title: Agreeable semigroups

authors: Jackson, Marcel

subjects: mathematics

abstract: This paper concerns the theory of partial maps under composition and more generally, the RC-semigroups introduced by Jackson and Stokes [Semigroup Forum 62 (2001) 279–310] (semigroups with a unary operation called (right) closure). Many of the motivating examples have a natural meet-semilattice structure; the inverse semigroup of all injective partial transformations of a set and the semigroup of all binary operations under composition are two examples. We here view the semilattice meet as an additional operation, thereby obtaining a variety of algebras with one unary and two binary operations. The two non-semigroup operations are then shown to be captured by a single binary operation, via the notion of an agreeable semigroup. We look at a number of properties of these structures including their congruences (which are uniquely determined by their restriction to certain idempotents), a relationship with so-called interior semigroups, and a natural category associated with a large variety of RC-semigroups (which includes all inverse semigroups). For example, we show that the existence of equalisers in this category is intimately connected with the existence of the natural meet-semilattice structure.

text: Agreeable semigroups This paper concerns the theory of partial maps under composition and more generally, the RC-semigroups introduced by Jackson and Stokes [Semigroup Forum 62 (2001) 279–310] (semigroups with a unary operation called (right) closure). Many of the motivating examples have a natural meet-semilattice structure; the inverse semigroup of all injective partial transformations of a set and the semigroup of all binary operations under composition are two examples. We here view the semilattice meet as an additional operation, thereby obtaining a variety of algebras with one unary and two binary operations. The two non-semigroup operations are then shown to be captured by a single binary operation, via the notion of an agreeable semigroup. We look at a number of properties of these structures including their congruences (which are uniquely determined by their restriction to certain idempotents), a relationship with so-called interior semigroups, and a natural category associated with a large variety of RC-semigroups (which includes all inverse semigroups). For example, we show that the existence of equalisers in this category is intimately connected with the existence of the natural meet-semilattice structure.

year: 2003

title: Late Miocene turnover of molluscan faunas, New Zealand: Taxonomic and ecological reassessment of diversity changes at multiple spatial and temporal scales

authors: Hendy, Austin J.W.

subjects: diversity

abstract: Previous estimates of molluscan biodiversity during the Neogene in New Zealand have revealed a pattern of significant diversity decline during the latest Miocene. This study uses an occurrence-based dataset (derived from published literature) to examine this pattern in further detail with both traditional synoptic measures and subsequent sampling standardization. Synoptic analyses of regional-scale data reveal diversity trajectories similar to those previously established, and rarefaction techniques demonstrate that the inferred pattern of Late Miocene diversity decline and Early Pliocene rebound is only somewhat biased by variations in sampling intensity. The pattern is also affected by temporal variations in the preservation of shelf paleoenvironments, with representation of highly diverse shallow-water facies varying considerably between biostratigraphic stages. The sampling and corresponding synoptic genus richness of biogeographic areas within the New Zealand region is also uneven. Within a single sedimentary basin sampled at high temporal resolution (Wanganui Basin), new data suggest that Late Miocene faunas were as diverse as those of the Early Pliocene, contrasting with the pattern of diversity decrease and subsequent increase observed at the regional spatial scale in prior studies. However, an ecological analysis of the new data demonstrates that turnover and restructuring of benthic communities did take place at the end of the Late Miocene. These findings suggest that spatial scale and temporal resolution are important considerations in determining the magnitude of diversity and ecological change observed in paleontologic studies. Contemporaneous biodiversity may not be similarly expressed at varying spatial or temporal scales in the fossil record. Rather, regional patterns of diversity change are governed by a complex interplay of not only large-scale environmental factors (e.g. temperature control), but also independent basin-scale processes (e.g. basin subsidence) and local sampling intensity.

text: Late Miocene turnover of molluscan faunas, New Zealand: Taxonomic and ecological reassessment of diversity changes at multiple spatial and temporal scales Previous estimates of molluscan biodiversity during the Neogene in New Zealand have revealed a pattern of significant diversity decline during the latest Miocene. This study uses an occurrence-based dataset (derived from published literature) to examine this pattern in further detail with both traditional synoptic measures and subsequent sampling standardization. Synoptic analyses of regional-scale data reveal diversity trajectories similar to those previously established, and rarefaction techniques demonstrate that the inferred pattern of Late Miocene diversity decline and Early Pliocene rebound is only somewhat biased by variations in sampling intensity. The pattern is also affected by temporal variations in the preservation of shelf paleoenvironments, with representation of highly diverse shallow-water facies varying considerably between biostratigraphic stages. The sampling and corresponding synoptic genus richness of biogeographic areas within the New Zealand region is also uneven. Within a single sedimentary basin sampled at high temporal resolution (Wanganui Basin), new data suggest that Late Miocene faunas were as diverse as those of the Early Pliocene, contrasting with the pattern of diversity decrease and subsequent increase observed at the regional spatial scale in prior studies. However, an ecological analysis of the new data demonstrates that turnover and restructuring of benthic communities did take place at the end of the Late Miocene. These findings suggest that spatial scale and temporal resolution are important considerations in determining the magnitude of diversity and ecological change observed in paleontologic studies. Contemporaneous biodiversity may not be similarly expressed at varying spatial or temporal scales in the fossil record. Rather, regional patterns of diversity change are governed by a complex interplay of not only large-scale environmental factors (e.g. temperature control), but also independent basin-scale processes (e.g. basin subsidence) and local sampling intensity.

year: 2009

title: Studies on the health and bacterial symbionts of  toheroa (Paphies ventricosa)

authors: Bennion, Matthew Joseph

subjects: Shellfish health

abstract: Disease outbreaks in marine species can have devastating consequences for host populations, host-associated species assemblages, ecosystem functioning, and for human users of these marine resources. At present, the risk factors associated with disease outbreaks, such as warming and pollution, are increasing. Given the increasing risk of disease outbreaks and the role that parasites play in marine ecosystems, there is a vital need to gain knowledge of marine diseases for species conservation, and the monitoring, management, and forecasting of disease. The field of marine disease ecology is growing, but many facets of our understanding remain in their infancy. Faced with a lack of baseline health data, efforts to combat disease outbreak in the ocean are impeded, even though the future of food security hinges on an ability to source food from the ocean. With a shift towards aquaculture, in particular bivalve aquaculture, knowledge of ambient health of wild and farmed species will dictate both yield, and our ability to protect wild stocks. 
Disease outbreak poses added risk to species that are already in peril. The toheroa (Paphies ventricosa) is a threatened surf clam endemic to Aotearoa (New Zealand). Once bountiful, overharvesting and population collapse put an end to the large-scale fisheries of the early and mid-1900s. The protections enacted on toheroa populations should have ensured their recovery, but recovery has not occurred. Disease has been suggested as one possible explanation. However, without knowledge of disease dynamics in toheroa populations, restorative efforts risk failure, or worse, inflicting further damage. Intracellular microcolonies of bacteria (IMCs) have been linked to numerous shellfish mass mortality events (MMEs) in Aotearoa in recent years, and were first detected in toheroa in 2017. This discovery raised questions regarding the role IMCs might be playing in preventing the recovery of toheroa populations. 
To address this uncertainty, this thesis set out to investigate what pathogens and parasites are present in toheroa, and determine what effect they might be having on toheroa health. A histopathology survey was conducted to gather fundamental baseline health information on toheroa populations across their entire distribution. IMCs were found to be the only potential pathogens of note. Histology data coupled with Bayesian models indicated that the probability of higher IMC intensity was associated with decreased toheroa condition. Using PCR, DNA sequencing, and in situ hybridisation, IMCs were characterised as bacteria in the genus Endozoicomonas. In many marine organisms, Endozoicomonas spp. are cosmopolitan members of associated-bacterial communities, often fulfilling biogeochemical cycling functions in host tissues. In toheroa populations, Endozoicomonas spp. abundance was found to be seasonal, but site specificity indicated habitat characteristics (specifically, the presence of freshwater outflows) might be a significant driver of their abundance. The bacterial community of toheroa was subsequently investigated using 16S rRNA gene sequencing, and candidates common to other coastal bivalve molluscs were found to be dominant, including Spirochaetaceae, Mycoplasmataceae, and Endozoicomonadaceae (in order of relative dominance). Freshwater outflows appeared to be such a significant driver of microbiome taxonomic dissimilarity, that specimens collected from sites 1240 km apart hosted more similar bacterial communities than specimens from sites with and without streams on the same beach and within the same region. The key indicator taxa driving microbiome dissimilarity were found to be Endozoicomonas spp. and sulfate-reducing bacteria in the phylum Desulfobacterota. 
Gas bubbles were also observed on the shells of toheroa at the same time that IMCs were first detected. At that stage, temperature and total dissolved gaseous pressure was thought to contribute to their manifestation. To gain a better understanding of this phenomenon, a spatio-temporal survey was conducted which revealed an association of high gas bubble intensity with the austral-autumn/winter and freshwater outflows. A new hypothesis is therefore presented that links gas bubbles to sulfate-reducing bacteria and hydrogen sulfide (H₂S), a by-product of anaerobic digestion. Given the apparent influence of freshwater on toheroa intrinsic health, the capacity for streams to deliver pollutants to toheroa beds was assessed. Results gained from inductively coupled plasma-mass spectrometry (ICP-MS) suggest that despite the modified nature of adjacent land, streams do not deliver significant loads of bioavailable trace metals to toheroa beds in the intertidal zone. Instead, nutrition in the form of large phytoplankton blooms in autumn/winter is thought to be the primary source of bioavailable trace metals for toheroa.
No observations of significant pathogenesis, associated with Endozoicomonas species, were made throughout this research. Furthermore, during the timeframe of this research (apart from intermittent mortality events reported), there is no evidence of an ongoing disease epidemic in toheroa populations. While not providing evidence for the factor preventing the recovery of toheroa, this research does have implications for the ongoing conservation and management of toheroa. It seems reasonable to assume that infectious disease is not a major factor contributing to the limited recovery of toheroa throughout Aotearoa. Instead, associations made between freshwater outflows, nutrition, and detritus indicate that habitat requirements provided by freshwater streams are having significant effects on toheroa health, survival, and homeostasis. Furthermore, evidence presented suggests that the Endozoicomonas spp. present in toheroa and other Aotearoa shellfish are likely to be an important endosymbiont. In the future, studies on remaining toheroa populations should prioritise nutritional health. Namely, what role symbionts play in toheroa nutrition, and how niche requirements shape symbiont community composition and function in toheroa tissues. Answers to these questions could profoundly increase the success of toheroa restoration and conservation efforts.

text: Studies on the health and bacterial symbionts of  toheroa (Paphies ventricosa) Disease outbreaks in marine species can have devastating consequences for host populations, host-associated species assemblages, ecosystem functioning, and for human users of these marine resources. At present, the risk factors associated with disease outbreaks, such as warming and pollution, are increasing. Given the increasing risk of disease outbreaks and the role that parasites play in marine ecosystems, there is a vital need to gain knowledge of marine diseases for species conservation, and the monitoring, management, and forecasting of disease. The field of marine disease ecology is growing, but many facets of our understanding remain in their infancy. Faced with a lack of baseline health data, efforts to combat disease outbreak in the ocean are impeded, even though the future of food security hinges on an ability to source food from the ocean. With a shift towards aquaculture, in particular bivalve aquaculture, knowledge of ambient health of wild and farmed species will dictate both yield, and our ability to protect wild stocks. 
Disease outbreak poses added risk to species that are already in peril. The toheroa (Paphies ventricosa) is a threatened surf clam endemic to Aotearoa (New Zealand). Once bountiful, overharvesting and population collapse put an end to the large-scale fisheries of the early and mid-1900s. The protections enacted on toheroa populations should have ensured their recovery, but recovery has not occurred. Disease has been suggested as one possible explanation. However, without knowledge of disease dynamics in toheroa populations, restorative efforts risk failure, or worse, inflicting further damage. Intracellular microcolonies of bacteria (IMCs) have been linked to numerous shellfish mass mortality events (MMEs) in Aotearoa in recent years, and were first detected in toheroa in 2017. This discovery raised questions regarding the role IMCs might be playing in preventing the recovery of toheroa populations. 
To address this uncertainty, this thesis set out to investigate what pathogens and parasites are present in toheroa, and determine what effect they might be having on toheroa health. A histopathology survey was conducted to gather fundamental baseline health information on toheroa populations across their entire distribution. IMCs were found to be the only potential pathogens of note. Histology data coupled with Bayesian models indicated that the probability of higher IMC intensity was associated with decreased toheroa condition. Using PCR, DNA sequencing, and in situ hybridisation, IMCs were characterised as bacteria in the genus Endozoicomonas. In many marine organisms, Endozoicomonas spp. are cosmopolitan members of associated-bacterial communities, often fulfilling biogeochemical cycling functions in host tissues. In toheroa populations, Endozoicomonas spp. abundance was found to be seasonal, but site specificity indicated habitat characteristics (specifically, the presence of freshwater outflows) might be a significant driver of their abundance. The bacterial community of toheroa was subsequently investigated using 16S rRNA gene sequencing, and candidates common to other coastal bivalve molluscs were found to be dominant, including Spirochaetaceae, Mycoplasmataceae, and Endozoicomonadaceae (in order of relative dominance). Freshwater outflows appeared to be such a significant driver of microbiome taxonomic dissimilarity, that specimens collected from sites 1240 km apart hosted more similar bacterial communities than specimens from sites with and without streams on the same beach and within the same region. The key indicator taxa driving microbiome dissimilarity were found to be Endozoicomonas spp. and sulfate-reducing bacteria in the phylum Desulfobacterota. 
Gas bubbles were also observed on the shells of toheroa at the same time that IMCs were first detected. At that stage, temperature and total dissolved gaseous pressure was thought to contribute to their manifestation. To gain a better understanding of this phenomenon, a spatio-temporal survey was conducted which revealed an association of high gas bubble intensity with the austral-autumn/winter and freshwater outflows. A new hypothesis is therefore presented that links gas bubbles to sulfate-reducing bacteria and hydrogen sulfide (H₂S), a by-product of anaerobic digestion. Given the apparent influence of freshwater on toheroa intrinsic health, the capacity for streams to deliver pollutants to toheroa beds was assessed. Results gained from inductively coupled plasma-mass spectrometry (ICP-MS) suggest that despite the modified nature of adjacent land, streams do not deliver significant loads of bioavailable trace metals to toheroa beds in the intertidal zone. Instead, nutrition in the form of large phytoplankton blooms in autumn/winter is thought to be the primary source of bioavailable trace metals for toheroa.
No observations of significant pathogenesis, associated with Endozoicomonas species, were made throughout this research. Furthermore, during the timeframe of this research (apart from intermittent mortality events reported), there is no evidence of an ongoing disease epidemic in toheroa populations. While not providing evidence for the factor preventing the recovery of toheroa, this research does have implications for the ongoing conservation and management of toheroa. It seems reasonable to assume that infectious disease is not a major factor contributing to the limited recovery of toheroa throughout Aotearoa. Instead, associations made between freshwater outflows, nutrition, and detritus indicate that habitat requirements provided by freshwater streams are having significant effects on toheroa health, survival, and homeostasis. Furthermore, evidence presented suggests that the Endozoicomonas spp. present in toheroa and other Aotearoa shellfish are likely to be an important endosymbiont. In the future, studies on remaining toheroa populations should prioritise nutritional health. Namely, what role symbionts play in toheroa nutrition, and how niche requirements shape symbiont community composition and function in toheroa tissues. Answers to these questions could profoundly increase the success of toheroa restoration and conservation efforts.

year: 2021