersion29) and LMMs on distance data, using ln-transformations where required to achieve normality. LMMs were used on non-normal percentage data, which were ln- and then logit-transformed (using log[(P + e)/(1 − P + e)], where e is the lowest non-zero number, halved)30. We used toad id, site (sampling location) and sampling trip (2019 versus 2020) as random factors.Anuran transect dataCounts of toads in burned versus unburned areas were compared both directly via GLMMs with a negative binomial distribution and relative to the numbers of frogs sighted along the same transects (binding the columns in R as ‘number of toads, number of amphibians – number of toads’ and using a GLMM with a binomial distribution). We used site as a random factor.Telemetry dataFor telemetry data, we analysed response variables via LMMs, and ln-transformed data where relevant to achieve normality.Dissection dataWe used LMMs for SUL, body mass, body condition and organ mass residuals (e.g., fat body mass relative to body mass). For prey item data, we used a poisson distribution with row number as a random factor, as the negative binomial and beta distribution GLMMs were overdispersed (see31). We used LMM for number of prey items and number of prey groups, with site as a random factor. Where models failed to converge, we reduced or removed the error term(s). Analyses were restricted to toads ≥ 70 mm SUL, because animals below this size were difficult to sex. We also performed nominal logistic regression to explore variation in sex ratio and male secondary sexual traits.Reproductive conditionWe used LMM for male secondary sexual characteristic display, using site as a random factor. For ovary presence, we used a binomial GLMM with a logit link, using site as a random factor. We used a LMM of the residual values from ovary mass relative to body mass (ln-transformed), using site as a random factor.Ethics declarationsAll procedures were performed in accordance with the relevant guidelines and regulations approved by Macquarie University Animal Ethics Committee (ARA Number: 2019/040-2) and in accordance with ARRIVE guidelines. More