Two of the pollen transfer functions developed by Wilmshurst et al. (2007) (section 5.5.4) are used in the
current study to derive mean annual temperatures for Eltham: (a) partial least squares regression (PLS), and (b) the weighted modern analogue technique (W-MAT) where the ten closest modern analogues of the fossil pollen assemblage are identified, and the mean of the modern annual temperature for the ten analogues is weighted by relative abundance.
The Eltham taxa used in the transfer function models are shown, along with the correlation coefficients between
mean annual temperature and pollen frequencies (Wilmshurst et al. 2007) (Table 10). The correlation
coefficients are also shown at the foot of individual taxon graphs within the pollen diagrams to highlight the temperature preferences within each broad vegetation type. In addition, bud freezing temperatures for selected taxa are shown (from Table 2).
Table 10. Correlation between Mean Annual Temperature and Pollen Types for Taranaki Sites, and Selected Bud Freezing Temperatures
Pollen Taxa correlation MAT
Fr ee zi ng T em
p (°C) Pollen Taxa correlation MAT
Fr ee zi ng T em p (°C)
Phyllocladus trichomanoides 0.64 -10.0 Pseudowintera -0.02
Cyathea dealbata 0.63 Weinmannia -0.04 -8.0
Metrosideros undiff. 0.57 -8.0 Coprosma -0.07 -8.0
Dacrydium cupressinum 0.51 -8.0 Prumnopitys ferruginea -0.09 -7.0 Libocedrus plumosa 0.49 -7.0 Libocedrus bidwillii -0.09
Nestegis 0.46 Plagianthus -0.09 -5.0
Ascarina lucida 0.43 -3.0 Hoheria -0.12
Griselinia 0.42 Hebe -0.15
Knightia excelsa 0.39 -8.0 Dracophyllum -0.24 -10.0
Freycinetia 0.33 Nothofagus subg. Fuscospora -0.38 -10.0
Dacrycarpus dacrydioides 0.31 -7.0 Asteraceae -0.39
Syzygium maire 0.29 Poaceae -0.49
Dodonaea viscosa 0.28 Nothofagus menziesii -0.51 -12.1
Elaeocarpus 0.22 -5.0 Halocarpus -0.59 -25.0
Collospermum 0.21 Phyllocladus alpinus -0.65 -20.0
Cyathea smithii 0.21 Pittosporum 0.20 -7.0 Monolete spores 0.17 Quintinia 0.15 -8.0 Hedycarya arborea 0.14 -3.0 Dactylanthus taylorii 0.14 Pseudopanax 0.13 Dicksonia squarrosa 0.12 Podocarpus totara 0.09 -7.0 Leucopogon fasiculatus 0.08 Fuchsia 0.07 Prumnopitys taxifolia 0.06 -11.1 Myrsine 0.04 Dicksonia fibrosa 0.03 Hymenophyllum 0.02
Source: Wilmshurst et al. (2007); Sakai & Wardle (1978). This list is a subset of Wilmshurst et al. (2007) list, that is, only
includes those taxon or taxa groups enumerated at Eltham or the coastal Taranaki sites. The MAT correlations shown in
bold are statistically significant at the 99.9% probability level, and are the ‘critical taxa’ referred to in Newnham et al.
7.7. Biodiversity Indices
The purpose of this section is to briefly describe how the diversity indices used in this study are calculated, as well as some consideration of the relative strengths and weaknesses of the various indices.
(i) Species richness is the most basic measure of biodiversity; it is simply a count of the number of species. Species richness can be generalised higher taxonomic levels (Hammer & Harper 2006); in this study, ‘palyno-
richness’ (Flenley 2003) or the number of taxa are given. A well-established weakness of species richness as a
measure of diversity is that richness does not take into account relative abundance and therefore is susceptible to the size of the sample: the more individuals counted, the greater the number of taxa likely to be enumerated (Peet 1974; Tipper 1979; Brewer & Williamson 1994). Techniques that account for different sample sizes are:
(ii) Rarefaction Curves are used for both standardising sample sizes, and as an index in their own right.
Rarefaction curves show the expected number of taxa as a function of n, under assumptions of homogeneity and
randomness (Brewer & Williamson 1994). When the rarefaction curve flattens out at larger values of n, this
indicates that the original sample captured most of the taxa. Heck et al. (1975) and Tipper (1979) calculated
E (Sn) or expected number of species using:
(7) where Ni is the number of individuals in species i of the un-rarefied sample.
In other words, during the initial part of the pollen count, taxa richness rapidly increases but the rate of taxa richness slows and reaches an asymptote where additional counting uncovers no new taxon. This ‘moment of
saturation’ (Weng et al. 2006) varies amongst ecosystems, with the asymptote occurring at a low pollen count in
a low diversity, temperate ecosystem such as a beech forest, compared with a higher pollen count in a high diversity ecosystem such as a tropical rainforest. Figure 38 shows the rarefaction curve for Eltham Swamp dryland pollen taxa (red) with 95% confidence intervals (blue). Note that the curve begins to flatten off at n =
200, with a taxa count of around 20. This compares with the goal of a minimum dryland pollen count of 200, excluding ferns, so we can be 95% confident that on average, pollen counts of 200 capture most dryland taxa present (mean dryland pollen count at Eltham = 223.3).
40 80 120 160 200 240 280 Specimens (n) 0 3 6 9 12 15 18 21 24 27 Ta xa (9 5% c on fi de nc e)
Rarefaction analysis of fossil pollen has been used to determine Holocene floral diversity in Crose Mere, central England and the Isle of Skye in western Scotland; Late Glacial diversity in Abernathy Forest, eastern Scotland (Birks & Line 1992); Late Holocene vegetation in Finland (Grönlund & Asikainen 1992); and southern Sweden (Lindbladh & Bradshaw 1995). A search of the literature did not reveal any similar study in New Zealand.
(iii) Menhinick’s richness (MR) index
Menhinick (1964) compared several diversity indices for species of insects against two criteria: (i) the indices
must be applicable for a given ‘universe’ (population) regardless of sample size; and (ii) the indices must
differentiate between populations that had different numbers of species for a given number of individuals. Menhinick examined species/log individuals, species -1/natural log of individuals, log species/log individuals, and species/ square root of individuals; only the latter index met both of the criteria, therefore he proposed that species richness (sample size, S) increases with n, but does so non-linearly, at the square root of n:
(8)
Menhinick’s index has been used by various researchers (Kumar et al. 2006; Deb & Sundriyal 2011; Dobhal et
al. 2011; Caçador et al. 2013) to measure vegetation richness of extant, northern hemisphere forests.
(iv) Margalev’s richness (MR) index:
(9)
Hammer & Harper (2006) point out that whether the number of taxa in a sample increases more like the square
root of the sample size as in Menhinick’s index) or the logarithm of the sample size (as in Margalev’s index)
depends upon relative taxa abundances, so neither solution is always applicable.
(viii) Berger-Parker (DBP) index (Berger & Parker 1970) is a measure of how common the most abundant
taxon is:
(10) Where N = total number of individuals in a sample, and NMAX is the total number of individuals in the most
common taxon. As a consequence, if one taxon dominates a community, it is not very diverse as measured by the Berger-Parker index. Since more diverse communities have a lower Berger-Parker index, a complement form is often used, that is
(11) Therefore, values of DBPC range from 0 (low diversity) to 1 (high diversity). The non-complement form is given
in the present study, that is, equation (10) rather than equation (11).
(ix) Simpson diversity (DS)index (Simpson 1949) calculates the probability of any two individuals selected at random from a population belonging to the same taxon:
(12) where Pi2 is the proportion of individuals in the ith species. Since Ds and diversity are inversely related, a
complement index called the Gini-Simpson index is often used (and is used in the current study), that is
(13) Like the Berger-Parker index, both the Simpson and Gini-Simpson index are biased towards the most abundant species, so therefore are of limited use when the population has many rare species, although DS and DGS are
more accurate than DBP because they utilise a broader array of taxa, whereas DBP only uses data for the most
prominent taxon.
A second broad group of diversity indices are known as information statistic indices. These indices are based on the concept that diversity can be estimated in a similar manner to calculating uncertainty in a code; as a consequence rare species are weighted more in information statistic indices than they are in dominance indices (Stirling & Wilsey 2001):
(x) Shannon index (Hs)
(14) where Pi is the proportion of individuals in the ith species, and ln is the natural logarithm. A strength of HS is
that even the rarest taxon contributes to the index. It is essentially a measure of the information required to define an assemblage (Berger & Parker 1970). The Shannon index is a measure of the number of common taxa, whereas the Simpson index is a measure of the very common taxa (Brewer & Williamson 1994). Values for
natural communities typically range between 1.5 (low diversity) and 3.5 (high diversity).
Since diversity indices combine two concepts – taxa richness and abundance evenness – and since the emphasis on either component varies from one index to the next, finding a balance is problematic. In addition, applying these indices to fossil pollen data is complicated by problems inherent in palynology in general, such as differential pollen production, dispersal and preservation. As a consequence, Weng et al. (2006) suggest the
simplest measure, Species Richness, may provide the most meaningful pollen diversity information. The same palynological limitations prompted Birks & Line (1992) to recommend avoiding the use of diversity indices
such as Shannon’s or Simpson’s indices in favour of rarefaction analysis.
In contrast, Buckland et al. (2005) note that although no single index is able to encompass all the dimensions of
diversity change, both Simpson’s and Shannon indices perform well against five out of the six criteria they
suggest are appropriate to measure diversity indices against29. Neither index satisfied criterion 2; this is unfortunate given the pollen diagram for Eltham (Figure 39) shows that pollen influx is not constant over time, but increases towards the top of the core. Buckland et al. (2005) suggested applying a modified version of the
Shannon index that satisfied all six criteria; in particular the estimator decreased if absolute abundance of all taxa declined at the same rate. However, the modified Shannon index had no theoretical foundation and was purely a pragmatic solution to satisfy all six criteria (Buckland et al. 2005) and has not been rigorously tested
(Buckland et al. 2011). Given the foregoing discussion, it seemed most prudent to provide a selection of
diversity measures for Eltham.
A weakness of applying biodiversity indices to palynological data is that the indices were generally designed to describe populations where identification to species level is possible, however in palynology ‘taxa’ may relate
to different taxonomic levels, that is, species (Dacrycarpus dacrydioides), genus (Libocedrus, Pittosporum),
Family (Asteraceae) or groupings based on pollen morphology (Nothofagus subg. Fuscospora, Leptospermum-
type). Furthermore, there may be an indeterminable number of species within a higher taxonomic level, for example Asteraceae or Coprosma. This makes it difficult to make definitive inferences about diversity change,
however the alternative would be to only enumerate those taxa identifiable to species level, and this could also limit the usefulness of this type of analysis and also result in misleading inferences.
29 Non-statistical criteria are (i) for a system that has a constant number of species, overall abundance and species evenness,
but with varying abundance of individual species, the index should show no trend; (ii) if overall abundance is decreasing, but the number of species and species evenness are constant, the index should decrease; (iii) if species evenness is decreasing, but the number of species and overall abundance are constant, the index should decrease; and (iv) if the number of species is decreasing, but overall abundance and species evenness are constant, the index should decrease. Statistical criteria are (v) the index should have an estimator whose expected value is not a function of sample size; and