Evaluating at-sea sampling designs for Marbled Murrelets using a spatially explicit model

Spatial environmental gradients can greatly affect the distribution of organisms, but studies investigating how the spatial arrangement of samples along these gradients influences power of monitoring programs to detect trends are lacking. Spatial gradients in environmental processes may remain relatively constant, or change over different time intervals and spatial dimensions. We investigated the influence of transect layout and replication on the power to detect population declines in the Marbled Murrelet (Brachyramphus marmoratus), a threatened seabird found in a highly dynamic nearshore environment. In Marbled Murrelet populations in our study area, no a priori gradient along the shoreline was apparent, whereas a predictable decline in abundance offshore occurred. We characterized the spatial and temporal variation in the offshore gradient by: (1) fitting flexible curves to historical abundance data from 13 site–year combinations in California and Oregon and (2) applying clustering routines to the fitted offshore probability distributions to reveal three distribution patterns that varied among sites and annually within sites. Power of sampling schemes was derived by a simulation where nine transect designs of equal effort detected population declines over 10 years within an 80 km × 2.5 km sampling unit either with or without stratification, based on data-generating distributions that were an approximation to the observed data. Our simulations suggested several designs had high power to detect trends at an annual decline rate of 2, 4, and 6%, produced relatively unbiased population estimates and slopes of the trend, and were logistically feasible: (1) stratified and unstratified zigzags and (2) ten 8 km transects placed at random distances parallel to shore in two strata. For murrelets, layouts that adequately sample along-shore and offshore in both high-density and low-density areas were most robust to heterogeneity and shifting environmental gradients in both along-shore and offshore dimensions. Our approach shows how pilot survey data and an understanding of spatial gradients or heterogeneity can help design a powerful sampling layout.