Spatial analysis of nuclear and mitochondrial RFLP genotypes in populations of the chestnut blight fungus, Cryphonectria parasitica

Spatial structure of both nuclear and mitochondrial RFLPs were studied in several populations of the chestnut blight fungus, Cryphonectria parasitica, using a variety of spatial autocorrelation tests designed to detect nonrandom patterns. Fungal individuals were sampled from cankers on infected chestnut trees, and the location of each tree was mapped. Single-locus nuclear RFLPs, nuclear fingerprints, and mitochondrial DNA haplotypes were determined for each individual. Individuals with the same DNA fingerprint genotypes occurred closer together than would be expected at random in four of the five plots, while mitochondrial DNA haplotypes were aggregated in all five plots. Genetic distances between individuals, expressed as one minus the proportion of shared restriction fragment size classes for fingerprints and mitochondrial haplotypes, were significantly correlated with Euclidean distances between individuals in four of the five populations, but these correlations were very weak (r < 0.18). The same DNA fingerprint and single-copy nuclear RFLP alleles occurred on the same trees or immediately neighbouring trees more often than would be expected at random. Most of the aggregation for all three genetic markers occurred among individuals within the same cluster of chestnut stems or on neighbouring trees. Lack of spatial autocorrelation in one population was probably due to sampling on a larger scale that was too coarse to detect any patterns. Significant aggregation of genotypes in C. parasitica is most likely caused by some degree of restricted dispersal within populations. The implications of restricted dispersal are discussed in relation to the breeding system and isolation by distance in populations of. C. parasitica.     

GENE DISPERSAL AND SPATIAL GENETIC STRUCTURE

Spatial autocorrelation statistics have been studied in theoretical population genetic models and widely used in experimental studies of spatial structure in many plant and animal populations. However, the statistical properties of spatial autocorrelation statistics have remained uncharacterized. Little is known about how values of spatial autocorrelation statistics in population samples depend on the level of dispersal and scheme of sampling. In this paper, we characterize the statistical properties of join-count spatial autocorrelation statistics for population genetic surveys under various conditions of dispersal and sampling. The results indicate generally high statistical power. These results can provide a method to estimate gene dispersal based on standing spatial patterns of genetic variation observed within populations.     

Mitochondrial restriction fragment length polymorphism (RFLP) and sequence variation among closely related avian species and the genetic characterization of hybrid Dendroica warblers

To address several interconnected goals, we used mitochondrial DNA (mtDNA) sequences to explore evolutionary relationships among four potentially hybridizing taxa in a North American avian superspecies (Dendroica occidentalis, D. townsendi, D. virens, and D. nigrescens). We first compared the results of a previous restriction fragment length polymorphism (RFLP)-based study with 1453 nucleotides from the mitochondrial cytochrome oxidase subunit I (COI), ATP-synthase 6 (ATPase 6), and ATP-synthase 8 (ATPase 8) genes. Separate phylogenetic analyses of the RFLP and sequence data provided identical and well-supported hierarchical species-level reconstructions that grouped occidentalis and townsendi as sister taxa. We then explored several general features of mitochondrial evolution via a comparison of the RFLP and sequence data sets. Qualitative rate differences that seemed evident in highly autocorrelated comparisons of RFLP vs. sequence pairwise distances were not supported when autocorrelation was removed. We also noted a high variance in corresponding RFLP and sequence distances after the removal of autocorrelation effects. This variance suggests that caution should be used when combining RFLP and sequence-based data in studies that require the large-scale synthesis of divergence estimates drawn from sources employing different molecular techniques. Finally, we used our parallel RFLP and sequence data to design and validate a rapid and inexpensive polymerase chain reaction-RFLP (PCR-RFLP) protocol for determining species-specific mitochondrial haplotypes. This PCR-RFLP technique will be applied in ongoing studies of the occidentalis/townsendi hybrid zone, where the historic and geographical complexity of the interbreeding populations necessitates the genotyping of thousands of individual warblers.     

Marked genetic polymorphism of the swine steroid 21-hydroxylase gene, and its location between the SLA class I and class II regions

Restriction fragment length polymorphism (RFLP) analysis of the swine 21-hydroxylase (CYP21) region was conducted on 31 unrelated SLA class I typed pigs, mainly Large Whites, including 15 haplotypes. Ten haplotypes were from SLA genotypic homozygotes and five were from SLA class I phenotypic homozygotes. DNA digestion with Hin dIII, TaqI and PstI, and hybridization to a 4.5-kb swine CYP21 genomic probe yielded respectively two, four and three RFLP patterns. Six patterns were identified with combined RFLP. In addition, analysis of the CYP21 region in families comprising several SLA recombinants demonstrated that the CYP21 gene lies in the DNA segment between the SLA class I and class II regions. These overall results reinforce our previous conclusion about the existence in the pig of a single 21-hydroxylase gene. The characterization of at least six CYP21 allelic patterns provides a new tool for studying the associations between the SLA region and zootechnical traits.     

Molecular mapping of class II polymorphisms in the human major histocompatibility complex. I. DR beta

We have studied 27 cell lines homozygous by consanguinity for the major histocompatibility complex to establish the restriction fragment length polymorphism (RFLP) patterns seen with six different restriction enzymes (Bam HI, Bg1 II, Eco RI, Hinc II, Hind III, Pvu II) and DR beta chain probes. The probes used were a full-length cDNA DR beta probe and a probe specific for the 3' untranslated region. The RFLP obtained represent the first standard patterns for the individual haplotypes DR1 through 7 and DR9 as defined by genetically homozygous lines. The patterns obtained reflect the DR specificities closely, as well as the DRw52 and DRw53 specificities. These latter specificities are associated with the most prominent patterns of RFLP. Bands are present which are unique for the haplotypes DR1, DR2, DR4, DR7, DRw52, and DRw53, and could be used for typing these haplotypes in heterozygotes. Subtypes can be identified for all of the haplotypes except DR1. These subtypes indicate that there is an extensive amount of polymorphism in the DR subregion that has not been identified serologically.     

Conditionally autoregressive models improve occupancy analyses of autocorrelated data: An example with environmental DNA

Site occupancy‐detection models (SODMs) are statistical models widely used for biodiversity surveys where imperfect detection of species occurs. For instance, SODMs are increasingly used to analyse environmental DNA (eDNA) data, taking into account the occurrence of both false‐positive and false‐negative errors. However, species occurrence data are often characterized by spatial and temporal autocorrelation, which might challenge the use of standard SODMs. Here we reviewed the literature of eDNA biodiversity surveys and found that most of studies do not take into account spatial or temporal autocorrelation. We then demonstrated how the analysis of data with spatial or temporal autocorrelation can be improved by using a conditionally autoregressive SODM, and show its application to environmental DNA data. We tested the autoregressive model on both simulated and real data sets, including chronosequences with different degrees of autocorrelation, and a spatial data set on a virtual landscape. Analyses of simulated data showed that autoregressive SODMs perform better than traditional SODMs in the estimation of key parameters such as true‐/false‐positive rates and show a better discrimination capacity (e.g., higher true skill statistics). The usefulness of autoregressive SODMs was particularly high in data sets with strong autocorrelation. When applied to real eDNA data sets (eDNA from lake sediment cores and freshwater), autoregressive SODM provided more precise estimation of true‐/false‐positive rates, resulting in more reasonable inference of occupancy states. Our results suggest that analyses of occurrence data, such as many applications of eDNA, can be largely improved by applying conditionally autoregressive specifications to SODMs.     

Analysis of Pathotypic and Genotypic Diversity of Xanthomonas oryzae pv. oryzae in China

Virulence analysis and restriction fragment length polymorphism (RFLP) were used to evaluated the population structure of Xanthomonas oryzae pv . oryzae ( Xoo ) from the main rice-growing region in China. The pathotype of Xoo was determined for 103 strains by inoculating 13 near-isogenic rice lines using IR24 as the recurrent parent. Sixty-one pathotypes was shared by these strains, on the basis of the consensus of three clustering statistics, and four clusters for pathotype were formed. Cluster 2 consists of strains with high molecular polymorphorism and many pathotypes that are either virulent to a majority of the 13 major resistance ( R ) genes or avirulent only to Xa21 , and is geographically dispersed. The resistance gene Xa21 has broader resistance than others to the strains tested. A probe from a member of the avrBs3/pthA type III effector family, 1376 bp Sph I-digested fragment, was used to screen the genomes of 52 strains tested. Four common bands were found in the DNA fingerprint pattern of Xoo , suggesting basic patterns of evolutionary relationship for members of avrBs3/pthA family and/or the pathogen. Each distinct RFLP banding pattern of each strain was considered as a haplotype; 42 haplotypes were revealed by the probe and divided into four lineages by the same statistics method. It was observed that some isolates with different pathotypes shared the same haplotype and others with different haplotypes harboured identical pathotype. There was a weak correlation between virulent pathotypes and molecular haplotypes.     

Restriction fragment length polymorphism analysis of major histocompatibility complex class II genes from inbred chicken lines

High molecular weight DNA was extracted from sperm from chickens of 14 inbred lines. The DNA was digested with each of four restriction enzymes (Pvu II, Hind III, Bgl II, and Bam HI), electrophoresed for 18 or 45 h, blotted onto nitrocellulose, and hybridized to a chicken major histocompatibility complex (MHC, B complex) class II beta-chain probe (beta 2-exon specific). Restriction fragment length polymorphisms (RFLPs) were found with each of the restriction enzymes used. Birds with the same B haplotype always showed the same RFLP pattern; however, some birds of different B haplotypes also shared the same RFLP pattern. To test for the Mendelian inheritance of the RFLP patterns, the F2 progeny of an informative cross were analysed. The RFLP patterns corresponded with the serologically determined B haplotypes of the F2 birds, thereby showing the Mendelian inheritance of the polymorphic bands.     

Concordant evolution of mitochondrial and nuclear genomes in the wheat pathogen Phaeosphaeria nodorum

We compared patterns of mitochondrial restriction fragment length polymorphism (RFLP) diversity with patterns of nuclear RFLP diversity to investigate the effects of selection, gene flow, and sexual reproduction on the population genetic structure and evolutionary history of the wheat pathogen Phaeosphaeria nodorum. A total of 315 fungal isolates from Texas, Oregon, and Switzerland were analyzed using seven nuclear RFLP probes that hybridized to discrete loci and purified mitochondrial DNA that hybridized to the entire mtDNA genome. Forty-two different mitochondrial haplotypes and 298 different nuclear haplotypes were detected. The two most frequent mtDNA haplotypes were present in every population and represented 32% of all isolates. High levels of gene flow, low levels of population subdivision, no evidence for either host specificity or cyto-nuclear disequilibrium were inferred from the analysis of both genomes. The concordance in estimates of these population genetic parameters from both genomes suggests that the two genomes experienced similar degrees of migration, genetic drift and selection.     

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test.     

Pattern‐oriented modelling of population genetic structure

Although several statistical approaches can be used to describe patterns of genetic variation and infer stochastic differentiation, selective responses, or interruptions of gene flow due to physical or environmental barriers, it is worthwhile to note that similar processes, controlled by several parameters in theoretical models, frequently give rise to similar patterns. Here, we develop a Pattern‐Oriented Modelling (POM) approach that allows us to determine how a complex set of parameters potentially driving empirical genetic differentiation among populations generate alternative scenarios that can be fitted to observed data. We generated 10 000 random combinations of parameters related to population size, gene flow and response to gradients (both driven by dispersal and selection) in a spatially explicit model, and analysed simulated patterns with F_ST statistics and mean correlograms using Moran's I spatial autocorrelation coefficients. These statistics were compared with observed patterns for a tree species endemic to the Brazilian Cerrado. For a best match with observed F_ST (equal to 0.182), the important parameters driving simulated scenario are mainly related to population structure, including low population size with closed populations (low N_m), strong distance decay of gene flow, in addition to a strong effect of the initial variance of allele frequencies. These scenarios present a low autocorrelation of allele frequencies. Best matching of correlograms, on the other hand, appears in simulations with a large population size, high N_m and low population differentiation and F_ST (as well as more gene flow). Thus, targeting the two statistics (correlograms and F_ST) shows that best matches with empirical data with two distinct sets of parameters in the simulations, because observed patterns involve both a relatively high F_ST and significant autocorrelation. This conflict can be resolved by assuming that initial variance in allele frequencies can be interpreted as reflecting deep‐time historical variation and evolutionary dynamics of allele frequencies, creating a relatively high level of population differentiation, whereas current patterns in gene flow creates spatial autocorrelation. This make sense in terms of the previous knowledge on population differentiation in D. alata, especially if patterns are explained by a combination of isolation‐by‐distance and allelic surfing due to range expansion after the last glacial maximum. This reveals the potential for more complex applications of POM in population genetics. © 2014 The Linnean Society of London, Biological Journal of the Linnean Society, 2014, 113 , 1152–1161.     

Indo-West Pacific patterns of genetic differentiation in the high-dispersal starfish Linckia laevigata

Genetic variation in four natural populations of the starfish Linckia laevigata from the Indo-West Pacific was examined using restriction fragment analysis of a portion of the mtDNA including the control region. Digestion with seven restriction enzymes identified 47 haplotypes in a sample of 326 individuals. Samples collected from reef sites within each location were not significantly differentiated based on Φ_ST or spatial distribution of haplotypes, indicating that dispersal is high over short to moderate distances. Evidence of gene flow is further supported by the low divergence among haplotypes and the lack of any clear geographical structuring among different haplotypes in the gene phylogeny. However, analysis of molecular variance ( AMOVA ), Φ_ST and contingency χ² analyses of the spatial distribution of haplotypes demonstrate the presence of significant broad scale population genetic structure among the four widespread locations examined. RFLP data are consistent with high gene flow between the Philippines and Western Australia and moderate gene flow between the Great Barrier Reef (GBR) and Fiji, but only limited gene flow between either the Philippines or Western Australia and either the GBR or Fiji. The presence of mtDNA structure contrasts with previous allozyme data which suggest that dispersal among widely separated locations is equivalent to dispersal among populations within the highly connected GBR studies. This discordance between patterns of gene flow inferred from these two markers cannot be fully accounted for by differences in effective population size for mtDNA. This might suggest that while mtDNA variation may represent contemporary patterns of gene flow, allozyme variation among populations is yet to reach equilibrium between drift and migration over the range surveyed.     

Consequences of a catadromous life-strategy for levels of mitochondrial DNA differentiation among populations of the Australian bass, Macquaria novemaculeata

The influence of a catadromous life-strategy on levels of spatial genetic structuring in fish is poorly understood. In an effort to gain a better appreciation of how this specialized life-strategy determines population genetic structuring, we assessed variation in the mitochondrial DNA (mtDNA) control region in a catadromous perciform, the Australian bass Macquaria novemaculeata . Nineteen putative haplotypes were resolved using temperature gradient gel electrophoresis from 10 geographically distinct populations. Significant heterogeneity was revealed in haplotype frequencies and their spatial distributions among many locales. Gene partitioning statistics ( AMOVA ) for both raw haplotype frequency data and frequency data with sequence divergences were concordant, indicating that M. novemaculeata populations were moderately genetically structured (Φ_ST = 0.05, 0.06; P < 0.001, respectively). Isolation by distance seems to be a strong structuring force in M. novemaculeata , culminating in no detectable phylogeographic structuring among haplotypes. Low sequence divergences were observed among many haplotypes and it is suggested that these are the result of pruning of maternal lineages by cyclical variations in female reproductive success. This study highlights the importance of life-history patterns and, in particular, spawning locality, in determining spatial structuring of mtDNA variation in catadromous species.     

Restriction fragment length polymorphism of the major histocompatibility complex of the pig

Human HLA cDNA probes were used to analyze the restriction fragment length polymorphism (RFLP) of the SLA major histocompatibility complex in swine. Cellular genomic DNA from 19 SLA homozygous pigs representing 13 different haplotypes was digested with restriction endonucleases Eco RI, Hind III, or Bam H1, separated by electrophoresis, and transferred onto diazobenzyloxymethyl paper by the Southern blot technique. The blots were probed with ³²P-labeled class I or beta-DR class II cDNA. Depending on the haplotypes and the endonucleases used, seven to ten restriction fragments hybridized with the class I probe, and five to seven with the beta-DR probe. Their sizes ranged from 3.4 to 22 kilobase-pairs. Few bands were common to all 13 haplotypes. With all but one haplotype, identical autoradiogram patterns were obtained from unrelated, but phenotypically SLA-identical pigs, suggesting that most of the RFLP revealed were controlled by the SLA region. Further polymorphism was found in a group of seven unrelated pigs which typed serologically as SLA A15 CI B18 homozygotes but could be divided into two subgroups, with five animals in one subgroup and two in the other, when the genomic DNA was hybridized with the class I probe. When the class 11 beta-DR probe was tested on the same seven pigs, another subdivision was seen, and this correlated with MLR data. These results demonstrate that HLA class I and class II probes can be used to identify certain well-established SLA haplotypes and to identify subclasses within at least one SLA haplotype.Abbreviations MHC major histocompatibility complex - MLR mixed lymphocyte reaction - kbp kilobase pair(s) - RFLP restriction fragment length polymorphism     

Polymorphic DNA haplotypes at the phenylalanine hydroxylase (PAH) locus in European families with phenylketonuria (PKU)

DNA haplotype data from the phenylalanine hydroxylase (PAH) locus are available from a number of European populations as a result of RFLP testing for genetic counseling in families with phenylketonuria (PKU). We have analyzed data from Hungary and Czechoslovakia together with published data from five additional countries--Denmark, Switzerland, Scotland, Germany, and France--representing a broad geographic and ethnographic range. The data include 686 complete chromosomal haplotypes for eight RFLP sites assayed in 202 unrelated Caucasian families with PKU. Forty-six distinct RFLP haplotypes have been observed to date, 10 unique to PKU-bearing chromosomes, 12 unique to non-PKU chromosomes, and the remainder found in association with both types. Despite the large number of haplotypes observed (still much less than the theoretical maximum of 384), five haplotypes alone account for more than 76% of normal European chromosomes and four haplotypes alone account for more than 80% of PKU-bearing chromosomes. We evaluated the distribution of haplotypes and alleles within these populations and calculated pairwise disequilibrium values between RFLP sites and between these sites and a hypothetical PKU "locus." These are statistically significant differences between European populations in the frequencies of non-PKU chromosomal haplotypes (P = .025) and PKU chromosomal haplotypes (P much less than .001). Haplotype frequencies of the PKU and non-PKU chromosomes also differ significantly (P much less than .001. Disequilibrium values are consistent with the PAH physical map and support the molecular evidence for multiple, independent PKU mutations in Caucasians. However, the data do not support a single geographic origin for these mutations.(ABSTRACT TRUNCATED AT 250 WORDS)     

Joint Report of the Fourth International Bovine Lymphocyte Antigen (BoLA) Workshop, East Lansing, Michigan, USA, 25 August 1990

Blood samples from 54 animals were exchanged between 15 laboratories in nine countries to improve and expand BoLA class I and class II typing. A total of 27 out of 33 (82%) of previously accepted BoLA-w specificities were represented within the cell panel. Seventeen new serum-defined BoLA specificities were accepted by the workshop participants, thus expanding the number of internationally recognized BoLA specificities to 50. The large number of new specificities detected resulted from the number of serological reagents used (n = 1139) and the genetic diversity of the cell panel. Confidence derived from the high percentage of agreement between the laboratories on antigen detection (97.3%; r = 0.84) permitted the removal of the workshop (w) notation from 23 BoLA-w specificities and their acceptance as full status BoLA-A antigens. Two new non-BoLA antigens were also detected, one completely included within the red blood cell factor S' (BoLy-S'), whereas a second (BoLy-w1) did not show any association with tested red blood cell factors. A comparison between serological, isoelectric focusing (IEF) and DNA typing for BoLA class II polymorphism was conducted with a subset of workshop cells. Correlation between the three methods was significant for three combinations of alleles. Three other serologically defined class II specificities were correlated with DR and/or DQ restriction fragment length polymorphism (RFLP) types, whereas six additional IEF types were correlated with DR and/or DQ RFLP types (r greater than or equal to 0.50). Several new IEF, DRB, DQA and DQB RFLP patterns were identified. In 46 animals that were typed for BoLA-DR and DQ genes by RFLP analysis, 46 different BoLA haplotypes were tentatively defined. These 46 haplotypes were distinguished by 31 serologically-defined BoLA-A alleles (and 2 'blanks'), 15 DRB RFLP types (plus up to 10 new DRB RFLP patterns) and 23 DQA-DQB haplotypes.     

Dispersal, philopatry, and infidelity: dissecting local genetic structure in superb fairy-wrens (Malurus cyaneus)

Dispersal influences evolution, demography, and social characteristics but is generally difficult to study. Here we combine long-term demographic data from an intensively studied population of superb fairy-wrens (Malurus cyaneus) and multivariate spatial autocorrelation analyses of microsatellite genotypes to describe dispersal behavior in this species. The demographic data revealed: (1) sex-biased dispersal: almost all individuals that dispersed into the study area over an eight-year period were female (93%; n = 153); (2) high rates of extragroup infidelity (66% of offspring), which also facilitated local gene dispersal; and (3) skewed lifetime reproductive success in both males and females. These data led to three expectations concerning the patterns of fine-scale genetic structure: (1) little or no spatial genetic autocorrelation among females, (2) positive spatial genetic autocorrelation among males, and (3) a heterogeneous genetic landscape. Global autocorrelation analysis of the genotypes present in the study population confirmed the first two expectations. A novel two-dimensional local autocorrelation analysis confirmed the third and provided new insight into the patterns of genetic structure across the two-dimensional landscape. We highlight the potential of autocorrelation analysis to infer evolutionary processes but also emphasize that genetic patterns in space cannot be fully understood without an appropriate and intensive sampling regime and detailed knowledge of the individuals genotyped.     

Restriction fragment length polymorphism of the caprine ß-globin gene cluster associated with the Hb ß-globin variants in Norwegian dairy goats

Restriction fragment length polymorphism (RFLP) analysis was used to characterize the beta-globin cluster in Norwegian dairy goats. In 122 individuals, different RFLP patterns were detected after BglII and PstI digestion and hybridization with a caprine beta-globin probe. The location of the polymorphic BglII and PstI sites were determined. The different RFLPs were in linkage disequilibrium with each other and with the beta-globin locus as studied at the protein level. A preferential association between certain RFLP haplotypes and beta-globin variants was observed. Polymorphic DNA fragments in the epsilon-globin genes were detected after MspI digestion and hybridization with a caprine epsilon-probe, and eight different band patterns were observed. Correlation between different MspI haplotypes and the beta-globin variants was determined.     

Restriction fragment length polymorphism analysis of major histocompatibility complex class II genes from inbred chicken lines

Summary. High molecular weight DNA was extracted from sperm from chickens of 14 inbred lines. The DNA was digested with each of four restriction enzymes ( Pvu II, Hind III, Bg /II, and Bam HI), electrophoresed for 18 or 45h, blotted onto nitrocellulose, and hybridized to a chicken major histocompatibility complex (MHC, B complex) class II β-chain probe (β2-exon specific). Restriction fragment length polymorphisms (RFLPs) were found with each of the restriction enzymes used. Birds with the same B haplotype always showed the same RFLP pattern; however, some birds of different B halotypes also shared the same RFLP pattern. To test for the Mendelian inheritance of the RFLP patterns, the F2 progeny of an informative cross were analysed. The RFLP patterns corresponded with the serologically determined B haplotypes of the F2 birds, thereby showing the Mendelian inheritance of the polymorphic bands.     

On the scaling patterns of species spatial distribution and association

Understanding how species distribution (occupancy and spatial autocorrelation) and association (that is, multi-species co-distribution) change across scales is fundamental to unlocking the pattern formation in population ecology and macroecology. Based on the Bayesian rule and join-count statistics, I present here a mathematical model that can demonstrate the effect of spatial scale on the observation of species distribution and association. Results showed that the intensity of spatial autocorrelation and species association declines when the grain in the spatial analysis increases, although the category of species distribution (aggregated or segregated) and association (positive or negative) remains the same. Random distribution and species independence were proved to be scale-free. Regardless of the possible patterns of species distribution and association, species tend to be randomly distributed and independent from each other when scaling-up (an increasing grain), reflecting a percolation process. This model, thus, grasps the statistical essence of species scaling pattern and presents a step forward for unveiling mechanisms behind species distributional and macroecological patterns.