PREAMBULO ANTECEDENTES
2 MARCO TEORICO
2.10. Categorías específicas de áreas que existen
Recall in Section 5.2.2 of Chapter 5, the trials survey is conducted by position- ing a trial trap some pre-determined distance and random direction away from a known-location animal. After a set period of time (e.g., one night), the trap is checked to see if the known-location animal was captured or not. One trial is set per individual, per time period (e.g., night). The animals upon which trials are performed were selected in proportion to their expected frequency in the main survey data (i.e., highly detectable individuals were over-represented in the trials survey). Although this is a realistic scenario to what would occur when implementing the method in the field, it will lead to bias in population es- timates when underlying between-group heterogeneity is ignored (see Simulation 2, page 114). Since the underlying true detection function is unknown to the field observer, different methods will perform differently under different detection function scenarios. Four methods for selecting trial distances were investigated:
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Figure 6.2: Plot of a single realisation of the main survey simulation, based on three detection function scenarios. The main survey was a 10 trap by 15 trap grid (trap location shown as an “x”), with a 250 m horizontal and vertical inter-trap spacing, located in a survey area of 3,000 m by 4,300 m. The total number of individuals in the main survey was 2,000 (equal ratio between groups of animals where applicable, i.e., scenarios “Medium” and “Low”). Panel A) All individuals had a single “High” probability detection function, and 22 individuals were detected (solid circle). Panel B) Individuals were separated into two groups, the first with “High” detectability (eight individuals detected, solid square), the second with “Medium” detectability (three individuals detected, solid triangle). Panel C) Individuals were separated into two groups, the first with “High” detectability (seven individuals detected, solid square), the second with “Low” detectability (four individuals detected, solid triangle). See Section 6.2.1 and Figure 6.1 for detectability group definition. Undetected individuals are shown as a small solid grey circle.
Uniform: Trial distances are selected uniformly between 1 m and w(the trun- cation distance, here 125 m). For example, if 40 trials are conducted per individual (i.e., one trial every night for 40 nights), the distance between each trial trap would be ≈ 3.2 m (Figure 6.3A). If the true underlying detection probability decreases rapidly with increasing distance from the trap, and the probability of detection is essentially zero at distances much shorter than w (i.e., trials at distances > 60 m in Figure 6.3A), a large proportion of trials may be with traps placed in the “tail” of the detection function. This is an inefficient use of survey effort as most trials at these long distances will be unsuccessful, and the trial surveys will provide little information for estimating the detection function.
Stopping Rule with 5 consecutive unsuccessful trials: Trial distances are distributed as per the “Uniform” method, except that they start at 1 m, and continually increase in distance (e.g., a 3.2 m interval) until five consecutive trials were unsuccessful on the individual, or the distance w was reached. Trials on that individual then stop, and a new individual is selected (Figure 6.3B). The average number of trials per individual is 12, 11, and nine for the “High”, “Medium” and “Low” detection function scenarios, respectively1. Depending on the underlying true detection func- tion, the method may perform badly if the stopping rule is too short to capture the tail of the detection function (i.e., not enough trials at longer distances). Also, the cost (effort) of the survey prior to starting can only be approximated, because it is not exactly known how many trials will be completed on each individual.
1
Average number of trials per individual for each detection function scenario were calculated using simulation. Trials were performed on 10,000 individuals and the average number of trials per individual was calculated.
Stopping Rule with 8 consecutive unsuccessful trials: As per the previ- ous method, however eight consecutive unsuccessful trials were required before the survey was stopped and a new individual was selected (Figure 6.3C). The average number of trials per individual is 15, 14, and 13 for the “High”, “Medium” and “Low” detection function scenarios, respectively. Similar issues to “Stopping Rule 5” occur (i.e., can only approximate cost of survey prior to starting, and the stopping rule used may be inappropriate for the true detection function).
Adaptive: Half the trial survey effort was allocated using the “Uniform” method, and a preliminary detection function was fitted (Figure 6.4A). The remain- ing survey effort was then allocated between 0 and w m, according to the cumulative distribution function (CDF) of detection distances, estimated using the data from the initial uniform trials. Values systematically dis- tributed between 0 and 1 were back-transformed through the fitted CDF to generate trial distances (Figure 6.4B). This results in more trials at shorter distances, and fewer trials at distances in the tail of the detection function. The detection function used in the final abundance estimation is based on all trials conducted in both the uniform and adaptive phases of the trial survey. For example, if 40 trials are conducted per individual, 20 are allocated using the uniform method, and 20 are allocated based on the CDF of the detection distances, and trial results are combined to estimate the detection function (Figure 6.4C).
6.2.4 Estimating abundance
Using data obtained from the trial and main survey simulations, two abundance estimators were used as per methods detailed in Section 5.3.2 on page 81. They are: ˆ N2 = A Ac n X i=1 1 Eb[ ˆP(gi)] ˆ N3 = A Ac n X i=1 Eb " 1 ˆ P(gi) #
where A is the area of the survey region (=3,000×4,300 m2), Ac is the area of
the covered region (=kπw2, wherekis the number of sample points in the main survey andw= 125), and ˆP(gi) is the estimated probability of detecting theith
animal captured in the main survey, given it is in groupg. If the group covariate is unknown, then the detection function is assumed to depend only on distance, and no other covariates. Variance estimation followed using a bootstrap, as presented in Section 5.3.3.
99 function with parameters specified by the “High” detection function scenario. In this example, a maximum of 40 trials were
performed per individual. Panel A) Trial distances were selected uniformly between 1 m and 125 m. Three were successful. Panel B) Trials started at distance 1 m, and increased until five consecutive trials were unsuccessful. In this instance, 14 trials were undertaken (seven were successful) before the survey ceased. On average, 12 trials are conducted per individual using this method, and for these detection function parameters. Panel C) As per B) but eight consecutive trials were required before the trial survey ceased. In this instance, 15 trials were undertaken (five were successful) before the survey ceased. On average, 15 trials are conducted per individual using this method, and for these detection function parameters.
100 Half of the trial survey effort (i.e., here, 20 trials) were uniformly positioned between 1 m andw. Two trials (solid circles) were
successful (18 trials, hollow circles, were unsuccessful). A preliminary detection function is fitted to the preliminary trial survey data (from multiple individuals) and a new set of trials is selected uniformly between 0 and 1, that were back-transformed through the fitted CDF of detection distances (Panel B). Most trials in the second phase of the survey are at shorter trial distances (Panel C, seven trials shown as solid triangles were successful, 13 were unsuccessful).