A functional–structural model of ephemeral seagrass growth influenced by environment

Abstract

Background and Aims

Ephemeral seagrasses that respond rapidly to environmental changes are important marine habitats. However, they are under threat due to human activity and are logistically difficult and expensive to study. This study aimed to develop a new functional–structural environmentally dependent model of ephemeral seagrass, able to integrate our understanding of ephemeral seagrass growth dynamics and assess options for potential management interventions, such as seagrass transplantation.

Methods

A functional–structural plant model was developed in which growth and senescence rates are mechanistically linked to environmental variables. The model was parameterized and validated for a population of Halophila stipulacea in the Persian Gulf.

Key Results

There was a good match between empirical and simulated results for the number of apices, net rhizome length or net number of internodes using a 330 d simulation. Simulated data were more variable than empirical data. Simulated structural patterns of seagrass rhizome growth qualitatively matched empirical observations.

Conclusions

This new model successfully simulates the environmentally dependent growth and senescence rates of our case-study ephemeral seagrass species. It produces numerical and visual outputs that help synthesize our understanding of how the influence of environmental variables on plant functional processes affects overall growth patterns. The model can also be used to assess the potential outcomes of management interventions like seagrass transplantation, thus providing a useful management tool. It is freely available and easily adapted for new species and locations, although validation with more species and environments is required.

INTRODUCTION

Seagrasses are marine angiosperms that constitute a critical marine habitat, but their range is declining globally (Orth et al., 2006; Waycott et al., 2009). They are a key component of marine food webs that stabilize sediments and sequester substantial amounts of carbon by trapping organic matter and their high productivity (Orth et al., 1984; Fonseca, 1989; Duarte and Cebrián, 1996; Fourqurean et al., 2012). They are the primary food of dugongs, manatees and some sea turtles, which are threatened with extinction, and their ecosystem services are financially valuable (Costanza et al., 1997; Green and Short, 2003; Connell and Gillanders, 2007; IUCN, 2010). The global range of seagrass is declining due to dredging, land reclamation, recreational boating, commercial fishing, contaminant discharge, algal blooms, invasive species, global warming and poor land management (Fonseca et al., 2004; Orth et al., 2006; Connell and Gillanders, 2007; Waycott et al., 2009; Sheppard et al., 2010; Short et al., 2011). Small fast-growing ephemeral seagrasses that respond rapidly to environmental changes are important marine habitats, but are under threat due to human activity and are logistically difficult and expensive to study (Sheppard et al., 2010; Whitehead 2015). Understanding how seagrass growth dynamics are affected by environmental drivers is critical for effective habitat management (Lee et al., 2007). For example, temperature is considered to be a major factor controlling seagrass seasonality because it affects the rates of seagrass photosynthesis and respiration (Phillips et al., 1983; Marsh et al., 1986; Lee et al., 2005, 2007). The way that environmental drivers influence overall plant growth patterns often involves complex interactions between these drivers and a number of interacting local-scale growth and senescence processes.

Computer simulation growth models can help understand these complex interactions between environmental drivers, local-scale growth and senescence processes and emergent overall plant growth patterns, and thus help predict and manage seagrass growth. Numerical models have been used to help understand the function of seagrass meadows and to predict human impacts (Wetzel and Neckles, 1986; Fong et al., 1997; Best et al., 2001; Newell and Koch, 2004). Spatially explicit modelling of seagrass growth helps to simulate and ‘observe’ developmental progress, which may be logistically difficult or temporally impossible to record empirically (Fonseca et al., 2004; Kendrick et al., 2005). Some spatially explicit simulations of seagrass used a grid approach with occupied and unoccupied cells to predict range expansion or contraction and recovery times for damaged meadows of slow-growing seagrass reefs that take centuries to develop (Fonseca et al., 2004; Kendrick et al., 2005). Functional–structural plant models (FSPMs) represent plant growth and development at much finer levels of detail (Godin and Sinoquet, 2005; Dejong et al., 2011). These models integrate rules for lower levels of biological structure, such as the function and structure of cells, branches or plants, to predict higher-level outcomes, such as the development of branches, whole plants, forests, fields or meadows (Godin and Sinoquet, 2005; Hanan and Prusinkiewicz, 2008; Dejong et al., 2011). The clonal growth of seagrasses is well suited to functional–structural plant modelling and lower-level components are typically rhizome segment (internode), rhizome growth rate, branching frequency and branching angle (Sintes et al., 2005, 2006, 2007; Brun et al., 2006). Brun et al. (2006) and Sintes et al. (2006) built influential FSPMs using this clonal seagrass structure. Sintes et al. (2007) developed a spatially explicit FSPM for seagrasses that incorporated rhizome branching, mortality of rhizome apical meristems and internal signalling to represent the dominance of some apical meristems over others. Renton et al. (2011) designed and applied a spatially explicit FSPM for identifying the optimal planting arrangements for transplanting the slow-growing Posidonia australis. However, to date there are no FSPMs suitable for simulating the growth patterns of small ephemeral fast-growing seagrasses, in which seasonally varying growth and senescence cycles caused by environmental variation are the main driver of growth patterns.

This study aimed to develop a new spatially explicit FSPM able to represent ephemeral seagrasses, including a mechanistic link between environmental drivers and seagrass growth and senescence. We wanted the model to be able to help users test their understanding of how environmental factors drive seasonal growth cycles and also to predict the potential outcomes of management interventions. We also wanted the model to be easily re-parameterized and used to represent other seagrass species and environmental conditions. We aimed to test the model by applying it to a shallow subtidal population of the seagrass Halophila stipulacea from the western Persian Gulf. This population exhibits rapid biomass response to the marked seasonal environmental differences it experiences. This makes it ideal for testing whether our model could successfully integrate data on environment and lower-level growth processes (at the plant component level, such as changes in shoot mortality) to predict seasonally varying higher-level behaviour (such as lateral expansion or contraction of whole plants).

METHODS

Model overview

The stochastic spatially explicit functional–structural model simulates the dynamics of ephemeral seagrass growth and productivity in response to environmental drivers that vary over time. The two key components of the model are apices (live apical meristems) and internodes (individual rhizome segments – as a real seagrass rhizome grows, its leaves are encased in a leaf sheath that encircles the rhizome; once the leaf sheaths senesce, they leave a clearly marked scar on the rhizome which defines the limits of an internode). The model simulates the branching structural development of seagrass plants by representing how each growing apex produces new internodes, leaves and additional apices over time. The number of initial apical meristems in the simulated plot area, the plot area dimensions and the duration of the simulation are defined by the user and are limited only by computer power. The structure and behaviour of the simulated seagrass is defined by a series of rules regarding branching pattern, internode angle and internode length. The model mechanistically links seagrass growth and senescence rates with a locally relevant environmental variable through a user-defined relationship. The death of apical meristems is determined stochastically according to a base probability that can be modified at certain times throughout the simulation to represent temporary effects, such as storms, herbivory or competition.

Model implementation

The model is implemented in the open-source, platform-independent and freely downloadable statistical computing and graphics software package R (R Core Team, 2013). Two comma-separated values (csv) files contain parameterization data describing seagrass growth habit and a third csv file provides the environmental data. The csv format was selected because it is broadly recognized and easily adjusted using common data management software such as Microsoft Excel. This makes it easier for operators with little or no computer programming experience to re-parameterize the model for new species and locations, a key aim of this project. Before starting the simulation, operators adjust the data in the csv files to represent the lower-level growth habit of their case study species, define the environmental conditions of their case study location and simulation period, set the size of the area or empirical plot to be represented, and define the initial number of apical meristems within this area. The R model code files and examples of the required csv parameter and environmental input files are provided as Supplementary Data S1.

Case study species

We aimed to create a general model able to represent many ephemeral seagrasses, but in order to test it we parameterized it to represent Halophila stipulacea. This species responds rapidly to changes in environmental conditions and thus provided a good first case study for developing a model with a mechanistic link between seagrass productivity and environmental conditions. Halophila stipulacea is a small seagrass naturally occurring in the western Indian Ocean from Mozambique to south-western India (den Hartog, 1970). It is an invasive species in the Mediterranean and Caribbean Seas, where it was initially introduced via commercial and recreational boating activities and then expanded its range by vegetative and sexual reproduction (Lipkin, 1975; Ruiz and Ballantine, 2004; Willette and Ambrose, 2012). It forms meadows in coastal areas that are subject to massive developments involving substantial dredging and construction (Sheppard et al., 2010). Growth occurs rapidly from the tips (apices) of underground stems (rhizomes), and it has demonstrated exceptional ecological flexibility in tolerating a wide range of tolerance to salinity and depth irradiance and a high potential for dissemination to new locations (Willette and Ambrose, 2009; Willette et al., 2014). Measuring growth over more than a few weeks, however, presents a number of difficulties because of the combination of high turnover of shoots and disintegration of the underground stems that connect shoots (Whitehead, 2015).

According to observations of plant growth and structure derived from field sampling conducted in Sumaisma Bay, Qatar (25°55′ N, 51°29′ E), leaf-bearing shoots were produced from apical meristems on rhizomes buried ~5 mm below the surface of the seabed (Whitehead, 2015). Apices produced two elliptical leaves, each flanked by a temporary leaf scale. Mean internode length was 9.7 mm (± standard deviation of 6.5 mm). The direction of each new internode generally alternated from the previous internode by 20 ± 22°. Branching angle was 87 ± 20° and there was an 84 % probability that a new branch would be produced on the opposite side of the parent stem to the previous branch. A single root was formed on each internode but persisted to maturity on only 52 % of internodes. Surviving roots reached a mean length of 25 ± 16 mm. At its mean maximum growth rate, a new internode with leaf scales, leaf pair and root was produced every 6.1 d (n = 10), but on occasions this was as soon as 2 d. Mean apical density recorded from small, isolated stands of 100 % cover in May 2012 was upscaled to derive an m⁻² value of 1120 ± 560 apices per m² (n = 10). Senescence of the oldest part of the rhizome occurred concurrently with new growth at the rhizome apex throughout the year. This pattern of senescence from the base resulted in separation of branches, with each branch forming a new independent plant, and thus constituted an important, novel structural feature for our model. Most spatially explicit plant models either do not include senescence or have been developed for perennial species, where any senescence included in the model occurs from the loss of apical meristems, i.e. shoot mortality (Fernández et al., 2011; Renton et al., 2011; Sarlikioti et al., 2011).

Case study location

The Persian Gulf is an epicontinental sea located between 24 and 30° N and 48 and 57° E and experiences minimal water exchange with the Indian Ocean and net evaporation due to high solar radiation and negligible freshwater input (Purser and Seibold, 1973). Sumaisma Bay is a shallow, east-facing bay with mangroves, intertidal mudflats and subtidal seagrass meadows. Salinity at the study site remained >40 practical salinity units (PSU) and temperature ranged between 11 °C in winter and 37 °C in summer. Sampling was conducted at a site with mean water depth of ~0.2 m below chart datum, which is considered to be broadly representative of other shallow seagrass habitats throughout the western Gulf (Price and Coles, 1992). The high seasonal variability of environmental variables experienced in Sumaisma Bay made it an ideal site for parameterizing a model of the growth and senescence of ephemeral seagrass and how it is influenced by environmental factors.

Model details

In the simulation, each apex grows horizontally across the seafloor largely independently of other apices, producing new apices, internodes and leaves as it grows. Growth and structural development depend on the values specified for model parameters (Tables 1 and 2). Growth rate is driven by environmental data, which was assumed to be temperature in our case study. Each apex is associated with a cumulated degree-days sum that is updated each day by adding the difference between the day’s mean temperature and the model parameter base.enviro.value, when the mean temperature is greater than base.enviro.value. The apex produces a new internode when the cumulated value of this sum reaches the value of the model parameter DDpernode. Once a new internode is produced, the cumulative value of this sum is reset and accumulation recommences. The length of each new internode and the change in growth direction relative to the previous internode are determined stochastically by drawing from normal distributions with means and standard deviation defined by the four model parameter values len.mean, len.sd, nodeanglemean and nodeanglesd. The position of the apex then changes to be the far end of the new internode.

Table 1.

List of general model parameters, with description and the values sourced from field sampling used for our case study of H. stipulacea in Sumaisma Bay, Qatar.

Model parameter	Description	H. stipulacea value used
radforcount	Radius for counting apical density	50 mm
maxnum	Maximum number of apices within the radforcount area	9
nodeanglemean	Mean angle of internode growth compared with the alignment of the previous internode. Node angle alternates, producing a zigzag growth pattern	20°
nodeanglesd	Standard deviation of the angle of internode growth	22°
branchanglemean	Mean angle at which the branch grows out from the parent branch	87°
branchanglesd	Standard deviation of the angle of branching	20°
branchaltprob	Probability of a branch growing on alternating sides of the parent branch	0.84
base.enviro.value	Minimum reported value for the environmental driver of growth, which was water temperature in this case study	13 °C
DDpernode	Number of degree days required to produce one internode	112
Pbudmort	Random probability of apical death	0.05
biomass.root.pernode	Mean mass of a root per internode	0.95 mg
biomass.internode.permm	Mean rhizome biomass	0.38 mg mm−1
biomass.leaf.per.node	Mean biomass of a leaf pair	7 mg
leaf.duration.days	Estimated persistence time of a leaf	25 d
max.dieback.perday	Maximum rate of internode dieback (number of internodes apex−1 d−1) applied from the oldest internode	0.26
base.dieback	Minimum internode dieback rate applied year round from the oldest internode	0.105
dieback.transition.rate	Rate of transition from max.dieback.perday to base.dieback	0.1
dieback.transition.value	The value of the environmental parameter at which dieback rate transitions from max. dieback.perday to base.dieback	>20 °C

Table 2.

List of branch order model parameters, with description and the values sourced from field sampling used for our case study of H. stipulacea in Sumaisma Bay, Qatar. No differences between branch orders were observed in this case study so the mean and standard deviation values provided here were used for all branch orders

Model parameter	Description	H. stipulacea value used
len.mean	Mean internode length	9.7 mm
len.sd	Standard deviation of internode length	2 mm
count.mean	Mean number of internodes between branches	2
count.sd	Standard deviation of the number of internodes between branches	2

Sometimes a new apex is produced at the same time as a new internode; these new apices produce new branches, which grow out from the parent stem. Whenever a new branching apex is produced, the number of internodes that it will produce before branching again is determined stochastically by drawing from a normal distribution defined by the parameters count.mean and count.sd. To allow alternate branching structures, the side of the parent stem to which a new branch will grow is determined stochastically, with the probability that the branch will be on the opposite side to the previous branch defined by the parameter branchaltprob. The angle of the branch relative to the parent stem is also determined stochastically, drawn from a normal distribution defined by the parameters branchanglemean and branchanglesd.

All new nodes produced have a leaf attached to them and each leaf has a pre-determined life-span defined by the model parameter leaf.duration.days. Leaves do not influence plant function but have been included for visualization purposes. Leaf life-span does not vary between leaves.

The model assumes a fixed minimum chance of apex mortality at each time step, which is defined by the model parameter Pbudmort. It is also assumed that crowding or competition for light and other resources increases the chance of mortality when an apex has more other apices in its vicinity. Mortality due to crowding is simulated using two parameters: radforcount defines the area surrounding an apex to consider and maxnum represents the approximate maximum number of apices that can occur within this area. For each apex, at each time step, the number n_other of other apices within a radius of radforcount is calculated, and then the probability of mortality is then calculated according to this equation:

$$p_{\text{mort}}=\text{Pbudmort}+{\left(n_{\text{other}}/\text{maxnum}\right)}^{\text{3}}\times \left(\text{1}-\text{Pbudmort}\right),$$

where p_mort is the probability of mortality for the apex at this time step. Whether or not mortality of that apex occurs at that time step is then determined stochastically, according to the calculated probability. This ensures that as the number of other apices within radforcount of an apex approaches maxnum, then the probability of mortality approaches one, ensuring that apex/bud density does not exceed maxnum. Increased likelihood of apical mortality due to temporary or stochastic influences such as storms, competition or other factors can also be represented, as we describe later, for the impacts of crab burrowing and algal smothering.

Senescence proceeds from the base towards the tips of the branching structure. The oldest internodes senesce first, resulting in gradual isolation of branches from the parent stem. The time required for senescence of an internode is also mechanistically linked to environmental data (also temperature in our case study). The senescence rate is defined by the equation:

$$R_s=d_b+(d_{mx}-d_b)\times \left(\frac{1}{1+\text{exp}(d_{tr}(E-E_t))}\right)$$

where R_s is senescence rate, d_b is the minimum or base senescence rate (base.dieback), d_mx is the maximum senescence rate (max.dieback.perday), d_tr is the rate of transition between the maximum and minimum senescence rate (dieback.transition.rate), E represents the value of the environmental variable on that day of simulation and E_t represents the value of the environmental variable around which the transition is centred (dieback.transition.value).

For example, in our case study higher senescence rates occurs on days when water temperature is below dieback.transition.value. For every degree above dieback.transition.value, the senescence rate decreases at a rate determined by the value of dieback.transition.rate until it approaches base.dieback, and for every degree below dieback.transition.value the senescence rate increases in a similar way until it approaches max.dieback.perday.

Model parameter values are specified in the files basicparams.csv and byorderparams.csv, and the environmental data that drive the simulation are included in envirodata.csv. Species-specific data concerning internode lengths and the number of internodes between branching points are contained in byorderparams.csv. Because some seagrasses exhibit structural and functional differences between branches of different orders (Renton et al., 2011), users can enter different values describing the number of internodes and internode lengths for up to four branch orders into this file. The other parameter file, basicparams.csv, contains general parameters controlling structural geometry, senescence, biomass and mortality.

Model output

The model produces a two-dimensional image showing the growing structure of the plant(s) (Fig. 1). Simulated seagrass can grow beyond the designated visualized plot area; there is no limit on how far apices can grow. This means that apices can grow back into the visualized plot area from outside the plot area. It also means that the simulation will continue until the user-defined run duration is completed or until all apices have senesced, regardless of whether live apices appear within the visualized plot area. For all simulations in this paper, a visualized experimental plot area of 300 mm × 300 mm was used.

Fig. 1.

Two-dimensional ‘snapshots’ illustrating the dynamic simulated growth of four initial apical meristems within a 300 mm × 300 mm experimental plot, with growth captured at 20, 60, 120 and 200 d after initial planting. Black dotted lines represent senesced and decayed rhizomes, light green solid lines represent live rhizomes, dark green circles represent leaves and red circles represent growing apical meristems. Note that at day 20 (top left) all plants have branched once, but one of the resulting apices has already died on one plant. By day 60 (top right), two plants have lost all live apices; one of these has separated into two separate structures. The two survivors have grown out of the plot, and one of these has then grown back into the plot from outside. By day 120 two plants are completely dead and senescenced, and by day 200 one of the surviving plants has grown to reach the area where one of the dead senesced plants was growing.

At completion of each time step, the model records the numbers of apices, internodes and leaves, rhizome lengths, leaf density, apical density, percentage cover (the percentage of 1 cm × 1 cm squares that contain at least one leaf) and biomass. Biomass is calculated based on parameters representing the mass of each plant part (biomass.rootpernode, biomass.internode.permm, biomass.leaf.per.node), which are simply multiplied by the number of each plant part within the plot area. Upon completion of a model run, the record of numbers, lengths and biomass is output to a csv file for further analysis.

Model parameterization

Morphological data for H. stipulacea were collected by conducting detailed measurements of H. stipulacea in a total of 50 transplanted and reference seagrass plots at ~2-month intervals between 26 June 2010 and 21 May 2011. (Reference plots are undisturbed plots that are used as references against which to compare restored plots.) A further ten seagrass plots were transplanted on 5 April 2011 and sampled on 20 April 2011 and 21 May 2011 to obtain detailed growth rate data for spring 2011. Further details of field survey methodology and project design are provided in Whitehead (2015). The following descriptors of plant morphology were sampled in the field (with the corresponding model parameter name provided in brackets obtained by summarizing the sampled data): internode angle (nodeanglemean, nodeanglesd), internode length (len.mean, len.sd), branch location (count.mean, count.sd), branch angle from the parent stem (branchanglemean, branchanglesd, branchaltprob), leaf presence or absence (leaf.duration.days), leaf length, and location of apical meristems (Tables 1 and 2). The change in the total number of internodes in a seagrass plot area between sampling events was used to derive values for parameters max.dieback.perday and base.dieback. Data were recorded on DuraRite^© underwater paper and were transcribed into electronic spreadsheets upon return to the office. Biomass data were collected by harvesting five of the transplanted plots at ~2-month intervals. Biomass samples were separated into three categories, namely leaves, rhizomes and roots. Mean and standard deviation were determined for mass mm⁻¹ and length to specify values for the biomass.rootpernode, biomass.internode.permm and biomass.leaf.per.node parameters for this case study. Although other environmental variables, such as light or nutrient availability, may be equally important drivers of seagrass growth dynamics, water temperature was selected as the environmental driver of growth for this case study because it is a key influence on seagrass seasonality (Lee et al., 2007), it is simple to measure and, unlike light irradiance data, the logged data are not confounded by low levels of biofouling. Water temperature was logged every 30 min of the sampling programme using a Hoboware^© temperature pendant (UA-002-64), which was installed 100 mm above the seabed. The temperature logger failed between 17 February and 4 April 2012 and missing data were estimated by linear interpolation. Temperature data were used to determine base.enviro.value and the temperature data were coupled with the net change in the number of internodes between sampling events to derive values for parameters DDpernode and dieback.transition.value. Values for Pbudmort and dieback.transition.rate were estimated based on observation.

In summer and winter, apical mortality was observed to increase because of bioturbation by crabs and burial by decomposing macroalgae. In summer, the effect of crab burrowing was estimated to increase apical mortality throughout an established meadow by 1 %. To account for this effect in our case study application, an additional apical mortality factor of 1 % above the base probability of apical mortality was simulated when water temperature exceeded 28 °C. In winter and early spring, epiphytic diatoms and macroalgae were observed to smother the underlying seagrass and increase apical mortality by ~5 %. Thus, in our simulations the probability of apical mortality was increased by 5 % when water temperature fell below 20 °C. Because algal smothering was not observed when water temperature was below 20 °C in autumn, the additional 5 % apical mortality was applied only between days 190 and 300 of the simulation.

Model validation

In order to help validate the model, each individual transplanted and reference seagrass plot was simulated for the same duration as the empirical sampling programme, and simulation results were compared with empirical data for each corresponding plot. This validation method tests whether the model could successfully integrate lower-level processes and values to predict higher-level outcomes. That is, observed values regarding component-level aspects of plant morphology such as internode length, angles and branching frequency and direction were used in parameterizing the model, and the parameterized model was then used to predict the structure and function of entire shoots and the number of apices, number of internodes and total rhizome length in a plot. These higher-level outcomes thus arose as emergent properties of the parameterized model, rather than being directly represented. Our validation consisted of testing whether these emergent characteristics of the model matched the corresponding characteristics of the real plants. We acknowledge that while this validation method addresses the aims of this study, it does not test the ability of the model to predict growth in new independent situations.

The simulation was run for the same duration as the field-sampling programme. The number of initial apices in each simulation was as close as possible to the actual number of initial apices recorded in the field, with the constraint that the model assumes initial apices are distributed in a grid. No more than five initial apices were modelled in a single row or column of the grid to avoid excessive apical death due to crowding, and this may have caused some deviation from field data in those few plots where this situation occurred. Where the initial number of apices was an odd number greater than five, the next closest allowable number of apices was used, alternating between the next highest followed by the next lowest. For example, if two plots contained seven initial apices, the initial number of apices was six in the first simulation (three columns on each of two rows) and eight (four columns by two rows) in the second simulation. The Welch t-test was used to test whether there was a significant difference between the observed and simulated values for net rhizome length, net number of apices and net number of internodes.

Effect of planting density and temperature

We conducted analyses of the general model to test and demonstrate its ability to predict the effects of varying planting density and temperature. Fifty replicate simulation runs were conducted for each of three planting patterns (four, nine and 16 plants in the simulated plot, on a 2 × 2, 3 × 3 and 4 × 4 grid, respectively). Fifty replicate simulation runs were then conducted for the 4 × 4 planting grid, for each of three temperature scenarios (original, +2 °C, +4 °C). These 300 simulations were conducted for just 200 d in all cases. In each case the temperature data used were the first 200 d of the original temperature data, with the temperature difference applied to every day where applicable. Analysis of variance was used to test whether differences in outputs were statistically different at 100 and at 200 d.

RESULTS

The graphical output of the parameterized model representing the dynamic structural growth and development of the seagrass plants qualitatively matched the growth patterns of H. stipulacea observed at the study site (Fig. 1; see also the example animated gifs in Supplementary Data S1). There was a reasonable match between empirical and simulated results over the 330-d simulation for net number of apices, net rhizome length and net number of internodes, although simulated data were generally more variable than observed data (Fig. 2). The Welch t-test indicated no significant difference between the observed and simulated values, indicating that there was no systematic over- or under-prediction by the model.

Fig. 2.

Validation results for (A) net number of apices, (B) net rhizome length and (C) net number of internodes. The boxes represent the interquartile range for observed and modelled plants over 330 d. The whiskers extend to the most extreme data point that is no more than 1.5 times the interquartile range from the box, while data points more than 1.5 times the interquartile range are shown individually as open circles.

The analyses of the general model demonstrated its ability to predict the effects of varying planting density and temperature (Figs 3 and 4). Varying planting density had a greater and more consistent effect on mean biomass and percentage cover than varying temperature. The effect of varying both planting density and temperature on both mean biomass and mean percentage cover was statistically significant (P < 0.01), because of the large number of replicate simulations runs, but there was also large variability among replicate runs within planting density or temperature scenarios (Figs 3 and 4). Increasing planting density increased mean biomass and percentage cover, as would be expected, and also decreased the variability between replicate runs (Figs 3 and 4). Increasing temperatures increased mean biomass and percentage cover, as would be expected, and also increased the variability between replicate runs (Figs 3 and 4).

Fig. 3.

Two-dimensional ‘snapshots’ illustrating the results of varying the initial planting density (2 × 2 = 4, 3 × 3 = 9 and 4 × 4=16 plants per 300 mm × 300 mm plot for left, central and right columns, respectively), and variation between replicate model runs (rows) on plant structures shown after 200 d of growth. Black dotted lines represent senesced and decayed rhizomes, light green solid lines represent live rhizomes, dark green circles represent leaves and red circles represent growing apical meristems. Note the stronger stochastic effects of early apex mortality and plants growing out of the plot when planting density is lower. The four replicates shown for each density were chosen at random from the 50 replicate runs conducted.

Fig. 4.

Percentage cover and biomass changes over time for five replicates for each of three planting densities (top; 2 × 2 = 4, 3 × 3 = 9 and 4 × 4 = 16 plants per 300 mm × 300 mm plot) or temperature scenarios (bottom; original temperatures, original temperatures +2 °C, original temperatures, original temperatures +4 °C). The five replicates shown for each density or temperature scenario were chosen at random from the 50 replicate runs conducted.

The model was also able to capture basal senescence patterns in a way that qualitatively matched field observations (Fig. 5 and animated gifs in Supplementary Data S1).

Fig. 5.

Two-dimensional ‘snapshot’ illustrating the simulated growth of four initial apical meristems within a 300 mm × 300 mm experimental plot, captured at 60 d after initial planting. Black dotted lines represent senesced and decayed rhizomes, light green solid lines represent live rhizomes, dark green circles represent leaves and red circles represent growing apical meristems. Note that at this time in this simulation run, all four plants have senesced from the base to a point where they are now two separate structures, meaning there are now eight separate branching structures. See also animated gifs in Supplementary Data S1.

DISCUSSION

This study successfully developed a new spatially explicit FSPM able to represent ephemeral seagrasses, including a mechanistic link between environmental drivers and seagrass growth and senescence. The mechanistic link between plant function and environmental variables means that the model can predict growth in new environments and varying environments, whereas earlier seagrass FSPMs could only be parameterized to represent growth in one specific set of environmental conditions, and thus did not allow for seasonal variability (e.g. Renton et al., 2011). This mechanistic link represents a useful development of spatially explicit FSPMs for seagrasses because it allows users to test their understanding of how environmental factors drive seasonal growth cycles. Another important development in this model is the ability to represent the senescence from the base observed in ephemeral seagrasses, and the resulting splitting of branching structures into independent organisms. This was not possible in our previous seagrass FSPM (Renton et al., 2011), nor to our knowledge in any previous FSPMs.

We wanted the model to be easily re-parameterized and used to represent other seagrass species and environmental conditions. To help achieve this, the model was implemented within the freely available computer graphics and statistics package R (R Core Team, 2013) and most parameterization data are entered into csv spreadsheets that can be easily modified in any of the widely used spreadsheet programs. Since R is a relatively simple programming language and environment that is freely available and increasingly widely used, it should also be relatively easy to recode aspects of the model that cannot be adapted as required solely through simple manipulation of parameter values. We believe that these factors will facilitate further use, validation and development of the model.

We tested the model by applying it to represent a shallow subtidal population of the seagrass H. stipulacea from the western Persian Gulf, an extreme environment where small fast-growing seagrasses appear during part of the year, and then disappear during the cooler months (den Hartog, 1970; Erftemeijer and Shuail, 2012). Management issues for this species in this region include large-scale mechanical transplanting for mitigation of shallow areas of seagrass impacted by human activities and developments [such as the extension of Doha airport, which provided the context for this study (Whitehead, 2015)]. In this environment, H. stipulacea takes on an annual life history, presenting many difficulties in tracking the outcome of transplanting for mitigation or habitat restoration. We therefore wanted the model to be able to help users test their understanding of the environmental drivers of seagrass seasonality and also to predict the potential outcomes of management interventions. Our results show that the model is indeed able to integrate data on the way that lower-level growth processes (at the plant component level) were affected by seasonally varying environmental drivers to predict seasonally varying higher-level behaviour (at the level of whole plants). It is also able to predict the effects of management options such as varying transplanting density, or reducing seasonally important drivers of increased mortality such as predation or competition.

The good match between simulated and empirical data observed during model validation was encouraging, but improvements are possible. The model uses a linear function to predict seagrass growth dynamics based on water temperature, while in reality such relationships are non-linear and influenced by multiple environmental variables (Lee et al., 2007). Although this version of the model effectively represents seagrass growth relative to environmental seasonality, its accuracy might be further improved by better data on how different environmental factors influence growth and senescence. The high variability in simulation results may be explained by the stochastic nature of the simulation, particularly regarding apical mortality. The stochasticity of the model allows it to represent the natural variation in seagrass growth forms, but it appears that these processes may be less stochastic in reality than modelled, possibly due to stabilizing feedback processes that decrease growth, branching and/or apex survival when plants are larger.

The validation we conducted showed that our model successfully integrated lower-order values and processes to predict higher-order outcomes, and we would expect the mechanistic nature of the model to give it some predictive value in different locations and environments. However, to properly test this, validation against new data collected from different locations and environments would be needed. Parameterization data were derived from vegetative fragments or seagrass growing at the fringes of an existing meadow and therefore the model may not accurately represent seagrass behaviour in an established meadow. Field investigations identified rare, isolated stands of tightly branching seagrass with short internodes and high apical density that persisted through winter. We did not observe any simulation runs that mirrored this growth form, which also indicates the importance of further model refinement. The model improves on previous seagrass FSPMs (Renton et al., 2011) by representing senescence from the base and dependence on environmental conditions, but as in Renton et al. (2011) the model has been designed and validated for seagrass species that do not have a vertical rhizome growth strategy and would thus require further development to account for a three-dimensional growth pattern.

The visual representation of the dynamic branching structure of seagrass rhizomes provided by the model helps stakeholders to quickly appraise the potential outcomes of management interventions such as seagrass transplantation. This simplifies the communication of potential project outcomes to stakeholders who may have a limited understanding of ecological processes. For example, in the case study reported here, the model clearly demonstrates that transplantation of H. stipulacea in the Persian Gulf would be unlikely to produce a persistent meadow by vegetative reproduction, because most transplanted fragments would completely senesce by the end of the first winter. This outcome is pertinent for proponents and environmental authorities when considering the potential impacts and mitigation measures of coastal construction projects, and it is relevant to two large-scale coastal construction projects in Qatar where seagrass transplantation was recently conducted (Seagrass Watch, 2009).

The model has many potential uses. In its current state, the model is useful for scientific purposes such as understanding how local-level processes result in emergent higher-order outcomes. It is also useful for more applied purposes such as forecasting potential impacts of environmental changes on seagrass productivity or predicting seagrass transplantation outcomes with different planting densities or arrangements (Renton et al., 2011). With further testing and development, this model could be linked to hydrodynamic models at various spatial scales and used in environmental impact assessments to assess potential ecological impacts (Burkhard et al., 2011; Verduin and Backhaus, 2000). The model could also be developed to assist with invasive species management. For example, a range of chemical and mechanical options were trialled for managing the invasive marine alga Caulerpa taxifolia in Australia (Glasby et al., 2005) and H. stipulacea is itself an invasive species in the Mediterranean and Caribbean Seas (Ruiz and Ballantine, 2004; Willette and Ambrose, 2009, 2012). With an understanding of how the control methods influence short-term local growth processes of the invasive species, and possibly other non-target species, the long-term outcomes of each control method could be simulated to help predict their effectiveness prior to full-scale implementation, potentially improving project outcomes and reducing unnecessary effort and environmental impact.

SUPPLEMENTARY DATA

Supplementary data are available online at www.aob.oxfordjournals.org and consist of the following. S1: three animated gifs illustrate the simulated growth of four initial apical meristems for a period of 200 d within a 300 mm × 300 mm experimental plot. Black dotted lines represent senesced and decayed rhizomes, light green solid lines represent live rhizomes, dark green circles represent leaves and red circles represent growing apical meristems. Note that as the plants grow they also senesce from the base, creating separate structures. (See also Fig 5.) Model code and parameter files are also included.