flapper: practitioner FAQsvignettes/flapper_algorithms_faqs.Rmd
flapper_algorithms_faqs.RmdThis vignette addresses frequently asked questions (FAQs) for
practitioners seeking to apply the flapper algorithms. For
further details, consult Lavender et al. (2023). To submit a
new question, go to https://github.com/edwardlavender/flapper/issues or
contact edward.lavender@eawag.ch.
There is no theoretical obstacle to the incorporation of
receiver-specific detection ranges or detection probability models that
vary by receiver (or other environmental variables). In flapper,
receiver-specific detection containers are passed as objects to the
relevant algorithm function (i.e., ac(),
acdc()). At the time of writing, the helper function used
to create detection containers (acs_setup_containers())
assumes the detection range is constant across receivers, but custom
detection containers could be created and passed to the algorithm
similarly. The same goes for detection probability kernels. Since these
objects are created in advance, custom inputs are efficiently
incorporated. However, for larger and/or more complex
containers/kernels, calculations may take longer.
Assuming that the clocks of receivers are aligned, a simultaneous detection of an individual at multiple receivers implies that the individual must have been located within the intersection of those receivers’ detection containers (at that moment in time), accounting for the set of possible previous and future locations. Within this region, the probability that the individual was in any given location depends on the detection probability model.
This depends on the algorithm, the size and shape of study area, the arrangement of receivers, the detection range and the movement capacity of the tagged animal. These factors affect both how quickly an animal can move away from an area and where it can go (i.e., the definition of ‘anywhere’). Take a circular study area of radius 1000 m with a single receiver at the centre where an individual is both located and detected. If we take a maximum swimming speed of 1 ms-1 and assume this can be maintained indefinitely then, by time \((s)=distance (m)/speed (ms^{-1})\), the individual could be located anywhere in the area after a detection gap of 1000 s (about 17 minutes). This calculation provides an indication of the duration between detections beyond which the set of possible locations for the individual (and our uncertainty in its location) is greatest and is effectively encapsulated by the AC/ACDC algorithm (assuming a ‘negligibly small’ detection container). Allowing for locational uncertainty within a detection container, then the time by which the individual could reach the boundaries of the study area could be smaller (because the starting position could be further away from the receiver), though the area in which the individual could be located following the detection is also reduced by the detection container (and the shape of the detection probability kernel within that region). If you refine the AC-branch outputs using the ACPF or ACDCPF algorithm, the set of possible locations of the individual may expand less rapidly in the gaps between detections, depending on the probability of different rates of movement (as defined by the movement model), the presence of additional constraints (such as the locations of receivers that did not record detections, the depth at each time step or movement barriers) and the stochastic sampling process. At the time of writing, we recommend researchers consider the duration of detection gaps in relation to these criteria and avoid implementing the algorithms over ‘long’ detection gaps when information on the location of an individual is limited. Ultimately, however, the definition of ‘long’ depends not only on the aforementioned criteria but also a study’s objectives. For example, in this study, we deliberately implement the algorithms over the complete detection time series for a one-month period for an example individual to test the hypothesis that the individual could have remained in the study area (a Marine Protected Area) over this time interval. For post-hoc evaluation of the influence of each time step on algorithm outputs, you can examine the shape of the probability distribution of the set of possible locations in which the individual could have been located through time.
The flapper algorithms simply resolve the set of locations in which a tag could have been located through time, given the data and supporting information (e.g., detection probability). They make no judgement about whether a tagged individual has died or expelled the transmitter. If you have a stationary tag regularly transmitting within the detection container of a receiver, then the set of possible locations for the tag is restricted by this information and this is what is recapitulated by the flapper algorithms. Overlapping receivers and/or ancillary observations place additional restrictions on the possible locations of a tag which can make it possible to determine location more precisely. However, if there are gaps in detections due to imperfect detection probability, then the flapper algorithms may also (correctly) permit limited movements beyond the receiver’s detection container (unless you have defined a movement model in which the probability of ‘movement’ is lower under certain conditions, for instance for individuals that were tagged in poor condition or after a certain period of time due to an increase in tag expulsion or mortality risk).
We reiterate: the algorithms simply provide an honest assessment of the set of possible locations that are consistent with the data through time. With any individual time series, this is the complete extent of our knowledge, and that is the point of the flapper algorithms. If you, as a researcher, have external information about the likelihood of tag expulsion or death from study of the detection patterns of multiple individuals, in which serially repeated detections are unusual, then you are at liberty to infer expulsion or mortality. In unclear cases with detection gaps, reconstructing the set of possible locations through time may help to suggest whether tag expulsion/mortality is a more likely explanation of the data (given the scale of possible movements away from receivers) than other possibilities, although some back-of-the-envelope calculations may be simpler. If you are confident about tag expulsion or mortality, we would generally recommend against implementing the flapper algorithms, although there are circumstances in which this could be useful (for example, identification of the possible location(s) of a stationary tag facilitates opportunistic study of detection probability).
Passive acoustic telemetry has opened the door to studies of individuals over extended time scales that may encompass seasonal, reproductive and ontogenetic changes in movement. In theory, these changes can be handled in the flapper algorithms through the incorporation of a time-varying movement model. However, behavioural switches need to be specified as part of the algorithm implementation: the flapper algorithms do not estimate movement parameters; they simply use the data to reconstruct the set of locations through time that is consistent with known properties of movement (and other algorithm components). That being said, in practice, we recommend structuring analyses on the basis of existing knowledge of animal movement and life history. If there are notable seasonal changes in movement, for instance, the simple approach is to implement separate, season-specific algorithms. Under specific conditions, no information is lost with this approach with existing routines. More generally, any information lost (from the end of one time series to the start of another) is negligible. Over longer, multi-annual time series, implementations of the flapper algorithms, as illustrated here, are likely to be prohibitively expensive in computational terms. Further work is needed to develop tailored methodologies that can handle these volumes of data. This includes computational optimisation of existing routines and consideration of the influence of algorithm resolution and data processing (e.g., thinning detections, as suggested by Aspillaga et al. [2019a]) on reconstructed patterns.
This is an important, and very general, query about how to reconcile datasets (such as animal tracks and environmental data products) that differ in resolution and uncertainty. There is a limited amount of specific advice we can offer in this context, but there are some important points that need to be made, starting with the resolution at which movements can be resolved. In this study, we develop the algorithms in discretised form, with locations represented on a uniform grid. The consequence of this approach is that grid resolution determines the resolution of the outputs and uncertainty (as measured by the number of locations on the grid in which an individual could have been located and their associated probabilities) is propagated accordingly. A large number of possible locations (with similar probabilities) reflects a high degree of uncertainty and a smaller number of locations (and/or a skewed probability distribution) reflects a lower degree of uncertainty. The degree of uncertainty at any one time depends on the strength of the constraints on individual location, including observations, array design, movement capacity and other parameters. This means that the spatial scale of uncertainty can be much smaller than the detection container of a receiver, or rather larger. In the ACPF algorithm, for instance, the growth, expansion and intersection of acoustic containers depends on array design, detection range, movement capacity and the detection time series. In the ACDCPF algorithm, the incorporation of depth time series can dramatically reduce uncertainty, as shown in this study. Both flapper algorithms are unique in that all of these properties of the system mechanistically determine uncertainty. Moreover, (almost) no further reductions in uncertainty can be achieved without the imposition of additional constraints (such as new data): the dynamics of the system are comprehensively represented. Incidentally, in all other methods, uncertainty is necessarily higher because only a subset of the full suite of constraints on individual location is incorporated. This point is not obvious because uncertainty is typically unquantified or only quantified indirectly by other methods, so the true level of uncertainty in an individual’s location is unknown.
What are the implications of high uncertainty for analyses of habitat use? It is true that when uncertainty is high and substrates are spatially heterogeneous, we can be less certain about the habitat use of an individual and the flapper algorithms will reflect this uncertainty. But here we are limited by the data and not the methodology. In fact, from a methodological perspective, the propagation of uncertainty is highly desirable because it safeguards against overconfident or misplaced inferences. As we show for the mean-position algorithm, failure to consider movements away from receivers can suggest highly biased patterns of habitat use (Fig. 3).
So how can we reconcile the resolution and uncertainty of the flapper algorithms with habitat data that differ in resolution and uncertainty? As noted above, this is a difficult question that pervades the fields of movement ecology and spatial modelling. In previous work investigating possible habitat preferences in flapper skate, we studied the distribution of environmental conditions within detection containers (Lavender et al., 2021). The flapper algorithms resolve movement both within and beyond detection containers, facilitating more holistic analyses of habitat preferences. In general, our approach is to use habitat data at the resolution and extent at which it is available. Where habitat data provide an important constraint on individual location and are used as part of a flapper algorithm, we suggest implementing the flapper algorithms at a similar resolution (where practical). For example, in this study, we incorporated a bathymetry layer at the original (5 x 5 m) resolution and resolved movements across the same grid. This approach trades off computation time with precision. In our study system, depth time series impose a strong constraint on location. This constraint dramatically weakens if you aggregate the data, which greatly reduces the utility of depth observations for reconstructing movements. We recommend practitioners consult the documentation of the process_surface() function for advice in this context.
Where the outputs of the flapper algorithms are combined with environmental data to infer habitat use, we also broadly favour using data at their original resolution. It is not clear what could be gained by aggregating (or disaggregating) data. As explained above, the precision with which movements are resolved by the flapper algorithm can change through time but uncertainty is propagated. Moreover, environmental datasets are often complex data products that incorporate observations, interpolation and modelling. Aggregation of these datasets can mask important variation and add another layer of complexity when it comes to understanding uncertainty that is usually swept under the rug. That being said, where aggregation (or disaggregation) is necessary, we encourage the use of simulations and comparisons (where feasible) to evaluate the influence of resolution on results.
Recall that in the PF-branch algorithm, a large number of particles are sampled at each time step. Consequently, if the gaps between detections span a large number of time steps, a large number of possible paths may be reconstructed between receivers that are consistent with the data (based on the connections between sequentially sampled particles). This is one of the key innovations of our method because it provides ‘a fuller exploration of possible movements than permitted under the assumption that individuals follow least-cost paths between detection containers’. The set of possible paths depends on the information that is available to constrain the location of the animal in the gaps between detections (i.e., the detection probability model and receiver positions, the movement model and additional constraints, such as depth observations and coastline). If there are few constraints on individual locations and the gaps between detections span multiple time steps, then different paths will ‘wander’ across the landscape, generating a relatively smooth surface that reflects our uncertainty in the possible location of the individual through time. If there are more constraints, the set of possible paths may be more tightly focussed and highlight several more-or-less likely ‘routes’ between receivers. Direct linear or least-cost transitions between detection containers are only likely to emerge if the time between detections is short (relative to the movement capacity), such that the individual could (or must have) moved directly from one to another during the detection gap.
The short answer to this is ‘no’. To see why, first consider passive acoustic telemetry in isolation. In an acoustic array, the information we have on an individual’s location is limited to detections at receivers, detection probability and movement capacity (in the context of barriers to movement, such as coastline). Of these sources of information, most approaches for modelling acoustic time series (including the mean-position algorithm) only consider detections at receivers, which means there is typically a high degree of uncertainty in the individual’s location through time (even if this is not represented). By considering the detection and movement processes that generate observations, the ACPF algorithm more effectively represents uncertainty, but it still exists. However, if we consider additional sources of information on individual location (which is possible within the flapper algorithms), our uncertainty can decrease. (This is naturally quantified by a reduction in the number of locations in which the individual could have been located, accounting for their relative probabilities.) Imagine we collect both acoustic and archival (depth) time series. Now, when an individual is detected, we know not only that it must be within the detection container of a receiver but we can identify the subset of locations that is also consistent with the observed depth. The same principle is true in the gaps between detections. These additional restrictions can lead to differences in maps of space use. It is not that a map constructed with acoustic time series alone is ‘wrong’ whilst one constructed with both acoustic and archival time series is ‘right’. With the flapper algorithms, both maps are valid representations of the individual’s possible locations, given the data, it’s just that depth observations place an additional restriction on location that refines the map. More generally, datasets that place multiple, distinct restrictions on location suggest more refined maps of space use. These differences are not only inevitable but desirable.
Quantification of the extent to which the addition of new datasets updates maps of space use is valuable because it indicates the relative amount of information contained within different datasets, which can guide tag and array deployment programmes. In our illustrative analyses of flapper skate, it is clear that the integration of both acoustic and archival data refines reconstructed patterns of space use (Fig. 3). This demonstrates the benefits of a coupled acoustic and archival tagging programme in our study area. Building on this work, where feasible, we encourage practitioners leading tag and array deployment programmes to evaluate the merits of designing systems that collect detections alongside ancillary data (such as depth observations). Obvious considerations concern the accuracy of ancillary data and the resolution of background (e.g., depth) layers. In general, if background data layers are relatively homogeneous, then collecting ancillary information is unlikely to refine maps of space use substantially and improvements to the receiver network may be a better use of limited resources (except perhaps in situations where background data resolution, while currently a limiting factor, is expected to improve). In contrast, if background data layers are heterogeneous, then coupling passive acoustic telemetry with ancillary information on individual habitat use has the potential to refine inferences and investments in ancillary recording capacities may be worthwhile. We support the use of simulation to explore the relative value of different datasets (though comparison of maps reconstructed from different combinations of information) and note the potential to integrate this research with economic modelling to design optimal array/tag deployment programmes that maximise the information gleaned for a given budget.
Where beneficial, we also encourage practitioners to exploit the flexibility of the flapper algorithms to incorporate multiple datasets by considering not only acoustic and archival time series, but other spatially or temporally heterogeneous data types as well (such as salinity or temperature). The construction of the algorithms provides a straightforward means to ‘slot in’ ancillary data in the same way that we incorporate depth time series. All you need is a model that compares ancillary observations and a background layer to describe the probability of an individual being in any given location through time, according to that particular dataset. This information can be combined with equivalent surfaces from the AC algorithm (via eqn 13 in Lavender et al. 2023) and PF can be implemented for the combined surfaces in the usual way. When you do this, do not feel disconcerted if the results change: it is a sign that your efforts have been worthwhile.
The choice of algorithm depends on data availability and study objectives. For reconstructing patterns of space use, the different algorithms suggest different patterns because they incorporate different information. Let’s use Fig. 3 in Lavender et al. (2023) to illustrate this point and clarify algorithm choice. Recall that Fig. 3A shows a map reconstructed from the depth time series; Fig. 3B–C show maps reconstructed from acoustic detections; and Fig. 3D shows a map based on both datasets. If you only have depth time series, or you are interested in the extent to which a region (such as a Marine Protected Area) represents the depths used by an individual, the DC algorithm (Fig. 3A), is the appropriate choice. If you only have detection data at receivers, you have the choice of a number of existing methods, such as the mean-position algorithm (Fig. 3B), or our ACPF algorithm (Fig. 3C). As noted in Lavender et al. (2023), the relative utility of these methods may vary in different settings but in clustered receiver arrays the mean-position algorithm may perform poorly (Fig. 3B) and the ACPF algorithm (Fig. 3C) is the clear choice here. If you have both depth and detection time series, the ACDCPF algorithm is a refinement. Thus, for flapper skate, the ACDCPF algorithm is the best choice when it comes to reconstructing patterns of space use and Fig. 3D is the most-refined map of space use for the analysed individual. In summary, the best algorithm for reconstructing patterns of space use depends on the data you have available: if you only have depth time series, use the DC algorithm; if you only have acoustic time series, use the ACPF algorithm; if you have both depth and acoustic data, then use the ACDCPF algorithm, which can integrate both types of data.
We have emphasised above that different algorithms can produce different patterns of space use (and we should not be disconcerted by this). The purpose of Fig. 3E is to take this point one step further and illustrate that differences in patterns of space use reconstructed by different methods have wider implications, using the example of sediment use. What Fig. 3E is showing is the proportion of each sediment type that is found within the core range suggested by each algorithm, as delineated in Figs 3B–D, relative to the proportional availability of each sediment type in the study area at large. According to the mean-position algorithm, the proportion of muddy sand in the individual’s core area substantially exceeds background levels. But the mean-position algorithm is strongly biased by the locations of receivers and this result is thus an artefact of COA’s localised distribution. By accounting for possible movement away from receivers, the flapper algorithms produce more informative maps of space use, as explained previously, and these suggest a different conclusion. According to both flapper algorithms, the use of muddy sand is not considerably higher than we might expect (given the prevalence of this sediment type in the study area) and the results instead point ‘towards the exploitation of multiple benthic habitats, in concordance with recent work’ (Thorburn et al., 2021). That being said, the most refined map of space use (Fig. 3D), which integrates information from both acoustic and archival time series, suggests that mud is used proportionally more than the other sediment types, relative to background availability. We should be cautious of overinterpreting this result for a single individual, but it highlights a potential habitat preference that is worthy of further study.
Simulations are a device we can use to explore algorithm behaviour and utility in different settings, but care is needed in the interpretation of such analyses. In the flapper algorithms, unlike other methods, it is necessarily true that maps reconstructed by (correctly specified) algorithm implementations will encompass the true path (given sufficient samples). In general terms, it is also true that we should expect a ‘reasonable’ match between simulated and reconstructed patterns, and that this match should often be better than for methods that do not encapsulate the processes that generate observations. However, what is ‘reasonable’ depends on the information provided by observations (and other algorithm components). In systems with ‘high’ information, there are strong restrictions on the possible locations of an individual though time and we expect a close match between simulated and reconstructed patterns. In contrast, in systems with low information (the typical case), there are fewer such restrictions and a wider range of movements could have generated the observations. In this kind of situation, movements beyond a simulated path allowed by the observations can lead to differences between that path, which is only one realisation of a particular data-generating process, and the reconstructed pattern, which encapsulates the range of movements that could have generated the observations. Thus, you should not be surprised if simulated and reconstructed patterns do not match perfectly.
There are important consequences of the representation of uncertainty in the flapper algorithms when it comes to comparing the fidelity with which different algorithms reconstruct a simulated path. As we show in this study, in any individual case, COAs from the mean-position algorithm may align more closely with the true path than particle samples from the flapper algorithms (for instance, because the latter permit movement into areas where the individual could have, but did not, venture). Since particle samples represent the distribution of possibilities, it is only on average (if one imagines many simulated outcomes of a data-generating process) that we expect (correctly specified) flapper algorithms to reconstruct the true path more accurately (especially in non-uniform arrays) than methods that do not recapitulate the data-generating process. That being said, we cannot at this stage discount the possibility that the mean-position algorithm (or other methods) may outperform the flapper algorithms in unexpected settings. We encourage the use of simulations to compare the behaviour of different approaches in different scenarios to guide analyses. A key avenue for future research is to develop quantitative metrics for the comparisons of simulated and modelled patterns of space use in different settings.
Alongside the fidelity with which the true path is reconstructed in any particular situation, the wider advantages and disadvantages of each method should be used to guide the choice of methodology. Important criteria include implementation ease, speed and study objectives. For example, by accounting for movement in the gaps between detections, the flapper algorithms are well-suited to studies of residency, whereas alternative methods (such as the mean-position algorithm, network analysis and Aspillaga et al.’s (2019a) synthetic-path method) are not.
The mobility parameter controls how far an individual can move in any given time step. Intuitively, under-estimation of mobility will lead to overly concentrated patterns of space use, while over-estimation of mobility will lead to overly diffuse patterns of space use. However, these two outcomes are not necessarily equally plausible. Algorithm sensitivity also depends on additional constraints, such as array design.
First, note that it can be quite hard to under-estimate the mobility parameter. If you, for example, halve mobility, the PF algorithm may fail to converge: during the simulation of individual movements, you may reach a time step in which the set of locations in which the individual could be located at a subsequent time step (given previously sampled locations) does not overlap with the set of locations within which the individual must have been located (given the data), because mobility is too restricted (assuming you sample a sufficient number of particles). This situation is more likely to arise in studies in which constraints on an individual’s location through time (e.g., detections or ancillary time series) successfully restrict the number of possible routes between sequential locations.
While it can be difficult to under-estimate mobility, it is possible to over-estimate it. The effects of doing so will be most apparent in the AC-branch algorithms and depend on constraints (such as array design). In a sparse array that records few detections, there is little information to constrain movement and an over-estimated mobility parameter will produce more diffuse patterns of space use. However, the coupling of AC- and PF- branch algorithms can limit the influence of an over-estimated mobility parameter because the latter incorporates a movement model in which longer-range movements, while permitted, can be made less likely. This is what the movement model for flapper skate does in Lavender et al. (2023).
Finally, it is important to note that these considerations are not unique to our methods. The flapper algorithms simply make the influence of movement constraints explicit, but the interpretation of passive acoustic telemetry data in general (and particularly of patterns such as residency) depends on knowledge of movement constraints. This has point been emphasised by recent publications (Lavender et al., 2021).
For practitioners seeking to apply our methods in new settings, we make the following recommendations:
get_mvt_mobility_*() functions as a guide.The algorithms are always ‘robust’ in the sense that the reconstructed set of possible locations of an individual is a complete, mechanistic description of all inputted information about the location of the animal through time (i.e., all detections, all gaps between detections and all ancillary data, given the detection probability model, the movement model and other parameters). Consequently, unless the algorithm is mis-specified (see below), the set of possible locations will include the ‘true’ movement path, even in sparse arrays with few detections. However, care is required in the interpretation of the ‘set of possible locations of an individual through time’: while this, by definition, will include the ‘true’ movement path, it is not guaranteed (nor even desirable) that the pattern of space use exhibited by the set of possible locations should match the pattern of space use exhibited by the ‘true’ path.
While a correctly specified algorithm will reconstruct a set of possible locations that includes the ‘true’ path (assuming you sample a sufficiently large number of particles in the PF step), the algorithms are sensitive to misspecification like any other method. However, the consequences of mis-specifying algorithm components, such as the detection range, detection kernels or movement parameters, vary. See ‘Sensitivity’ for further commentary.
The ‘usefulness’ of the algorithms in different settings is a separate issue. If tags malfunction, receivers are sparse and or detection probability is limited, the flapper algorithms, like other methods, are of limited utility: the set of possible locations will simply span the ‘permitted’ area (mainly beyond receiver detection containers) with more-or-less uniform probability. The quality of the inputs unavoidably influences the utility of the outputs.
These comments notwithstanding, as for other emerging movement modelling approaches in passive acoustic telemetry systems, more needs to be learnt about the utility of the flapper algorithms in different settings. As argued in Lavender et al. (2023), an improved understanding of the relative utility of different methods in different settings will help to move the field forwards.
The resolution of available data affects the temporal resolution of the analysis. The transmission interval of acoustic tags sets a sensible lower bound for this. In theory, a more frequent transmission interval makes it possible to resolve movement paths at a higher temporal resolution. However, in practice, the appropriate resolution of an analysis will depend upon whether or not more frequent transmissions are accompanied by more frequent detections, the resolution of other datasets (such as depth time series), analytical objectives and computational constraints. As for other methods, the optimisation of study design and algorithm parameters for improved inference is an avenue in which future research will be beneficial.
Recall that the flapper algorithms are designed to recapitulate the movement and detection processes that give rise to detections. This means that, by definition, reconstructed patterns of space use will contain the ‘true’ movement path (assuming they have been correctly specified: see ‘Sensitivity’). As in Lavender et al. (2023), you can explore the correspondence between a ‘known’ and reconstructed movements under different conditions using simulation. In real-world settings, fine-scale positioning records collected during drift tests of detection probability can also be used for this purpose. The probability distribution of the set of possible locations through time provides a measure of our certainty in the location of an individual: a flat surface emerges when there are few constraints on an individual’s possible location and reflects low certainty; a more concentrated surface emerges when the set of possible locations for an individual is more constrained and reflects higher certainty. However, even for more concentrated distributions, it is not guaranteed (nor even desirable) that the pattern of space use exhibited by the simulated locations will match the pattern of space use exhibited by the ‘true’ path (see ‘Optimisation’).
The central contribution of the flapper framework is the mechanistic perspective that recapitulates the processes that generate observations. This perspective has a number of methodological benefits:
These methodological innovations have important practical consequences:
We encourage users to consider these potential advantages in the context of those of other methods, alongside their respective disadvantages, to evaluate the relative merits of existing approaches in different settings.
The flapper algorithms encapsulate a new, bottom-up, mechanistic perspective of passive acoustic telemetry systems. This perspective has notable conceptual and practical advantages that have the potential to support applied research in the future (see above). However, our main hope is that this unique perspective will motivate a conversation about how we model passive acoustic telemetry data and encourage new research into the dynamics, performance, sensitivity, optimisation and uses of alternative methods in different settings, which are areas that have hitherto received insufficient attention. In this context, we highlight eight avenues for future methodological research that emerge from this study:
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