Carbonatites are the most silica-poor magmas known and are amongst Earth’s most enigmatic igneous rocks. They crystallise to rocks dominated by the carbonate minerals calcite and dolomite. We review models for carbonatite petrogenesis, including direct partial melting of mantle lithologies, exsolution from silica-undersaturated alkali silicate melts, or direct fractionation of carbonated silicate melts to carbonate-rich residual melts. We also briefly discuss carbonatite–mantle wall-rock reactions and other processes at mid-to upper crustal depths, including fenitisation, overprinting by carbohydrothermal fluids, and reaction between carbonatite melt and crustal lithologies.
INTRODUCTION
Carbonatites are silica-poor igneous rocks composed predominantly of primary carbonate minerals, typically >50% modal calcite and dolomite. They are the most silica-undersaturated magmas in the Earth’s crust. The bulk of the worlds’ supply of rare earth elements (REEs) and Nb is derived from carbonatites. The Earth has approximately 600 known occurrences of carbonatites (Humphreys-Williams and Zahirovic 2021 this issue) that range in age from Archean to the present day, and are found on all continents and, in rare cases, on oceanic islands with atypically thick lithosphere [i.e., the Canary Islands (Spain) and Cape Verde]. The most common geodynamic setting for carbonatites is within intraplate regions, commonly cratonic margins, and many are associated with the early stages of rifting and plate separation. Carbonatites have been linked to mantle plumes and the formation of large igneous provinces (Bell and Simonetti 2010).
Carbonatites are a diverse group of rocks that include extrusive, intrusive, and carbohydrothermal varieties (formed by reaction with CO2 + H2O–rich fluids). The only known currently active carbonatite volcano is Oldoinyo Lengai (Tanzania), which historically erupted natrocarbonatite. However, there are ~50 examples of carbonatite extrusives reaching back to 1.8 Ga in the geological record.
The majority of carbonatites (74%) are associated with a wide variety of alkaline igneous silicate rocks that range from ultramafic to felsic (e.g., lamprophyres, olivine melilitites, olivine nephelinites, phonolites, syenites, and their intrusive equivalents). The most common are nephelinite, syenite, and melilitite, the parental melts of which could have been derived by small degrees of partial melting of the hydrousand carbonate-bearing mantle (Woolley and Kjarsgaard 2008). Progress towards understanding the formation and evolution of carbonatite magmas has been complicated by their petrological diversity and that of the associated silicate rocks, and by the common presence of cumulate, flow banded, and rheomorphic textures in carbonatites. Field, petrological, and geochemical studies have shown strong links between carbonatites and their associated alkaline silicate rocks. These carbonatite–alkali–silicate complexes could be related by liquid immiscibility, or by extensive fractionation of CO2-bearing silicate melts that have left residual carbonate-rich liquids. Alternatively, some carbon-atites occur without associated silicate rocks and/or carry mantle xenoliths and xenocrysts and are inferred to be derived directly from the mantle (Harmer and Gittins 1997). These carbonatites crystallise magnesian calcite as the liquidus phase at low pressures (Harmer and Gittins 1997) and this, coupled with field and textural evidence for cumulates and crystal mushes, lends support for a primary mantle origin for some carbonatites. Furthermore, these primary carbonatites may sometimes be spatially ‘associated’ with primary alkali silicate rocks, but have no genetic relationship to them.
Despite their diversity in mineralogy and lithological association, most carbonatites have stable (carbon and oxygen) and radiogenic isotopic compositions that unequivocally indicate a mantle origin for their parental magmas (e.g., Bell and Simonetti 2010). Moreover, young (<200 Ma) carbonatites have Sr, Nd, and Pb isotopes that closely resemble those of oceanic islands basalts, with HIMU (‘high μ’, where μ = 238U/204Pb) and EM1 (‘enriched mantle type 1’) being the dominant mantle endmembers. This suggests they contain significant components that originated in the sub-lithospheric mantle. Noble gas and N isotopic compositions also indicate a sub-lithospheric source for the parental melts, associated with either upwelling asthenospheric mantle or with plumes arising from the deeper mantle (Bell and Simonetti 2010).
The aim of this article is to review models for the petro-genesis of carbonatites and their evolution before and during crustal intrusion or eruption. Current models for the genesis of carbonatites are illustrated in Figure 1 and include the following:
Primary carbonatite magmas emplaced into the crust directly from their mantle sources. Partial melting of carbonate-bearing peridotite or eclogite in the mantle has been shown to produce alkali-bearing, dolomitic to calcio-dolomitic melts (e.g., Wallace and Green 1988; Yaxley and Brey 2004).
Separation of an immiscible carbonatite magma from CO2-bearing, silica-undersaturated, silicate magmas (e.g., Freestone and Hamilton 1980). Immiscibility is induced by fractionation of the parental primary or evolved liquid, driving its composition to a two-liquid solvus leading to separation of silica-undersaturated silicate melt and carbonatite melt (Kjarsgaard and Peterson 1991; Brooker and Kjarsgaard 2011).
Residual melts from the fractional crystallization of evolved, carbonated, undersaturated, alkali-rich silicate liquids without immiscibility (Watkinson and Wyllie 1971).
In any of these three cases, the parental carbonatite and alkali silicate melts may be further modified in the upper mantle or crust by fractional crystallization, reaction with and/or assimilation of wall rock, and loss of alkali-rich fluids to surrounding crust via a process referred to as fenitisation. Extended fractionation of sodic or potassic alkaline silicate magmas (and of carbonatites themselves) can produce low-temperature CO2, H2O-rich (and F-rich) residual fluids, commonly referred to as carbohydrothermal fluids (Woolley and Kjarsgaard 2008). These fluids may precipitate carbonates, and also can, thus, form ‘carbonatite rocks’. Whether these are residual melts (also called ‘brine-melts’) or residual fluids is a topic of ongoing research and debate (e.g., Anenburg et al. 2020a).
We will review evidence from experimental petrology, geology, and geochemistry for these models (Fig. 1) and demonstrate that they all apply in different situations.
CARBONATE MELTS FROM THE MANTLE
Evidence from high-pressure experimental petrology has shown unequivocally that in both compositionally simple systems such as Na2O–CaO–MgO–SiO2–CO2 and in “complex” natural systems with ≥10 major and minor components, low degrees of melting of carbonate-bearing peridotite or eclogite can produce alkali-bearing, dolomitic, and calcio-dolomitic carbonate melts. The melts form at a pressure (P) ≥2 GPa (Fig. 2) and a temperature (T) and oxygen fugacity that occurs along oceanic and continental upper mantle conductive geotherms (Wallace and Green 1988; Dasgupta et al. 2004).
Melting of carbonate peridotite near its solidus to produce carbonate melts is limited to pressures ≥2.0 GPa, where the reaction
intersects the peridotite + CO2 ± H2O solidus and limits dolomite stability relative to CO2-rich fluid at lower pressures (Fig. 2). At higher pressures and subsolidus temperatures, magnesite forms via the vapour-absent reaction
Near-solidus melts from 2 to 6 GPa are dolomitic to calciodolomitic, with SiO2 ~5%–10%, Ca/Mg <1, and a total alkali content of typically 5–7 wt% (Wallace and Green 1988; Dasgupta et al. 2004) (Fig. 2).
Carbonatite melts are of very low density and viscosity and are able to wet silicate grain boundaries at melt fractions as low as 0.02% (Hunter and McKenzie 1989). They can, therefore, segregate from their sources at near-solidus conditions and, being buoyant, can migrate rapidly along silicate grain boundaries by porous flow. If dolomitic carbonatites ascend at such low melt fractions, they are likely to migrate along P–T paths close to the local geotherm, rather than along liquid adiabats. When they intersect Reaction (1), the dolomite component in the carbonatite melt will react with, and replace, orthopyroxene in the wall rock to produce metasomatic olivine and clinopyroxene, releasing a CO2-rich fluid. This process may even eliminate orthopyroxene locally, leading to the formation of apatite-bearing wehrlite, as has been documented in spinel-peridotite xenolith suites from eastern Africa and southeastern Australia (Yaxley et al. 1991; Rudnick et al. 1993).
Clearly, in this situation, Reaction (1) represents a barrier to migration through, and the extraction of, carbonatites and carbonated undersaturated silicate melts from lherzolitic or harzburgitic mantle. However, Dalton and Wood (1993) showed that the conversion of peridotite to wehrlite, which can result from Reaction (1), may armor magma conduits and pathways and thereby allow their ascent, without intersecting Reaction (1). Instead, dolomitic carbonatite melts can evolve to more CaCO3-rich compositions by reacting with the wehrlite wall rock (Dalton and Wood 1993) (Reaction 3).
The spatial relationship of carbonatites to crustal-scale faults or structures, coupled with buoyant magma rapidly transported through the mantle lithosphere, may also hinder Reactions (1) and (2), allowing alkali-bearing dolomitic magmas to reach high crustal levels or the surface (Fig. 1).
The HIMU isotopic signature of oceanic islands basalts suggests that they are derived from mantle sources containing ancient recycled oceanic crust. An alternative model for the formation of carbonatites is by partial melting of carbonate-bearing eclogite in the upper mantle (Dasgupta et al. 2004; Yaxley and Brey 2004). In this model, carbonated eclogite derived from subducted altered oceanic crust is recycled back into the mantle and stored for billions of years in the mantle before being incorporated into carbonatite source regions. Experiments have shown that carbonatite melts can be formed by partial melting of carbonated mantle eclogite (Dasgupta et al. 2004; Yaxley and Brey 2004). These studies have shown that near-solidus melts at 2.5 GPa to 5.0 GPa are sodic calciodolomitic carbonatites, and are markedly more calcic than the dolomitic melts produced by partial melting of carbonated peridotite. Yaxley and Brey (2004) suggested that carbonatite liquids formed from carbonated eclogite heterogeneities in ambient peridotite mantle may freeze to dolomite or magnesite when segregating from the eclogite source and percolating into any surrounding peridotite wallrock. Alternatively, the carbonatites may remain liquid and then migrate to the surface.
CARBONATE MELTS FORMED VIA LIQUID IMMISCIBILITY
Carbonatite liquids can form from carbonated silicate magmas if such magmas reach the two-liquid solvus that separates carbonate and silicate liquids. Melting of peridotite with only a few 1,000 ppm C, at low melt fractions and high pressures (≈2.5–3.5 GPa) yields carbonated, SiO2-undersaturated silicate melts, such as olivine melilitite or olivine nephelinite (Green 2015), with several wt% dissolved CO2. Segregation and migration of these melts into the crust, coupled with crystal fractionation of silicate phases, increases CO2 in the residual silicate liquid such that a carbonate liquid is exsolved. Thus, a carbonatite magma forms, with its associated conjugate silica-undersaturated silicate magma (e.g., Kjarsgaard et al. 1995; Weidendorfer et al. 2016).
There have been numerous experimental studies on the immiscibility of silicate–carbonate liquids at crustal and upper mantle pressures (see Brooker and Kjarsgaard 2011 and references therein). These studies have been broadly aimed at understanding the effects of variable bulk compositional parameters [alkali, SiO2 and H2O contents, Ca/Mg, Fe/Mg, pressure (including PCO2) and temperature] on the extent of the carbonate–silicate two-liquid field, and the compositions of liquids and solid phases.
Experimental studies at crustal pressures using natural rock powders have shown that immiscibility between silicate and carbonatite melts can reproduce compositions closely resembling those found in nature (Freestone and Hamilton 1980; Kjarsgaard and Peterson 1991). The rock compositions used as starting material in the two-liquid experimental studies include nephelinite or phonolite combined with natrocarbonatite from Oldoinyo Lengai (Freestone and Hamilton 1980; Kjarsgaard et al. 1995) and nephelinites from the Shombole Volcano (Kjarsgaard and Peterson 1991). These studies indicate that the immiscibility field closes off at low alkali contents with the production of conjugate Na-bearing calcic carbonatites and nephelinites. They also indicated that the two-liquid field narrows in compositional space with increasing temperature and decreasing pressure (Fig. 3). Notably, liquid immiscibility, while feasible at mantle pressures (2–3 GPa), is favoured at moderate pressures (mid-crust to lower-crust). At mantle pressures, high CO2 solubility in the silicate melt may preclude CO2-saturation and immiscibility (Brooker and Kjarsgaard 2011).
Strong support for the important role of liquid immiscibility in the generation of carbonatites associated with alkaline silicate magmas is provided by an analysis of ocean island volcanics by Schmidt and Weidendorfer (2018), who showed that the formation of carbonatites is restricted to those hotspot islands which have lavas with the lowest Siand highest alkali-contents among their primitive melts (Cape Verde and Canary Islands). In these cases, crystal fractionation of strongly silica-undersaturated primitive melts having high alkali contents drives the evolving melts into the silicate–carbonatite miscibility gap, whereas less alkaline magmas fractionate toward the alkali-feldspar thermal divide and do not exsolve a carbonatite.
The carbonatite lavas erupted from Oldoinyo Lengai are also considered to result from liquid immiscibility with the carbonatite exsolved from parental nephelinite magma (Potter et al. 2017). Supporting evidence is found in melt inclusions trapped in minerals crystallising from the lavas (e.g., gregoryite, schorlomite, nepheline, clinopyroxene) which preserve clear textural evidence of immiscibility between nephelinitic and carbonatite (and halide) liquids (Potter et al. 2017). The lavas erupted at Oldoinyo Lengai contain phenocrysts of gregoryite [(Na2K2Ca)CO3] and nyerereite [Na2Ca(CO3)2] in a complex groundmass of Na–Ca-carbonate solid solutions, Na2CO3, khanneshite, fluorite, Na-sylvite, K-halite, apatite, nepheline, sulfides, and other phases (Potter et al. 2017; Weidendorfer et al. 2017; Kamenetsky et al. 2021 this issue). The origin of the carbonatite lavas ultimately relates to liquid immiscibility from parental nephelinite magma that exsolved alkali-carbonate liquid.
The highly sodic carbonatite lavas at Oldoinyo Lengai are commonly viewed as anomalous because they do not resemble any other carbonatites, which are typically much lower in Na2CO3 and richer in CaCO3. The majority of carbonatites are alkali-depleted due to many possible processes, e.g., accumulation of crystallized calcite or dolomite, alkali loss to exsolved fluids or late-stage melts, or even weathering. The lavas of Oldoinyo Lengai are notoriously unstable under atmospheric conditions and are difficult to preserve in the surficial environment because of the H2O-soluble nature of the sodic carbonate minerals they crystallise. The lavas have been observed to evolve very rapidly after eruption as a result of alkali leaching, leaving residual calcic carbonate rocks, with the primary melt compositions only preserved as inclusions in minerals.
An example of carbonatite formation by silicate–carbonate liquid immiscibility as recorded in melt inclusions is the Kerimasi Volcano (Tanzania), only a few kilometres south of Oldoinyo Lengai. At Kerimasi, melt inclusions trapped in perovskite consist of immiscible silicate–carbonate pairs: melilitite and conjugate alkali-bearing (7–10 wt%) calciocarbonatites (Guzmics et al. 2015). However, silicate and carbonate melt inclusions in nepheline, apatite, and magnetite further reveal a range of compositions, including melt inclusions similar to the natrocarbonatites that erupted from Oldoinyo Lengai (Guzmics et al. 2015). The difference in exsolved carbonatite compositions is attributed to the more calcic parental melilitite at Kerimasi Volcano compared with the peralkaline nephelinite parent at Oldoinyo Lengai. This illustrates the important effects of the parental undersaturated alkali silicate melt composition on the nature of the exsolved conjugate carbonate liquids (Kjarsgaard and Peterson 1991).
FRACTIONAL CRYSTALLISATION OF SILICATE MELTS LEADING TO RESIDUAL CARBONATITE MELTS
In some cases, silica-undersaturated alkali melts may undergo fractional crystallisation without intersecting a two-liquid field. Fractionation may proceed sufficiently to produce an evolved, residual carbonatitic liquid. Experimental studies of this process are rare. Watkinson and Wyllie (1971) investigated the nepheline–calcite join at 25 wt% H2O and showed that a H2O-bearing liquid with a composition of 90% nepheline + 10% calcite at ~0.1 GPa could undergo fractionation with a successive assemblage of nepheline, melilite, and hydroxyhaüyne or cancrinite, leading to a calcite-rich residual liquid. This was a way to explain the sequence of rock-types observed in the Oka carbonatite complex in Quebéc (Canada), where nephe-line-, melilite + nepheline-, melilite + hydroxyhaüyne or cancrinite-, and calcite + cancrinite + melilite-bearing rocks correspond, respectively, to the ijolite, nepheline–okaite, okaite, and carbonatite. Further experimental work is necessary to assess the characteristics of CO2- and H2O-bearing silicate melt compositions, their fractionating phases, and the pressure–temperature conditions that might allow for liquid lines of descent that do not intersect a two-liquid solvus, thereby evolving all the way to residual carbonatite liquids without immiscibility.
CARBONATITE MAGMA DIFFERENTIATION
The fact that many carbonatites in the Earth’s crust are rich in CaCO3 (sövites, or calciocarbonatites) is consistent with their derivation as calcite cumulates from broadly dolomitic parental melts (Harmer and Gittins 1997). As described earlier, melts parental to carbonatites that formed in the mantle are likely to be alkali-dolomitic to calcio-dolomitic in composition. Liquids close to the compositional join CaCO3–MgCO3 are unlikely to crystallize dolomite as a liquidus or sub-liquidus phase at low pressures.
Experimental studies of the alkali carbonate–CaCO3 systems (Weidendorfer et al. 2017 and references therein) have shown that calcite (and apatite) is a crystallising phase over a large compositional and temperature range. Formation of Na-rich carbonatite (similar to those erupted at Oldoinyo Lengai) from a more calcic parental carbonatite melt was long considered highly controversial because of the existence of a thermal barrier in the Na2CO3–K2CO3–CaCO3 system at low pressures (see Fig. 3). In this system, Na-bearing calcic carbonatite liquids would be expected to crystallise calcite as the liquidus phase and evolve to a eutectic liquid with <10 mol% Na2CO3 at about 800 °C, a substantially lower Na2CO3 content and higher temperature than the erupted lavas at Oldoinyo Lengai (490–595 °C).
However, Weidendorfer et al. (2017) have elegantly demonstrated that when this system includes additional volatile and other components known to be present in the natural lavas, such as Cl, F and P2O5, the thermal divide is suppressed. They demonstrated that low-pressure crystallisation of 47.7 wt% calcite, 11.9 wt% apatite and minor clinopyroxene from a calcitic carbonate liquid with 8–9 wt% Na2O + K2O and as little as 2.7 wt% F and 4 wt% Cl will terminate at a lower temperature eutectic (≈500 °C) where a natrocarbonatite melt is saturated in Na2CO3 and nyerereite.
This raises the possibility that Oldoinyo Lengai’s highly sodic lavas are, in fact, not particularly anomalous. The processes of immiscibility and fractional crystallisation inferred or observed in this complex may, in fact, be broadly representative of other Na-poor, calcio-carbonatites which are associated with silica-undersaturated silicate magmas and were emplaced in the crust in the geological past. The low alkali contents of most carbonatites and the rarity of natrocarbonatites such as those of Oldoinyo Lengai simply reflects their likely origins as calcite-rich cumulates; a loss of Na-rich fluids to the surrounding wall rock during fenitization (see next section); the unstable nature of sodic compositions and their susceptibility to syn- and postmagmatic crystallization and fluid alteration, and especially to weathering and leaching, which may have removed evidence of their former highly sodic character.
In Figure 4, we illustrate highly simplified versions of possible scenarios in which carbonatites may be produced, including by immiscibility from a range of silica-under-saturated silicate magmas, and in settings associated with rifting, mantle plumes, and cratonic margins. In general, the compositions of the associated silicate rocks are determined by the thickness of the overlying lithosphere, which limits the depth and degree of partial melting.
SECONDARY PROCESSES AND CRUSTAL INTERACTIONS WITH CARBONATITES
Understanding carbonatites and their genesis and evolution is further complicated by the fact that carbonatites emplaced at shallow levels in the crust can undergo extensive re-equilibration and interaction with carbohydrothermal and other aqueous fluids, including meteoric waters, and also with the crust into which they are emplaced. A classic version of these processes is referred to as ‘fenitization’, whereby an alkali-rich fluid is expelled from the carbon-atite melt into the surrounding country rock and metasomatizes it, forming Na- or K-rich silicate minerals such as pyroxenes, amphiboles, and alkali feldspars.
Carbonatites commonly display complex multistage evolutionary histories that can involve magmatic, carbohydrothermal, and hydrothermal stages, which can be identified by detailed petrological and geochemical study. Many carbonatites of magmatic origin have been modified by late-stage magmatic and/or sub-solidus metasomatic processes involving CO2-rich and water-rich fluids. These fluids can lead to the remobilization and formation of secondary phases and the concentration of REEs, P, Sr, Ba and F. Experimental studies have shown that REEs are readily concentrated by hydrothermal processes and that transport and deposition of REEs is facilitated by formation of alkali-REE complexes having ligands of Cl−, F− or CO32− (Anenburg et al. 2020a). In addition to fenitization, some carbonatites have been inferred to have interacted so extensively with crustal rocks that they were ephemeral, effectively reacting out of existence (Anenburg et al. 2020b).
Hydrothermal processes involving chloride- and carbonate-rich fluids are thought to have played an important role in the formation of iron-rich carbonatites (siderite- or ankerite-bearing carbonatites aka ‘ferrocarbonatites’). However, iron-rich residual carbonatite could also form by extended fractional crystallisation of Ca–Mg carbonate melts, because Fe is highly soluble in residual chlorideand water-rich carbonate melts. Ferrocarbonatites likely formed by multistage processes during their crystallization, notably involving late overprinting by carbonate- and chloride-rich hydrothermal fluids and pervasive fenitization of the country rock. Similarly, it is clear that multistage processes involving magmatic carbonatite overprinted by later carbo-hydrothermal and/or hydrothermal events commonly play an important role in the development of REE and other associated mineral deposits.
CONCLUSIONS AND FUTURE DIRECTIONS
Carbonatites can have multiple origins and complex evolutionary histories. Most carbonatites are directly associated with sodic alkaline silicate rocks (nephelinites, melilitites) and the case for their formation by liquid immiscibility is well supported. Much of the compositional diversity of the more primitive sodic alkaline rock types associated with carbonatites that formed by liquid immiscibility (i.e., aillikite, melilitite, nephelinite, basanite) can be explained in terms of depth and degree of partial melting of the mantle. Other more evolved rock types (e.g., syenites) may reflect more extensive crystal fractionation prior to separation of an immiscible carbonatite melt. Alternatively, extended fractionation of evolved carbonated silicate magmas may result in the formation of carbonatitic rocks from residual melts, without immiscible separation of carbonate from silicate melts. Within this broad spectrum of ‘carbon-atitic’ rocks are the REE–F-rich carbonate rocks that may be precipitates from COH fluids. These rocks can be of significant economic interest due to their enrichment in REEs and other metals, such as Nb; however, formation of these ores typically involves multiple stages of enrichment.
Experimental petrology has shown that primary carbon-atite melts of alkali-rich, dolomitic to calcio-dolomitic carbonate composition can be formed by low degrees of partial melting of carbonate-bearing peridotite and eclogite at pressures greater than about 2 GPa. But, because most carbonatites are intrusive (plutonic) and were modified by crystal accumulation from the primary melts, clear evidence for a primary mantle origin may be absent. Possibly as much as a quarter of known carbonatite occurrences are not associated with putative conjugate silicate magmas (Woolley and Kjarsgaard 2008) and, therefore, arguably do not present evidence of formation by liquid immiscibility. Carbonatites without associated silicate rocks and which carry mantle xenoliths and xenocrysts have been inferred to be derived directly from the mantle (Harmer and Gittins 1997), as per Figure 1.
Advances in in situ age determinations using the U–Pb isotope system in perovskite and high-precision 40Ar/39Ar and Sr–Nd–Hf–Pb and carbon and oxygen isotopic analyses coupled with trace element analysis of mineral phases continue to better define the temporal and chemical relationships between coexisting carbonatite and silicate rocks. For example, are the associated rocks cogenetic, or comagmatic, or simply coeval? Isotope systematics also give important information about the likely sources of melts parental to carbonatites. They are also key to deciphering the complex history of carbonatite-related ore deposits. Such integrated studies are providing new insights into the nature and origin of the diverse spectrum of carbonatites, the role of carbonate in the mantle, and the sources of carbon in carbonatites. Similarly, Ca isotopic compositions of carbonatites (Amsellem et al. 2020) and chemical and isotopic compositions of inclusions and their diamond host (e.g., using O isotopes) (Timmerman et al. 2021 this issue) are providing increasing evidence of recycling of crustal carbonates during subduction into the deep, convecting mantle as a major source of carbon in carbonatite rocks.
Acknowledgments
BAK thanks the Geological Survey of Canada Targeted Geoscience Initiative rare metal activity for support. We thank Suzette Timmerman, Michael Anenburg and John Eiler for comments on an earlier draft, and Richard Brooker and Daniel Weidendorf for formal reviews. Jodi Rosso is thanked for editorial work.