Mark recapture models

3.2.2.1. Robust design mark-recapture models

The abundance of bottlenose dolphins in the overall area and in St Andrews Bay was estimated using robust design (RD) models (Pollock, 1982, Kendall et al., 1995, Kendall et al., 1997). Within the RD, closed population models are applied to the secondary encounter occasions within each primary sampling period to provide an estimate of abundance ( . In this analysis, as in Chapter 2, each annual field season from May to September was treated as a primary sampling period, which was divided into multiple secondary sampling occasions by pulling together all sightings within each month. As detailed in Chapter 2, all photographs taken during the encounters with bottlenose dolphins were first graded for their photographic quality. All high quality pictures with grades 3.1, 3.2 and 3.3 (see Appendix 1c) were matched to a catalogue of known individual dolphins based on the natural marks on their dorsal fin. Only high quality pictures from marked individuals (i.e. with permanent marks such as nicks and notches) were used to construct capture histories, to define whether or not a marked individual was captured within a sampling period and area of interest. The number of secondary sampling occasions within each year and the number of marked individuals included in the analysis for both the overall study area and the subarea of St Andrews Bay are summarized in Table 3.1.

To estimate the abundance of animals using the overall area, a first attempt was made to fit models that could account for both temporary emigration and heterogeneity of

capture probabilities. The fitted models had two mixtures (Pledger, 2000) to account for heterogeneity of capture probabilities, allowed capture probabilities to vary between sampling occasions, and had either constant or time varying random or Markovian temporary emigration. However, the resulting models were over-parameterized with each model having between 294 to 338 parameters, and all models failed to estimate a large proportion of the temporary emigration and mixture parameters (not shown). Thus, models accounting for both temporary emigration and heterogeneity of capture probabilities were not considered further. Instead, the abundance of bottlenose dolphins was estimated from the most supported RD model accounting for temporary emigration

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in Chapter 2 (Model φ (.) g''(t)=g'(t) p(txs)in Table 2.4 from Chapter 2; see Chapter 2 for definitions of parameters). The effects of not accounting for heterogeneity of capture probabilities or not accounting for temporary emigration were also investigated (see section 3.2.5. ).

The St Andrews Bay area represents only a part of the population’s distributional range, and animals are known to move between areas within the range (Cheney et al., 2013). If animals spent time in other parts of the range, such as the Moray Firth, they might not have been available for sampling in St Andrews Bay for some of the years of the period 2009 to 2013. To account for this, a candidate set of models with no emigration, random and Markovian temporary emigration (Kendall et al., 1997) were fitted to the subset of capture histories of individuals encountered in St Andrews from 2009 to 2013. In all models, capture probabilities were allowed to vary between and within primary periods, based on the results from Chapter 2. Annual estimates of abundance of marked animals were derived from the most supported model from the candidate set, using Akaike’s Information Criterion adjusted for small sample size (AICc, Burnham and Anderson, 2002) for model selection.

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Table 3.1. Photo-identification survey effort conducted between 1990 and 2013 in the overall study area and between 2009 and 2013 in St Andrews Bay area (also included in the overall effort). Survey effort dates, number of secondary sampling occasions (i.e. months), and total and newly marked individuals annually captured in each area are shown.

Overall study area

Year Effort 2ary

occ Marked inds New inds 1990 03 May-14 Aug 4 47 13 1991 17 May-12 Sep 5 37 6 1992 14 May-24 Sep 5 51 6 1993 02 May-23 Sep 5 36 5 1994 02 Jun-24 Sep 4 36 2 1995 12 May-20 Sep 5 47 6 1996 07 May-05 Sep 5 39 5 1997 24 May-24 Sep 5 26 2 1998 18 May-22 Sep 5 28 2 1999 01 May-22 Sep 5 34 6 2000 01 May-19 Sep 5 34 5 2001 01 May-17 Sep 5 72 20 2002 01 May-09 Sep 5 65 8 2003 01 May-28 Sep 5 74 10 2004 02 May-11 Sep 5 87 7 2005 03 May-17 Sep 5 54 1 2006 04 May-25 Sep 5 84 8

2007 02 May-28 Sep 5 82 5 St Andrews Bay area

2008 06 May-26 Sep 5 41 1 Effort 2ary

occ

Marked inds

New inds

2009 02 May-30 Sep 5 89 13 21 Jun-24 Aug 3 43 43

2010 05 May-21 Sep 5 92 6 17 Jun-01 Sep 4 42 9

2011 03 May-29 Sep 5 89 3 10 Jun-31 Aug 3 42 4

2012 02 May-27 Sep 5 103 10 09 May-27 Sep 5 40 6

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3.2.2.2. Closed population models using CAPTURE

Only seven trips were conducted in Aberdeenshire between 2012 and 2013, providing too few sampling occasions to use a robust design approach to estimate the abundance of bottlenose dolphins in each year. Instead, a single abundance estimate was produced for both years combined. Each trip was a sampling occasion, resulting in a total of seven sampling occasions that were used to fit a closed population mark-recapture model. Program CAPTURE (Rexstad and Burnham, 1991), implemented within program MARK (White and Burnham, 1999), was used to determine the most appropriate closed population model to estimate the abundance of marked animals. By combining both years, the assumption of population closure was likely to be violated between the years, although that should only introduce a small bias on the abundance estimate. Closed population models within CAPTURE allow capture probabilities to be constant (Mo), to vary by time (Mt), or behaviour (Mb), to include individual heterogeneity (Mh), or be a combination of the basic models (Mth, Mtb, Mbh). The presence of heterogeneity in capture probabilities was further investigated by fitting a closed population model with two mixtures (Pledger, 2000) in program MARK (White and Burnham 1999).

Trip # Encounters Marked inds New inds

14 July 2012 1 5 5 08 Aug 2012 1 7 2 20 Sep 2012 1 5 2 09 Jun 2013 2 9 6 25 Jun 2013 3 5 2 09 Jul 2013 2 6 1 18 Jul 2013 2 7 1

Figure 3.5. Number of marked and newly marked individuals captured in each trip in Aberdeenshire in 2012 and 2013.

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