Increased dominance of heat-tolerant symbionts creates resilient coral reefs in near-term ocean warming.

Climate change is radically altering coral reef ecosystems, mainly through increasingly frequent and severe bleaching events. Yet, some reefs have exhibited higher thermal tolerance after bleaching severely the first time. To understand changes in thermal tolerance in the eastern tropical Pacific (ETP), we compiled four decades of temperature, coral cover, coral bleaching, and mortality data, including three mass bleaching events during the 1982 to 1983, 1997 to 1998 and 2015 to 2016 El Niño heatwaves. Higher heat resistance in later bleaching events was detected in the dominant framework-building genus, Pocillopora, while other coral taxa exhibited similar susceptibility across events. Genetic analyses of Pocillopora spp. colonies and their algal symbionts (2014 to 2016) revealed that one of two Pocillopora lineages present in the region (Pocillopora "type 1") increased its association with thermotolerant algal symbionts (Durusdinium glynnii) during the 2015 to 2016 heat stress event. This lineage experienced lower bleaching and mortality compared with Pocillopora "type 3", which did not acquire D. glynnii. Under projected thermal stress, ETP reefs may be able to preserve high coral cover through the 2060s or later, mainly composed of Pocillopora colonies that associate with D. glynnii. However, although the low-diversity, high-cover reefs of the ETP could illustrate a potential functional state for some future reefs, this state may only be temporary unless global greenhouse gas emissions and resultant global warming are curtailed.

On incorporating forecasts into linear state space model Markov decision processes.

Weather forecast information will very likely find increasing application in the control of future energy systems. In this paper, we introduce an augmented state space model formulation with linear dynamics, within which one can incorporate forecast information that is dynamically revealed alongside the evolution of the underlying state variable. We use the martingale model for forecast evolution (MMFE) to enforce the necessary consistency properties that must govern the joint evolution of forecasts with the underlying state. The formulation also generates jointly Markovian dynamics that give rise to Markov decision processes (MDPs) that remain computationally tractable. This paper is the first to enforce MMFE consistency requirements within an MDP formulation that preserves tractability. This article is part of the theme issue 'The mathematics of energy systems'.

Population dynamics of the reef crisis: Consequences of the growing human population.

An unequivocal link exists between human population density and environmental degradation, both in the near field (local impacts) and far field (impacts due to teleconnections). Human population is most widely predicted to reach 9-11 billion by 2100, when the demographic transition is expected in all but a handful of countries. Strongest population growth is in the tropics, where coral reefs face dense human population and concomitant heavy usage. In most countries, >50% will be urbanized but growth of rural population and need for food in urban centres will not alleviate pressure on reef resources. Aquaculture will alleviate some fishing pressure, but still utilizes reef surface and is also destructive. Denser coastal populations and greater wealth will lead to reef degradation by coastal construction. Denser populations inland will lead to more runoff and siltation. Effects of human perturbations can be explored with metapopulation theory since they translate to increases in patch-mortality and decreases in patch-colonization (=regeneration). All such changes will result in a habitat with overall fewer settled patches, so fewer live reefs. If rescue effects are included, bifurcations in system dynamics will allow for many empty patches and, depending on system state relative to stable and unstable equilibria, a part-empty system may either trend towards stability at higher patch occupancy or extinction. Thus, unless the disturbance history is known, it may be difficult to assess the direction of system trajectory-making management difficult. If habitat is decreased by destruction, rescue effects become even more important as extinction-debt, accumulated by efficient competitors with weaker dispersal ability, is realized. Easily visible trends in human population dynamics combined with well-established and tested ecological theory give a clear, intuitive, yet quantifiable guide to the severity of survival challenges faced by coral reefs. Management challenges and required actions can be clearly shown and, contrary to frequent claims, no scientific ambiguity exists with regards to the serious threat posed to coral reefs by humankind's continued numerical increase.

A tropical eastern Pacific invasive brittle star species (Echinodermata: Ophiuroidea) reaches southeastern Florida.

The invasive brittle star Ophiothela mirabilis (family Ophiotrichidae), a tropical Indo-Pacific endemic species, first reported in Atlantic waters off southern Brazil in 2000, has extended its range northward to the Caribbean Sea, to the Lesser Antilles in 2011, and was first reported in south Florida in January 2019. Its occurrence in southeast Florida extends along nearly 70km of coastline, from near the Port of Miami, Miami-Dade County, northward to Deerfield Beach, Broward County. It occurs abundantly as an epizoite on octocorals, attaining population densities of 25 individuals and more per 10-cm long octocoral stem. The surface texture of octocoral hosts (rough, smooth) did not affect the densities of the ophiuroid epizoites, and there were significantly greater abundances on octocorals during two winter sampling periods than in the summer. Beige and orange-coloured morphs are sometimes present on the same octocoral stem. Gut content analysis supported a suspension feeding mode, revealing essentially identical ingested items in both colour morphs with a preponderance of amorphous detritus and filamentous algae. Molecular genetic evidence (COI & 16s) has established the identity of O. mirabilis and its relationship to invasive Brazilian populations. The orange and beige morphs form two distinct, but closely related lineages that may represent two separate introductions. The orange morph shares haplotypes with Brazilian and Caribbean specimens suggesting a further range expansion of the 'original' invasion. The beige morph, however, shares haplotypes with specimens from the Mexican Pacific and Peru and potentially represents a secondary introduction. Traits promoting dispersal and establishment of this species in new habitats are manifold: vagility and ability to cling tightly to diverse host taxa (e.g. sponges, cnidarians, bryozoans, and echinoderms), frequent asexual reproduction (fissiparity), suspension feeding, including a wide range of dietary items, possession of integument-covered ossicles and arm spines offering protection from predators, and an effective competitive edge over associated microbiota for substrate space.

Some environmental and biological determinants of coral richness, resilience and reef building in Galápagos (Ecuador).

Throughout the Galápagos, differences in coral reef development and coral population dynamics were evaluated by monitoring populations from 2000-2019, and environmental parameters (sea temperatures, pH, NO3-, PO43-) from 2015-19. The chief goal was to explain apparent coral community differences between the northern (Darwin and Wolf) and southern (Sta. Cruz, Fernandina, San Cristóbal, Española, Isabela) islands. Site coral species richness was highest at Darwin and Wolf. In the three most common coral taxa, a declining North (N)-South (S) trend in colony sizes existed for Porites lobata and Pocillopora spp., but not for Pavona  spp. Frequent coral recruitment was observed in all areas. Algal competition was highest at Darwin, but competition by bioeroding sea urchins and burrowing fauna (polychaete worms, bivalve mollusks) increased from N to S with declining coral skeletal density. A biophysical model suggested strong connectivity among southern islands with weaker connectivity to Wolf and even less to Darwin. Also, strong connectivity was observed between Darwin and Wolf, but from there only intermittently to the south. From prevailing ocean current trajectories, coral larvae from Darwin and Wolf drift primarily towards Malpelo and Cocos Islands, some reaching Costa Rica and Colombia. Mean temperature, pH, and PO43- declined from N to S. Strong thermocline shoaling, especially in the warm season, was observed at most sites. A single environmental factor could not explain the variability in observed coral community characteristics, with minimum temperature, pH and nutrient levels the strongest determinants. Thus, complex environmental determinants combined with larval connectivity patterns may explain why the northern Galápagos Islands (Darwin, Wolf) have higher coral richness and cover and also recover more rapidly than central/southern islands after region-wide disturbances. These northern islands are therefore potentially of critical conservation importance as important reservoirs of regional coral biodiversity and source of larvae.

State of corals and coral reefs of the Galápagos Islands (Ecuador): Past, present and future.

Coral populations and structural coral reefs have undergone severe reductions and losses respectively over large parts of the Galápagos Islands during and following the 1982-83 El Niño event. Coral tissue loss amounted to 95% across the Archipelago. Also at that time, all coral reefs in the central and southern islands disappeared following severe degradation and eventual collapse due primarily to intense bioerosion and low recruitment. Six sites in the southern islands have demonstrated low to moderate coral community (scattered colonies, but no carbonate framework) recovery. The iconic pocilloporid reef at Devil's Crown (Floreana Island) experienced recovery to 2007, then severe mortality during a La Niña cooling event, and is again (as of 2017) undergoing rapid recovery. Notable recovery has occurred at the central (Marchena) and northern islands (Darwin and Wolf). Of the 17 structural reefs first observed in the mid-1970s, the single surviving reef (Wellington Reef) at Darwin Island remains in a positive growth mode. The remainder either degraded to a coral community or was lost. Retrospective analyses of the age structure of corals killed in 1983, and isotopic signatures of the skeletal growth record of massive corals suggest the occurrence of robust coral populations during at least a 500-year period before 1983. The greatest potential threats to the recovery and persistence of coral reefs include: ocean warming and acidification, bioerosion, coral diseases, human population growth (increasing numbers of residents and tourists), overfishing, invasive species, pollution, and habitat destruction. Such a diverse spectrum of disturbances, acting alone or in combination, are expected to continue to cause local and archipelago-wide mortality and degradation of the coral reef ecosystem.

Seasonal Variability in Calorimetric Energy Content of Two Caribbean Mesophotic Corals.

Energetic responses of zooxanthellate reef corals along depth gradients have relevance to the refugia potential of mesophotic coral ecosystems (MCEs). Previous observations suggested that MCEs in the Caribbean are thermally buffered during the warmest parts of the year and occur within or just below the chlorophyll maximum, suggesting abundant trophic resources. However, it is not known if mesophotic corals can maintain constant energy needs throughout the year with changing environmental and biological conditions. The energetic content of tissues from the stony coral species Orbicella faveolata and Agaricia lamarcki was measured on the southern insular shelf of St. Thomas, US Virgin Islands (USVI), using micro-bomb calorimetry. Three sites for each species, at depths of 6m, 25m, 38m and 63m, were selected to capture energetic differences across the major vertical range extent of both species in the USVI-and sampled over five periods from April 2013 to April 2014. Mesophotic colonies of O. faveolata exhibited a significant reduction in energetic content during the month of September 2013 compared to mid-depth and shallow colonies (p = 0.032), whereas A. lamarcki experienced similar energetic variability, but with a significant reduction in energy content that occurred in July 2013 for colonies at sites deeper than 25m (p = 0.014). The results of calorimetric analyses indicate that O. faveolata may be at risk during late summer stress events, possibly due to the timing of reproductive activities. The low-point of A. lamarcki energy content, which may also coincide with reproduction, occurs prior to seasonal stress events, indicating contrasting, species-specific responses to environmental variability on MCEs.

A depth refugium from catastrophic coral bleaching prevents regional extinction.

Species intolerant of changing climate might avoid extinction within refugia buffered from extreme conditions. Refugia have been observed in the fossil record but are not well documented or understood on ecological time scales. Using a 37-year record from the eastern Pacific across the two most severe El Niño events on record (1982-1983 and 1997 1998) we show how an exceptionally thermally sensitive reef-building hydrocoral, Millepora intricata, twice survived catastrophic bleaching in a deeper-water refuge (> 11 m depth). During both events, M. intricata was extirpated across its range in shallow water, but showed recovery within several years, while two other hydrocorals without deep-water populations were driven to regional extinction. Evidence from the subfossil record in the same area showed shallow-water persistence of abundant M. intricata populations from 5000 years ago, through severe El Niño-Southern Oscillation cycles, suggesting a potential depth refugium on a millennial timescale. Our data confirm the deep refuge hypothesis for corals under thermal stress.

Poorly cemented coral reefs of the eastern tropical Pacific: possible insights into reef development in a high-CO2 world.

Ocean acidification describes the progressive, global reduction in seawater pH that is currently underway because of the accelerating oceanic uptake of atmospheric CO(2). Acidification is expected to reduce coral reef calcification and increase reef dissolution. Inorganic cementation in reefs describes the precipitation of CaCO(3) that acts to bind framework components and occlude porosity. Little is known about the effects of ocean acidification on reef cementation and whether changes in cementation rates will affect reef resistance to erosion. Coral reefs of the eastern tropical Pacific (ETP) are poorly developed and subject to rapid bioerosion. Upwelling processes mix cool, subthermocline waters with elevated pCO(2) (the partial pressure of CO(2)) and nutrients into the surface layers throughout the ETP. Concerns about ocean acidification have led to the suggestion that this region of naturally low pH waters may serve as a model of coral reef development in a high-CO(2) world. We analyzed seawater chemistry and reef framework samples from multiple reef sites in the ETP and found that a low carbonate saturation state (Omega) and trace abundances of cement are characteristic of these reefs. These low cement abundances may be a factor in the high bioerosion rates previously reported for ETP reefs, although elevated nutrients in upwelled waters may also be limiting cementation and/or stimulating bioerosion. ETP reefs represent a real-world example of coral reef growth in low-Omega waters that provide insights into how the biological-geological interface of coral reef ecosystems will change in a high-CO(2) world.

A natural history model of stage progression applied to breast cancer.

Invasive breast cancer is commonly staged as local, regional or distant disease. We present a stochastic model of the natural history of invasive breast cancer that quantifies (1) the relative rate that the disease transitions from the local, regional to distant stages, (2) the tumour volume at the stage transitions and (3) the impact of symptom-prompted detection on the tumour size and stage of invasive breast cancer in a population not screened by mammography. By symptom-prompted detection, we refer to tumour detection that results when symptoms appear that prompt the patient to seek clinical care. The model assumes exponential tumour growth and volume-dependent hazard functions for the times to symptomatic detection and stage transitions. Maximum likelihood parameter estimates are obtained based on SEER data on the tumour size and stage of invasive breast cancer from patients who were symptomatically detected in the absence of screening mammography. Our results indicate that the rate of symptom-prompted detection is similar to the rate of transition from the local to regional stage and an order of magnitude larger than the rate of transition from the regional to distant stage. We demonstrate that, in the even absence of screening mammography, symptom-prompted detection has a large effect on reducing the occurrence of distant staged disease at initial diagnosis.

Simulation-based parameter estimation for complex models: a breast cancer natural history modelling illustration.

Simulation-based parameter estimation offers a powerful means of estimating parameters in complex stochastic models. We illustrate the application of these ideas in the setting of a natural history model for breast cancer. Our model assumes that the tumor growth process follows a geometric Brownian motion; parameters are estimated from the SEER registry. Our discussion focuses on the use of simulation for computing the maximum likelihood estimator for this class of models. The analysis shows that simulation provides a straightforward means of computing such estimators for models of substantial complexity.

Coral reefs: corals' adaptive response to climate change.

The long-term response of coral reefs to climate change depends on the ability of reef-building coral symbioses to adapt or acclimatize to warmer temperatures, but there has been no direct evidence that such a response can occur. Here we show that corals containing unusual algal symbionts that are thermally tolerant and commonly associated with high-temperature environments are much more abundant on reefs that have been severely affected by recent climate change. This adaptive shift in symbiont communities indicates that these devastated reefs could be more resistant to future thermal stress, resulting in significantly longer extinction times for surviving corals than had been previously assumed.

Defense by symbiotic crustacea of host corals elicited by chemical cues from predator.

Observations and experiments carried out on a coral reef off the Pacific coast of Panamá demonstrated that shrimp (Alpheus lottini) and crab (Trapezia spp.) symbionts that protect their host coral (Pocillopora elegans) can detect an approaching sea star predator (Acanthaster planci) by chemical cues. Simulated feeding attacks by Acanthaster in sealed transparent bags elicited only 0.5 defensive responses (snipping at spines and tube feet, jerking the sea star, and snapping) per 3 min; defensive behavior increased significantly to 4 and 5 responses, respectively, for Acanthaster in perforated bags and for Acanthaster in direct contact with coral. Neutralized (boiled) Acanthaster elicited only 3 defensive interactions per 3 min compared with 12 interactions for live Acanthaster. Simulated feeding attacks by Oreaster, a non-corallivorous sea star, elicited only 0.5 defensive responses per 3 min, whereas Oreaster introduced with "Acanthaster water" increased the level of defensive responses to 7. These results suggest that chemical, and to a lesser extent visual (physical presence and movements of sea star), cues stimulate the defensive behavior of the symbiotic crustaceans. The ability to detect a predator at a distance is probably advantageous because in responding only to an actual threat it minimizes the time the defending symbionts spend in an exposed position on the terminal branches of the host coral and because it alerts the crustaceans to sea stars feeding at night.