An artificial intelligence approach to palaeogeographic studies: a case study of the Late Ordovician brachiopods of Laurentia

Abstract According to the earliest hypothesis which was based on qualitative studies of the Late Ordovician brachiopod fauna, the younger and larger species of Hiscobeccus, which was one of the epicontinental brachiopod fauna of North America, evolved from the older and smaller species of Rhynchotrema, which lived in precratonic regions. The results of quantitative studies and multivariate analyses based on the morphological characteristics of the brachiopods support this hypothesis. In this study, an artificial intelligence model based on neural networks was conducted in order to determine the relationship between the morphological characteristics of the Late Ordovician brachiopods of the Laurentia and their geographical localities. This neural network model estimates the palaeogeographic localities of the brachiopods by generating a mathematical formula between the morphometric characteristics of brachiopods and their geographical distribution. Based on the results of this study, the neural network can estimate the geographical localities of the test samples of brachiopod with a high accuracy of 82%. By creating a more comprehensive dataset based on the morphometric parameters of the brachiopods of Laurentia and other regions of the world and using the neural network model, the palaeogeographic localities of brachiopods can be estimated with high accuracy. Keywords: Brachiopods, Neural network, Morphometrics, Palaeogeography, Late Ordovician Introduction Traditionally, paleontology has been a descriptive science, and much of the previous research has been based on qualitative approaches. In recent years, more quantitative methods have been used by paleontologists, in order to have a more comprehensive understanding of the relationships between fossils and their palaeogeography, palaeoecology, palaeobiology, and evolutionary history. Based on the previous studies, which have been largely qualitative, Hiscobeccus evolved from Rhynchotrema, probably in the late Chatfieldian (middle Caradoc), and developed into a large, spherical, and highly lamellated shell (Amsden 1983; Jin 2001). Despite these early studies, there are still many questions regarding the evolutionary lineage of Rhynchotrema-Hiscobeccus. For example, what was the rate of morphological transformation from Rhynchotrema to Hiscobeccus? Did morphological changes occur similarly in different regions with different palaeoenvironments on the Laurentian plate? What was the palaeoecological position of different species of the Rhynchotrema-Hiscobeccus lineage in different palaeogeographic environments? How did sea-level changes affect the evolution of the Rhynchotrema-Hiscobeccus lineage? In a study by Sohrabi and Jin (2013), a dataset was conducted based on morphological features of Rhynchotrema and Hiscobeccus specimens from North America and they used multivariate analysis to distinguish morphological trends from Rhynchotrema to Hiscobeccus. Based on the primary measurements, they extracted secondary parameters in order to examine morphological changes (e.g. increase in shell size, lamellosity, and globosity) from Rhynchotrema to Hiscobeccus. Based on these secondary parameters such as shell size index (SSI), shell convexity index (SCI), shell lamellosity index (SLI), and shell lamella density (SLD), they studied the differences between younger and older forms of Rhynchotrema and early forms of Hiscobeccus during the Late Ordovician time. In their study, based on the morphological changes, the relationships between different forms of Rhynchotrema and Hiscobeccus in different regions and with different palaeogeographic distribution patterns of species were investigated. In previous studies, the Late Ordovician brachiopods from different regions of North America have been qualitatively and quantitatively examined, and also a detailed dataset related to the morphological characteristics of brachiopod fossils from different regions of North America has been previously collected. Therefore, a dataset based on the North American brachiopods was used in this study. The fact that most of the studies on the Late Ordovician brachiopods from different regions of Iran have been qualitative, and also the quantitative data related to the morphological characteristics of Iranian brachiopods are very limited, the Late Ordovician brachiopods of Iran were not used in this study. For the present study, an artificial intelligence approach was used to investigate and analyze the palaeogeography and evolutionary process of the Rhynchotrema-Hiscobeccus lineage during the Late Ordovician in North America (Laurentia). Artificial intelligence has the ability to learn from any pattern between a set of input and output data and involves various techniques including neural networks. In this study, a neural network method was used to estimate the location of the Rhynchotrema-Hiscobeccus lineage and also their palaeogeographical analysis. The use of neural network-based artificial intelligence allows paleontologists to have a better and more comprehensive understanding of the palaeogeographic distribution of the brachiopods. By adding more brachiopods data from other geographical locations around the world to the current dataset, a more inclusive dataset can be created for future studies, which would enhance the predictivity power of the neural network model to cover wider geographic locations. Materials & Methods The data used in this study are based on a morphometric dataset of Rhynchotrema and Hiscobeccus specimens collected by previous studies (see Sohrabi and Jin 2013). This dataset includes biometric measurements of the Upper Ordovician (upper Sandbian–upper Katian) rhynchonellid brachiopods from nine localities in North America (Brett et al. 2004; Bergstrom 1971; Mitchell & Bergstrom 1991) (Figs. 1 and 3). The Rhynchotrema specimens in this study are as follows: Mn-10 from the Platteville Formation, Upper Sandbian, Minnesota; W (NAPC-9) from the Lexington Formation, lower Katian, Kentucky; Mara-1 (0–2) from the Verulam Formation, lower Katian, Lake Simcoe Region, Ontario; Ottawa-1 from the Verulam Formation, lower Katian, Ottawa Region; GSC Loc. 1603 specimens from the Verulam Formation, lower Katian, Bay of Quinte, southern Ontario. The specimens of Hiscobeccus in this study are as follows: GSC Loc. 205924 from the Advance Formation, Trentonian age, northern Rocky Mountains, British Columbia; GSC Loc. 113531 from the Amadjuak Formation, Edenian–Maysvilian age, Baffin Island; GSC Loc. C-205929 from the Stony Mountain Formation, Richmondian age, southern Manitoba; W (C-7a-77) specimens from the Waynesville and Liberty formations, Richmondian age, Ohio (Figs. 1 and 2). Discussion of Results & Conclusions In this study, a neural network model was developed based on palaeogeography and evolutionary analysis of brachiopods in North America, and a back-propagation neural network model was created to estimate the location of the Rhynchotrema and Hiscobeccus specimens, based on a set of nine morphometric data (Nouri-Taleghani et al. 2015; Abdizadeh et al. 2017; Farzi et al. 2017) (Fig. 4). In this method, after entering the dataset, an artificial intelligence model learns the morphological features of brachiopods related to each geographical region and then estimates the geographical location of the brachiopods for new specimens. The neural network tries to relate these morphometric data to their location in order to predict their initial location by providing new morphometric measures to the neural network model. If the initial location of the brachiopods has been displaced by various factors, neural networks can estimate the initial location of those brachiopods with high accuracy. In this method, the input (morphometric data) and output (brachiopod location) are divided into a training set (to learn the input and output patterns), a validation set (for overtraining prevention), and a test set (for reliability measurement of the neural network). Localities identified based on laboratory measurements of Rhynchotrema-Hiscobeccus brachiopods are: 15862 (Baffin); 0–104507 (Baffin); 0–104517 (Baffin); GSC 113531–113541 (Baffin); GSC 205924 (Advance Formation, Rocky Mountains), GSC 1603 (Bay of Quinte, Ontario), NAPC-Pre Stop 1B (Bromley Member, Lexington limestone, Kentucky), Ottawa-1 (Ottawa), Mara 1(0–2) (Lake Simcoe area, Ontario), MN-10 (Minnesota), GSC Loc. C-205929 (Stony Mountain, Manitoba), C-7a- 77 (Waynesville and Liberty, Ohio). Codes 1 to 12 were assigned to the 12 locations, in order to be identified by the neural network program in MATLAB software. Two-thirds of the data were used for training and one-third of the data were used for validating and testing in the neural network model. From a total of 160 brachiopod samples, 52 samples (33%) were randomly selected as test samples, and 108 samples were used for training the neural network model. The morphometric data including L, L1, W, W1, W2, T, T1, AA and LN were used as the input data (Fig. 3). The matrix diagram indicates the interrelationships of morphometric data measured on 160 brachiopod samples and there is a good correlation between the input data of the neural network model (Figs. 4 and 5). Twelve neurons in the input layer, and one neuron in the output layer were used. Figure (6) shows the TANSIG and PURLIN transfer functions which were considered from layers one to two and from layers two to three. In order to measure the reliability of the neural network model, the mean square error performance function was used. For training the neural network model, the Bayesian training function (trainbr) was used. Based on the training algorithm and after 146 periods, the training error decreased, but the validation error increased (Fig. 7). The optimized weights and bias values ​​were obtained when the network training was stopped when a period was at 146. The graphical images showing the gradient, mu, Gam

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