268
EP. Agterberg . EM. Gradstein
4
Palaeogeographic Distribution Patterns of Taxa
Even when kc is set relatively high, the probability that two taxa co-occur may remain very small. One possible explanation of this is that many taxa existed within restricted geographic domains occupying parts of the entire study area. If the
two domains of two taxa had little overlap, very few sections would contain both
taxa. Because of the small frequencies of taxa and pairs of taxa in wells (and
smaller frequencies of superpositional relations between events), it is, at
present, not feasible in most practical applications to establish reliable two-dimensional patterns that could be incorporated in RASC for further analysis.
However, it is useful to study such patterns in their own right, because this provides guidelines for selecting wells for analysis and the setting of threshold parameters.
Geographic distribution patterns of fossil events can be studied separately to
establish their traceability across the study region. As indicated by the positive
skewness of frequency distribution for number of different taxa per section, the
main difficulty to be resolved in establishing traceability is to eliminate the effect
of relatively low probability of observing an event in a well for most taxa. Not detecting a taxon in the samples for a given well does not mean that the taxon did
not exist at the location where the well was drilled. The probability to be estimated can be regarded as the product of the probability of being within the domain
where the taxon existed and the probability of detecting it. The logistic model
can be used for estimating probability of occurrence of a fossil event at any sampling point including the locations of wells within the study area.
Bonham-Carter et al. (1986) applied correspondence analysis to foraminiferal
data from 36 offshore wells on the Labrador Shelf, Grand Banks, and Scotian
Shelf for biostratigraphic correlation and for investigating systematic trends in
distribution related to palaeogeography. Best results were obtained by applying
this technique to assemblage zones for separate time-slices defined on clusters
in a RASC zonation. Geographic trends in faunal distribution, differing according to latitude, were shown to exist. Their reordered data matrices (taxa versus
scores along first axis of correspondence analysis) clearly indicate that there are
three types of taxa: those present in wells randomly distributed across the entire
study area, and those definitely missing in wells either in the southern or the
northern part of the study area (Bonham-Carter et al. 1986).
Suppose that the geographic locations of the wells are coded as x (for easting
or longitude) and y (northing or latitude), and that the presence/absence data
for a taxon are coded as 1 (present) or 0 (absent). Then the following logistic
equation can be fitted for each taxon: Pr(taxon is present) = exp{j(x,y)}I[1+exp
(f(x,y)}] where Pr denotes probability and j(x,y) represents a function of the geographical co-ordinates. The two functions applied in this paper are (I) f(x,y) =
a+bx+cy, and (II) f(x,y)=a+by. In these expressions a, band c are the coefficients
of the logistic model which can be estimated by the maximum likelihood method. According to Model II, the probability changes as a function of latitude only.
Model I allows for change in the east-west direction as well. Use of the logistic
EP. Agterberg . EM. Gradstein
4
Palaeogeographic Distribution Patterns of Taxa
Even when kc is set relatively high, the probability that two taxa co-occur may remain very small. One possible explanation of this is that many taxa existed within restricted geographic domains occupying parts of the entire study area. If the
two domains of two taxa had little overlap, very few sections would contain both
taxa. Because of the small frequencies of taxa and pairs of taxa in wells (and
smaller frequencies of superpositional relations between events), it is, at
present, not feasible in most practical applications to establish reliable two-dimensional patterns that could be incorporated in RASC for further analysis.
However, it is useful to study such patterns in their own right, because this provides guidelines for selecting wells for analysis and the setting of threshold parameters.
Geographic distribution patterns of fossil events can be studied separately to
establish their traceability across the study region. As indicated by the positive
skewness of frequency distribution for number of different taxa per section, the
main difficulty to be resolved in establishing traceability is to eliminate the effect
of relatively low probability of observing an event in a well for most taxa. Not detecting a taxon in the samples for a given well does not mean that the taxon did
not exist at the location where the well was drilled. The probability to be estimated can be regarded as the product of the probability of being within the domain
where the taxon existed and the probability of detecting it. The logistic model
can be used for estimating probability of occurrence of a fossil event at any sampling point including the locations of wells within the study area.
Bonham-Carter et al. (1986) applied correspondence analysis to foraminiferal
data from 36 offshore wells on the Labrador Shelf, Grand Banks, and Scotian
Shelf for biostratigraphic correlation and for investigating systematic trends in
distribution related to palaeogeography. Best results were obtained by applying
this technique to assemblage zones for separate time-slices defined on clusters
in a RASC zonation. Geographic trends in faunal distribution, differing according to latitude, were shown to exist. Their reordered data matrices (taxa versus
scores along first axis of correspondence analysis) clearly indicate that there are
three types of taxa: those present in wells randomly distributed across the entire
study area, and those definitely missing in wells either in the southern or the
northern part of the study area (Bonham-Carter et al. 1986).
Suppose that the geographic locations of the wells are coded as x (for easting
or longitude) and y (northing or latitude), and that the presence/absence data
for a taxon are coded as 1 (present) or 0 (absent). Then the following logistic
equation can be fitted for each taxon: Pr(taxon is present) = exp{j(x,y)}I[1+exp
(f(x,y)}] where Pr denotes probability and j(x,y) represents a function of the geographical co-ordinates. The two functions applied in this paper are (I) f(x,y) =
a+bx+cy, and (II) f(x,y)=a+by. In these expressions a, band c are the coefficients
of the logistic model which can be estimated by the maximum likelihood method. According to Model II, the probability changes as a function of latitude only.
Model I allows for change in the east-west direction as well. Use of the logistic