# Mark Recapture Technique Assumptions And Critical Thinking

## Introduction

Population size is often the variable of interest in long-term population monitoring programmes, yet it is difficult to accurately measure in many animal species. Unbiased estimators of population size (*N*) are generally obtained by correcting count data using estimates of detection probability (Seber 1982; Lancia, Nichols & Pollock 1994), with many methods involving some form of capture–recapture sampling (Williams, Nichols & Conroy 2002). Conventional and spatially explicit capture–recapture modelling methods rely on uniquely marked animals (Williams, Nichols & Conroy 2002; Royle & Young 2008) and are well established in the literature. In these methods, individuals are uniquely identified during two or more encounter occasions and the data consist of the set of resulting capture histories, each representing the temporal or spatiotemporal sequence of detections and non-detections. While these methods produce highly accurate estimates of population size, the repeated efforts to capture and tag individuals may be incompatible with conservation strategies for sensitive species and can be costly, especially for long-term monitoring (Pollock *et al.* 2002). Moreover, it can be difficult to capture a large enough sample of individuals and trapping and marking may affect animal behaviours, which can bias estimates of population size; therefore, non-invasive methods for estimating population size that do not rely on trapping are preferred (Greenwood & Robinson 2006).

Multiple new approaches, including the use of digital photography (Goswami, Madhusudan & Karanth 2007), digital sound recording (Efford, Dawson & Borchers 2009) and DNA sampling (Waits 2004) are now available for conducting capture–recapture surveys without physically capturing animals. Recently developed spatially explicit capture–recapture modelling methods use spatiotemporal animal locations to estimate the density of central locations (e.g. individual activity centres) of animals (Efford 2004; Dawson & Efford 2009), but locations are either from physically tagged, naturally marked or uniquely vocal individuals surveyed using a sampling array. Alternatively, the model of Royle & Young (2008) accounts for a two-dimensional spatial point process from the central locations of animals collected without a sampling array; however, this method still requires that all animals be marked. Such methods may be impractical for monitoring dense populations of species that lack natural characteristics for uniquely identifying individuals. For example, capture–recapture methods have been rarely used to estimate the size of avian populations due to the difficulty of capturing and marking individuals (Gibbons & Gregory 2006).

One method that has been used to estimate population size with capture–recapture methods without capturing individuals is the mapping of geographic locations (i.e. point coordinates) of conspicuous inanimate objects related to abundance (e.g. nests; Lancia, Nichols & Pollock 1994; Williams, Nichols & Conroy 2002:291). Applying this technique to untagged animals requires the assumption that individuals utilize a unique spatial area; the parameter estimated is the number of occupied home ranges or territories rather than overall population abundance. However, as animals are mobile and not physically marked, this method presents the problem of inexact identification, which violates a key assumption of capture–recapture models: that ‘tags’ are correctly identified and not lost (Pollock & Kendall 1987). When point coordinates from untagged individuals are used as tags, each movement within the study area by an animal can equate to a lost or incorrectly identified tag in subsequent capture–recapture sampling occasions. This would cause the omission of recaptures and incorrect addition of new captures, both of which may lead to biased high estimates of abundance (Williams, Nichols & Conroy 2002:306).

The earliest example of using geographic locations of animals to build encounter histories we are aware of is from Hewitt (1967), who conducted repeated surveys of breeding red-winged blackbirds *Agelaius phoeniceus* and applied the Lincoln–Petersen estimator to estimate abundance (Petersen 1896). Fletcher & Hutto (2006) expanded on this by using point coordinates of multiple species of birds recorded during double observer surveys along a river. These studies attempted to resolve the problem of inexact identification using a combination of landmarks, vegetation cover, speed of a survey vehicle, bird behaviours, distances between locations and the removal of some observations to assign encounters as recaptures or new marks. Although Hewitt’s (1967) population estimates were consistent (Francis 1973), these solutions lacked standardization within and among surveys and may have contributed to unknown levels of bias in the resulting population estimates. Subsequently, the use of point coordinates for constructing capture–recapture encounter histories has not been widely adopted or applied to encounter histories with more than two encounter occasions. A standardized method of processing such spatially explicit count data from two or more encounter occasions is needed before point coordinates can be used to reliably estimate the size of animal populations, especially for long-term monitoring.

We developed a two-stage approach to constructing spatially explicit capture–recapture encounter histories from locations of unmarked animals acquired over two or more encounter occasions for analysis with conventional capture–recapture models. The locations are recorded as point coordinates and the parameter of interest is abundance of individual activity centres. The development of point-coordinate capture–recapture (PCCR) encounter histories is simple, flexible and extensible. We demonstrate this method with a PCCR survey of burrowing owls *Athene cunicularia* in the Imperial Valley of California, USA. This species has special conservation status (US Fish and Wildlife Service 2002) and is difficult to monitor due to variable and occasionally high densities across large areas and the lack of uniquely identifiable characteristics among individuals (Holroyd, Rodríquez-Estrella & Sheffield 2001). These owls are conspicuous in the breeding season, when they actively defend their nests during the day (Coulombe 1971; Martin 1973), thus using their nest burrow as an activity centre. However, they also occasionally travel between breeding territories (Coulombe 1971; Rosenberg & Haley 2004). We examined the robustness of the PCCR method to movements beyond those observed in our owl example by performing bootstrapping on an independent data set of owl locations derived from continuous observations throughout the day. We also carried out simulations to evaluate the utility of this technique for other species under variable detection probabilities, levels of territorial overlap and distribution of activity centres within a survey area.

## Materials and methods

### Data and method

We developed a two-stage approach for constructing spatially explicit capture–recapture encounter histories from point locations of unmarked individuals. First, a summary statistic of the maximum distance moved (MDM) by individuals from their activity centres is calculated from an empirical distribution of distances moved during a time representative of when population surveys will take place (e.g. incubation period for birds). Second, sampling is conducted during two or more PCCR encounter occasions under closed-population conditions (Otis *et al.* 1978) that involve recording only a single point-coordinate location for each unmarked individual during each occasion. Two-stage approaches have been used to develop other population estimators (Johnson, Pollock & Montalbano 1989; Pearse *et al.* 2008), and reliance on the is analogous to using prior information on animal movements for estimating space use and resource selection (Boyce *et al.* 2003; Horne *et al.* 2007; Forester, Im & Rathouz 2009).

The locations from the PCCR surveys are processed with proximity rules, defined in the following section and informed by the site specific , to estimate the location of activity centres and construct the PCCR encounter histories. Once obtained, the can be applied to long-term monitoring programmes of abundance of activity centres as long as environmental conditions remain stable. We emphasize that the PCCR method is based on an ‘area search’ without a predefined sampling array, and observed coordinates may be anywhere within the delineated sampling area. Here, detection is a function of the species characteristics and survey protocol, and methods to increase detection probabilities and avoid double counting of individuals are survey protocol issues that we consider later.

We suppose that a population consists of *N* individuals (or breeding pairs), where each has a centre of activity or home range centre. During PCCR surveys (stage two), a point coordinate is not observed for every individual due to imperfect sampling of individuals, nor do we necessarily observe individuals at their activity centres. Utilization around the activity centre is assumed to be unimodal; observations are drawn from a utilization distribution with the highest probabilities centred on the activity centre (A). We do not assign a biological meaning to this concept but rather provide a concise mathematical definition for estimating the activity centre as

where *x*_{ij} and *y*_{ij} represent the point coordinates from individual *i* on the *j*th sampling occasion. With each additional occasion, this centroid of observed locations should tend towards the activity centre. Only the first observed location of an individual is recorded during a survey occasion, and approaches to ensure this are design and protocol issues. Home range boundaries and activity centres are assumed to remain constant during the period of population sampling, but individuals are presumed to move within their home range.

#### Maximum distance moved

The is a critical parameter in the PCCR process because it represents half the distance within which two captures on different occasions will be considered the same individual. That is, the is the radius of a circle around the activity centre where an individual is expected to occur. This parameter should be estimated from an independent sample of individuals in the study area during a season equivalent to when PCCR sampling would occur and, once established, can be repeatedly applied to long-term monitoring.

The maximum distances of observed individuals are independent normals so that maximum distance ∼ Normal(MDM, *σ*^{2}); a maximum likelihood estimate of MDM is

where *d*_{i} is the maximum distance for individual *i* from a sample of *n* individuals.

#### Point-coordinate capture–recapture encounter histories

The second stage of the PCCR method involves using the to process the *k* point-coordinate locations from the *j* encounter occasions into encounter histories according to the following proximity rules:

*Encounter occasion 1*. Each of the *k* locations recorded on the first of *j* PCCR encounter occasions is from a different individual and is assigned a unique individual ‘tag’ identification number (*i*).

*Encounter occasion 2*. The *k*_{1} and *k*_{2} locations from the first two occasions and the distance (*D*) between locations from each occasion are used to construct PCCR encounter histories (EH_{PCCR}), such that

For activity centres detected on both occasions (11), the locations are used to calculate , which replaces the corresponding *k*_{j−1 } for the subsequent sampling occasion. Thus, the spatiotemporal data set used to develop PCCR encounter histories is comprised of single locations from home ranges encountered on only one of the two occasions (10 or 01, depending on the occasion detected) and for those encountered on both occasions (11).

*Encounter occasion 3+.* Here, we consider PCCR data from three or more occasions (i.e. *j *>* *2). Let all and *k*_{j}s from the previous occasion (*j* − 1) be *k*_{j−1}, and use the *k* locations from occasion *j* and the distances between the *k*_{j−1} and *k*_{j} locations to develop PCCR encounter histories (), so that

We assume that the population is demographically closed (Otis *et al.* 1978; Seber 1982), sampling occasions are independent, all individuals occupy home ranges, double counting of individuals within a sampling occasion does not occur, and detection probabilities (*p*) within an occasion are homogeneous among individuals across the sampling area (but may differ between occasions). Thus, repeated encounters of individuals within population *s* are viewed as independent encounters of a binomial random variable with parameters *N*_{s} (abundance) and *p*_{s}, and can be used to construct PCCR encounter histories for analysis with conventional closed capture–recapture models.

### Burrowing owl field study

We conducted PCCR surveys of burrowing owls in the Imperial Valley of California, USA. The Imperial Valley is largely cultivated for agricultural production. The terrain was relatively flat, with incised channels constructed for conveyance of irrigation water. As is commonly the case with burrowing owls in agricultural environments, nesting was restricted largely to within or along the banks of irrigation drains, canals and ditches that border agricultural fields and roads. We conducted owl surveys along seven randomly selected 1- to 2-km nesting areas.

#### Known size of burrowing owl population

For comparison with PCCR estimates, we conducted intensive banding efforts and located all nest burrows to determine the size of the population in the survey area. We captured resident male owls between 11 February and 11 April 2007 using noose carpets and Bal-Chatris traps (Collister 1967; Bloom 1987). Each owl was fitted with US Fish and Wildlife Service and coloured alphanumeric leg bands. We determined the sex of each banded owl by the presence of a brood patch and behavioural observations from at least three additional diurnal surveys in April. Of 40 pairs present along the survey routes, we banded 32 males and were unable to capture the remaining eight owls. We retained the eight unbanded males for acquiring locations because they used burrows situated between burrows occupied by banded owls, thus enabling us to distinguish them.

#### Estimation of maximum distance moved

One observer continuously tracked each male owl with binoculars and a spotting scope, recording perch locations every 15 min as well as other perch locations that coincided with movements >1 m during a 13-h consecutive observation period between sunrise and sunset in April 2007. Owls were observed from vehicles parked approximately 160 m away because owls in agricultural areas tend not to respond to parked vehicles at that distance (Coulombe 1971; Conway & Simon 2003). We used the global positioning system (GPS) location of the observer and the distance and bearing to an owl to determine perch locations. The flat agricultural landscape enabled us to maintain sight of owls even when they travelled far distances. We considered the burrow entrance with the greatest amount of sign (e.g. an owl retreated or flushed from burrow, regurgitated pellets, feathers, nest lining, whitewash or footprints with the absence of cobwebs) in each territory to be the primary activity centre, and recorded its GPS location. We measured the distance between an owl’s primary nest burrow and its perch locations using ArcGis 9.2 (ESRI, Redlands, CA, USA), and used these to calculate .

#### Point-coordinate capture–recapture surveys of burrowing owls

We conducted four PCCR encounter occasions (one occasion per consecutive day) in each nesting area from 14 April to 3 May 2007. These surveys were conducted on different days and with different observers than the continuous tracking, with survey hours from ½-h after sunrise to 11:30 PST and 16:00 to ½-h before sundown to avoid issues with reduced availability of owls for detection due to being inside their burrows during midday (Coulombe 1971). Surveys were completed during the incubation stage of the breeding cycle (April; Coulombe 1971), when females incubate inside the nest burrow and males remain sentinel outside the nest entrance (Martin 1973). We surveyed in the same direction by vehicle each time, travelling 11 km h^{−1}, with one observer and one driver without the aid of optical equipment. Detection was presumed to be constant out to the edge of agricultural fields (∼15 m) and survey vehicles advanced towards owl territories while surveying along the linear nesting areas.

We stopped at every burrowing owl detected, and recorded the date, time, GPS coordinates of the observer and rangefinder distance and compass direction to the perch location where the owl was first observed. We used these data in ArcGis 9.2 to determine the point coordinates of each owl location in each occasion. To avoid double counting within an occasion, we did not count owls only seen flying and visually tracked owls that flew ahead on the survey route after they had been recorded. Although we expected only male owls to be present outside the burrow during surveys, we further avoided double counting of territories that could arise by the occasional presence of the female by recording owls <20 m apart as a single observation. This was based on a previous study in a portion of this area that found the preponderance of distances between burrows to be >20 m (Rosenberg & Haley 2004). When an owl was <20 m from an active nest detected by the observers during the survey, we recorded the location of the nearest nest burrow instead of the owl to improve the repeated assignment of owl encounters (e.g. recaptures) in the PCCR encounter history.

#### Point-coordinate capture–recapture estimate of burrowing owl population size

To process the locations into PCCR encounter histories, we developed an ArcGIS shapefile of owl locations for each PCCR encounter occasion and applied the proximity rules with the calculated above using an Arc Macro Language (ESRI) script. We fit closed-population models available in program mark 4.3 (Cooch 1999; White & Burnham 1999) to the PCCR encounter history, and considered the PCCR encounter history as a closed capture data type. We applied a sin link function and fit models that assumed that and recapture probability () were equal and constant [] or varied over time [], where time referred to occasions one, two, three and four. We used second-order Akaike’s information criterion corrected for small sample sizes (AIC_{c}; Akaike 1973; Burnham & Anderson 2002) to determine the most parsimonious model, and considered it to be the best model to obtain a PCCR estimate of We used a plot of deviance residuals to heuristically assess model fit.

### Burrowing owl simulation

To examine the sensitivity of population estimates to movements beyond those found in the owl example, we used locations from the consecutive observations of the 40 owls initially collected to estimate MDM. We simulated four PCCR sampling occasions from these data by bootstrapping a single location from the observed locations of each owl (Efron & Tibshirani 1993), and repeated this four times with replacement to simulate four PCCR survey occasions. We than randomly removed a sample of 12 owls from each occasion to simulate equal and constant and (=0·7, estimated using a pilot study). We considered the estimated in the owl example as the true MDM, applied our proximity rules to these four bootstrapped sampling occasions, and repeated these steps to construct a sample of PCCR encounter histories (*n *=* *15 iterations, at which point the variance had stabilized).

We used these data to assess the sensitivity of PCCR estimates to biased estimates of MDM, varying levels of *p*, and different population densities. To investigate the effects of biased estimates of MDM, we varied the MDM from 20–400% of the true MDM. We also assessed the effect of using an MDM estimated from maximum distances measured without knowledge of where the activity centre occurred during the first stage of the PCCR process by calculating the mean distance between all movement locations, which assumes that the activity centre is in the geometric centre of the home range. For these tests, we constructed closed capture–recapture models in program mark that assumed , as described above.

We compared the resulting PCCR population estimates to the known population size (*n* = 40), and assessed the sensitivity of the estimates to various *p*s by varying *p* from 0·6 and 0·9 while holding the true MDM constant. To evaluate sensitivity to population density, we used two subareas to reflect the bimodal nature of nest densities in the survey area. Density categories were low (7·0 home ranges per km) and high (15·0 home ranges per km). We again used the true MDM and compared the resulting estimates to the known number in each subarea.

### Animal activity centre simulation

We used simulations to test whether the PCCR method could be extended to other species and environmental conditions beyond those which were represented in our empirical and simulated owl examples. We defined each simulated data set as having a true *N *=* *149, and established two spatial arrangements for grouping home ranges across a landscape: linear (to resemble distributions in narrow riparian corridors, hedge rows in an agricultural matrix, etc.) and two-dimensional patches. To these, we applied four levels of home range overlap (0%, 14%, 39% and 58%) and four levels of constant *p* (0·2, 0·4, 0·6 and 0·8; with *p *= *c*). We applied a two-dimensional distribution of locations, such that point locations∼Normal(30, 7·6), to each simulated home range to represent the utilization distribution of a central-place forager (Orians & Pearson 1979; Schoener 1979). We assumed that movements within home ranges were temporally and directionally independent, and generated random point coordinates for each survey in each home range. As the simulated utilization distributions were normal, the MDM was equal to the radius of the circle (30 m) and neighbouring activity centres were located 60 m apart. We used this MDM to construct PCCR encounter histories, and fit the same closed capture–recapture model used in the burrowing owl simulation to each encounter history. We also explored the sensitivity of PCCR population estimates to levels of sampling effort by varying the number of sampling occasions (*n *=* *3–6) in a patch configuration while holding *p *=* *0·5 and overlap at 39%. All analyses were based on 30 repetitions performed using Arc Macro Language programming. Results of all analyses are presented as means with 95% confidence intervals.

## Results

### Burrowing owl field study

Maximum distances owls moved from the nest throughout the day were normally distributed, with an of 58·4 m (46·2–70·5 m). Observers were able to locate birds at 95·4% of all time points during continuous observations. The best closed captures model fit to the burrowing owl PCCR encounter history provided an unbiased estimate of population size (, 39–41; Table 1). A symmetric and narrow pattern of deviance residuals close to zero suggested that the model fit the data well.

2 | 16·9 | 1·0 | 0 | |

(time) | 5 | 15·7 | 0·08 | 4·9 |

### Burrowing owl simulation

When we applied MDMs smaller than the true MDM to estimate population size, estimates were biased high; bias decreased as the MDMs increased from 10 to 55 m (<6% below the true MDM), at which point the population estimates were unbiased and precise (Fig. 1). Estimates remained unbiased until the applied MDM exceeded 75 m (>30% of the true MDM). The mean maximum distance between locations of each individual was 89 m, which produced estimates that were negatively biased (Fig. 1). When we set the MDM to an exaggerated 400% above the true MDM, estimates were biased low by approximately four owls (9%) from the true population size.

Population estimates modelled with *P *=* *0·6 and 0·9 were nearly identical to the true population size (Fig. 2), and density had no measurable effect on population estimates, which remained identical to the known numbers [seven owls per km, known *N *=* *6, 6·1 (5·8–6·5) and 15 km^{−1}, known *N *=* *7, 7·1 (6·8–7·5)].

### Animal activity centre simulation

Estimates of population size were unbiased and precise when *p* was high (≥0·8), regardless of the level of overlap between simulated home ranges or how they were distributed (Fig. 3). When population estimates were biased, estimates were always below the true population size. Bias increased with territorial overlap and decreased as *p* increased, and was slightly lower when home ranges were distributed linearly (Fig. 3). Precision increased as *p* and home range overlap increased (Fig. 3). Increased survey effort (i.e. number of occasions) improved precision, but had little effect on bias (Fig. 4). A summary of predicted bias in population estimates under various conditions is listed in Table 2.

Unbiased | High | Low | None (unbiased) |

Unbiased | High | High | Negative (slight) |

Unbiased | Low | Low | Negative |

Unbiased | Low | High | Negative |

Biased low | High | Low | Positive |

Biased low | High | High | Positive |

Biased low | Low | Low | Positive |

Biased low | Low | High | Positive |

Biased high | High | Low | Negative (slight) |

Biased high | High | High | Negative |

Biased high | Low | Low | Negative |

Biased high | Low | High | Negative |

## Discussion

Capture–recapture methods that do not rely on trapping are desirable for research and long-term monitoring of many species (Greenwood & Robinson 2006). We designed a two-stage process that accurately estimates population size with encounter histories constructed from the point coordinates of unmarked animals recorded during population surveys. Like conventional capture–recapture encounter histories, PCCR encounter histories can be analysed with closed-population models currently available in statistical packages such as program mark (Cooch 1999; White & Burnham 1999). The method is most appropriate for conspicuous species that utilize an activity centre. This is the first documentation of a standardized approach for using point coordinates of unmarked animals to construct capture–recapture encounter histories and generate unbiased population estimates in the presence of violating assumptions of no tag loss and correct tag identification.

The burrowing owl is a difficult species to monitor, especially in high-density areas because of the absence of distinguishable natural marks or vocalizations among individuals. The PCCR method presented here provides an alternative to conventional capture–recapture encounter histories and spatially explicit capture–recapture modelling that does not require animals to be captured. In our empirical example, we used this method to obtain an accurate estimate of population size from point-coordinate locations of burrowing owls in the Imperial Valley of California, USA. Although owls occasionally travel between breeding territories (Coulombe 1971; Rosenberg & Haley 2004), we found that owls moved short distances from their nests ( = 58·4 m), as was expected during the incubation period (Martin 1973), and had high probabilities of detection. Population surveys of this species conducted when owls are more mobile or in different habitat types would require season- and habitat-specific MDMs to be estimated prior to analysing PCCR data.

Our burrowing owl simulations evaluated the performance of the PCCR method under situations in which the probabilities of detection, density of home ranges and distances moved differed from that in the owl example. We considered *p *=* *0·6 and 0·9, which is approximately 15% below and 28% above the *p* found in the owl example. These simulations suggest that the PCCR method produces unbiased estimates of burrowing owl population size, with confidence intervals overlapping true population size. Density (7 or 15 owls per km) also did not bias estimates.

Population estimates were unbiased when a distance between 1% below and 30% above the empirically estimated MDM was used, but applying a distance that was more than 1% below the estimated MDM led to misclassification of recaptures as new captures that biased population estimates high. By contrast, distances that were biased higher than the MDM led to low levels of bias (less than 10%). However, estimating the MDM as the mean distance between all movement locations without incorporating the location of the activity centre led to biased estimates of population size, indicating that activity centres were not on average located in the geometric centre of the home range. As the activity centre of many species is probably not in the geometric centre of the home range, we caution against using the mean distance between all movement locations, and cannot overemphasize the importance of accuracy in estimating the MDM from an activity centre. Even though the maximum likelihood estimator we used is asymptotically unbiased, the MDM may vary across population densities and habitats within a species’ range, and thus should be estimated directly for the population of interest. If the MDM is highly variable across space, bias may be avoided if the population can be divided into distinct areas (i.e. no neighbouring animals) that are similar in space use, with a different MDM applied to each area. In cases where individual heterogeneity in MDM is high but spatially unstructured, the application of the MDM in the PCCR method could lead to overestimates of population size; researchers may wish to conduct simulations of their system to determine whether this is an issue. Finally, MDM should be accurate as long as environmental conditions are stable but should be re-estimated periodically during long-term monitoring programmes to ensure that changes are detected.

## Summary

**1.** Estimating population size is a fundamental objective of many animal monitoring programmes. Capture–recapture methods are often used to estimate population size from repeated sampling of uniquely marked animals, but capturing and marking animals can be cost prohibitive and affect animal behaviours, which can bias population estimates.

**2.** We developed a method to construct spatially explicit capture–recapture encounter histories from locations of unmarked animals for estimating population size with conventional capture–recapture models. Prior estimates of the maximum distance individuals move in the population is used to set a summary statistic and process subsequent capture–recapture survey data. Animal locations are recorded as point coordinates during survey occasions, and the parameter of interest is abundance of individual activity centres.

**3.** We applied this method to data from a point-coordinate capture–recapture survey of burrowing owls *Athene cunicularia* in the Imperial Valley of California, USA. We also used simulations to examine the utility of this technique for additional species with variable detection probabilities, levels of home range overlap and distributions of activity centres within a survey area.

**4.** The estimates from empirical and simulation studies were precise and unbiased when detection probabilities were high and territorial overlap was low.

**5.** This method of estimating population size from point locations fills a gap in non-invasive census and long-term monitoring methods available for conspicuous species and provides accurate estimates of burrowing owl territory abundance. The method requires high detection probabilities, low levels of home range overlap and that individuals use activity centres. We believe that these requirements can be met, with suitable survey protocols, for numerous songbird and reptile species.

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