M

Here, the dependence of the cell probabilities on parameters fl via Eq. (3.1.1) is indicated explicitly by the notation L(fl|y) can be maximized effectively

1 Strictly speaking, we might prefer to qualify our analyses by noting that 'presence' here means observed or apparent presence but we are temporarily avoiding the conceptual and practical implications of that.

using standard numerical methods, e.g., as implemented in R using a number of nonlinear optimization routines, as we illustrate in the following section.

3.1.1 Modeling Species Distribution: Swiss Breeding Birds

We consider data from the Swiss Monitoring Haufige Brutvogel (MHB) - the Swiss Survey of Common Breeding Birds2. We will refer to this program as the Swiss Breeding Bird Survey, or Swiss BBS in some instances.

The Swiss BBS is an annual survey conducted during the breeding season. Sample units are 1 km2 quadrats that are sampled 2 or 3 times each by volunteer observers. Each observer surveys on foot a route of variable length (among quadrats) but consistent for all surveys of a given quadrat. Observers can also choose the intensity of sampling, i.e., the amount of time they spend surveying their chosen route. Thus, route selection, length, and situation within the quadrat are largely up to each observer. Data are collected using a method of territory mapping (Bibby et al., 1992) that involves significant interpretation on the part of the biologist, but yields a rich data structure that is amenable to a number of different analytic renderings. Routes aim to cover as large a proportion of a quadrat as possible and remain the same from year to year. During each survey, an observer marks every visual or acoustic contact with a potential breeding species on a large-scale map and notes additional information such as sex, behavior, territorial conflicts, location of pairs, or simultaneous observations of individuals from different territories. Date and time are also noted for each survey.

Detailed descriptions of the survey, the resulting data, and a number of different analyses can be found in Kery and Schmid (2004), Kery et al. (2005), Royle et al. (2005), Kery and Schmid (2006), Royle et al. (2007b), Royle and Kery (2007), and Kery (2008). Here we use data on the willow tit (Parus montanus) from 237 quadrats. Table 3.1 shows a subset of the data with the number of observed territories for each of 3 sample periods. For the present purposes, we have quantized the counts in Table 3.1 to simple presence/absence data, so that if the count is 1 or greater, it was set to 1 while observations of 0 remain so. For any model fitting, the covariates elevation and forest were standardized to have mean 0 and unit variance.

We will address a number of features of the data relevant to various analyses in this and subsequent chapters. First, the counts were typically made on different days for each quadrat. Second, both route length and survey effort (duration

2 We are immensely grateful to Hans Schmid and Marc Kery of the Swiss Ornithological Institute for making these data available to us.

Table 3.1. Swiss bird survey data consisting of 3 replicate quadrat counts of the willow tit (Parus montanus) during the breeding season and covariates elevation (meters above sea level) and forest cover (percent). Only a subset of quadrat counts are shown here. The symbol 'NA' indicates a missing value in an R data set.

Table 3.1. Swiss bird survey data consisting of 3 replicate quadrat counts of the willow tit (Parus montanus) during the breeding season and covariates elevation (meters above sea level) and forest cover (percent). Only a subset of quadrat counts are shown here. The symbol 'NA' indicates a missing value in an R data set.

repl

rep2

rep3

elevation

forest

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