Fig 1.
Map overview of the study area, showing the 5302 settlements areas, 7 aggregated regions and 28 districts used in this research.
Fig 2.
Workflow for Bulgarian settlement flow and terrain ruggedness analysis, showing data acquisition, processing, spatial interaction modeling analysis, and validation and the results steps.
Table 1.
Census years included in this analysis, the count of geocoded settlements per year and population totals.
Fig 3.
Showing the Open Source Routing Machine (OSRM)-based distances on the y-axis, against the Euclidean distances on the x-axis in kilometres for every origin–destination pair in our model.
Fig 4.
Overview of Bulgaria’s mountainous areas by average TRI value per settlement.
Higher TRI values are considered more rugged areas in the country. Settlements are classified in 5 categories in a quantile distribution.
Fig 5.
Settlement-level model performance across intercensal periods (1934–1992) according to SRMSE, MAE, and MAPE values.
Colours range from purple (high accuracy) to yellow (low accuracy).
Table 2.
A combined table showing the best evaluation outputs based on predicted and observed populations based on census records.
Fig 6.
Network visualisation of predicted migration flows between settlements in Bulgaria.
Only flows over 1 are shown, highlighting major urban attractors such as Sofia and Plovdiv.
Fig 7.
Histograms and density plots showing settlement-level inflows, outflows, and net migration.
Table 3.
Predicted (model) vs. observed (Philipov, 1976) interregional migration flows aggregated to seven macro-regions; best unconstrained configuration from 1965–1975 applied.
Sofia is listed separately due to its distinct urban dynamics. Bottom panel reports cellwise relative differences (Eq 7); “–” indicates undefined values where the observed flow is zero.
Fig 8.
Box plots per year pair, ranging from the 5th to the 95th percentile whiskers.
They highlight the TRI compared with net migration analysis at the settlement level. Settlements were divided into 5 equal quantile groups based on TRI.
Fig 9.
Example showing the directional attraction of Plovdiv, compared with neighbouring settlements in the highest ruggedness quantile (Q5).
Fig 10.
Figure showing the top-ranking destinations of migrants of rugged or mountainous regions, per year pair.