Using molecular diet analysis to inform invasive species management: A case study of introduced rats consuming endemic New Zealand frogs

Abstract The decline of amphibians has been of international concern for more than two decades, and the global spread of introduced fauna is a major factor in this decline. Conservation management decisions to implement control of introduced fauna are often based on diet studies. One of the most common metrics to report in diet studies is Frequency of Occurrence (FO), but this can be difficult to interpret, as it does not include a temporal perspective. Here, we examine the potential for FO data derived from molecular diet analysis to inform invasive species management, using invasive ship rats (Rattus rattus) and endemic frogs (Leiopelma spp.) in New Zealand as a case study. Only two endemic frog species persist on the mainland. One of these, Leiopelma archeyi, is Critically Endangered (IUCN 2017) and ranked as the world's most evolutionarily distinct and globally endangered amphibian (EDGE, 2018). Ship rat stomach contents were collected by kill‐trapping and subjected to three methods of diet analysis (one morphological and two DNA‐based). A new primer pair was developed targeting all anuran species that exhibits good coverage, high taxonomic resolution, and reasonable specificity. Incorporating a temporal parameter allowed us to calculate the minimum number of ingestion events per rat per night, providing a more intuitive metric than the more commonly reported FO. We are not aware of other DNA‐based diet studies that have incorporated a temporal parameter into FO data. The usefulness of such a metric will depend on the study system, in particular the feeding ecology of the predator. Ship rats are consuming both species of native frogs present on mainland New Zealand, and this study provides the first detections of remains of these species in mammalian stomach contents.


| INTRODUC TI ON
Although the decline of amphibians has been of international concern for more than two decades, the mechanisms of these declines are often difficult to identify, or they are difficult to disentangle as they may be acting synergistically (Alford, Dixon, & Pechmann, 2001;Alford & Richards, 1999;Stuart et al., 2004). This is exacerbated by a number of amphibian traits that can make them difficult to study, such as spending large portions of time in refugia inaccessible to researchers (e.g., under benthic mud, under deep rock piles), emerging from refugia only ephemerally (on both seasonal and daily timescales), and often being nocturnal. These and other factors have led to an alarming number of species (23%) being placed in the IUCN's Data Deficient category, which is much higher than for the other comprehensively studied vertebrate groups, birds, and mammals (Bishop et al., 2012).
Invasive species are considered one of the most important threats to global biological diversity (Vitousek, Dantonio, Loope, & Westbrooks, 1996;Park, 2004) and are ranked as the third most important detrimental factor affecting amphibian populations (after habitat modification and pollution; Chanson, Hoffman, Cox, & Stuart, 2008). Conservation managers are often tasked with delegating the allocation of resources to the control of invasive species, yet modeling the effects of invasive species on native species can be complex (Lohr et al., 2017). Decisions to implement such control measures are often based on diet studies (Allen & Leung, 2012;Park, 2004). Using morphological methods, successful identification of prey depends on an array of factors including: prey size; the durability of identifiable parts (Major, 1990); the level of digestion prey has been subjected to prior to examination (Veron, 1969); the part of the prey ingested (Day, 1966); and the degree of mastication by the predator (Hansson, 1970;Kasper, Reeson, Cooper, Perry, & Austin, 2004). For example, ship rats (Rattus rattus) have often been implicated in the decline of native vertebrate fauna worldwide (Towns, Atkinson, & Daugherty, 2006), but the level of mastication effected by this group makes prey identification from rodent stomach contents notoriously difficult (Hansson, 1970).
Molecular diet analysis can provide the additional tools required to detect prey in predator gastrointestinal or fecal samples, and the diets of a number of rodent species have been investigated using DNA (Lopes et al., 2015;Soininen et al., 2009;Zarzoso-Lacoste, Corse, & Vidal, 2013). However, there are many considerations to be taken into account when applying DNA-based diet approaches, such as primer choice, target region, the occurrence of false positives or false negatives, and assay sensitivity (King, Read, Traugott, & Symondson, 2008;Pompanon et al., 2012;Symondson, 2002). A particular challenge is that the abundance of predator DNA can mask prey DNA detections (Vestheim & Jarman, 2008). To overcome this, species-or group-specific primers are often used, targeting the prey of interest, rather than employing broad-range primers that are likely to co-amplify DNA from the predator species. Nevertheless, even if predator DNA is not co-amplified, the relatively high concentration of nontarget DNA can still affect assay sensitivity (Juen, Hogendoorn, Ma, Schmidt, & Keller, 2012;Nejstgaard et al., 2008).
The focus of many diet studies is the contribution of prey species to a given predator species in terms of survival, distribution, energetics, and other aspects of ecological relevance. In such studies, the occurrence and documentation of rare prey species is justifiably considered as being of minor importance. However, when the focus is on determining the impacts of a predator species on prey species of high conservation value, rare occurrences of the prey species can still have major implications for prey populations, especially when the predator density is high, as is often the scenario where invasive species are concerned (Pitt & Witmer, 2007;Pintor, Sih, & Kerby, 2009). Thus, the relative contribution of a prey species to an invasive predator species' diet does not necessarily provide sufficient information to make conservation management decisions (Allen & Leung, 2012). Or worse, it has the potential to mislead conservation practitioners into considering the threat of an invasive species as being minor, due to the high-value prey species in question occurring at low frequency in the diet.
One of the most common metrics to report in diet studies (both morphological and molecular) is Frequency of Occurrence (FO), the number of diet samples in which a prey species is detected, divided by the total number of diet samples analyzed (Hansson, 1970).
Although caution is often advised when interpreting FO data, it has been used for describing dietary composition (Baker, Buckland, & Sheaves, 2014), for ranking the relative importance of various prey to a single predator species (Sinclair & Zeppelin, 2002), for comparing seasonal and regional diet variation of a predator species (Sinclair & Zeppelin, 2002), and for comparing diets among predator species (Murphy, Keedwell, Brown, & Westbrooke, 2005). However, unless additional parameters are incorporated, FO can only ever be a relative measure and cannot be used to estimate the potential impact of a predator species on the prey population (Greenstone, 1996;. This is because FO does not take into account time, an important parameter for determining predation rates (Dempster, 1960;Jones & Toft, 2006).
Here, we examine the potential of FO data derived from molecular diet analysis to inform invasive species management, using invasive ship rats and endemic frogs in New Zealand as a case study.
New Zealand's fauna evolved in the absence of mammals (excluding marine mammals and bats; see Clout & Saunders, 1995), and there are now 31 introduced mammalian species present as wild or feral populations (King, 2005;Parkes & Murphy, 2003) Only four species of native frog remain in New Zealand (all endemic) and only two of those are found on the mainland, in highly fragmented remnant populations; Archey's frog (Leiopelma archeyi) and Hochstetter's frog (Leiopelma hochstetteri), which are listed as Critically Endangered and Least Concern, respectively (IUCN, 2017).
Hochstetter's frog is semi-aquatic, usually restricted to streams and seepages in woodland habitats (Crossland, Mackenzie, & Holzapfel, 2005;Green & Tessier, 1990;Tessier, Slaven, & Green, 1991), and has a nonfeeding tadpole stage (Bell & Wassersug, 2003;Stephenson, 1955). This species has the most widespread distribution of the Leiopelma species, being found in scattered populations over an extensive area of the North Island (Bishop et al., 2013). New Zealand also has three species of introduced frogs (Litoria & Ranoidea), two of which are declining in their native ranges in Australia and are listed as "Endangered" or "Vulnerable" (IUCN, 2017).
The primary threats to Leiopelma are considered to be introduced mammalian predators, infectious disease (chytridiomycosis), and habitat modification (Bishop et al., 2013), but agents of decline have not been conclusively demonstrated (Bishop et al., 2013;Newman et al., 2010). Although it seems, from sporadic reports, that ship rats may represent the greatest mammalian predation threat to New Zealand's frogs , the current impacts of introduced predators on New Zealand frog populations are largely unknown (Baber, Moulton, Smuts-Kennedy, Gemmell, & Crossland, 2006;Bishop et al., 2013;Haigh, Pledger, & Holzapfel, 2007;Tocher & Pledger, 2005). The evidence to date is largely circumstantial: The extinction of three native frog species occurred synchronously with the arrival of introduced fauna (in association with human settlers), as did the range contraction of the currently extant species (Bell, 1994b;Easton et al., 2018;Towns & Daugherty, 1994;Worthy, 1987b).

Indirect predation studies have been carried out comparing
Leiopelma abundance in areas where mammalian predators had been removed with areas where no predator control had been implemented (reviewed by . The results to date have varied widely in terms of estimating the effects of mammalian predators on Leiopelma abundance (see discussion section herein). A major difficulty with comparing frog abundance estimates is that a difference in abundances may not reflect a difference in population size, but only in detection probability, which can vary both spatiotemporally and by observer (Buckland, Goudie, & Borchers, 2000;Crossland et al., 2005; Nájera-Hillman, Yoccoz, Nichols, & Boulinier, 2001). For instance, McLennan (1985) calculated a fourfold difference in abundances of Hochstetter's frogs based on results collected from different observers. Leiopelma are also long-lived (three generations are estimated at 30-45 years for Archey's frog) and produce few eggs (1-22;Bell, 1985;Bell, 1994a;Bell & Wassersug, 2003), so population monitoring necessitates very long-term studies. Even so, invasive species are more likely to be generalist predators (Dukes & Mooney, 1999), and as such tend to be buffered from fluctuations in the abundance of any one prey species (Inayat et al., 2011). Thus, native amphibian prey populations would not necessarily be expected to fluctuate in tandem with introduced generalist mammals. Diet analysis has the potential to provide estimates of the impact of invasive predators on prey species, as it does not necessarily require long-term studies, and is not affected by observer bias or frog detection probability across habitats.
To examine the potential of FO data derived from molecular diet analysis to inform invasive species management, we addressed the following objectives: (Bell, 1985(Bell, , 1994aNewman et al., 2010) design and validate PCR primers for detecting frog DNA (in terms of specificity, sensitivity, and taxonomic coverage); compare morphological and molecular diet analyses for detecting frog remains in field-collected ship rat stomach contents; and assess whether the incorporation of a temporal parameter into FO data can provide more informative metrics for making conservation management decisions.

| Field study
Four sites were visited within two study areas: Whareorino Forest and the Waitakere Ranges. Whareorino Forest is an extensive area of unlogged podocarp-hardwood forest (Pryde, Lettink, & O'Donnell, 2006) situated in King Country, central North Island, New Zealand, and is managed by local DOC authorities. This area is inhabited by both Hochstetter's and Archey's frogs (Thurley, 1996;Thurley & Bell, 1994). The Waitakere Ranges, Auckland, New Zealand, is largely covered by the Waitakere Ranges Regional Park, administered by the Auckland Regional Council. The Waitakere Ranges are not inhabited by Archey's frogs, but this area was chosen because there are far more distribution data available for Hochstetter's frogs in the Waitakere Ranges than in Whareorino Forest (Allen, 2006;Green, 1994;Green & Tessier, 1990;Moreno, 2009;Tessier et al., 1991). Sites in the Waitakere ranges were centered along streams known to be inhabited by Hochstetter's frogs.
At each site, a trapping web consisting of 81 rat snap traps (Victor; Woodstream Corporation) was installed. Each web consisted of 16 trap lines radiating from a central point, each line comprised of five traps, plus an additional trap at the center of the grid.
For the initial two trapping sessions, traps had a 25-m spacing, but the results of these sessions indicated that a low proportion of the rat population present was being trapped. Consequently, for subsequent trapping sessions (n = 3) the spacing was decreased to 20 m. Rat traps were baited with peanut butter and placed under wire mesh tunnels with a plastic covering pegged into the ground to reduce the risk to nontarget species. All traps were left baited, but unset for the first night (following Hickson, Moller, & Garrick, 1986;Tobin, Koehler, Sugihara, Ueunten, & Yamaguchi, 1993). Traps were then set for five consecutive nights. Each morning, traps were checked, carcasses removed, and traps reset if necessary. Dissection was carried out at a field station within each study area, whereby whole stomachs (excluding esophagus and intestine) were removed and stored in 95% ethanol. Instruments were washed in ethanol and flamed between dissections.
To ensure that trapping was being carried out on nights that frogs were emerging from diurnal retreats, a 50-m transect was surveyed each night during trapping. Each survey consisted of visual searches for frogs using torches, as Leiopelma rarely produce sounds (Stephenson & Stephenson, 1957). Transects were located near to (within 100 m) trapping grids, but not inside them, to avoid disturbance to trapping. Indices were standardized by always commencing frog counts 1-1.5 hr after dusk (as Leiopelma frogs will have left their daytime retreats by this time, given favorable conditions; Cree, 1989) and always completing transects within 30-40 min.
All procedures employed during fieldwork were ethically reviewed and approved by the University of Otago Animal Ethics Committee (ET 25/09).

| In silico primer evaluation
Different assays will have different sensitivities for detecting a particular prey species. In order to maximize the detection of frog DNA from stomach content samples, we used two approaches: one using species-specific primers for each of the two target species, followed by Sanger sequencing; and one using group-specific primers targeting Anura in general, followed by Illumina MiSeq sequencing.
Species-specific primer pairs were developed targeting short fragments of the mitochondrial 12S rRNA gene (Table 1) In order to develop an assay to target a broad range of frog species, both for the current study (to detect all four genera of frogs present on mainland New Zealand), and for future studies (in New Zealand or elsewhere), the program AMPLICON (Jarman, 2004) was used to generate primers intended for selectively amplifying anuran DNA from mixed DNA samples. Representative sequences for the 16S rRNA gene from every major anuran superfamily, along with homologous sequences from other species from all animal classes (obtained from NCBI database), were used as input for AMPLICON, with anuran sequences designated as the target group and sequences from all others treated as the excluded group. It should be noted that we initially targeted representative 12S sequences, but no suitable primers were found; hence, 16S sequences were subsequently used.
Resultant primers were tested for specificity and taxonomic coverage in silico using ECOPCR (Ficetola et al., 2010), allowing for up to one mismatched base per primer. Specificity was assessed by testing

| In vitro primer evaluation
To assess the specificity of the species-specific primers, PCRs were performed on DNA from of all five frog species present on mainland New Zealand, as well ship rat DNA. Tissue samples were obtained from the University of Otago (Supporting Information Table S1).
DNA was extracted using the DNeasy Blood and Tissue Kit (Qiagen), following the manufacturer's instructions. Gradient PCRs were performed and specificity for the respective species' DNA was confirmed by gel electrophoresis using SYBR Safe (Life Technologies). To assess the specificity and coverage of the group-specific anura primers, PCRs were performed on DNA from tissue of 61 frog species from 29 divergent families (Supporting Information Table   S1), as well as DNA extracted from tissue of ship rat and a number of other nontarget mammals known to be present in the study sites: Norway rat (R. norvegicus), hedgehog (Erinaceus europaeus), and human (Homo sapiens). Tissue samples were obtained from multiple sources (Supporting Information Table S1). DNA was extracted using the DNeasy Blood and Tissue Kit (Q iagen), following the manufacturer's instructions. Gradient PCRs were performed and specificity for the anuran DNA was confirmed by gel electrophoresis using SYBR Safe (Life Technologies). One primer pair (EGETER-2019-16S-F/R; To test the sensitivity of the assay, we conducted a limit of detection experiment, similar to that performed by Sint, Raso, and Traugott (2012). This experiment consisted of two tests, one using serially diluted total DNA and one using serially diluted amplicon.
The concentration of total DNA for two distantly related species (Ranoidea raniformis and Leiopelma hochstetteri) was measured based on the average of three measurements using the QuBit HS DNA Assay (Thermo Fisher Scientific) and diluted to 2, 0.2, 0.02, 0.002, and 0.0002 ng -µl . Separately, PCR product produced by the EGETER-2019-16S primers from each of the two species was gel-extracted using the QIAquick Gel Extraction Kit (Qiagen). The number of amplicon copies in the product was estimated using the QuBit HS DNA Assay (Thermo Fisher Scientific) in conjunction with DNA CALCULATOR (Sint et al., 2012) and dilutions of 1,000, 500, 100, 50, 25, 10, and 1 copy -µl were made. Five PCR replicates were carried out for each dilution in each test. DNA templates were not mixed prior to PCR: A separate set of replicates was done for each frog species for each test. Furthermore, the entire experiment was carried out twice, once using 1 µl of template for each PCR and once using 1 µl of template plus 1 µl of ship rat total DNA (50 ng -µl ).
It should be noted that we also trialed previously published batrachia-specific primers (Valentini et al., 2016), but were unable to avoid nonspecific amplification of mammalian DNA using the PCR conditions detailed herein (across a gradient of annealing temperatures).

| Diet analysis
In the laboratory, morphological analysis of stomach contents was undertaken with the aim of identifying frogs as prey using a  Kocher et al., 1989), using PCR conditions as detailed by . This provided an estimation of the number of samples resulting in amplifiable DNA in general.
Amplicons from this PCR were visualized on gels but were not sequenced as they are longer (c. 400 bp) than usually recommended for diet analysis studies (King et al., 2008) and would also be expected to amplify ship rat DNA in high proportions.
PCR products from stomach content samples, produced using the species-specific primer pairs, were cleaned and Sanger-se-

| Data analysis
Frequency of Occurrence (FO) of frogs as prey for each trapping session was calculated using Equation 1: where P is the number of stomach samples testing positive for frog DNA, and R is the number of rats trapped.
We considered that a sample testing positive must represent a minimum of one event when a rat ingested frog tissue; therefore, where i is the trap night.
Equation 2 assumed that a sample being positive, that is, resulting in sequence(s) matching a frog species, was the result of an ingestion event occurring during the sampling period (i.e., on the night the sample was obtained). We consider that this assumption was likely to hold true due to the following rationale: • Archey's frogs are active only between dusk and dawn (Cree, 1989), and ship rats are also primarily nocturnal (Dowding & Murphy, 1994;Hooker & Innes, 1995).
• Daylight hours during the study periods ranged from 12 to 15.5 hr.
• Detection probability of frog tissue in ship rat stomach contents using DNA-based diet analysis under laboratory conditions was previously found to be very low c. 12 hr after ingesting frog tissue (<0.1; . Furthermore, detection probabilities in the laboratory study were likely to be higher than under field conditions as rats in the laboratory were fed ad libitum, which is known to increase detection probabilities over time (Dodd, 2004).
• Therefore, even if a rat ingested frog tissue just before daybreak, but was not caught in a trap until the earliest possible time during the following trapping session (dusk of the same day), frog DNA would not be detected.
This is similar to approaches used by Dempster (1967; see also Ashby, 1974;and Sopp, Sunderland, Fenlon, & Wratten, 1992;Dempster, 1960), but does not assume that the detection of an ingestion event is equivalent to predation of an individual.

| Detecting frog remains in ship rat stomach contents
In total, 191 ship rat stomach content samples were obtained: 60 at  (Tables 2 and   3; Supporting Information Figure S2).
Using morphological analysis, none of the rat stomach contents were found to contain remains of frogs. The species-specific approach coupled with Sanger sequencing had a similar success rate to the group-specific approach coupled with MiSeq sequencing (six positives each), but in two cases one of the approaches detected a species the other missed. One sample tested positive for both Hochstetter's frog and Archey's frog ( further analyses were conducted on frog emergence data due to the low number of nights with detected ingestion events. It should be noted that one sample resulted in sequences that were assigned to ship rat, but these were filtered out during the bioinformatic processing. Read numbers from the MiSeq run were lower than expected at only c. 340 reads/sample before filtering and c. 200 final reads/sample (Table 3). This was caused by primer dimers from different primer sets belonging to samples from other unrelated projects that used up a large proportion of the reads in the overall run (data not shown). Nonetheless, as the results are corroborated by the species-specific primers coupled with Sanger sequencing, this was not deemed to be a major issue.
One drawback of molecular diet analysis is the potential for the occurrence of false positives through sample contamination. We
Amplification and reliable Sanger sequences were obtained from 57/61 (93%) of the species tested in vitro (Supporting Information Table S1). The species not amplified belonged to Ascaphidae, Ranidae, Strabomantidae, and Ptychadenidae, which partially concurs with the in silico analysis where the primers amplified 100%, 42%, 85%, and 51% of these families, respectively.
At lower annealing temperatures (<61°C), DNA from tissue of nontarget (mammalian) species was occasionally amplified, but this did not occur using the final PCR conditions. In silico, 100% of amplifications belonged to the phylum Chordata, 81% of these attributed to the class Amphibia. The remaining amplifications consisted primarily of fish species (Figure 2), indicating there may be some nontarget amplification of this group.
The DNA barcode amplified by EGETER-2019-16S primers appears to offer good resolution, unambiguously identifying 83% of the Anura Database to species level and 94% to genus level in silico.
Sequences obtained for each species from tissue samples were also unique with a mean p-distance of 57 base differences (using pairwise deletion of gaps in comparison). The majority of sequences were assigned to the expected taxonomy (Supporting Information Table S1). Figure S3 for a neighbor-joining tree highlighting the efficacy of the target region as a DNA barcode. TA B L E 3 Details of rat stomach samples testing positive for frogs as prey using three diet analysis approaches. All rats were adults

| Validation of primers
We present two new species-specific primers and one group-specific primer for frogs. The group-specific primer pair appears to exhibit good coverage, high taxonomic resolution, and reasonable specificity. It was also shown to detect frog DNA at relatively low concentrations, even in the presence of high amounts of predator DNA. However, there were differences in assay sensitivity among the two species tested in the limit of detection experiment, suggesting that variability in the template target DNA or in primer binding sites affects the detection of different prey species, especially when predator DNA is co-extracted in high relative proportions. Such biases have often been noted using group-specific primers (see Pinol, Mir, Gomez-Polo, & Agusti, 2015).
For this study, it was pertinent to ensure that predator DNA was not being amplified, which required relatively high annealing temperatures for all primer sets. If the primers were to be used for other sample types, such as environmental DNA from water bodies, it may be beneficial to test the primers at less stringent conditions to maximize detection of anuran species.

| Comparison of diet analysis approaches
From feeding trials, molecular diet analysis has been shown to outperform morphological diet analysis when attempting to detect amphibians as prey in ship rat stomach and fecal samples , which concurs with the present field-based study. In fact, studies comparing morphological and molecular diet analyses have generally found that DNA-based methods improve prey detection success, either by detecting prey more frequently, or by detecting a higher number of prey species (Boyer, Yeates, Wratten, Holyoake, & Cruickshank, 2011;Carreon-Martinez, Johnson, Ludsin, & Heath, 2011;Casper, Jarman, Gales, & Hindell, 2007;Casper, Jarrnan, Deagle, Gales, & Hindell, 2007;Dunn, Szabo, Mcveagh, & Smith, 2010;Purcell, Mackey, Lahood, Huber, & Park, 2004;Scribner & Bowman, 1998;Soininen et al., 2009;Tollit et al., 2009). In the present study, morphological analysis failed to identify any frog remains in ship rat stomach contents. This is likely because ship rats often do not ingest skeletal components of frog prey, preferring to consume only soft tissue, and even if bones are ingested, they are highly fragmented, making it impossible to discern diagnostic traits .
The species-specific and group-specific molecular diet analysis approaches agreed with each other in five out of the seven detections of frog DNA from ship rat stomach contents. Given the low number of total detections, it is not possible to state whether the disagreements were due to differences in assay sensitivity or PCR F I G U R E 1 Family coverage of the of EGETER-2019-16S primer pair in the order Anura according to in silico PCR using the Anura Database. One base mismatch per primer was allowed. The percentages of each family amplified by the primers are indicated above the bars

| Incorporation of temporal parameters
FO data provide a metric that can be difficult to interpret, as it does not include a temporal perspective. In this study, we incorporated a temporal parameter into the commonly used FO metric, similar to approaches used by Dempster (1967; see also Ashby, 1974;and Sopp et al., 1992;Dempster, 1960). For each trapping session, this allowed expression in units of minimum number of ingestion events per rat per night (TFO). This unit provides a more intuitive metric, as it constitutes a temporal rate (the minimum number of ingestion events during a given time period), rather than a relative rate (the minimum number of ingestion events per predator). Deagle et al. (2018) noted that when prey are eaten sporadically and in discrete foraging events (as is the case for the present study), FO data may provide meaningful indications of how often a taxon is being consumed. We are not aware of other DNA-based diet studies that have incorporated a temporal parameter into FO data.
Another benefit of TFO data, as calculated herein, is that the maximum detection period (maximum time that prey is detectable in stomach contents since prey was ingested) is used to ascertain the shortest interval possible between sampling periods. This means that prey DNA detection can be assigned confidently to an ingestion event that occurred within the sampling period, while also maximizing the temporal resolution. Measuring a maximum detection period requires relatively simple feeding trial data, as the aim is only to find the point at which prey are no longer detectable. This is in contrast to measuring 50% detection probabilities from feeding trial data (Gagnon, Doyon, Heimpel, & Brodeur, 2011;Greenstone, Payton, Weber, & Simmons, 2014  Total DNA concentration (ng/reaction) von Berg, Traugott, Symondson, & Scheu, 2008;Waldner, Sint, Juen, & Traugott, 2013;Welch, Schofield, Chapman, & Harwood, 2014), which requires relatively high sample sizes at multiple time points ranging from very high to very low detection probabilities.
Furthermore, while 50% detection probabilities can be useful for adjusting relative prey FO data, it is less clear whether it can be reasonably applied to directly adjust a temporal rate, such as TFO, as feeding trial data are unlikely to accurately reflect prey DNA detection across the spectrum of field conditions. This is less of an issue when using a maximum detection period, as the shortest interval possible between sampling periods can be chosen such that detecting prey from a previous sampling period is extremely unlikely.
While it is tempting to assume that each prey detection in molecular diet analysis represents at least one prey individual, this assumption cannot be confirmed for this study as partially eaten Archey's frog carcasses have been found previously with rat bite marks (Fitzgerald & Campbell, 2002;Thurley & Bell, 1994), indicating the possibility of multiple rats consuming tissue from a single frog within one night. Nonetheless, estimating a minimum predation rate (minimum number of individuals consumed during a given time period) from TFO data should be possible in many study systems, particularly those with predators that consume only live whole prey (Codron, Codron, Sponheimer & Clauss 2016;Deagle et al. 2018). If feces are being utilized for diet analysis, rather than stomach contents, then additional considerations are required, but the principles remain the same-an ingestion event can be assigned to a sampling period as long as the fecal sample was produced during the sampling period and the maximum detection period does not extend into the previous sampling period. We recommend that future studies focussed on measuring the impact of predators using molecular diet analyses should take maximum prey detection times into consideration during the design of field sampling, to ensure that each prey detection can be assigned to a specific sampling period.
It should be noted that the estimates we obtained can be considered very conservative. We did not attempt to apply 50% detection probabilities from previous feeding trial data to our field data, which would have adjusted FO values upwards (Gagnon et al., 2011;Greenstone et al., 2014Greenstone et al., , 2007Greenstone et al., , 2010Szendrei et al., 2010) and we assumed that a prey DNA detection was the result of at least one ingestion event, when it may have been the result of numerous events.
This means that the true rate of ingestion events is very likely to be higher than the minimum rate estimated herein. Nonetheless, a con- is to utilize the genetic information of the prey population to estimate the minimum number of prey individuals required to produce the observed variation in a sample (Carreon-Martinez, Wellband, Johnson, Ludsin, & Heath, 2014). We envisage that the most accurate DNA-based predation approaches in the future will build on existing methods by combining temporal parameters, FO data, sequence read count data, and individual-level genetic information. Other studies have compared the abundances of Hochstetter's frogs in areas with or without rodent control, but results to date have been varied (Baber et al., 2008;Mussett, 2005; Nájera-Hillman, ). This may be due to difficulties with monitoring Hochstetter's frog abundances as detection probabilities can vary spatially or temporally (Anderson, 2001(Anderson, , 2003Bailey, Simons, & Pollock, 2004;Crossland et al., 2005;Hyde & Simons, 2001). Nájera-Hillman,  found no difference in the relative abundance of Hochstetter's frogs among areas with and without rodent control. Conversely, Mussett (2005) and Baber et al. (2008) found that Hochstetter's frog abundance was higher in mammal-controlled areas. However, the results of Mussett (2005) were complicated by the fact that the highest ship rat abundance coincided with the highest frog abundance and at some mammal-controlled sites ship rat abundance was similar to sites without mammal control.

| Predation on New Zealand native frogs
Longson, Brejaart, Baber, and Babbitt (2017) (Allen, 2006;Green, 1994;Green & Tessier, 1990;Moreno, 2009;Tessier et al., 1991), which may help to explain the low number of ingestion events detected in this study. However, more sampling would be required to ascertain whether ingestion events are indeed a consistently rare event across various sites and seasons.  (Pledger, 2011). However, as they are long-lived and produce few eggs (Bell, 1985(Bell, , 1994aBell & Wassersug, 2003), such a frequency of ingestion events may still have a significant impact on the population. With the current data, this remains difficult to interpret and these rates are also likely to change over time, given the annual fluctuation of rat densities (e.g., Daniel 1972;Smith 1986) and varying food sources available. Results of a previous experiment indicated that population sizes of Archey's frogs decreased outside a rodent-controlled area, while they remained stable or increased inside the rodent-controlled area, although it should be noted that the study was confined to a small sample size of two 100-m 2 monitoring grids per treatment (Pledger, 2011). Sites 1 and 2 of the present study were situated close to the grid from that experiment, and our results provide some support for those findings.
The results of this study were provided to the New Zealand Department of Conservation and this, along with multiple lines of evidence indicating the negative impact of introduced mammals on a range of native species, has led to the inclusion of Whareorino Forest in New Zealand's mammal control program.

| CON CLUS IONS
Ship rats are consuming both species of native New Zealand frogs still present on the mainland. This is the first time these species have been detected in mammalian stomach contents. Molecular diet analysis outperformed morphological techniques. Although frog predation by ship rats was rare, it may still have a significant impact on the frog populations. We were able to incorporate a temporal parameter into FO diet data, which allowed the calculation of ingestion events per rat per night. We are not aware of other DNA-based diet studies that have incorporated a temporal parameter into FO data. The usefulness of such a metric will depend on the study system, in particular the feeding ecology of the predator. We provide recommendations for future diet studies focussed on measuring the impact of predators on prey species.

ACK N OWLED G M ENTS
The research was carried out with the approval of the University of

AUTH O R CO NTR I B UTI O N S
BE designed the study and the primers, carried out the field work, and led the manuscript writing. PJB and BCR guided the research.
BE, CR, SP, PP, and JP conducted the laboratory work. LJE contributed to the analysis of the results. All authors provided manuscript input and edits and participated in discussions that developed the work.

DATA ACCE SS I B I LIT Y
Fasta files containing all Sanger-sequenced tissue-derived se-