Erroneous behaviour of MixSIR, a recently published Bayesian isotope mixing model: a discussion of Moore & Semmens (2008)

The application of Bayesian methods to stable isotopic mixing problems, including inference of diet has the potential to revolutionise ecological research. Using simulated data we show that a recently published model MixSIR fails to correctly identify the true underlying dietary proportions more than 50% of the time and fails with increasing frequency as additional unquantified error is added. While the source of the fundamental failure remains elusive, mitigating solutions are suggested for dealing with additional unquantified variation. Moreover, MixSIR uses a formulation for a prior distribution that results in an opaque and unintuitive covariance structure.     

Combining sources in stable isotope mixing models: alternative methods

Stable isotope mixing models are often used to quantify source contributions to a mixture. Examples include pollution source identification; trophic web studies; analysis of water sources for soils, plants; or water bodies, and many others. A common problem is having too many sources to allow a unique solution. We discuss two alternative procedures for addressing this problem. One option is a priori to combine sources with similar signatures so the number of sources is small enough to provide a unique solution. Aggregation should be considered only when isotopic signatures of clustered sources are not significantly different, and sources are related so the combined source group has some functional significance. For example, in a food web analysis, lumping several species within a trophic guild allows more interpretable results than lumping disparate food sources, even if they have similar isotopic signatures. One result of combining mixing model sources is increased uncertainty of the combined end-member isotopic signatures and consequently the source contribution estimates; this effect can be quantified using the IsoError model (). As an alternative to lumping sources before a mixing analysis, the IsoSource mixing model () can be used to find all feasible solutions of source contributions consistent with isotopic mass balance. While ranges of feasible contributions for each individual source can often be quite broad, contributions from functionally related groups of sources can be summed a posteriori, producing a range of solutions for the aggregate source that may be considerably narrower. A paleohuman dietary analysis example illustrates this method, which involves a terrestrial meat food source, a combination of three terrestrial plant foods, and a combination of three marine foods. In this case, a posteriori aggregation of sources allowed strong conclusions about temporal shifts in marine versus terrestrial diets that would not have otherwise been discerned.     

Using Bayesian stable isotope mixing models to estimate wolf diet in a multi-prey ecosystem

Stable isotope analysis (SIA) of wolf (Canis lupus) tissues can be used to estimate diet and intra-population diet variability when potential prey have distinct δ¹³C and δ¹⁵N values. We tested this technique using guard hairs collected from 44 wolves in 12 northwestern Montana packs, summer 2009. We used hierarchical Bayesian stable isotope mixing models to determine diet and scales of diet variation from δ¹³C and δ¹⁵N of wolves and potential prey, white-tailed deer (Odocoileus virginianus), mule deer (Odocoileus hemionus), elk (Cervus canadensis), moose (Alces alces), snowshoe hare (Lepus americanus), and other prey. As a check on SIA results, we conducted a separate diet analysis with temporally matched scats (i.e., collected in summer 2008) from 4 of the same packs. Wolves were centered on the ungulate prey in the isotope mixing space. Both methods revealed differences among pack diets and that wolves may consume moose in greater proportions than predicted by available biomass. Stable isotope analysis, and scat results were not entirely concordant; assumptions related to tissues of use in SIA, hair growth period in wolves, and scat sampling may have contributed to a mismatch between methods. Incorrect fractionation values, insufficient separation of prey in the isotope mixing space, choice of prior information in the Bayesian mixing models, and unexplained factors may have distorted diet estimates. However, the consistently high proportion of moose in pack diets suggests that increased population monitoring would benefit management of moose and wolves. Our results also support suggestions of other researchers that species-specific fractionation values should be used whenever possible, and that SIA may sometimes only provide indices of use for general groups of prey (e.g., large ungulates). © 2012 The Wildlife Society.     

Process,correlation and parameter fitting in species distribution models: a response to Kriticos et al

In a recent article (Dormann et al., 2012, Journal of Biogeography, 39, 2119–2131), we compared different approaches to species distribution modelling and depicted modelling approaches along an axis from purely ‘correlative’ to ‘forward process‐based’ models. In their correspondence, Kriticos et al. (2013, Journal of Biogeography, doi: 10.1111/j.1365‐2699.2012.02791.x ) challenge this view, claiming that our continuum representation neglects differences among models and does not consider the ability of fitted process‐based models to combine the advantages of both process‐based and correlative modelling approaches. Here we clarify that the continuum view resulted from recognition of the manifold differences between models. We also reinforce the point that the current trend towards combining different modelling approaches may lead not only to the desired combination of the advantages but also to the accumulation of the disadvantages of those approaches. This point has not been made sufficiently clear previously.     

Fire as a dimension of historical ecology: a response to Bowman et al. (2011)

Bowman et al. (Journal of Biogeography, 2011, 38 , 2223–2236) attempt a synthesis of the current status of study into human use of fire as an ecosystem management tool and provide a framework for guiding research on the human dimensions of global fire. While we applaud this ambitious effort, we believe the proposed ‘pyric phase and transition’ model to be too deterministic and simplistic to account for the complexity and diversity in human–fire relationships. After reviewing theoretical problems with the proposed framework, we question policy implications of their conclusions concerning tropical forest systems. We suggest that a theoretically informed perspective should build on an historical fire ecology framework for investigating social and ecological aspects of human–environment interactions.     

Response to Collins et al. (2011)

We note serious problems in Collins et al. (Journal of Biogeography, 2011, doi: 10.1111/j.1365‐2699.2011.02506.x ): failure to use over 80% of the available data; failure to use one of the two available archipelagoes; mistaken inclusion of four species; and reliance on a grossly inadequate number of null matrices. Curing the paper of these problems would have strengthened the evidence for checkerboards and the role of competition.     

Management implications of the Macquarie Island trophic cascade revisited: a reply to Dowding et al. (2009)

1. The management of non-indigenous species is not without its complications. In Bergstrom et al. 's (2009) study, we demonstrated that feral cats Felis catus on sub-Antarctic Macquarie Island were exerting top-down control on the feral rabbit Oryctolagus cuniculus population, and that the eradication of the cats led to a substantial increase in rabbit numbers and an associated trophic cascade.
2. Dowding et al. (2009) claim our modelling was flawed for various reasons, but primarily that a reduction in the application of the rabbit control agent, Myxoma virus, coinciding with cat removal, was a major driver of rabbit population release.
3. We explore this proposition (as well as others) by examining rates of Myxoma viral release between 1991 and 2006 (with an attenuation factor for the years, 2003–2006) in association with presence/absence of cats against two estimates of rabbit population size. Myxoma viral release was a significant factor in the lower estimates of rabbit population, but the effect was small, and was not significant for higher rabbit population estimates. By contrast, the presence or absence of cats remained highly significant for both estimates.
4. Synthesis and applications. We re-affirm our position that top-down control of rabbit numbers by cats, prior to their eradication, was occurring on Macquarie Island. Nonetheless, we agree with Dowding et al. (2009) that systems with multiple invasive species represent complex situations that require careful scrutiny. Such scrutiny should occur in advance of, during, and following management interventions.     

Using connectivity to identify climatic drivers of local adaptation: a response to Macdonald et al.

Macdonald et al. (Ecol. Lett., 21, 2018, 207–216) proposed an analytical framework for identifying evolutionary processes underlying trait‐environment relationships observed in natural populations. Here, we propose an expanded and refined framework based on simulations and bootstrap‐based approaches, and we elaborate on an important statistical caveat common to most datasets.     

The development and raison d'être of 'habitat hectares': A response to McCarthy et al. (2004)

We welcome the constructive comments of McCarthy et al . (2004), and are grateful for the opportunity to respond.     

Demystifying the marine‐terrestrial biodiversity gradient: response to Vermeij et al.

We respond to seven criticisms made by Vermeij et al. ( 2018 ) regarding Miller & Wiens ( 2017 ). Their criticisms generally reflect misunderstandings, unsupported speculations, and topics that were explicitly addressed in our paper.