Demographics and Population Dynamics Project the Future of Hard Coral Assemblages in Little Cayman

Individual hard coral colonies from four representative reef sites around Little Cayman were surveyed yearly between 2010 and 2015, a period of non-disturbance between two elevated seawater temperature anomalies. Photographic censuses produced 7069 annual transitions that were used to describe the demographics (size class frequencies, abundance, area cover) and population dynamics under non-disturbance environmental conditions. Agariciids, Porites asteroides, and Siderastrea radians have replaced acroporids as the predominant massive corals. Recruitment rates were generally low (<1 colony per m), except for a fourfold recruitment pulse of S. radians that occurred in 2011. On average, 42% of coral recruits survived their first year but only 10% lived longer than four years. Temporal comparisons allowed correction factors to be calculated for in-situ methods that overestimate recruitment of colonies ≤2 cm in diameter and overlook larger colonies. Size class transitions included growth (~33%), stasis (~33%), partial mortality (10% 33%), and whole colony mortality, which decreased with increasing colony size (typically <10% for colonies with surface areas >30 cm). Transition matrices indicated that Little Cayman assemblages have declining hard coral populations (λ < 1) but as stable size class distributions progress toward higher proportions of colonies with >150 cm surface areas, live area cover may remain relatively stable. Projection models indicated that downward population trends would be exacerbated even by mild disturbance (5% 10% mortality) scenarios. The fate of hard corals on Little Cayman’s reefs was determined to be heavily dependent on the health and transitions of agariciid colonies. Conservation strategies that currently focus on restoration of Caribbean acroporids should be expanded to include agariciids, which were previously considered “weeds”.


Introduction
Since the 1970s, Caribbean corals have been subjected to regional and local mass mortality events associated with disease outbreaks, temperature-induced bleaching, hurricanes, and anthropogenic stressors, which have resulted in a decline in average coral cover from 35% to 16% [1].The previously dominant reef builders, Acropora cervicornis and A. palmata, have been disproportionately susceptible to these disturbances and have been placed on the IUCN's Red List as critically endangered.Coral dominance has shifted from these highly susceptible branching and tabular species to more resistant and resilient massive taxa.The fates of the surviving massive corals shall shape future Caribbean coral communities.
Little Cayman is an ideal location within the Caribbean to study the population dynamics of hard coral populations because it lacks many of the anthropogenic stressors to which other reefs are exposed.Little Cayman is located 120 km northeast of Grand Cayman, 145 km south of Cuba, and 10 km southwest of Cayman Brac (Figure 1).The remote island is approximately 16 km long by 1.6 km wide, with a maximum elevation of 12 m, and is surrounded by shallow and narrow reef shelves, some of which drop off to vertical walls (e.g.Bloody Bay Wall) that reach 300 m deep.More than half of the shallow reefs have been designated as protected areas (e.g.marine parks, replenishment zones) since 1986 [2].Little Cayman has a small resident population (<200 people) and lacks agriculture, freshwater input rivers or streams, commercial fishing, industry, and ports; providing a rare opportunity to decouple the impacts that anthropogenic stressors (e.g.nutrient run off, sedimentation, pesticides, pollution, resource extraction, development) and environmental stressors have on the health of coral reefs.
Live coral cover in Little Cayman has rebounded from its low point of 14% in 2004 to an average of 25%, among the highest in the Caribbean, despite sharing a similar disturbance history with reefs region wide [1]  Outbreaks of white, yellow, and black band diseases and white plague have followed hurricane and bleaching events in 1981-82, 1990, 1996, and 1999-2000.The study reported herein took place annually from 2010 through 2015 during non-disturbance environmental conditions (i.e. between the two most recent elevated temperature anomalies and during a period when no hurricanes, disease outbreaks, or other mortality events occurred).The objectives of this study were to 1) describe the demographics and dynamics of the hard coral communities around Little Cayman, 2) use the vital rates, based on temporal comparisons of individual colonies, to develop size class transition probability matrices, and 3) project the recovery potential of these coral assemblages for several disturbances scenarios.

Annual Surveys
Scleractinian coral populations were surveyed annually along the reef crests at four locations around Little Cayman for six consecutive years, between 2010 and 2015, during the non-disturbance period between two elevated seawater temperature anomalies (i.e. annual surveys began one year after the 2009 bleaching event and ended two months prior to first signs of coral paling in 2015) (Figure 1, Table 1).Permanent monitoring stations were installed, with permission from the Cayman Islands Department of Environment, in order to allow for repetitive photographic surveys of benthic areas and specific coral colonies.Digital images were taken each summer along three 10 m × 1.5 m belt transects radiating from a central point within each monitoring station at depths of 9 -15 m using a rigid photo-framer that oriented the camera at a fixed distance of 50 cm above the benthos.The 0.5 m × 0.75 m base of the framer served as a border within each image to provide known dimensions for subsequent image analysis.Monitoring stations were haphazardly located to avoid crossing over sand channels which are unsuitable for scleractinian settlement.

Image Analysis
Each scleractinian coral which appeared as a whole colony within a given belt transect was traced using the Area Analysis function in Coral Point Count (CPCe) [5], which calculated colony area cover (planar view).Image resolution was clear enough to identify colonies as small as 0.1 cm 2 to species; however, some of the smaller Agaricia, Undaria, and Helioseris spp.colonies lacked the morphological characteristics that help to differentiate the species, so these taxa were pooled into the "agariciid" group.Colonies which first appeared within a given transect after the initial 2010 survey were considered recruits.Colonies were presumed to have died if they were absent after the initial survey, overgrown by Trididemnum solida tunicates or macroalgae, or no longer had live tissue visible on the skeletons.

Size Class Determination
Hard corals were grouped into eight size-dependent classifications ("SC") (Table 2) based on area cover.To determine the most appropriate groupings, size classifications were compared for areas associated with radius increments of 1 cm and 2 cm, assuming colonies closely resembled circular structures with Area = πr 2 .
Each of the top 10 most abundant taxa was distributed across either size class grouping, except for Siderastrea radians, the third most abundant taxa.If the larger size classes (based on 2 cm radius increments) were used, >97% of all Hard coral colonies were grouped into eight size classes based on their measured area cover and estimated radii (assuming circular colonies, A = πr 2 ).SC = size class.
S. radians colonies would be combined into the smallest size class (SC1) and their growth and partial mortality rates would be masked as size class stability which could, in turn, mask the overall vitality rates of Little Cayman's corals.
Therefore, size classes based on 1 cm radius increments were used for the analysis described herein.

Transition Matrices
Size class transition matrices were developed for the two most abundant taxa ( ) An 8 × 8 matrix has eight eigenvalues, λ i , or solutions to the matrix.The dominant eigenvalue (i.e. the largest, positive eigenvalues that is a real number) is the growth rate of the size class-structure population [6] [10]: 1) for λ > 1, the population is growing, 2) for λ = 1, the population is stable, and 3) for λ < 1, the population is declining.The ratio of the dominant eigenvalue to the absolute value of the second largest eigenvalue, known as the damping ratio, provides the rate of convergence of the population toward a stable stage distribution (i.e. the larger the damping ratio, the quicker a population will return to its stable state after a disturbance) [6] [7].Sensitivities and elasticities are measures of perturbation analyses that quantify the relative contribution of each vital rate to the population growth by adjusting each rate by a specific amount and by a specific proportion, respectively [6] [7].The dominant eigenvalues (i.e.population growth rates), stable size class distributions, sensitivities, and elasticities for the transition matrices were calculated using the PopTools add-in for Excel [11].

Demographics within Monitoring Stations
A total of 7069 annual transitions were recorded during the six-year study.The sample population was comprised of 23 taxa groups (Figure 2, Table 3).Additional species (e.g. A. cervicornis, A. palmata, P. divaricata, P. porites) are  present, and may be prevalent in certain areas around the island, but were not recorded within the belt transects.
70% of all colonies within the study area were smaller than 30 cm 2 (SC1-SC3).
Each of the larger size classes (S4-S8) contributed less than 10% to the total population each year (Figure 3).The largest temporal size class fluctuation occurred in the smallest (SC1) corals, primarily due to a recruitment pulse of S. radians in 2011 (Figure 4).

Recruitment
Recruits were observed within the monitoring stations for all recorded taxa except D. cylindricus, D. labrynthiformis, F. fragum, I. sinosa, and Meandrina spp.; however, recruits of these taxa were observed elsewhere around Little Cayman during the study period.A recruitment pulse of S. radians occurred in 2011 during which recruit abundance was fourfold greater than during each subsequent year of the study (4 recruits per m 2 compared to 1 recruit per m 2 ) (Figure 4).All other taxa had annual recruitment of <1 recruit per m 2 between 2011 and 2015.
Further investigations are required to identify pulse cycles and possible contributing factors.
Previous studies have estimated coral recruitment in Little Cayman by counting colonies that are ≤2 cm in diameter [4], the equivalent of SC1 in this study.
recruits survived their first year; 27% survived to their second year; 16% survived to their third year; and 10% survived to their fourth year (Figure 5, Table 5).
Given the high rates of mortality, recruits may die before they reach sexual reproductive maturity; therefore, the authors caution against using recruitment pulses as indicators of reef recovery.

Size Class Transitions
Approximately one-third of the SC1-SC7 colonies grew between monitoring periods regardless of size class (Table 6).Agariciids and P. furcata were capable of growing six size classes within a single year, whereas the other taxa groups grew no more than three size classes within the same time frame.However, these large growth spurts were uncommon: 72% of the growing colonies transitioned to the next larger size class.
Approximately one-third of the SC1-SC7 colonies remained within the same size class.However, 60% -100% of those colonies which achieved surface areas >150 cm 2 (SC8) had size class stability, depending on the taxa group.
Partial mortality varied by size class.Approximately one-third of the SC4-SC7 colonies decreased in size.Among the smaller SC2-SC3 and larger SC8 colonies, 10% -15% experienced partial mortality and transitioned into a smaller size class.Occasionally, shrinkage of four size classes was recorded; however, 74% of the shrinking colonies transitioned to the next smaller size class.
Between one-third and half of SC1 colonies die each year, largely due to the high mortality of recruits.The probabilities of whole colony mortality decrease with increasing colony size and are typically <10% for those colonies with surface areas >30 cm 2 (SC4-SC8).An exception is the apparent increase in mortality for P. asteroides, which increases from negligible mortality for SC6-SC7 colonies to 20% mortality for SC8 colonies.This study was conducted during a period of non-disturbance environmental conditions (e.g.no temperature anomalies, disease outbreaks, extreme storms); therefore, the cause(s) for whole colony mortality require(s) further study.

Stable Size Class Distributions, Dominant Eigenvalues, and Damping Ratios
The stable size class distributions (i.e. the eigenvectors associated with the dominant eigenvalues), dominant eigenvalues and damping ratios were determined for agariciids, P. asteroides, and all 23 hard coral taxa pooled together (Table 7).
The dominant eigenvalues (λ) were <1, which result in gradual population decay [6].The damping ratios were 1.12 -1.36, indicating the hard corals approach asymptotic behavior (stability) at similar rates among the taxa groups (i.e.similar resilience/recovery rates following a disturbance) [12].

Sensitivities and Elasticities
Sensitivities and elasticities are measures of perturbation analyses that quantify the relative contribution of each vital rate to the population growth by a specific  amount and by a specific proportion, respectively [6] [7].Sensitivity and elasticity matrices, displayed graphically as surface plots (Figure 6), indicated that the dominate eigenvalues, λ, are most affected by changes in the upper right corners of the matrices which correspond to the stability of SC8, the partial mortality of SC8 colonies into smaller size classes, and the growth of SC7 into SC8 colonies.

Population Projections
The mean annual size class transition probability matrices were used to project populations within the monitoring stations through 2040 (Figure 7), the year by which the reefs around Little Cayman has been projected to experience annual severe coral bleaching [13] [14].These projections are idealized, best case scenarios which assume no environmental disturbances or changes in the vital rates (i.e.size class transition probabilities, recruitment rates).
1) The number of P. asteroides colonies is projected to decline by 23% over the 13 years following this study until a stable population distribution is reached.The largest changes in the population structure are projected to be a 16% decline in SC1, a 10% decline in SC2, and a 10% increase in SC8.The mid-sized colonies (SC3-SC7) are projected to increase by ≤4% each.The trend toward larger colonies is projected to nearly balance with the decline in the number of colonies, resulting in a ≤1% increase in the total area cover of P. asteroides in 2040 compared to 2015 (assuming the mean surface area of SC8 corals remains unchanged within this timeframe).
2) The number of agariciid colonies is projected to decline by 11% for six years, followed by a gradual 13-year recovery before stabilizing at 93% of

(
agariciids and Porites asteroides) and for all hard corals pooled together to represent Little Cayman overall.(S. radians, the third most abundant taxa, was comprised of small colonies in SC1-3 only; therefore, the respective size class transitions were not developed separately.)The use of eight size classes resulted in 8 × 8 matrices in which each element represents the mean probability of moving from a starting size class or "state" (column) to ending size class or "fate" (row)[6] [7].The matrices include growth (G) to the next largest size class, size class stability (S) by remaining within the same group, or partial mortality (PM) to a smaller size class.Corals may also experience fission (i.e. the regression of a single colony into multiple smaller ramets) or fusion (i.e. two or more ramets grow together)[8] [9].In these cases, which were rare in this study, the area cover for all ramets were pooled and compared to the size class for the respective parent colony which underwent fission or for the resulting fused colony and were recorded as a partial morality, size class stability or growth transition.The resulting probability matrices were used to project the number of corals in each size class during year t + 1, which equals the number in each size class at year t multiplied by the respective size class transition probabilities plus the mean number of corals which enter the population through recruitment (R) (Equation (1)).

Five-year mean
percentages (± STD) of colonies within each size class that are recruits.Mean percentages may be used as correction factors for in-situ recruit estimation surveys.AGAR = agariciids; PAST = P. asteroides; PFUR = P. furcata; SRAD = S. radians; SSID = S. siderea; OTHERS = 13 common and rare taxa of massive corals pooled together.

Table 1 .
Descriptions of repetitive monitoring sites.

Table 2 .
Size-dependent classifications for hard coral colonies. )

Table 3 .
Hard coral taxa within monitoring stations.= Greater than 100 individual colonies recorded within the belt transects during one or more years; Common = Between 5 and 100 colonies; Rare = Less than 5 colonies. Abundant

Table 6 .
Mean annual transition probability matrices.

Table 7 .
Stable size class distributions, dominant eigenvalues, and damping ratios.
Stable size class distributions and eigenvalues from mean annual transition probability matrices.