Field data from standardised surveys of stoats have been available for decades, but simple descriptive approaches and limited computer capabilities once hampered answering some critical questions. Now, new statistical approaches, run on ever-more powerful computers, can test hypotheses related to those questions. The probability of stoat capture is low, especially on widely spaced trap lines and when mice are not abundant. Stoat populations are patchy, and personality and experience make some individuals especially unlikely to enter a trap. Both of these factors violate essential assumptions of uniform or normal distribution and of equal detectabilities. Standard models of the population dynamics based on capture records can analyse the impacts of trapping on stoat populations. A more sophisticated model for managing unstable populations of stoats in beech forests (Chap. 5 ) from data with access to variations in age-specific mortality and fertility through the masting cycle can allow for natural mortality. Stoats eat fewer rodents per head than assumed, and cannot prevent post-seedfall rodent irruptions, depress their peak numbers, or delay the next irruption set off by the independent processes controlling mast seeding. Whether removing stoats releases higher numbers of rats or not varies with complex geographic patterns of rodent dynamics.