The study of the morphology of stone artifacts and their spatio-temporal changes in form has gained great importance in Paleolithic archaeology today. This growing attention is due to the prevalent use of advanced multivariate statistical methods in archaeology, the growing connection between archaeologists and the specialists of life sciences (e.g., animal biosystematics) and programming languages, advances in modern technology and data acquisition, as well as the ability of the statistical shape analysis methods to answer some questions that have not been possible to answer or the answers lacked acceptable dose of objectivity. Nowadays, using the help of stone artifacts shape analysis, it is becoming more and more feasible to deal with some hithertho-impossible questions in various domains such as cognitive topics, technological organization, human behavioral ecology, cultures’ history, the mechanisms of cultural transmission, as well as the investigation on phylogenetic evolution of artifacts. Here, a 3-d geometric morphometric approach is used to dealing with the diachronic variabilities of stone tools in shape. The tools are flake-based and are recovered from the two MIS 3 archaeological layers of Mirak, an open-air Paleolithic site near the modern city of Semnan in the northern fringes of Iranian Central Desert. The research is done using both computer-based post-excavation analysis and library research method. The research main question is whether there are morphological differences between the two sets of flake-based lithic tools. The results of the morphometric study using dimensional reduction and multivariate statistical methods indicated that there is no statistically significant difference between the tools of the two layers (deposits) mentioned; put in another way, the morphology of the tools has not changed over time. It seems this is due to the presence of metapopulations and the resultant survival of technological information in the region of study, the stability in flake core reduction methods, and finally, the original morphology of lithic raw material. 

1. Introduction
The study of the morphology of stone artifacts and their spatio-temporal variabilities in form have gained great importance in Paleolithic archaeology today. This growing attention is due to the prevalent use of advanced multivariate statistical methods in archaeology, the growing connection between archaeologists and the specialists of life sciences (such as animal biosystematics) and programming languages, advances in modern technology and data acquisition, as well as the ability of the statistical shape analysis methods to answer the questions more objectivity. Various methods have been developed to study the morphological variability of stone artifacts through space and time; one of them is called geometric morphometrics (GM), meaning the application of the geometrical principles to the statistical study of morphology. In one of the three general modes of GM, called landmark-based GM, the shape of artifacts is examined using comparable landmark and semilandmark points created on the Cartesian coordinate system. Such points, created on a two- or three-dimensional image of stone artifacts could help to grasp the inter- and intra-assemblage shape variabilities via the help of multivariate statistics. As a result, the researcher could be able to address the variables involve in creating various shapes. The ultimate goal of such studies is to inspect the mechanisms and reasons behind in creating such variabilities; among them are stochasticity, the original shape and type of raw material, reduction intensity and technique, function, ecology, cultural traditions and biomechanical and cognitive differences. Here, this method is used to investigate on the shape variabilities of the flake-based stone tools recovered from Mirak Paleolithic site.
2. Materials and Methods
Here, a 3-d GM approach is used to dealing with the diachronic variabilities of stone tools in morphology. The tools are flake-based and are recovered from the two archaeological layers of Mirak, both of Marine Isotope Stage 3. Mirak is an open-air Paleolithic site located near the modern-day city of Semnan, Iran, at the northern edges of Iranian Central Desert. The statistical population is comprising of 76 tools, 31 of which from the younger layer (layer 2), and the remainder (45 specimens) of layer 3 (late Middle Paleolithic Period). Thus, here we are dealing with two groups of comparable materials from one Paleolithic landscape to investigate their similarities and differences through time (diachronic approach). After the preparation of the 3-d models of the lithic tools via light scanning (desktop Shining 3D scanner), the cloud points were analyzed using a shape analysis software called AGMT-3d and the help of some dimensionality reduction techniques such as principal component analysis. Finally, the data were assessed using some formal significance tests.
3. Results and Discussion
The results of the landmark-based GM study using dimensional reduction and multivariate statistical methods indicated that there are no statistically significant differences between the lithic tools of the two layers mentioned; put in another way, the morphology of the tools has not changed drastically over time. This may bear some implications for raw material original shape, the reduction techniques, population dynamics, and their adaptive strategies. As far as the general morphology has remained unchanged, this may imply the impact of the original lithic raw material shape, the presence of metapopulations in the landscape throughout MIS 3, and the flow of information regarding core reduction techniques. Due to the radical size differences between the lithic raw material scatters in the landscape and Mirak flake-based tools, it seems the form of lithic raw materials was not the main factor determining the shape of the tools. Additionally, the absence of flake cores makes the comparison of the shape and dimensions of the candidate raw materials and tools difficult, due to the fact that cores are intermediate forms influenced from the original lithic raw material form and have great impact on the morphology of the detached flake blanks. In addition to what mentioned, based on the fluctuations in climatic-environmental characteristics in the landscape throughout MIS 3, it seems the comparability of the blanks of the flake-based tools is not solely due to similar adaptive strategies in the two different time periods (layers 2 and 3), since the environement was probably different in Mirak landscape with rather unpredictable incidents in the two periods. Therefore, the comparability of the flake blanks in the two discontinuous archaeological sets in Mirak could probably be attributed to the population dynamics and the presence of metapopulations in the landscape which prevented the loss of previous information and techniques.     
4. Conclusion
Based on what mentioned, it seems at least part of the comparability of the flake debitages is due to the presence of metapopulations in the landscape and this fact that the populations did not abandon the region completely during the periods with unfavorable environmental characteristics. The reasons behind the sticking with the region was probably due to the existence of some small refugia, the candidates of which are the western part of the Iranian Central Plateau or the more northern landscapes than Mirak near the locations of the modern population centers in the region today. Therefore, despite the time gap between the two archaeological sets, part of the comparability of flake blanks shape in Mirak is due to the survival of information regarding the reduction techniques with the help of the interrelated populations in the region.