Accurately estimating effective population size (N_e) is essential for understanding evolutionary processes and guiding conservation efforts. This study investigates N_e estimation methods in spatially structured populations using a population of moor frog (Rana arvalis) as a case study. We assessed the behaviour of N_e estimates derived from the linkage disequilibrium (LD) method as we changed the spatial configuration of samples. Moor frog eggs were sampled from 25 breeding patches (i.e., separate vernal ponds, ditches or parts of larger fens) within a single population, revealing an isolation-by-distance pattern and a local spatial genetic structure. Varying buffer sizes around each patch were used to examine the impact of sampling window size on the estimation of effective number of breeders (N_b). Our results indicate a downward bias in LD N_b estimates with increasing buffer size, suggesting an underestimation of N_b. The observed bias is attributed to LD resulting from including genetically divergent individuals (mixture-LD) confounding LD due to drift. This emphasises the significance of considering even subtle spatial genetic patterns. The implications of these findings are discussed, emphasising the need to account for spatial genetic structure to accurately assess population viability and inform conservation efforts. This study contributes to our understanding of the challenges associated with N_e estimation in spatially structured populations and underscores the importance of refining methodologies to address population-specific spatial dynamics for effective conservation planning and management.

The study site of c. 200 ha is part of the nature reserve and military domain ‘Klein Schietveld’ in Kapellen near Antwerp, Belgium (51.358 N, 4.495 E; Fig. S1). In March 2017, heathland pools, fens and temporary ponds were screened for the presence of egg clutches possibly belonging to moor frogs. In total, eggs were sampled in 26 locations where clusters of clutches were found. These locations consisted of separate vernal ponds, ditches or parts of larger fens; they are called ‘breeding patches’ from now on. In each breeding patch, up to 50 intact and distinguishable clutches were sampled and three eggs per clutch were taken. The eggs were stored in pond water in a refrigerator until DNA-extraction (maximally a few days after sampling). DNA-extraction was performed on two eggs per clutch. The jelly coats were first removed using a scalpel. DNA was extracted from the embryo’s using DNeasy Blood & Tissue Kit (Qiagen) with a lysis step of one hour and eluted in 70 μl AE buffer (elution performed twice). The integrity of DNA of 10 % of the samples was assessed on 1 % agarose gels, while the DNA concentration of all tissue samples was measured with Quant-iT Picogreen dsDNA Assay Kit (Invitrogen, Thermo Fisher Scientific) using a Synergy HT plate reader (BioTek). In order to make the distinction between samples from two different species, Rana arvalis and R. temporaria, DNA from one egg per clutch and from all larvae was analysed with the RFLP method of Palo and Merilä (2003).

The Rana arvalis eggs were genotyped at 19 microsatellite markers via multiplex PCR and genotyping analysis on an ABI 3500 Genetic Analyzer. Allele calls were scored using the GeneMapper v4.1 software with fragment sizes based on GeneScan 600 LIZ Size Standard. Negative controls were included in each 96‐well PCR to allow for detection of reagent contamination. Reproducibility was evaluated using 3 % blindly replicated samples, two to five times within and across well plates. One reference sample was further added to each well plate. Samples with genotypes for less than 50 % of the loci were reanalysed or replaced with genotypes of eggs of the same clutch where possible.

The average error rate per locus was 1%. Three markers, Rtempμ4, Rtempμ5 and Rt2Ca2-22, showed no polymorphism and alleles of locus Rtempµ9 could not be identified unambiguously. Locus RECALQ showed deviations from Hardy-Weinberg equilibrium (HWE) in 5 breeding patches and proportions of null alleles higher than 0.20 in at least 10 breeding patches. Also, RlatCa41 deviated from HWE in 7 breeding patches and null alleles in at least 6 patches. Both markers were excluded from further analysis.