Estimation of Species Richness of Permian Foraminifera in Non-Parametric Methods and Investigation of Its Change Trend in Central Alborz, Western Tethys

Species richness of foraminifera assemblages in the Permian succession, contains Dorud, Ruteh and Nessen Formations, in Central Alborz—North of Iran, was estimated and studied based on lithostratigraphy and microbiostratigraphy of Permian. We used four non-parametric estimators to investigate the species richness: Chao 2, Jackknife 1, Jackknife 2 and bootstrap. These methods estimates the species richness based on the presence/absence data of each taxon identified in the samples. We use the submenu of quadrat richness in “Past” [1] software to estimate richness in regional chronostratigraphic stages.The results show that the estimated diversity of foraminiferal assemblages with the exception of late Yakhtashian, increased constantly from Asselian to Murgabian with the highest diversity of foraminifera seen in the Murgabian. The main decrease in foraminiferal species richness happened during the Midian which corresponds to the kamura cooling event.

2) Beta diversity: shows species composition changes within a community or in a gradient [5] or along with changes in a variety of habitats [6].
3) Gamma diversity: this is defined as inter-province (across regions diversity) [7].Species richness is a numerical index and shows measure of alpha diversity.This means that to calculate it, the number of each species (number of individuals) in the samples is used.But, there are also other non-parametric methods for the calculation of richness that is used in this study.In these methods, the number of individuals is not need to calculate richness.
There are many examples of the application of this index in palaeontology.
Sepkoski [8] used richness at two genus and family levels for Phanerozoic marine animals and utilized the method of counting the number of taxa.Bentone [9] chose family taxonomic level for his study and used the number of family as richness index.Ruban [10] studies biodiversity of Jurassic foraminifera in northern Kazakhstan at the level of genus and species.Uhen [11] used the number of genera as amount of richness.Vilhena [12] measured species richness by counting the presence or absence of genera in intervals and compared it at palaeo latitudes.Ruban [13] used a similar method to calculate the richness of the Jurassic brachiopods.In this study species richness of Permian foraminifera is estimated from four important non-parametric methods including Chao 2, Jackknife 1, Jackknife 2 and bootstrap [7].In these methods, richness estimated without counting the number of species in samples, but based on the presence/absence of each taxon in the samples.For this purpose, two outcrops of the Permian strata were selected in Central Alborz and they litho and biostratigraphy was studied at high resolution.The species richness of the recovered for aminiferal assemblages was estimated using presence/absence data of the identified taxa in samples during regional chronostratigraphic (stage and sub stage) intervals.

Geological Setting
The Heev section is situated at the western margin and the Dorud section approximately in the center of Central Alborz representing the middle part of Alborz Mountains in the north of Iran.Aghanabati [15] divided the Iranian platform into three tectono-stratigraphic units including Northern Iran (Turan plate), Central Iran (Iranian plate) and Southern Iran (Zagros plate) by considering two main geo sutures: Palaeo-Tethys and Neo-Tethys (Figure 1(b)).In this subdivision, Central Iran plate contains several zones and subzones and one of them is the Alborz-Azerbaijan zone which is known as Alborz Block or Alborz Terrane too [16].The Alborz Mountains according to [15] and [17] can be subdivided into three main subunits containing the Western, Central and East-ern Alborz.The central Alborz is showing W-E structural trend and can be further divided into six subzones based on main faults and thrusts [18] (Figure 1(c)).Our studied sections are located at the southern Central subzone.

Palaeogeographic Setting
According to [19] the Alborz Mountains along with Central Iran, Sanandaj-Sirjan and NW Iran are comprising the Iranian plate since the early Permian and were disrupted from the Arabian plate by opening of the Neo-Tethys Ocean.This opening led to the formation of Cimmerian continents (Pangaea B) and spreading caused the motion of Iran, Afghanistan and other fragments toward NE (Figure 1(a)).Along with the opening of Neo-Tethys, subduction took place along the Palaeo-Tethys suture.Investigation of palaeomagnetic changes in the Central Alborz-Aru region by [19] shows that the Iranian plate were situated around 20˚S with a North-South trend in the Early Permian.During opening the Neo-Tethys and simultaneous Palaeo-Tethys subduction, it started to move to north rotating counter clockwise at the same time.So, during Late Permian it was placed in tropical latitude with a WE trend (Figure 1(a)).

Discussion and Methods
To investigate the species richness of foraminifera, two sections of the Permian succession in Central Alborz have been selected and sampled systematically.
Whereas biodiversity is a characterized by ecological and geological factors [20] and geological factors mainly contain fossil and rock records in palaeontology, so it is very important in palaeobiodiversity studies that selected data resources be perfect indicator of main diversity.In other word only perfect rock and fossil record can be representative of biodiversity at geological time.Hence we selected two studied sections by considering these two principals: rock and fossil record and by investigating all the previous studies.In addition since palaeobiodiversity can be considered as a basin scale study, so we did not have any restriction to select separated section for various intervals.As said above, Heev section is one of the thickest Ruteh outcrops (perfect rock record) in Central Alborz and have an acceptable fossil record of foraminifera according to previous studies such as [21].However in the Heev section, Dorud Formation though having great thickness does not contain all of the distinguished foraminifera biozones.Therefore we selected another and better section that has a more perfect fossil record.
After preparation of thin sections we studied them micropalaeontologically.
We identified all foraminifer genera and species in thin sections and then drew their extension line in a lithostratigraphic column (rang chart).Biostratigraphy is done based on lithostratigraphy and extension of taxa and index genus and species.We separated Permian stages (Asselian to Dzhulfian) and then inserted presence/absence data of taxa in Past [1] software data sheet (Table 1 and Tables 2(a)-2(f) see Appendix).So we could estimate species richness in four methods by quadrat submenu of diversity menu in Past [1] and then we plotted them in a curve diagram by using Excel.

Dorud Section
The type section of the Dorud Formation (or Dorud Group as recommended by [22]) (Figure 2

Heev Section
The Permian outcrop in the Heev section includes The Dorud, Ruteh and Nessen formations (Figure 2(a)) attaining a total thickness of 585 m.The Permian succession is underlain by dark volcanic unit of Jeirud Formation (Devonian) with a nonconformity contact (Figure 2(d)).Above, it is covered by a vermiculite, thin bedded limestone of the Elika Formation (Triassic) with a disconformity contact (Figure 2 and Figure 4).
The Dorud Formation (243 m) begins with a basal fine grained conglomerate changing upward into a quartzitic weathering buff colored sandstone followed by cross bedded sandstone, silty and shaly sandstone, Fusulinid and oncoid bearing gray limestone and massive thick bedded sandstone are present in the uppermost part.We did not study the Dorud Formation in this section because of its incomplete microfauna.
The transition to the Ruteh Formation (314 m) in the studied section disconformably overlies reddish brown Laterite zone on top of the Dorud Formation.
The Ruteh Formation typically contains dark gray fossiliferous limestone bearing common macrofauna of brachiopods, corals, trilobites and Zoophycus trace fossils (Figure 4).The Ruteh Formation is followed dark gray limestone (28 m) of Nessen Formation.The contact is disconformable because of laterite zone in between.
( Alborz [22], some studies have shown that the base of Ruteh Formation might be older.Vaziri [33] reported an Artinskian age of the Ruteh Formation in the Abyek-Gazvin area based on micropalaeontology.Again, Vaziri [21] accommodated themselves previous results with Radiolarian biozones in our studied area and the most important record belong to [34] who identified and reported

Species Richness Measurement Method
There are different methods to measure species richness.In the simplest case, it is equal to the number of observed species in the sample: R = S where R is richness and S is number of species counted in samples.However there are many examples of using other taxonomic levels in palaeontology.Two general approaches to calculate (estimate perhaps better expression) index there are: (1) by measuring the presence or absence of species in samples and (2) by counting the number of individuals of each species (abundance) in samples.We used the first method, where some random standard samples are selected and then species presence/absence data are extracted and richness in total of samples is calculated.
The four important equations for richness calculation in this method are [7]: S obs : total number of observed species L: the number of species that are present in a sample M: the number of species that exist in the two samples P i : proportion of specimens containing species i n: the number (size) of samples To estimate the indices with "Past" software [1] each row appropriates to a taxon and each column to a sample (represented by one?thin section in this study) and then the presence/absence of each taxon in each sample is entered in the relevant box.After entering all data (Table 1 and Tables 2(a)-2(f) see Appendix) and according to the range chart, columns (samples) of each stage were selected and grouped in the data sheet.In this step "Past" software [1] can estimate the above mentioned indices in species richness menu and quadrate submenu.The results for the Asselian through Dzhulfian stages are displayed in Table 3 and Figure 7 shows the curve diagram of them.Note that "Past" output for each quadrate (here is stage or substage) includes two groups of richness amounts: Original data set and Bootstrap replicates.Although there is little difference in numerical amount of the four indices and between two mentioned groups for each interval, all of them showing a similar trend.

Conclusion
The trend of species richness shows that all of four computational approaches have quite similar trends and slight differences in their amounts are the result of different equations used.The chart is showing a species richness increase from Asselian to Murgabian with a maximum value in the Murgabian.This is comparable  with high productivity in low latitude ocean [37].This could be due to the stability of the environment and good living conditions.In this condition, species richness increase by the time and by increasing the number of species and size of the population.During the Midian a sharp drop in the diversity is seen.This drop is comparable to the same results for bivalves [38] and brachiopods [39] and probably caused by the kamura cooling event [37].These are same as [40] results that showed two extinction in Maokovian and Changhsingian for both fusulinid and non-fusulinid foraminifera too.In Dzhulfian, foraminifer richness increases similar to other taxa at the global level.Diversity changes trend in this study is similar to the results of our previous study [41] at Abe-Garm section by using the method suggested by [42] for standing diversity calculation.

Figure 2 .
Figure 2. (a)-(d) Heev section, (e) Dorud section, outcrop details: (a) view of Heev section adapted from Google Earth, (b) contact of Ruteh and Nessen Formations at Heev section, (c) unconformable contact of Ruteh and Dorud Formations at Heev section, (d) eroisonal contact of Devonian volcanic unit with basal conglomerate of Dorud Formation at Heev section, (e) members of Dorud Formation at studied section (type section of Dorud Formation, north of Tehran).

Figure 3 .
Figure 3. Stratigraphic log of the Dorud Formation in Dorud Section, Central Alborz, North of Tehran, with foraminiferal biozones.

Figure 4 .
Figure 4. Stratigraphic log of the Ruteh and Nessen Formations in Heev Section, Central Alborz, SE of Gazvin with foraminiferal biozones.

Table 3 .
[1]aminifera species richness measures obtained from Past[1]for Asselian to Dzhulfian based on data extracted from studied sections.