596:
764:
are the grains. The R-code of the
Bayesian estimation model has been provided elsewhere. The key point of the Bayesian estimation model is that the scaling pattern of species distribution, measured by occupancy and spatial pattern, can be extrapolated across scales. Later on,
1103:
Lennon, J.J., Kunin, W.E., Hartley, S. & Gaston, K.J. (2007) Species distribution patterns, diversity scaling and testing for fractals in southern
African birds. In: Scaling Biology (D. Storch, P.A. Marquet & J.H. Brown, eds.), pp. 51–76. Cambridge University
153:
model, the cross-scale model and the
Bayesian estimation model. The fractal model can be configured by dividing the landscape into quadrats of different sizes, or bisecting into grids with special width-to-length ratio (2:1), and yields the following SPO:
68:
This pattern is often plotted as log-transformed grain (cell size) versus log-transformed occupancy. Kunin (1998) presented a log-log linear SPO and suggested a fractal nature for species distributions. It has since been shown to follow a
349:
The
Bayesian estimation model follows a different way of thinking. Instead of providing the best-fit model as above, the occupancy at different scales can be estimated by Bayesian rule based on not only the occupancy but also the spatial
133:
et al. confirmed that using the SPO is robust and reliable for assemblage-scale regional abundance estimation. The other application of SPOs includes trends identification in populations, which is extremely valuable for
1029:
Hui, C., McGeoch, M.A., Reyers, B., le Roux, P.C., Greve, M., Chown, S.L. 2009. Extrapolating population size from the occupancy-abundance relationship and the scaling pattern of occupancy. Ecological
Applications, 19:
437:
429:
129:
based on presence-absence data, or occupancy alone. This is appealing because obtaining presence-absence data is often cost-efficient. Using a dipswitch test consisting of 5 subtests and 15 criteria,
344:
848:
220:
1113:
Hui, C., McGeoch, M.A. & Warren, M. (2006) A spatially explicitly approach to estimating species occupancy and spatial correlation. Journal of Animal
Ecology 75: 140β147.
125:
between the mean and variance of species distribution, and Hui and McGeoch's droopy-tail percolation model. One important application of the SPO in ecology is to estimate
1187:
965:
Nachman, G. 1981. A mathematical model of the functional relationship between density and spatial distribution of a population. Journal of Animal
Ecology, 50: 453β460.
1191:
654:
1041:
Wilson, RJ., Thomas, CD., Fox, R., Roy, RD., Kunin, WE. 2004. Spatial patterns in species distributions reveals biodiversity change. Nature, 432: 393β396.
591:{\displaystyle q\,{(4a)_{+/+}}={\frac {{\Omega }^{10}-2\,{\Omega }^{4}\,{\mho }^{2}+{\mho }^{3}}{{\mho }^{2}\,\left(-{\Omega }^{4}+\mho \right)}}}
1020:
Hartley, S., Kunin, WE. 2003. Scale dependence of rarity, extinction risk, and conservation priority. Conservation
Biology, 17: 1559–1570.
1136:
Murray, Nicholas J.; Keith, David A.; Bland, Lucie M.; Nicholson, Emily; Regan, Tracey J.; RodrΓguez6,7,8, Jon Paul; Bedward, Michael (2017).
732:
is the conditional probability that a randomly chosen adjacent quadrat of an occupied quadrat is also occupied. The conditional probability
1205:
Murray, Nicholas (2017). "Global 10 x 10-km grids suitable for use in IUCN Red List of
Ecosystems assessments (vector and raster format)".
1081:
Hui, C. & McGeoch, M.A. (2007) A self-similarity model for occupancy frequency distributions. Theoretical
Population Biology 71: 61β70.
1010:
1092:
Hui, C. & McGeoch, M.A. (2007) Modeling species distributions by breaking the assumption of self-similarity. Oikos 116: 2097β2107.
1244:
1124:
Hui, C. (2009) On the scaling patterns of species spatial distribution and association. Journal of Theoretical Biology 261: 481β487.
364:
117:
Other occupancy-abundance models that can be used to describe the SPO includes Nachman's exponential model, Hanski and Gyllenberg's
1070:
Harte, J., Kinzig, A.P. & Green, J. (1999) Self-similarity in the distribution and abundance of species. Science 294, 334β336.
78:
114:, can also be applied for describing the SPO and the occupancy-abundance relationship for non-randomly distributed individuals.
873: = 1. In the same paper, the scaling pattern of join-count spatial autocorrelation and multi-species association (or
943:
Wright, D.H. 1991. Correlations between incidence and abundance are expected by chance. Journal of Biogeography, 18: 463β466.
905:
is used as a standardized, complementary and widely applicable measure of risk spreading against spatially explicit threats.
111:
1234:
49:
1009:
Hui, C., McGeoch, MA. 2007. Capturing the "droopy tail" in the occupancy-abundance relationship. Ecoscience, 14: 103β108.
275:
110:
in this Poisson model for randomly distributed individuals is also the SPO. Other probability distributions, such as the
987:
He, F., Gaston, K.J. 2003. Occupancy, spatial variance, and the abundance of species. American Naturalist, 162: 366β375.
1239:
898:
976:
Hanski, I., Gyllenberg, M. 1997. Uniting two general patterns in the distribution of species. Science, 284: 334β336.
1052:
Hasting, H.M. & Sugihara, G. (1993) Fractals: a User's Guide for the Natural Sciences. Oxford University Press.
775:
358:
et al. provide the following formula to describe the SPO and join-count statistics of spatial autocorrelation:
160:
954:
He, F., Gaston, K.J. 2000. Estimating species abundance from occurrence. American Naturalist, 156: 553β559.
1181:
70:
1042:
58:
the problem of relating phenomena across scales is the central problem in biology and in all of science
1061:
Kunin, WE. 1998. Extrapolating species abundance across spatial scales. Science, 281: 1513–1515.
1149:
138:
86:
999:
81:. For instance, if individuals are randomly distributed in space, the number of individuals in an
890:
41:
932:
Kunin, WE. 1998. Extrapolating species abundance across spatial scales. Science, 281: 1513β1515.
977:
126:
1210:
1167:
1157:
933:
639:
1071:
351:
17:
122:
1153:
1031:
149:
Models providing explanations to the observed scaling pattern of occupancy include the
118:
53:
45:
1114:
1093:
1228:
1172:
922:
921:
Levin, SA. 1992. The problem of pattern and scale in ecology. Ecology, 73, 1943β1967.
894:
874:
229:
is the box-counting fractal dimension. If during each step a quadrat is divided into
1214:
893:
increases rapidly as range size declines. In risk assessment protocols such as the
135:
21:
879:
the Bayesian model can grasp the statistical essence of species scaling patterns.
1125:
74:
1138:"The use of range size to assess risks to biodiversity from stochastic threats"
1082:
253:
is scale independent is not always the case in nature, a more general form of
40:) is the way in which species distribution changes across spatial scales. In
998:
Taylor, L.R. 1961. Aggregation, variance and the mean. Nature, 189: 732β735.
769:
provides the Bayesian estimation model for continuously changing scales:
766:
355:
130:
988:
955:
944:
150:
1162:
1137:
756:
is the absence probability in a quadrate adjacent to an occupied one;
77:
process. Furthermore, the SPO is closely related to the intraspecific
966:
121:
model, He and Gaston's improved negative binomial model by applying
424:{\displaystyle p\,{(4a)_{+}}=1-{\frac {{\Omega }^{4}}{\mho }}}
60:. Understanding the SPO is thus one central theme in ecology.
877:) were also provided by the Bayesian model, suggesting that "
237:) of sub-quadrats is also present in the fractal model, i.e.
354:
at one specific scale. For the Bayesian estimation model,
865:
are constants. This SPO becomes the Poisson model when
778:
642:
440:
367:
278:
163:
269:
is a constant), which yields the cross-scale model:
339:{\displaystyle P_{a_{j}}=f_{0}f_{1}\cdots f_{j}.\,}
842:
648:
590:
423:
338:
214:
233:sub-quadrats, we will find a constant portion (
8:
1186:: CS1 maint: multiple names: authors list (
843:{\displaystyle P_{a}=1-bc^{2a^{1/2}}h^{a}\,}
98: = 1 − exp(−
1190:) CS1 maint: numeric names: authors list (
889:The probability of species extinction and
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445:
444:
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410:
405:
402:
386:
372:
371:
366:
335:
326:
313:
303:
288:
283:
277:
211:
195:
191:
181:
168:
162:
885:Implications for biological conservation
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1179:
692: − 3) + p(a)
241: = 2(1 + log
215:{\displaystyle P_{a}=P_{0}a^{D/2-1}\,}
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564:
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79:occupancy-abundance relationship
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249:). Since this assumption that
112:negative binomial distribution
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50:modifiable areal unit problem
26:scaling pattern of occupancy
1142:Diversity and Distributions
899:IUCN Red List of Ecosystems
89:, with the occupancy being
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106:is the density. Clearly, P
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48:, it is similar to the
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87:Poisson distribution
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1154:2017DivDi..23..474M
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64:Pattern description
56:(1992) states that
1240:Population ecology
897:of Species or the
891:ecosystem collapse
840:
646:
588:
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123:Taylor's power law
42:physical geography
1163:10.1111/ddi.12533
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127:species abundance
34:area-of-occupancy
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309:
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245:/log
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