Fillable Form 2: the northern Florida Keys, USA Population (Inter Research Science Publisher)

Fill Online, Printable, Fillable, Blank Form 2: the northern Florida Keys, USA Population (Inter Research Science Publisher) Form

Use Fill to complete blank online INTER RESEARCH SCIENCE PUBLISHER pdf forms for free. Once completed you can sign your fillable form or send for signing. All forms are printable and downloadable.

Form 2: the northern Florida Keys, USA Population (Inter Research Science Publisher)

On average this form takes 1 minutes to complete

The Form 2: the northern Florida Keys, USA Population (Inter Research Science Publisher) form is 19 pages long and contains:

0 signatures
0 check-boxes
3 other fields

Country of origin: US
File type: PDF

Use our library of forms to quickly fill and sign your Inter Research Science Publisher forms online.

BROWSE INTER RESEARCH SCIENCE PUBLISHER FORMS

Related forms

Fill has a huge library of thousands of forms all set up to be filled in easily and signed.

Fill in your chosen form

Sign the form using our drawing tool

Send to someone else to fill in and sign.

find another form

ENDANGERED SPECIES RESEARCH

Endang Species Res

Vol. 19: 157–169, 2012

doi: 10.3354/esr00475

Published online December 20

INTRODUCTION

Corals are a recent addition to endangered species

lists. In 2006, the Atlantic elkhorn coral Acropora

palmata was classified as ‘threatened’ on the US

Endangered Species List

along with its congener A.

cervicornis. Currently, 82 additional corals are con-

sidered candidate species (NMFS 2010). In 2008,

corals were included on the International Union for

Conservation of Nature (IUCN) Red List for the first

time. Of all reef-building corals, 33% with sufficient

data were listed as threatened (Vulnerable, Endan-

gered, and Critically Endangered), a percentage

rivaled only by amphibians in the animal kingdom

(Carpenter et al. 2008, IUCN 2011).

Like many depleted corals, Acropora palmata was

neither historically rare nor tightly restricted in its

geographic range. Although there are unexplained

gaps in the fossil record (Hubbard et al. 2008), the

persistence, dominance, and sheer abundance of A.

palmata throughout time and space qualified it as the

dominant shallow-water reef builder in the Carib -

bean from the late Pleistocene through at least the

early Holocene (Adey et al. 1977, Jackson 1992, Hub-

bard et al. 2005, 2008). During this time, A. palmata

was dominant on 80% of shallow reefs surveyed

Population dynamics of threatened elkhorn coral in

the northern Florida Keys, USA

Tali Vardi

, Dana E. Williams

, Stuart A. Sandin

Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92037, USA

University of Miami, Miami, Florida 33149, USA

ABSTRACT: Caribbean elkhorn coral Acropora palmata (Lamarck, 1816) was once so widespread

and abundant that geologists use its fossils to measure sea levels from the Pleistocene through the

Holocene. Now it exists at a small fraction of its former abundance and is listed, along with a con-

gener, as ‘threatened’ under the US Endangered Species Act. We conducted annual demographic

surveys on the northern Florida Keys (USA) population from 2004 to 2010. Percent cover of the

benthos, number of colonies, and dominance by large individuals declined throughout the study

period. We created population matrix models for each annual interval of the study, which included

a severe hurricane year (2005–2006). Hurricane recurrence was simulated stochastically along

with multiple outplanting scenarios. Population depletion is predicted given a return time for

severe hurricanes of 20 yr or less. Elasticity analysis showed that the largest individuals have the

greatest contribution to the rate of change in population size. Active management through out-

planting can provide a positive population trajectory over the short term, especially if colonies are

reared for several years before transplanting. However, the former abundance of this species sug-

gests that background life history traits, specifically rates of growth versus shrinkage measured

herein, are fundamentally different from what they must have been in the past. Ultimately, recov-

ery of this species will depend on enacting local short-term management solutions while improv-

ing regional and global environmental conditions.

KEY WORDS: Acropora palmata · Caribbean · Demography · Disturbance · Recruitment ·

Stochastic · Matrix model

Resale or republication not permitted without written consent of the publisher

On 30 November 2012 NOAA proposed elevating this sta-

tus to ‘endangered’ and proposed listing an additional 66

species of coral

Endang Species Res 19: 157–169, 2012

throughout the Caribbean, often forming a monocul-

ture along reef crests and upper reef slopes (Jackson

1992). This percentage dropped to 40% by 1983, and

to less than 20% by 1990 (Jackson et al. 2001).

Although A. palmata is still present throughout its

range (Lang 2003), ecological data reveal a continu-

ing decline in abundance. As of 2005, most popula-

tions were at 2 to 20% of the 1970s baselines (Bruck-

ner & Hourigan 2000, Carpenter et al. 2008).

The Atlantic Acropora Status Review lists the fol-

lowing stressors to A. palmata: disease, temperature

anomalies and bleaching, natural and anthropogenic

branch breakage, competition, predation, excessive

sedimentation and nutrification, boring sponges,

toxic compounds in the water column, loss of genetic

diversity, and others (Acropora Biological Review

Team 2005). Lists, however, are a deceptively simple

presentation of environmental stressors, feedback

loops and synergies lurk between the commas (Kline

et al. 2006). Further, lists present a snapshot of a

dynamic system in which threats can intensify as

population abundance declines. For example, coral

bleaching episodes are frequently followed by dis-

ease outbreaks (Har vell et al. 1999, 2007, Jones et al.

2004). Storms can cause direct physical damage and

inflict longer-term damage by fragmenting large

colonies into smaller colonies that have higher rates

of mortality (Lirman 2003, Williams et al. 2006). Mul-

tiple storms can result in the decrease of asexual

recruitment via fragmentation (Williams et al. 2008).

Also, density of corallivorous snails, particularly

Coralliophila abbreviata, on Atlantic acroporids can

increase dramatically after hurricanes, impeding or

preventing population recovery (Knowlton et al.

1990, Baums et al. 2003, del Mónaco et al. 2011).

Matrix population modeling can offer a glimpse

of the immediate future of a population of Acropora

palmata colonies. Matrix models are constructed

with annual demographic data collected over a

time frame appropriate to the life history of an

organism. Data are converted into a matrix of tran-

sition probabilities, delineating the likelihood of

changing from one life stage or size class to

another. Each year the number of individuals in

each size class is multiplied by the transition

matrix, resulting in a projection of the population

size structure for the following year. Hughes (1984)

developed a size-based matrix model (an adaptation

of the classic age-based matrix model) for organ-

isms with a clonal life history, in which individuals

can not only grow and die, but also shrink and

fragment. For stony corals, shrinking is defined as a

reduction in the extent of the skeleton or a reduc-

tion in the extent of live tissue covering the skele-

ton. Fragmentation is a form of asexual reproduc-

tion wherein a portion of live coral (skeleton and

tissue) breaks off a colony, lands on the substrate,

attaches, and forms a new colony (Fig. 1).

158

⎫

⎬

⎭

a Grow

b Loop

c Shrink

d New Fragment

Fig. 1. Acropora palmata. Life cycle diagram

and corresponding matrices. Size classes 1 to 4

are represented by increasing circle sizes. (a−c)

Individuals can transition from one size class to

any other; they can grow, g; loop (stay in the

same size class), l; or shrink, s, comprising the

transition matrix, T. Although growing more

than 1 size class during a transition is mathe-

matically possible, in the model presented here

it is biologically possible only through fusion of

clonal fragments. (d) Arrival of new fragments,

represented by the fragmentation matrix, F, is

defined to include new asexually or sexually

derived colonies in any of the 3 smallest size

classes. (e) General form of the matrix model,

A. Subscripts are left off for clarity. Figure

modified with permission from Hughes (1984)

Vardi et al.: Elkhorn coral population model

Disturbance is a governing force in coral population

structure, and during these events, transition proba-

bilities are characteristically different from those dur-

ing background conditions (Hughes 1984, Fong &

Glynn 1998, Edmunds 2010). In the Carib bean, storms

and hurricanes are the major disturbance events on

coral reefs (Gardner et al. 2005) and are thus a critical

component for any coral population model. Although

Acropora palmata is dependent on a moderate level of

wave action for asexual reproduction (Highsmith et

al. 1980) and sloughing off sediment (Rogers 1983,

Acevedo et al. 1989), severe storms can cause high

rates of fragmentation (Lirman 2003) and extreme

damage (Woodley 1981, Lirman & Fong 1997).

We created a size-based matrix model with distur-

bance for the Acropora palmata population of the

northern Florida Keys, USA. We collected demo-

graphic data for 7 consecutive years, from 2004 to

2010, from which we estimated annual transition

rates for 6 annual intervals (2004–2005, 2005–2006,

2006–2007, 2007–2008, 2008–2009, 2009–2010). With

this rich data set, we simulated a stochastic environ-

ment by multiplying the population size structure

each year by a random draw from the 6 matrices.

During our study, the population experienced severe

hurricane conditions in 2005; thus 1 snapshot of these

disturbance dynamics was captured. Mild storms

occurred in the winter of 2004 and summer of 2008,

and were considered background conditions along

with 2006, 2007, and 2009. We used our population

model to determine critical life history stages, predict

future population abundance, explore management

actions, and provide a realistic time frame for recov-

ery planning for this population.

MATERIALS AND METHODS

Study site and sampling methodology

A rapid survey conducted throughout the Florida

Keys from 1999 to 2001 found Acropora palmata pri-

marily in high-relief spur and groove reefs and con-

centrated in the northern Keys (off Key Largo; Acro-

pora Biological Review Team 2005). In this area, 5 of

7 reefs were randomly selected for study. Fifteen

non-overlapping, 150 m

permanent plots distributed

among Molasses, French, Elbow, Key Largo Dry

Rocks, and Carysfort Reefs were established in 2004

(see Table S1 in the supplement at www.int-res. com/

articles/ suppl/n019p157_supp.pdf). Each plot was

circular with a radius of 7 m. At the outset of the

study, all plots had a minimum of 12 A. palmata

colonies. Areas of high A. palmata density (thickets)

are no longer typical in this area, and were purpose-

fully excluded so as to manageably track individuals

as defined above. Results are thus applicable only to

A. palmata stands exhibiting moderate density. For

a more detailed description of plot selection, see

Williams et al. (2008).

Individuals in this study were defined as neither

genets nor ramets, as a distinction between the 2

cannot be made in the field (Miller et al. 2007).

Rather, an individual was defined as any continuous

live tissue or patches of tissue on the same underly-

ing skeleton (for a complete definition see Williams

et al. 2006). Fragments, though clones, were consid-

ered reproductive output congruent with the defini-

tions presented by Carpenter et al. (2008) and High-

smith (1982) for all corals. Only ramets attached to

the substrate, as opposed to loose fragments, were

counted as individuals.

Measuring the size of an Acropora palmata colony

is not straightforward. Unlike a boulder coral, it does

not have a consistent shape, and unlike a tree, which

bears a morphological likeness to the prototypical A.

palmata colony, there is no standard measurement

such as diameter at breast height (Fig. 2). Because

corals experience partial mortality, an estimate of the

percentage of live tissue is incorporated into our

metric. We multiplied the longest axis of the colony

(length) and longest perpendicular axis (width) as

viewed from above, by a visual estimate of the per-

centage of live tissue, to estimate 2-dimensional pro-

jected live surface area, or colony size.

Each year, every colony, including any newly

attached individual, was identified and measured (as

described in detail by Williams et al. 2006). Surveys

were conducted in fall 2004, and each spring from

2005 to 2010. The fall survey was between 19 Sep-

tember and 22 October, spring surveys were con-

ducted between 1 May and 1 July, and all surveys

were completed within an average of 4 consecutive

weeks. In Spring 2005, only 6 of the 15 plots were

surveyed, and the remainder were surveyed in the

summer. Data from plots surveyed in the spring were

used for modeling, but both spring and summer data

were used for density estimates (see Table S1 for

these abundance data).

Designation of size classes

We used size, rather than age or stage, to classify

individuals, because size classifications lend them-

selves more easily to estimates of percent benthic

159

Endang Species Res 19: 157–169, 2012

cover of Acropora palmata on the reef, which is ulti-

mately our topic of interest. Further, Hughes & Con-

nell (1987) showed that size has a stronger influence

than age on coral population dynamics, and Lirman

(2000) demonstrated this for A. palmata specifically.

Size is also correlated with asexual recruitment in A.

palmata, because larger colonies have more branches,

and branches fragment to produce asexual recruits.

Further, living surface area is positively correlated

with the amount of gametes a colony produces

(Soong & Lang 1992). We used 2-dimensional pro-

jected surface area, which is directly proportional

with 3-dimensional surface area, as our size metric

(Holmes & Johnstone 2010, T. Vardi unpubl. data).

Four size classes were defined based on details of

the biology and life history of Acropora palmata. Size

class 1 (SC1) was defined to include all individuals

smaller than 100 cm

, and included both young-of-

year sexual recruits and colonies that may have

grown or shrunk into that size range. Given that the

highest linear extension rate measured in the Florida

Keys is 10 cm yr

−1

(Acropora Biological Review Team

2005), a new sexual recruit could grow rapidly for a

year, and still be a member of the smallest size class.

We chose an upper limit of 900 cm

for SC2 because

colonies up to this size typically have a low clonal

fecundity due to a lack of long branches. SC3 individ-

uals were defined with an upper limit of 4000 cm

and as such are more likely than SC2 colonies to

have long branches, leading to a higher probability

of asexual reproduction. SC4 individuals are defined

as those exceeding 4000 cm

, a size at which approx-

imately 90% of colonies produce gametes (Soong &

Lang 1992); SC4 colonies are thus the most likely to

reproduce by both sexual and asexual means.

Model development

Matrix population modeling (Hughes 1984, Caswell

2001) was used to explore Acropora palmata demo -

graphy, using the equation

160

Fig. 2. Acropora palmata. Examples of colonies in size classes 1 to 4, clockwise from top left. Size classes are defined as 0−100,

100−900, 900−4000, and >4000 cm

, and mean diameters observed were 6.5, 19, 46, and 106 cm for size classes 1 to 4, respectively

Vardi et al.: Elkhorn coral population model

t +1

= An

t +1

(1)

in which n

is a vector of the number of individuals in

each size class at time t. A square matrix with dimen-

sions equal to the number of size classes, A, is the

sum of a transition matrix, T, and a fragmentation

matrix, F (Fig. 1).

Each value in T, t

, represents a probability of tran-

sitioning from size class j to i in consecutive time

points. Transition probabilities are estimated by sum-

ming the number of times a particular transition

occurs over a sampling duration and dividing by the

number of individuals in j. Because the abundance

per size class changes each year, each transition is

based on a different sample size (see Abundance in

Table 1). Corals can grow (g), shrink (s), or stay the

same size (l); thus all positions in T can be >0

(Fig. 1a−c). Entries in the fragmentation matrix, f

are based on the number of new individuals that

arrive in the study area during the same time interval

(Fig. 1d). Since sexual and asexual recruits cannot be

distinguished in the field (Miller et al. 2007), we com-

bined these 2 categories.

The F matrix is traditionally known as the fertility

matrix. In corals, a measure of fertility would comprise

the probability of per-colony gamete release, multi-

plied by gamete survival. Recruitment would comprise

those 2 probabilities multiplied by the probability of

larval survivorship in the water column and settlement

survivorship. Here we redefine the fertility matrix as

the fragmentation matrix, F, since asexual reproduc-

tion dominates in Acropora pal m ata. Though critical

for long-term persistence, sexual recruitment events

are extremely rare (Bak & Engel 1979, Edmunds &

Carpenter 2001), and thus can be ignored for short-

term projections of this highly clonal species, as in-

cluding a sexual recruitment term does not affect the

results qualitatively. Therefore, the first row of the

fragmentation matrix, F

, incorporates several sepa-

rate biological processes and their associated proba-

bilities, i.e. the sum of all probabilities of sexual re-

cruitment listed above (since any new colony may

have been derived sexually) plus the probability of

existing colonies fragmenting multiplied by the sur-

vivorship of those fragments until the time of observa-

tion, and combines them.

For the F matrix, we assumed a closed population,

where new fragments arise from the existing stand of

large (SC3 and SC4) colonies and can be of any size

class (although new SC4 fragments were not observed

during this study). New SC3 fragments counted in a

given year were assumed to derive solely from pre-

existing SC4 colonies (see Fig. 1d). New fragments of

SC1 and SC2 were assumed to derive from existing

SC3 and SC4 colonies proportionally, based on the ra-

tio of mean size of SC4 colonies to that of SC3, at the

beginning of the time step. For i = 1 or 2, each year

= (f

× n

) + (f

× n

) (2)

where r

is the number of new i-class fragments at the

end of the time step, f

and f

are the probabilities

that an i-class fragment is produced by an SC3 or

SC4 colony, and n

and n

are the number of SC3 and

SC4 individuals at the beginning of the time step.

Given that q is the ratio of mean size of SC4 to that of

SC3 in a given year, we define:

= q × f

(3)

Finally, combining Eqs. (2) and (3), we calculate

the fragmentation rate of SC3 as:

= r

/ [n

+ (q × n

)] (4)

From the 7 surveys, 6 size-structured matrices

were developed, 1 for each time period: 2004–2005,

161

Size Observed Observed Abundance Stable size distribution

class size range (cm

) mean size (cm

) 2004

’05

’06

’06 ’07 ’08 ’09 ’10 ’04–05

’05–06

’06–07 ’07–08 ’08–09 ’09–10

Min Max Mean SE

1 0.2 100 43 1 22 25 28 94 72 66 87 62 0.19 0.37 0.12 0.22 0.37 0.17

2 100 900 369 9 46 49 31 110 93 98 101 93 0.36 0.22 0.23 0.34 0.33 0.26

3 900 4000 2158 49 33 37 21 66 67 60 50 44 0.29 0.14 0.21 0.16 0.13 0.17

4 4000 47 250 11 171 405 32 31 22 51 55 65 64 70 0.15 0.27 0.44 0.28 0.17 0.40

Total 133 142 102 321 287 289 302 269 λ = 1.05 0.71 1.00 1.05 0.97 1.01

Represents a smaller sample size

Table 1. Acropora palmata. Summary of northern Florida Keys coral size range, mean size, and abundance of individuals per size class, as

well as stable size distributions and population growth rate (λ) based on the respective population matrices in Table 2. In 2005, only 6 of the

15 plots were surveyed in the spring; therefore, transition and recruitment rates for 2004–05 and 2005–06 were calculated from colonies in

those 6 plots only. The 2 columns for 2006 show abundance in 6 plots and 15 plots, respectively. Abundances from all plots in 2004, 2005,

and 2006 are presented in Fig. 3b

Endang Species Res 19: 157–169, 2012

2005–2006, 2006–2007, 2007–2008, 2008–2009, and

2009–2010 (Table 2). Since the first time period was

6 mo, and all others were annual, the first matrix was

squared to make it comparable to the remaining

matrices (Caswell 2001). Performing this calculation

assumes that transition and recruitment from fall to

spring are equivalent to those from spring to fall. Pro-

jections were run without these data from 2004–2005

and showed the same qualitative output.

Log-linear analyses

We were interested in determining whether sites

differed significantly from one another or were sim-

ilar. If sites were deemed similar, then they could

be combined into a single population of Acropora

palmata in the northern Florida Keys. Using the T

matrices from each year, we built 2 log-linear equa-

tions based on transition counts (as in Caswell

2001). One equation included the effects of all pos-

sible factors (starting size class, ending fate, site,

and year of transition) and their interactions. The

other excluded site effects. If site effects are signifi-

cant, then the first, fully parameterized equation

will fit the data better than the second under-para-

meterized equation.

The saturated equation is written in terms of 4 fac-

tors: S, initial state or size class; F, ending fate, in -

cluding death, growth, or shrinkage to another size

class; X, site; and T, time. The probability that an

individual starts at state i, location k, and time l and

ends up with fate j is the product of the probabilities

that define those variables. The logarithm of the sum

of individuals with particular starting and ending

conditions is the sum of the effects of these variables

162

Years SC T F A λ

1 2 3 4 1 2 3 4 1 2 3 4

2004–05

a,b

1 0.60 0.07 0.00 0.00 + 0.06 0.28 = 0.60 0.07 0.06 0.28 1.05

2 0.15 0.69 0.10 0.06 0.06 0.30 0.15 0.69 0.16 0.36

3 0.01 0.11 0.74 0.11 0.23 0.01 0.11 0.74 0.34

4 0.00 0.00 0.11 0.83 0.00 0.00 0.00 0.11 0.83

Mort 0.24 0.13 0.05 0.00

2005–06 1 0.44 0.14 0.08 0.00 + 0.03 0.19 = 0.44 0.14 0.11 0.19 0.71

2 0.00 0.37 0.19 0.00 0.03 0.16 0.00 0.37 0.22 0.16

3 0.00 0.02 0.43 0.13 0.00 0.00 0.02 0.43 0.13

4 0.00 0.00 0.00 0.71 0.00 0.00 0.00 0.00 0.71

Mort 0.56 0.47 0.30 0.16

2006–07

1 0.60 0.12 0.00 0.00 + 0.01 0.05 = 0.60 0.12 0.01 0.05 1.00

2 0.13 0.61 0.11 0.00 0.02 0.11 0.13 0.61 0.13 0.11

3 0.00 0.12 0.79 0.04 0.00 0.00 0.12 0.79 0.04

4 0.00 0.00 0.09 0.96 0.00 0.00 0.00 0.09 0.96

Mort 0.28 0.15 0.01 0.00

2007–08 1 0.56 0.12 0.00 0.00 + 0.04 0.22 = 0.56 0.12 0.04 0.22 1.05

0.24 0.67 0.07 0.00 0.04 0.20 0.24 0.67 0.11 0.20

3 0.01 0.06 0.70 0.07 0.04 0.01 0.06 0.70 0.11

4 0.00 0.00 0.21 0.93 0.00 0.00 0.00 0.21 0.93

Mort 0.19 0.15 0.02 0.00

2008–09 1 0.68 0.12 0.02 0.00 + 0.09 0.41 = 0.68 0.12 0.10 0.41 0.97

2 0.12 0.58 0.22 0.00 0.06 0.31 0.12 0.58 0.28 0.31

3 0.00 0.11 0.54 0.09 0.03 0.00 0.11 0.54 0.12

4 0.00 0.00 0.07 0.91 0.00 0.00 0.00 0.07 0.91

Mort 0.20 0.18 0.15 0.00

2000–10 1 0.43 0.11 0.02 0.00 + 0.03 0.15 = 0.43 0.11 0.05 0.15 1.01

2 0.22 0.57 0.16 0.00 0.02 0.12 0.22 0.57 0.18 0.12

3 0.00 0.08 0.54 0.09 0.05 0.00 0.08 0.54 0.14

4 0.00 0.00 0.24 0.91 0.00 0.00 0.00 0.24 0.91

Mort 0.35 0.24 0.05 0.00

Probabilities based on a 6 mo time interval;

probabilities based on 6 plots;

fragmentation probabilities based on 6 plots

Table 2. Acropora palmata. Annual transition (T), fragmentation (F), and matrix population models (A). Each matrix comprises

transition and fragmentation probabilities, or rates, from one size class (SC; column) to another (row). Size-specific mortality

(Mort), calculated as 1 − (sum of transition probabilities), is presented underneath each T matrix. λ

: annual rate of change in

population size; size classes as in Fig. 2

Vardi et al.: Elkhorn coral population model

(Caswell 2001). This saturated equation can be

written as:

FSXT: log m

ijk

= u + u

S(i)

+ u

F( j)

+ u

X(k)

+ u

T(l)

SF(ij)

+ u

SX(ik)

+ u

ST(il)

+ u

FX( jk)

(5)

FT( jl)

+ u

XT(kl)

+ u

SFX(ijk)

+ u

SFT(ijl)

SXT(ikl)

+ u

FXT( jkl)

+ u

SFXT(ijkl)

The under-saturated equation excluding all X and

F interactions is

FST, SXT: log m

ijk

= u + u

S(i)

+ u

F( j)

+ u

X(k)

T(l)

+ u

SF(ij)

+ u

SX(ik)

(6)

ST(il)

+ u

FT( jl)

+ u

XT(kl)

SFT(ijl)

+ u

SXT(ikl)

where m

ijkl

is the number of individuals in state i from

location k at time l ending with fate j, u is the log of

the total number of observations in each table, u

S(i)

the effect of the ith state, and u

SF(ij)

is the effect of

the interaction of the ith state and the jth fate, and so

on.

The equations are parameterized using maximum

likelihood and compared using a chi-squared distrib-

uted goodness-of-fit test where:

(7)

Model analyses

Long-term rate of change in population abun-

dance, λ, and stable size distribution were calculated

by taking the eigenvalue and right eigenvector of

each matrix. In addition, stochastic growth rate, λ

was estimated from the average growth rate over a

long (50 000 yr) simulation (Caswell 2001, Stubben &

Milligan 2007). Since each matrix captures annual

variation in population dynamics (i.e. a stochastic

environment), λ

yields a more robust estimation of

the long-term rate of change than any annual matrix

or even the mean matrix can provide. In all cases,

simulations matched Tuljapurkar’s approximation for

the same parameter (see Caswell 2001). Several cal-

culations utilize the mean matrix, A

, which is simply

a matrix with dimension equal to that of A, wherein

each element a

is the arithmetic mean of the corre-

sponding a

from each matrix. Elasticity values

= a

/ λ × ∂λ/∂ a

(8)

were calculated to determine the relative contribu-

tion of each matrix element on lambda (Caswell

2001). These calculations utilized the ‘popbio’ pack-

age in R (Stubben & Milligan 2007).

Population projection and scenarios

From a management perspective, it is critical to

explore population projections among likely environ-

mental scenarios. For Acropora palmata, the most

important and variable physical forcings are hurri-

canes, specifically the frequency (defined as 1/h,

where h is the return time in years) of major hurri-

canes affecting a particular population (Gardner et

al. 2005). During the 2005–2006 interval, 4 major

hurricanes (category 3 or greater) traveled within 200

nautical miles (n miles) of the study area, 3 of which

caused significant damage to the existing population.

Single storms can produce a net gain in terms of pop-

ulation abundance, via branch breaks. However,

consecutive storms can (and did) result in a net loss,

when fragments are swept away before reattach-

ment can occur. Since the majority of the damage in

2005 was inflicted by 2 consecutive storms, we calcu-

lated the return time of 2 or more major storms occur-

ring within a 200 n mile radius of our study. Based on

annual data collected since 1851, this return time, h,

is 20 yr (NOAA 2011). Thus h = 20 represents a rela-

tively realistic scenario for a stochastic simulation. To

bound these results, we explored 2 alternate return

times. As a lower bound, we assumed that our study

period was representative, making the implicit

assumption that a year as severe as 2005–2006 recurs

every 6 yr (h = 6). As an upper bound, we assumed a

year as destructive as 2005–2006 would never return

(h = ∞). We thus simulated a stochastic environment

by randomly selecting 1 of the 6 annual matrices,

where the probability of selecting the hurricane

matrix was 1/h and the probabilities of selecting each

of the other 5 matrices were equal to each other and

defined as [1 − (1/h)] / 5. All hurricane scenarios were

run for 20 yr (until 2030) and for 50 yr (until 2060) to

contextualize the earlier time frame and to show any

potential differences between shorter- and longer-

term dynamics.

One of the few Acropora palmata management

actions available is outplanting colonies reared in

nurseries. We simulated outplanting both SC1 and

SC2 colonies at 3 density levels (1000, 2000, and 3000

outplants over the 2300 m

study area) that match

density levels currently used for Acropora cervicor-

nis (S. Griffin pers. comm.). We did not modify transi-

tion rates for outplants, but rather assumed that the

same rates of growth, shrinkage, and mortality would

apply. Mean rates of mortality measured in our study,

30 and 21% for SC1 and SC2, respectively, roughly

matched that of similarly sized A. cervicornis out-

plants (20%; T. Moore pers. comm.). The 20 yr pro-

2=× ×

⎛

⎝

⎞

⎠

∑

logobserved

observed

expected

cells

163

Endang Species Res 19: 157–169, 2012

jection period comprises 2 yr with no planting, 5 yr

with planting, and an additional 13 yr with no plant-

ing. Outplanting was incorporated into the model

explicitly by adding 1000, 2000, or 3000 individuals

to SC1 or SC2, for each time step (year) of the 5 yr

planting period. Results are shown after 5 and 20 yr

(in the years 2017 and 2030). All outplanting scenar-

ios were projected using the same matrices and Mar-

kovian processes as the hurricane scenarios with h =

20 yr. We used size-class specific abundances in 2010

to seed all population projections (see Table 1).

Percent cover was calculated by multiplying the

number of individuals in each size class in the final

year of the projection by the mean size of the corre-

sponding size class (see Table 1), and dividing the sum

of those numbers by the total study area (2309 m

This method assumes that colonies do not overlap,

thereby potentially overestimating total percent

cover for any projection. All calculations were con-

ducted using R (R Development Core Team 2011).

Projected estimates of population size and structure

are based on 10 000 simulations. All confidence inter-

vals (CI) presented are at the 95% level.

RESULTS

Annual surveys

During the course of our study from 2004 to 2010,

Acropora palmata cover decreased 40%, from 6.6 to

3.9%, and abundance decreased 21%, from 340 to

269 individuals (Fig. 3a,b). In addition, mean size

within each size class declined by 13, 19, 1, and 18%

for SC1 through SC4, respectively. The proportion of

individuals classified as reproductively viable (in -

cluding sexual and asexual reproduction, i.e. SC3

and SC4) declined from 52% in 2004 to 42% in 2010

(Fig. 3c).

Log-linear analyses

We used a goodness-of-fit to test the hypothesis

that site (or reef) was an important factor explaining

differences in the number of transitions from a partic-

ular state to a particular fate through time. The null

hypothesis was that the effects of site on fate do not

help explain the variability in the data; in other

words, that an under-saturated equation (FST, SXT ),

which excludes all interactions of site on fate, is suffi-

cient to describe observed transitions. There was

insufficient support to reject the null hypothesis at

the p = 0.05 level, suggesting that accounting for dif-

ferent sites does not significantly improve the power

of explanation. The results from this test (goodness of

fit = 241.622, df = 448, p = 1.00) suggest that variation

in transition rates among reefs was similar.

Matrices

Mortality was highest for the smallest size classes

and survivability increased with each successive size

class (Table 2). Probabilities of shrinkage from one

size class to the next were as high as 0.22, and rates

of growth from one size class to the subsequent were

as high as 0.24. Growing 2 size classes in 1 yr was un -

common (occurring twice) in comparison to shrinking

more than 1 size class, which happened a total of 8

times. The number of new fragments in a given year

ranged between 10 and 58, with smaller recruits con-

sistently outnumbering larger ones.

Most commonly, individuals tended to remain in

the same size class from one year to the next (Table 2).

Except mortality in SC1 and SC2 in 2005–2006, the

probabilities of stasis (the loop probabilities along the

main diagonal of the matrix) were larger than any

other probability per size class per year, over all

years and size classes. SC4 had the highest probabil-

ity of stasis, experiencing 0 mortality in all years

except 2005–2006. In Fig. S1 in the supplement at

www.int-res.com/ articles / suppl/ n019 p157 _ supp .pdf,

we show that e

, the elasticity of SC4 surviving and

not shrinking, was greater than the elasticity of any

other matrix element, e

, across all years, meaning

that adult survival had the largest contribution to

population growth rate, λ, compared with all other

transitions. This was true during background condi-

tions (Fig. S1a,c−f), as well as during severe storm

conditions (Fig. S1b). Elasticity analyses performed

on the mean matrices of the 3 hurricane scenarios

showed similar qualitative results to those emerging

from the deterministic 1 yr matrices shown in Fig. S1.

Thus, we present only the results from the 1 yr, deter-

ministic matrices in order to show the general pattern

of parameter elasticities and the extremes revealed

from these data. Importantly, if more precise elastici-

ties for particular stochastic scenarios are required

for management or other applications, targeted ana -

lyt i cal approaches are available (Tuljapurkar et al.

2003).

The dynamics of Acropora palmata during a severe

hurricane year were captured in the 2005–2006 pop-

ulation matrix (Table 2). Survivorship (1 − mortality)

during 2005–2006 for all size classes was markedly

164

Vardi et al.: Elkhorn coral population model

lower than that for all other years (0.44, 0.53, 0.70,

0.84 for –2006 for SC1 to SC4, respectively, versus

mean ± SE, 0.76 ± 0.04, 0.84 ± 0.03, 0.95 ± 0.03, 1.00

± 0.00 for the other 5 years). Similarly, the probability

of growth for all size classes in 2005–2006 was less

than that of background years by 1 order of magni-

tude (mean ± SE, 0.01 ± 0.00 versus 0.10 ± 0.01, based

on the mean matrix for those years).

Annual population growth rate, λ, calculated from

each matrix ranged from 0.71 to 1.05 (Table 1), and

was 0.96 based on the mean matrix. Thus, for every

100 colonies, an average of 4 died each year. Since

2005–2006 was an extreme year, stochastic growth

rate, λ

, depends on the probability of its recurrence,

1/h, and was estimated for h = 6 as 0.956 (95% CI =

0.955− 0.957), for h = 20 as 0.999 (95% CI = 0.998−

1.000), and for h = ∞ as 1.019 (95% CI = 1.018−1.020).

Thus, assuming a year like 2005–2006 recurs every

20 yr, the population is slowly declining.

Projections

Without intervention by 2060, and under a modest

hurricane recurrence scenario (h = 20), projected

benthic cover of Acropora palmata (mean = 4.5%,

95% CI = 0.9 to 11.2%) is nearly unchanged from

that in 2010 (3.9%; Fig. 3a). Predicted mean abun-

dance in 20 and 50 yr is also nearly equivalent to

starting abundance (Fig. 3b). Note that the estimated

stochastic growth rate for h = 20 was estimated as

slightly less than 1 (0.999), while short-term projec-

165

2060

2030

SC 4

SC 3

SC 2

SC 1

0.0

0.2

0.4

0.6

0.8

1.0

2017 2030

SC1 SC2

∞ 6

20 ∞

120

0.1

0.4

4.0

2004

2010

2005

2006

2007

2008

2009

1.0

2.0

3.0

0.2

0.3

100

0.0

0.2

0.4

0.6

0.8

1.0

0.0

123123 123123

0.2

0.4

0.6

0.8

1.0

0.00

0.05

0.10

0.15

Density (ind. m

–2

)Size class distribution

(proportion)

Percent cover

Recent past

Outplanting projections

Hurricane projections

× 10

Fig. 3. Acropora palmata. (a) Percent cover, (b) density, and (c) proportional size class distribution, as observed over the course

of the study from 2004 to 2010 (2005 spring and summer surveys combined; left panels), as projected after 5 yr of outplanting

(center panels), and as projected under different hurricane return times: 6, 20, and an infinite number of years (right panels).

The outplanting projections have a 2 yr lag time with no outplanting, followed by 5 yr of outplanting either size class 1 (SC1) or

size class 2 (SC2) outplants at 3 densities (1000, 2000, or 3000 outplants over the 2300 m

study area). Results are shown imme-

diately following 5 yr of outplanting (in the year 2017) and 13 yr after the end of outplanting (2030). The hurricane scenarios

are projected for 20 and 50 yr, to 2030 and 2060. All results are means based on 10 000 simulations. Error bars represent a 95%

confidence interval on percent cover and total abundance. Dotted lines represent (a) percent cover or (b) abundance as meas-

ured in 2010, and (c) 50%

Endang Species Res 19: 157–169, 2012

tions (20 and 50 yr) suggest slightly positive growth.

This distinction is due to the time scales of estima-

tion; λ

is calculated over a 50 000 yr simulation,

while these projections were on decadal scales.

Abundance and percent cover change predictably

with h. When h = 6, mean cover is reduced to less

than 2% by 2030 and less than 1% by 2060 (Fig. 3a).

When h = ∞, a modest increase in cover to 5.7% (95%

CI = 4.3 to 7.5%) is projected in 20 yr, and a doubling

of population abundance is projected for 2060

(Fig. 3b). The proportion of individuals in each size

class by the end of any projection of 20 yr or more

(including outplanting projections; Fig. 3c) is equiva-

lent to the stable size distribution derived from the

mean matrix. The convergence to a stable size distri-

bution could occur as early as 8.6 yr, using the

approach for estimating time to convergence from

Doak & Morris (1999).

Finally, size of outplants matters. At the most dense

outplanting scenario (1.3 outplants m

−2

or 3000 out-

plants over the 2300 m

study area), cover using SC2

outplants (mean 47%, 95% CI = 23−61%) is signifi-

cantly higher than that using SC1 outplants (mean

15%, 95% CI = 7−22%) after 5 yr of outplanting

(Fig. 3a). Analogous comparisons of the other SC2

outplanting densities, 0.43 m

−2

and 0.87 m

−2

(1000

and 2000 outplants over 2300 m

), revealed a similar

pattern resulting in higher percent cover, although

the CIs overlapped. Even in the worst-case scenarios

(i.e. lower confidence boundaries), 5 yr of SC2 out-

plantings are predicted to increase percent cover

from current conditions, represented by the dotted

line in Fig. 3a. This relationship holds at least until

2030. The same is not true for the SC1 outplanting

scenarios. Interestingly, although abundance is pre-

dicted to decline between 2017 and 2030 for all out-

planting scenarios (Fig. 3b), mean percent cover is

predicted to increase (Fig. 3a). Comparing the pro-

portional size class distribution in 2017, dominated

by SC1 and SC2 individuals, to that in 2030, which

has a more even size class distribution (Fig. 3c), we

see that the increase in percent cover is due to

growth of outplants into bigger size classes over time.

DISCUSSION

Modeling results

During the 7 yr of our study, we saw declines in

percent cover and mean size of individuals. The

demographic rates we measured reveal that while

this population of Acropora palmata could persist at

or near presently low levels of abundance for the

next 50 yr, without active management the popula-

tion will not recover to former levels of abundance.

Although λ is the standard currency of population

biology, it can be a misleading metric when applied to

the life history of clonal sessile organisms if size struc-

ture is not considered. Our most realistic assessment

of λ is just below 1.00 (at h = 20), not a drastic rate of

decline in population size for a threatened species.

However, we documented a shift in size structure

from the inception of the study, wherein larger, repro-

ductive size classes with high survivorship dominated

(52%), to the end of the study, wherein smaller, pre-

reproductive size classes with lower survivorship

dominated (58%). This trend is confirmed by the sta-

ble size distribution of the mean matrix, which pro-

vides the best estimate of how the size classes ulti-

mately will be distributed. Here, smaller size classes

also dominated (56%). Similarly, Hughes & Tanner

(2000) saw a shift in dominance from largest to small-

est size class in 2 coral species over a 16 yr study pe-

riod. These patterns are slow to emerge, yet are a crit-

ical sign of decline in the overall health of coral

populations, as smaller sizes in general have lower

survivorship and fecundity (Highsmith 1982).

Note that CIs widen as projection intervals lengthen,

a phenomenon common to all stochastic simulations.

The wide CIs on abundance and percent cover esti-

mates can be considered either representative of a

stochastic environment or an artifact of our model

choice. Prior coral simulation models set the return

time of a storm deterministically at varying intervals

and simulated background conditions in the interim

years (e.g. Hughes 1984, Lirman 2003, Ed munds

2010). There is utility in this approach, as it quantifies

the resilience of corals to storms. Further, this is the

only option unless more than 2 demographic surveys

have been conducted. We felt that our time series

was sufficiently long to simulate a stochastic environ-

ment and assign a probability of hurricane recur-

rence. This means that some simulations will have

more ‘bad years’ than others, and the resulting

response variables thus have a wide CI. Here we

present results using a CI of 95%, but from a man-

agement perspective, focusing on the lower limit of a

narrower CI may be more appropriate.

Management recommendations

The top 3 stressors to Acropora palmata in the

northern Florida Keys (fragmentation, disease, and

snail predation) have accounted for 85% of tissue

166

Vardi et al.: Elkhorn coral population model

loss since 2004 (Williams & Miller 2012). Fragmenta-

tion, due primarily to storms, cannot be stopped

(although rescued fragments can be stabilized), and

coral diseases are currently incurable. Snails, how-

ever, can easily be removed from colonies. Corallio-

phila ab bre viata is a known threat to al ready

depressed acroporid populations, capable of destroy-

ing remnant populations in the months and weeks

after a storm (Knowlton et al. 1990, Baums et al.

2003). Indeed, C. abbreviata density (relative to live

tissue area) in creased 4-fold over the course of the

present study, and accounted for 25% of lost live tis-

sue, excluding the 2005 storm season (Williams &

Miller 2012). Snail removal has been shown to pre-

serve 75% more live A. palmata tissue compared

with controls where snails are left in place (Miller

2001). Importantly, this management action can tar-

get SC4 colonies, which have the greatest influence

on population increase, as demonstrated by elasticity

analyses.

Outplanting is currently the only recovery strategy

being actively pursued by managers. Outplanting

can provide a short-term boost to currently de pressed

demographic rates in a small geographic area, while

long-term strategies to improve environmental con-

ditions are being pursued. We limited these pro -

jections to 20 yr, as models predict short-term trajec-

tories best, and the influx of colonies leads to a

widening of CIs. Unsurprisingly, after 5 yr of plant-

ing, in 2017, abundance is higher and distribution is

dominated by the size class that was planted (Fig. 3b).

Thirteen years after the cessation of planting, in

2030, the size class distribution stabilizes (Fig. 3c). At

this point, mean abundances have decreased relative

to the abundance in 2017; however, mean percent

cover estimations are greater in 2030 than those pro-

jected for 2017.

We found that planting 3000 SC2 colonies (mean

diameter 19 cm) resulted in significantly higher

mean percent cover by 2017 than planting 3000 SC1

colonies (mean diameter 6.5 cm) over the study area

(1.3 outplants m

−2

). Furthermore, although planting

SC1 colonies could increase cover to 60% by 2030

under the best conditions (upper CI boundary),

managers would be wise to focus on the value of the

lower CI boundary, which represents unfavorable

conditions (Fig. 3a). Here, cover could make a more

modest improvement (9%) over current conditions

(4%). In contrast to the SC1 scenario, planting 3000

SC2 colonies results in a worst-case scenario (lower

CI boundary) of 24% cover. Thus, according to our

model, a 5 yr dense SC2 outplanting regime does a

fair job of preventing population collapse in terms of

both percent cover and abundance until at least

2030. Outplanting, however, is a costly endeavor

that many Caribbean nations may not be able to

afford. If Acropora palmata nursery output and costs

were to match those of A. cervicornis, planting 3000

SC2 colonies per year for 5 yr would result in

roughly 30% cover and would cost approximately

US$3M (T. Moore pers. comm.). Due to its cost, out-

planting should be considered as part of a short-

term solution in a limited geographical region,

rather than a comprehensive solution for this basin-

wide problem.

Why does an influx of small individuals only

slightly improve population projections? The first

explanation is that the smaller size classes do not

have a significant influence over population growth

as demonstrated by elasticity analyses. The relatively

slow growth and high mortality of the individuals

limit their demographic potential for the population.

But the more relevant question is, why, even if we

eliminate the possibility of a ‘bad year’ (h = ∞), does

this population seem incapable of recovering? Quite

simply, the probability of shrinking, across all size

classes and years (mean ± SE, 0.089 ± 0.014), is

roughly equivalent but slightly greater, than that of

growing (0.082 ± 0.019). This implies that stressors

causing the loss of tissue (e.g. disease, predation) are

keeping pace with the ability of Acropora palmata to

thrive even in the absence of hurricanes. More

importantly, it implies that present vital rates during

non-hurricane years are fundamentally different

from those of the past, as recovery, even in the

impossible case of no future disturbance, appears

extremely unlikely to occur.

Our findings are somewhat in contrast to Lirman’s

(2003) stage-based population model of Acropora

palmata in the northern Florida Keys, and the differ-

ences could highlight an important aspect of this

organism’s population dynamics and potential for

recovery. Lirman parameterized his model from 1993

to 1997 on Elkhorn Reef, which at the time had a

higher density of colonies than the sites described in

the present study (D. Lirman pers. comm.). In Lirman’s

projections, storms recurring every 5 yr re sulted in a

4-fold increase, from 10 to 50 colonies, after 50 yr. In

contrast, in our study, parameterized a decade later

with storms occurring every 6 yr, abundance de -

creased by 80%, from 270 to 45 colonies (95% CI = 3

to 186 colonies), after 50 yr. The effects of the storms

and/ or the parameterization of storm effects could

account for this difference; however, relative changes

in transition matrix elements, especially in the influ-

ential rate of stasis for the largest colonies, between

167

Endang Species Res 19: 157–169, 2012

background and storm matrices, were comparable in

the 2 studies. Alternatively, A. palmata could exhibit

positive density dependence, as some observations

suggest (Baums et al. 2003, Williams et al. 2008),

wherein denser stands retain fragments and recover

more quickly from storms than less dense stands.

This hypothesis could be explored in a theoretical

modeling exercise, for example, or using a model

parameterized in an experimental outplanting design,

with various densities of outplants in replicate plots.

Further research in this area is critical, as a density-

dependent model may demonstrate that percent cover

could increase more quickly than our projections

suggest.

CONCLUSIONS

Despite being protected under the US Endan-

gered Species Act and being contained within no-

take marine reserves, our results show that without

intervention, Acropora palmata in the Florida Keys

will likely become functionally extinct in the near

future. With intervention, population projections are

highly variable, but active management offers the

only positive prospect in the short term. Removing

snails would likely have a net positive effect on

population trajectories, although this process is

resource intensive. Outplanting is projected to bol-

ster demographics in the short term, but should be

employed only in concert with the hard work of im -

proving environmental conditions over the medium

term (e.g. removing excess nutrients from sea water,

restoring herbivorous fishes and invertebrates that

remove macroalgae) and long term (e.g. reducing

sea surface temperature and ocean acidification to

pre-industrial age levels). Preserving and restoring

the A. palmata population of northern Florida will

undoubtedly be challenging, but will ensure the

livelihood of untold numbers of shallow reef fish

and invertebrates that depend on the complex habi-

tat it provides. Sixty-six coral species are currently

proposed for inclusion on the US Endangered Spe-

cies List, none of which has demographic data com-

parable to that of the A. palmata population studied

herein. As coral reefs face significant global threats,

the much studied and cared for reefs of Florida will

make an excellent example of how to bring a clonal,

sessile, endangered organism back from the brink

of extirpation. We hope that the model presented

here will provide context in the potential listing and

recovery planning of those candidate species as

well.

Acknowledgements. The authors thank Margaret Miller,

Brice Semmens, Nancy Knowlton, Jeremy Jackson, George

Sugihara, and Sach Sokol for helpful guidance and critical

thinking; and Jennifer Moore and NOAA's Coral Reef Con-

servation Program for generous funding.

LITERATURE CITED

Acevedo R, Morelock J, Olivieri RA (1989) Modification of

coral reef zonation by terrigenous sediment stress.

Palaios 4: 92−100

Acropora Biological Review Team (2005) Atlantic Acropora

status review. Report to National Marine Fisheries Serv-

ice, Southeast Regional Office, St Petersburg, FL

Adey W, Adey P, Burke R, Kaufman L (1977) The Hologene

reef systems of eastern Martinique, French West Indies.

Atoll Res Bull 218: 1−40

Bak R, Engel M (1979) Distribution, abundance and survival

of juvenile hermatypic corals (Scleractinia) and the

importance of life history strategies in the parent coral

community. Mar Biol 54: 341−352

Baums IB, Miller MW, Szmant AM (2003) Ecology of a coral-

livorous gastropod, Coralliophila abbreviata, on two

scleractinian hosts. I: Population structure of snails and

corals. Mar Biol 150: 1215−1225

Bruckner A, Hourigan T (2000) Proactive management for

conservation of Acropora cervicornis and Acropora

palmata: application of the U.S. Endangered Species Act.

Proc 9th Int Coral Reef Symp 2: 661−666

Carpenter KE, Abrar M, Aeby G, Aronson RB and others

(2008) One-third of reef-building corals face elevated

extinction risk from climate change and local impacts.

Science 321: 560−563

Caswell H (2001) Matrix population models: construction,

analysis, and interpretation. Sinauer Associates, Sunder-

land, MA

del Mónaco C, Noriega N, Narciso S (2011) Note on density

and predation rate of Coralliophila abbreviata and Coral-

liophila caribaea on juvenile colonies of Acropora

palmata in a deteriorated coral reef of Cayo Sombrero,

Morrocoy National Park, Venezuela. Lat Am J Aquat

Resour 39: 161−166

Doak D, Morris W (1999) Detecting population-level conse-

quences of ongoing environmental change without long-

term monitoring. Ecology 80: 1537−1551

Edmunds PJ (2010) Population biology of Porites astreoides

and Diploria strigosa on a shallow Caribbean reef. Mar

Ecol Prog Ser 418: 87−104

Edmunds PJ, Carpenter R (2001) Recovery of Diadema antil-

larum reduces macroalgal cover and increases abun-

dance of juvenile corals on a Caribbean reef. Proc Natl

Acad Sci USA 98: 5067−5071

Fong P, Glynn PW (1998) A dynamic size-structured popula-

tion model: Does disturbance control size structure of a

population of the massive coral Gardineroseris planulata

in the Eastern Pacific? Mar Biol 130: 663−674

Gardner TA, Coté IM, Gill JA, Grant A, Watkinson AR

(2005) Hurricanes and Caribbean coral reefs: impacts,

recovery, patterns, and role in long-term decline. Ecol-

ogy 86: 174−184

Geister J (1977) The influence of wave exposure on the eco-

logical zonation of Caribbean coral reefs. Proc 3rd Int

Coral Reef Symp, p 23– 29

168

➤

➤➤

➤

➤➤

➤

Vardi et al.: Elkhorn coral population model

Goreau T (1959) The ecology of Jamaican coral reefs I.

Species composition and zonation. Ecology 40:67–90

Harvell CD, Kim K, Burkholder JM, Colwell RR and others

(1999) Emerging marine diseases — climate links and

anthropogenic factors. Science 285: 1505−1510

Harvell CD, Jordán-Dahlgren E, Merkel S, Rosenberg E and

others (2007) Coral disease, environmental drivers, and

the balance between coral and microbial associates.

Oceanography 20: 172−195

Highsmith RC (1982) Reproduction by fragmentation in

corals. Mar Ecol Prog Ser 7: 207−226

Highsmith R, Riggs A, D’Antonio CM (1980) Survival of hur-

ricane-generated coral fragments and a disturbance

model of reef calcification/growth rates. Oecologia 46:

322−329

Holmes G, Johnstone RW (2010) Modelling coral reef eco-

systems with limited observational data. Ecol Model 221:

1173−1183

Hubbard D, Zankl H, Van Heerden I, Gill I (2005) Holocene

reef development along the northeastern St. Croix Shelf,

Buck Island, US Virgin Islands. J Sediment Res 75:

97−113

Hubbard D, Burke R, Gill I, Ramirez W, Sherman C (2008)

Coral-reef geology: Puerto Rico and the US Virgin

Islands. In: Riegl B, Dodge R (eds) Coral reefs of the USA.

Springer, Dania Beach, FL, p 263−302

Hughes T (1984) Population dynamics based on individual

size rather than age: a general model with a reef coral

example. Am Nat 123: 778−795

Hughes TP, Connell JH (1987) Population dynamics based

on size or age? A reef-coral analysis. Am Nat 129:

818−829

Hughes TP, Tanner JE (2000) Recruitment failure, life histo-

ries, and long-term decline of Caribbean corals. Ecology

81:2 250–2263

IUCN (International Union for Conservation of Nature)

(2011) The IUCN Red List of Threatened Species. Ver-

sion 2011.1. Available at www.iucnredlist.org (accessed

2 August 2011)

Jackson JBC (1992) Pleistocene perspectives on coral-reef

community structure. Am Zool 32: 719−731

Jackson JBC, Kirby MX, Berger WH, Bjorndal KA and oth-

ers (2001) Historical overfishing and the recent collapse

of coastal ecosystems. Science 293: 629−637

Jones RJ, Bowyer J, Hoegh-Guldberg O, Blackall LL (2004)

Dynamics of a temperature-related coral disease out-

break. Mar Ecol Prog Ser 281:63–77

Kline DI, Kuntz NM, Breitbart M, Knowlton N, Rohwer F

(2006) Role of elevated organic carbon levels and micro-

bial activity in coral mortality. Mar Ecol Prog Ser 314:

119–125

Knowlton N, Lang JC, Keller BD (1990) Case study of natu-

ral population collapse: post-hurricane predation on

Jamaican staghorn corals. Smithson Contrib Mar Sci 31:

1−26

Lang JC (ed) (2003) Status of coral reefs in the western

Atlantic: results of initial surveys, Atlantic and Gulf

Rapid Reef Assessment (AGRRA) program. Atoll Res Bull

496: 1−635

Lirman D (2000) Fragmentation in the branching coral Acro-

pora palmata (Lamarck): growth, survivorship, and

reproduction of colonies and fragments. J Exp Mar Biol

Ecol 251: 41−57

Lirman D (2003) A simulation model of the population dy-

namics of the branching coral Acropora palmata — effects

of storm intensity and frequency. Ecol Model 161: 169−182

Lirman D, Fong P (1997) Patterns of damage to the branch-

ing coral Acropora palmata following Hurricane

Andrew: damage and survivorship of hurricane-gener-

ated asexual recruits. J Coast Res 13: 67−72

Miller M (2001) Corallivorous snail removal: evaluation of

impact on Acropora palmata. Coral Reefs 19: 293−295

Miller MW, Baums IB, Williams DE (2007) Visual discern-

ment of sexual recruits is not feasible for Acropora

palmata. Mar Ecol Prog Ser 335: 227−231

NOAA (National Oceanic and Atmospheric Administration)

(2011) Historical hurricane tracks. Available at www. csc.

noaa. gov/hurricanes/# (accessed 29 March 2011)

NMFS (National Marine Fisheries Service (2010) Endan-

gered and threatened wildlife; notice of 90-day finding

on a petition to list 83 species of corals as Threatened or

Endangered under the Endangered Species Act (ESA).

Fed Regist 75: 6616−6621

R Development Core Team (2011) R: a language and envi-

ronment for statistical computing. R Foundation for Sta-

tistical Computing, Vienna

Rogers C (1983) Sublethal and lethal effects of sediments

applied to common Caribbean reef corals in the field.

Mar Pollut Bull 14: 378−382

Soong K, Lang JC (1992) Reproductive integration in reef

corals. Biol Bull (Woods Hole) 183: 418−431

Stubben C, Milligan B (2007) Estimating and analyzing

demographic models using the popbio package in R.

J Stat Softw 22: 1−23

Tuljapurkar S, Horvitz CC, Pascarella JB (2003) The many

growth rates and elasticities of populations in random

environments. Am Nat 162: 489−502

Williams DE, Miller MW (2012) Attributing mortality among

drivers of population decline in Acropora palmata in the

Florida Keys (USA). Coral Reefs 31: 369−382

Williams DE, Miller MW, Kramer KL (2006) Demographic

monitoring protocols for threatened Caribbean Acropora

spp. corals. Tech Memo NMFS-SEFSC-543. NOAA,

Miami, FL

Williams DE, Miller MW, Kramer KL (2008) Recruitment fail-

ure in Florida Keys Acropora palmata, a threatened

Caribbean coral. Coral Reefs 27: 697−705

Woodley JD, Chornesky EA, Clifford PA, Jackson JBC and

others (1981) Hurricane Allen’s impact on Jamaican coral

reefs. Science 214:749–755

169

Editorial responsibility: David Hodgson,

University of Exeter, Cornwall Campus, UK

Submitted: November 23, 2011; Accepted: November 2, 2012

Proofs received from author(s): December 12

, 2012

➤➤

➤

➤➤

➤

➤➤

➤

➤➤

➤

Download
Save PDF to desktop

Email
Email completed PDF

Send for Signing
Email for others to sign

Print
Print document

NAME

Form 2: the northern Florida Keys, USA Population (Inter ResearchScience Publisher)

View Audit Log
Print With Audit Log
Duplicate Document

Fillable Form 2: the northern Florida Keys, USA Population (Inter Research Science Publisher)

Fill Online, Printable, Fillable, Blank Form 2: the northern Florida Keys, USA Population (Inter Research Science Publisher) Form

Related forms

First 20 documents completely FREE!