The coincidence of environmental and climatic extremes and the response of primary producers in marine coastal habitats and open systems

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UNIVERSITÀ DIPISA

PH.D INMOLECULAR ANDBIOLOGICAL SCIENCES PROGRAM IN BIOLOGY

T

HE COINCIDENCE OF ENVIRONMENTAL AND

CLIMATIC EXTREMES AND THE RESPONSE OF

PRIMARY PRODUCERS IN MARINE COASTAL

HABITATS AND OPEN SYSTEMS

Doctoral Dissertation of: Martina Dal Bello

Supervisor:

Prof. Lisandro Benedetti-Cecchi

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Abstract

U

NDERSTANDINGhow global change affects primary productivity in natural sys-tems is of crucial importance. The majority of ecological studies on climate change focused the attention on the impact of mean changes in environmental conditions, but there is increasing evidence indicating that ecological responses may depend as much upon environmental variation and extremes. Extreme weather events, such as severe droughts, heavy rainfalls, heat waves and hot spells, are increasing in severity and frequency and are likely to cause severe impacts at all levels of biological organization. So far, most manipulative field experiments have examined the effects of individual extreme events, with little attention to the possible synergistic effects of mul-tiple extreme disturbances. My thesis addresses the need to examine the combined ef-fects of compounded extreme events on natural population. I focused on phytoplankton and intertidal epilithic microphytobenthos (EMPB) biofilms as model systems. EMPB has been used to test the hypothesis that the concomitance of distinct environmental extreme events elicits larger effects compared to the expected cumulative effect of in-dividual extreme events. The importance of stochastic and determinist environmental changes in driving extreme events has been evaluated through the environmental boot-strap method applied at the scale of the Mediterranean basin.

Research on biofilms started from basic descriptions of spatial organization, as un-derstanding these patterns is necessary to interpret the effects of climate extremes. Results indicated that microalgae develop scale-invariant structures, reflecting the in-fluence of multiple processes operating at different spatial scales and possibly self-organization. A manipulative experiment was set up in order to test the separate and combined effects of warming and runoff following heavy rainfalls. Although a gen-eral pattern of reduced EMPB biomass in the clustered than the non-clustered scenario emerged in the first trial of the experiment, the hypothesis that compounded extreme events would elicit larger impacts than extremities of individual disturbances was not supported. EMPB biomass was susceptible to both warming and runoff, but the effects of the combination of these stressors was complex and context-dependent. Thus, re-peating this experiment at different times will be necessary before generalities about EMPB responses to environmental extremes can be drawn.

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The environmental bootstrap method resampled short-term data of sea surface tem-perature and patterns of geostrophic currents to obtain an ensemble of hypothetical time series that, when combined with a predictive model of chlorophyll a concentra-tion, allowed me to make inferences on primary productivity response to environmental extremes. The output of this analysis is a map of the distribution of chlorophyll a con-centration values with 100 years return time periods for the Mediterranean basin, which highlights the areas that are likely to harbour exceptional greening events.

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CHAPTER

1

GENERAL INTRODUCTION

1.1

Current evidence of global climate change

1.1.1. Global trends

Global change is no longer a controversial issue: it is indisputable that the environ-ment is going through a period of rapid change (elevated CO2, ocean acidification,

in-creasing temperature and enhanced UV radiation), the pace of which is unprecedented in our geological history [40]. Among the anthropogenic impacts acting at the global scale, it is considered the one that probably has the greatest potential to alter the func-tioning of the Earth system; this is expected especially because climate change has a great potential to interact with many ecological processes, including other sources of anthropogenic disturbance [86].

According to the 2007 Fourth Assessment Report by the Intergovernmental Panel on Climate Change (IPCC [218]), global surface temperature increased 0.74 ± 0.18

◦_{C during the 20th century. Most of the observed temperature rise since the middle}

of the 20th century has been caused by increasing concentrations of greenhouse gases, which result from human activities such as the burning of fossil fuel, deforestation, urbanization and land use. Furthermore, climate model projections indicate that the global surface temperature is likely to rise a further 1.1 - 6.4◦C during the 21st century. Land surface precipitation has also increased since the beginning of the 20th century in the mid to high latitudes, but shows a decrease in Mediterranean areas, and some tropical and sub-tropical latitudes [65]. Since atmospheric water-holding capacity is expected to increase roughly exponentially with temperature and atmospheric water content is increasing in accord with this theoretical expectation, it has been suggested that human-influenced global warming may be partly responsible for increase in heavy precipitation [106].

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1.1. Current evidence of global climate change

Besides these trends, there have been alterations of natural oscillations of climate, cyclic on timescales from seasons to decades. Those that are the most important are the El Niño/Southern Oscillation (NAO) and the Pacific Decadal Oscillation (PDO) [167]. El Niño is a band of anomalously warm ocean water temperatures that periodically develops off the western coast of South America and can cause climatic changes across the Pacific Ocean. Two ENSO phases can be recognized (El Niño and La Niña) and they refer to variations in the temperature of the surface of the tropical eastern Pacific Ocean and in air surface pressure in the tropical western Pacific. The two variations are coupled: the warm oceanic phase, El Niño, accompanies high air surface pressure in the western Pacific, while the cold phase, La Niña, accompanies low air surface pressure in the western Pacific.

The NAO is a climatic phenomenon in the North Atlantic Ocean of fluctuations in the difference of atmospheric pressure at sea level between the Icelandic low and the Azores high. Through east-west oscillation motions of the Icelandic low and the Azores high, it controls the strength and direction of westerly winds and storm tracks across the North Atlantic.

The PDO is detected as warm or cool surface waters in the Pacific Ocean, north of 20◦ N. During a warm, or positive, phase, the west Pacific becomes cool and part of the eastern ocean warms; during a cool or negative phase, the opposite pattern occurs. It shifts phases on at least inter-decadal time scale, usually about 20 to 30 years. Although the extent to which all these preferred patterns of variability can be considered to be true models of the climate system is still a topic of active research, there is evidence that their existence can lead to larger-amplitude regional responses to forcing than would otherwise be expected. In particular, a number of the observed 20th-century climate changes can be viewed in terms of changes in these patterns [218].

Increases in air temperatures led to higher ocean temperatures. The world ocean started to warm since the mid-nineteenth century, accounting, over this period, for more than 80% of the changes in the energy content of the Earth climate system. During the period 1961-2003, the 0 to 3000 m ocean layer has taken up about 14.1 x 1022 J, equivalent to an average heating rate of 0.2 W/m2 (per unit area of the Earth surface). During 1993 to 2003, the corresponding rate of warming in the shallower 0 to 700 m ocean layer was higher, about 0.5 ± 0.18 W/m2 [95], [81]. These warming translated into changes in sea level [2] and in ocean salinity [47] and biogeochemistry [40], which were exacerbated by changes in carbon dioxide atmospheric concentrations.

Atmospheric levels of CO2have increased dramatically since the onset of the

Indus-trial Revolution and, from concentrations of 280 ppm in the late eighteenth century, are now 386 ppm [205]. Concentrations of CO2 in the atmosphere are predicted to reach

between approximately 750 and 1000 ppm by the year 2100, depending on the model used for future projections [7]. Such a shift in atmospheric CO2 translates into

sig-nificant changes in the inorganic carbon availability in seawater. Thus for a three-fold increase in atmospheric CO2from the pre-industrial level (a rise to 840 ppm), dissolved

CO2 (assuming equilibrium between gaseous and aqueous phases and a temperature of

18◦C) would be 28 µM. This would cause a drop in oceanic pH to 7.77 and a shift in the equilibria between CO2, HCO−3, and CO

2−

3 , such that the concentration of HCO − 3

would increase by 17% and that of CO2−₃ would decrease by 54% compared to pre-industrial values [122]. These changes in dissolved organic carbon in the oceans result

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in a decrease in the saturation state of both calcite and aragonite, important minerals in calcifying planktonic and non-planktonic marine organisms, as well as having implica-tion for photosynthesis and planktonic growth [63]. Increased global warming and CO2

concentration cause a range of direct effects, changing the rates of biological processes as well as indirect effects that in turn influence ocean stratification, storm frequency, water column mixing and dust deposition.

1.1.2. Changes in variability and extremes

Changes in various types of extreme climate events have been described in several regions of the world. Alexander et al. [32] gave a comprehensive view of global trends in extreme temperature and precipitation events analyzing a suite of climate change indices. Results showed widespread significant changes in temperature extremes as-sociated with warming, especially for those indices derived from daily minimum tem-perature. In the last 50 years there has been a significant decrease in the annual oc-currence of cold nights and a significant increase in the annual ococ-currence of warm nights (Fig. 1.1). Decreases in the occurrence of cold days and increases in hot days, while widespread, are generally less marked. Throughout the globe the distributions of minimum and maximum temperatures have not only shifted to higher values, con-sistent with overall warming, but the cold extremes have warmed more than the warm extremes over the last 50 years (Fig. 1.1).

Besides episodic extreme warm days, also heat waves and hot spells are predicted to increase in severity and frequency as a consequence of global change [7]. Heat waves are defined as periods of at least three to five days during which mean or maximum anomalies of at least 3 - 5◦C above normal are observed [7] and can significantly and abruptly alter biotic systems [65], [86].

Changes in precipitation extremes are much less coherent than for temperature, but globally averaged over the land area with sufficient data, the percentage contribution to total annual precipitation from very wet days (upper 5%) is greater in recent decades than in earlier decades (Fig. 1.2, top panel). Observed changes in intense precipitation (with geographically varying thresholds between the 90th and 99.9th percentile of daily precipitation events) for more than one half of the global land area indicate an increas-ing probability of intense precipitation events beyond that expected from changes in the mean for many extratropical regions (Fig. 1.2, bottom panel) [72]. This outcome supports the disproportionate changes in the precipitation extremes described in the majority of regional studies (see [218] for a complete list of papers), in particular for the mid-latitudes since about 1950.

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Figure 1.1: Observed trends (days per decade) from 1951 to 2003 in the frequency of extreme temperatures, based on 1961 to 1990 values, as maps of the 10th percentile: (a) cold nights and (b) cold days; and for the 90th percentile: (c) warm nights and (d) warm days. Trends were calculated only for grid boxes that had at least 40 years of data during this period and had data until at least 1999. Black lines enclose regions where trends are significant at the 5% level. Below each map are the global annual time series of anomalies (with respect to 1961 to 1990). The red line shows decadal variations. Trends are significant at the 5% level for all the global indices shown. From [32].

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Figure 1.2: Top panel: observed trends (% per decade) from 1951 to 2003 in the contribution to total annual precipitation from very wet days (95th percentile). Trends were only cal-culated for grid boxes where both the total and the 95th percentile had at least 40 years of data during this period and had data until at least 1999. Middle panel: Anomalies (%) of the global annual time series (with respect to the period 1961 to 1990) defined as the percentage change of contributions of very wet days from the base period average (22.5%). The smooth red curve shows decadal variations (Alexander et al. 2006). (Bottom) Regions where dis-proportionate changes in heavy and very heavy precipitation during the past decades were documented as either an increase (+) or decrease (–) compared to the change in the annual and/or seasonal precipitation [218]. Thresholds used to define “heavy” and “very heavy” precipitation vary by season and region.

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In parallel to increased extreme precipitation events, warming accelerates land sur-face drying and increases the potential incidence and severity of droughts [54]. There are numerous indices and metrics of drought, but the majority of studies use monthly precipitation totals and temperature averages combined into in index known as Palmer Drought Severity Index (PDSI). The PDSI, calculated from the middle of the 20th cen-tury, shows a large drying trend over many Northern Hemisphere land areas since the mid-1950s, with widespread drying over much of southern Eurasia, northern Africa, Canada and Alaska (Fig. 1.3), and an opposite trend in eastern North and South Amer-ica. Decreases in precipitation over land since the 1950s are the likely main causes for the drying trends, although large surface warming during the last two to three decades has also possibly contributed to the drying. One study shows that very dry land areas across the globe (defined as areas with a PDSI of less than -3.0) have more than dou-bled in extent since the 1970s, associated with an initial precipitation decrease over land related to the ENSO and with subsequent increases primarily due to surface warming [218].

Changes in tropical storm and hurricane frequency and intensity are masked by large natural variability. The El Niño-Southern Oscillation greatly affects the location and activity of tropical storms around the world. Globally, estimates of the potential destructiveness of hurricanes show a substantial upward trend since the mid-1970s, with a trend towards longer storm duration and greater storm intensity, and the activity is strongly correlated with tropical sea surface temperature. These relationships have been reinforced by findings of a large increase in numbers and proportion of strong hurricanes globally since 1970 even as total numbers of cyclones and cyclone days decreased slightly in most basins [218].

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Figure 1.3: The most important spatial pattern (top) of the monthly Palmer Drought Severity Index (PDSI) from 1900 to 2002. The PDSI is a prominent index of drought and measures the cumulative deficit (relative to local mean conditions) in surface land moisture by incorpo-rating previous precipitation and estimates of moisture drawn into the atmosphere (based on atmospheric temperatures) into a hydrological accounting system. The lower panel shows how the sign and strength of this pattern has changed since 1900. Red and orange areas are drier (wetter) than average and blue and green areas are wetter (drier) than average when the values shown in the lower plot are positive (negative). The smooth black curve shows decadal variations. The time series approximately corresponds to a trend, and this pattern and its variations account for 67% of the linear trend of PDSI from 1900 to 2002 over the global land area. It therefore features widespread increasing African drought, especially in the Sahel, for instance. Note also the wetter areas, especially in eastern North and South America and northern Eurasia. Adapted from [55].

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1.2. A new generation of climate change experiments: events, not trends

1.2

A new generation of climate change experiments: events, not trends

Although gradual trends in average values of climate parameters have for long been considered the main drivers of ecosystems response to global change, intensification of weather extreme is currently emerging as one of the most important facets of climate modification [86]. This is intuitive since it is sufficient to have a slight shift in mean and variance values of a climate variable to dramatically increase the probability of occurrence of extreme events (Fig.1.2.1). Variance per se has indeed received consid-erable interest as a driver of community change in ecological experiments [180], [181], [43], [42]. As a consequence, the number of studies “event-focused”, in contrast to “trend-focused”, has increased in recent years.

Before trying to summarize the recent literature of extreme events, it is useful to point out how extreme events are defined and the way they are detected in time series of environmental variables.

1.2.1. Synthetic definition of extreme event

Smith [24] defined an extreme climatic event as “an episode or occurrence in which a statistically rare or an unusually climatic period alters ecosystem structure and/or function well outside the bounds of what is considered typical or normal variability”. This definition integrates both the “driver” (i.e. the probability of occurrence of an event) and the “response” (i.e. long-term impacts on population dynamics) perspec-tives. Moreover it stresses the fact that extreme events are specific to particular or-ganisms or ecosystems because of differing physiological tolerances and evolutionary histories [202] and accounts for the relative event “abruptness” (i.e. the magnitude of change per unit time), which depends on the length of species life cycles and the successional stages of ecosystems [86].

The assessment of extremes is based on long-term observational series of weather elements [218]. However, a problem arises when trying to choose statistical criteria to define rarity: how rare an event must be to be defined “extreme”? A common approach to define rarity is to use percentile thresholds: extreme events are those occurring be-tween 1 and 10% of the time at a particular location in a particular reference period [218]. For example 1% is equivalent to a annual event happening once per 100 years (i.e. an event that has a 100-years return time period). Therefore, it is evident that what constitutes a climate extreme is highly dependent on the available climate record [24]. Global studies of daily temperature and precipitation extremes over land suffer both from a scarcity of data and from regions with missing data. The main reason is that in various parts of the world there is a lack of homogeneous observational records, due, for instance, to changes in observing practices and data resolution [65], [86]. Moreover, the rarer the event, the more difficult is to identify long-term changes, simply because there are fewer case to evaluate [19][160].

1.2.2. State of the art

The effects of extremes events are under increasing scrutiny and their ecological importance continues to rise in response to anthropogenically forced climate change [218]. Environmental variables do exceed important biological bounds in nature, and

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1.2. A new generation of climate change experiments: events, not trends

there are many cases in which ecological dynamics depend more upon extremes of environmental factors than on their means [225]. Extreme weather events differ from gradual climatic trends as their ecological consequences are expected to be out of pro-portion to their relative short duration [86]. Observational studies provided evidences of the potentiality of extreme weather conditions to impact all levels of the ecological hierarchy, from organisms [116] to ecosystems [195].

Extreme levels of certain variables can lead to impairment of function or outright mortality of individuals. As an example, many population extinctions of Edith’s Check-erspot butterfly (Euphydrias editha) have been associated with particular climatic events, from severe droughts [66] to extremely wet years [62]. Extreme events can trigger cas-cading phenomena with unpredictable for populations, communities, and ecosystems. In 1992 in a semi-arid, southwestern part of the US, heavy rainfall events led to extraor-dinary biomass production by plants, which in turn caused population booms of deer mice (Peromyscus maniculatus). Overcrowding and forage shortage in the following year led to an increase in the rodent activity in human buildings, and this facilitated the contact between humans and mice, which can carry hantavirus. Hantavirus car-diopulmonary syndrome is frequently lethal to humans, and a regional epidemic was observed in the area in 1993. The same chain of events was repeated between 1997 and 1999 [14].

Extreme events can influence community dynamics and biodiversity by selectively removing community dominants, thereby freeing up resources for other species [176], [161], [204], also introduced species [177]. A case study on the effects of Hurricane Omar in 2008 recorded the burial of native seagrass beds by unusually large sediment loads as a result of storm surges which led to the establishment of the invasive sea-grass Halophila spp [139]. In a marine coastal ecosystem in New Zealand, a heat wave caused the weekly maximum temperature to be 7◦C higher than that reported from pre-vious years: this led to widespread mortality that was an order of magnitude higher for a native mussel than for an introduced mussel species [120]. Extreme events can cause sufficiently dramatic ecological change that recovery is greatly delayed or impossible. Such effects arise when populations are pushed below some minimum density thresh-old (e.g., the Allee effect, [33]), or when a community or ecosystem enters an alternate stable state [195], [68].

Observational studies, such as those described before, although being able to cap-ture the potentially detrimental effects of extreme events, often lack replication and can-not control for characteristics of extremes (type, timing, magnitude) [24]. To overcome these limitations, in recent years the number of field experiments simulating climate extremes grew considerably (see for example [102], [36]). Compared to observational studies, these experiments offer the advantage of greater control over the nature of the climate extreme they impose, leading to a deeper comprehension of the effects of ex-tremes on population dynamics and ecosystem functioning. However, the majority of these studies examined the effects of single extremes, while largely overlooked the po-tential for complex responses to repeated extreme events [105]. Experimental studies imposing repeated winter warming events on Sub-Arctic shrubs and lichen communi-ties [44], [45] highlighted newly-observed plant growth and production patterns, which suggested that extreme events could compensate or even reverse predicted changes due to global warming trends [153]. Moreover, few have considered interactions between

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1.3. Study systems: epilithic microphytobenthos

different climate extremes (e.g. severe drought vs. heat wave in [149]). Finally, the majority of studies have been performed in terrestrial ecosystems, while, to date, the effects of extremes have not been formally tested in the marine realm.

1.3

Study systems: epilithic microphytobenthos

1.3.1. Why epilithic microphytobenthos (EMPB)

Predicting large scale population dynamics from the information gained at small spatial scales and understanding why large-scale outcomes contradict small-scale trends are among the most vexing problems in field ecology [8], [9]. When increasing the spa-tial extension of a study, some ecosystems properties intervene adding complexity and new unpredictable properties emerge.

Progress has been made in developing a theory to scale-up local population dy-namics to larger scales, which is called scale transition theory [200]. Application of this elegant approach is however complicated by the requirements of integrating mod-elling procedures with observational and experimental data. Another way to deal with problems of scale is to focus on study systems for which large scale dynamics occur over experimentally tractable spatial extents. This is the case for EMPB that mainly comprises microscopic organisms with relatively fast population dynamics that can be examined over a range of tractable scales, from a local scale of few mm to a large scale of tens of meters. Another advantage with EMPB is that changes in biomass can be evaluated continuously over a range of scales.

1.3.2. What we know about epilithic microphytobenthos

EMPB forming biofilms on rocky shores consists primarily of photosynthetic or-ganisms such as diatoms, cyanobacteria and macroalgal spores and germlings [213]. EMPB is a vital component of assemblages of species on rocky intertidal areas, con-tributing to primary production, providing food for many grazers [170] and influencing settlement of the dispersive larvae of many sessile invertebrates (e.g. barnacles, oysters) [126].

Biofilm biomass displays clear spatial and temporal patterns, which appear to be reasonably consistent in temperate areas worldwide. Several studies [145], [83] found greater abundances towards the lower levels of the shore and explained the observed trends as a response to periods of desiccation, increased temperature and light intensity at the higher levels of the shore. The same studies suggested a general trend for mi-croalgae to be less abundant during the warmer periods of the year, which again may reflect stress from desiccation.

Seasonal changes in EMPB may vary across heights on the shore, although patterns are not general. For example, in the northern hemisphere, greater seasonal variation has been observed on the upper shore, where stress during emersion was greater [145], [146]. In contrast, in the southern hemisphere, densities of EMPB on the upper shore varied little with season, and differences in chlorophyll a between heights were influ-enced more by changes in density lower on the shore (Australia [163], [83]; S. Africa [162]).

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1.4. Study systems: phytoplankton

Superimposed on this, however, is the effect of grazers: Thompson and co-authors [145] demonstrated that EMPB abundance is regulated by the interactive effect of sea-sonal variations in emersion stresses (principally insolation), combined with increased grazing activity during summer periods. EMPB biomass has proved to be positively related to number and growth of grazers [170] and can also influence ecological inter-actions among grazers, such as competition and facilitation [173].

The existing literature does not indicate consistent patterns in composition of as-semblages of EMPB among climatic regions in relation to environmental variables. In tropical Hong Kong, cyanobacteria were relatively more abundant during summer [217]. In Sydney, assemblages of EMPB at each latitude were typically dominated by cyanobacteria [83]. This was in contrast with many assemblages at temperate northern latitudes that were dominated by diatoms during winter [213], [146], which were more abundant lower on the shore and decreased with increasing insolation [145]. In the UK, cyanobacteria can also be prevalent during the summer [213], [145], [146].

Also wave-exposure seems to play an effect on biofilm abundance and the observed patterns have been attributed to direct effects of water flow, increasing nutrient supply and reducing desiccation, and changes in the density and identity of grazers along the wave exposure gradient. However, contrasting results can be found in the literature. In NW Europe, Jenkins and Hartnoll [219] found greater biofilm abundances at shel-tered than at exposed locations, while Thompson and other authors [146] showed the opposite trend, but this was on shores without macroalgal canopy. On the east coast of Australia, where macroalgal canopy is typically not present, biofilm abundance tends to be greater on sheltered shores compared to exposed one [83]. This pattern was the opposite of that observed in Australia by MacLulich [163], who found more chloro-phyll a on exposed shores. These contradictory outcomes have been related to different species dominance: for example, cyanobacteria-dominated EMPB assemblages in Aus-tralia opposite to diatoms-dominated assemblages, especially in winter, in the northern hemisphere [83].

In contrast to other regions of the world, little is known about the distribution of EMPB on rocky shores in the Mediterranean. Thus, one chapter of my thesis pro-vides an observational analysis of spatial and temporal patterns of EMPB on the rocky shore of Calafuria, south of Livorno. Two other chapters focus on ecological processes through field experiments.

1.4

Study systems: phytoplankton

1.4.1. Why phytoplankton

Primary productivity is the production of organic compounds from atmospheric or aquatic carbon dioxide, principally through the process of photosynthesis, with chemosynthesis being much less important. The organisms responsible for primary production are known as primary producers or autotrophs and form the basis of food webs. In terrestrial ecosystems, almost all primary production is now performed by vascular plants, with a small fraction coming from algae and non-vascular plants such as mosses and liverworts. In a reversal of the pattern on land, in the oceans the majority of primary production is performed by free-living microscopic organisms called phy-toplankton, since larger autotrophs, such as seagrasses and macroalgae are generally

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1.5. Aims of the thesis

confined to the littoral zone and adjacent shallow waters. Hence, contributing roughly half of the biosphere’s net primary production (NPP) (around 50 PgC/yr), photosyn-thesis by oceanic phytoplankton is a vital link in the cycling of carbon between living and inorganic stocks. Each day more than a hundred million tons of carbon in the form of CO2 are fixed into organic material by these ubiquitous, microscopic plants of the

upper ocean and each day a similar amount of organic carbon is transferred into marine ecosystems by sinking and grazing. In the light of the importance of primary produc-tivity and the vital role of phytoplankton, understanding the impact that global change will have on the ecological performance of these organisms is crucial.

Phytoplankton can be a useful model system for climate change studies for several reasons. First, phytoplankton natural populations are not exploited commercially. As-suming no direct human impacts via top-down consumers, such as fish, it is possible to draw non-biased links between long-term changes in primary productivity and cli-mate change [165]. Since phytoplankton is primarily composed of short-lived species, population size is less influenced by the persistence of individuals from previous years, which leads to thigh coupling between environmental change and plankton dynamics [76]. In addition to this, in the light of the fact that non-linear responses of biologi-cal communities are able to amplify subtle environmental perturbations [141], phyto-plankton can be more sensitive indicators of changes than the environmental variables themselves [76]. Finally, the ease of access and the wide spatial and temporal extent of ocean colour satellite data make phytoplankton an ideal model system to investigate long-term, broad-scale global change dynamics.

1.5

Aims of the thesis

The present thesis builds on previous correlative and experimental studies stressing the increasing importance of extreme events as main drivers of change in natural popu-lations in the contest of global warming and responds to the pressing need to investigate the compound effects of environmental extremes in marine systems. The primary aim of my thesis was to understand how extreme conditions of selected environmental and climate variables, in isolation and in combination, affect coastal primary productivity, both on a local scale (addressing EMPB ecology) and on a regional scale (dealing with phytoplankton dynamics).

Since scarce information is available about the distribution of EMPB on Mediter-ranean rocky shores, one aspect of my thesis (Chapter 3) focuses on the spatial and temporal patterns of EMPB distribution and abundance on intertidal rocky shores in the northwestern Mediterranean. Because EMPB is exposed to various sources of dis-turbance and stress on these shores, a related aspect of my thesis was to examine the recovery patterns of EMPB after experimental disturbance (Chapter 4). In both studies I took advantage of spatially nearly-continuous data obtained through field-based re-mote sensing and flexible statistical techniques (spectral and multifractal analyses) to elucidate EMPB ecological dynamics.

The results of these studies motivated and provided the basis for the interpretation of a manipulative experiment testing the effects of extreme events on Calafuria EMPB assemblages (Chapter 5). It is known from the literature that high temperature fluctua-tions and sediment deposition following runoff are two important sources of mortality

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1.5. Aims of the thesis

for rocky intertidal organisms and their impact is likely to be amplified by climate change. The weather extremes leading to increased aerial temperature and runoff are predicted to increase in frequency, intensity and duration in the Mediterranean basin, for which models project a scenario characterized by heavy precipitation events between prolonged hot and dry periods [218]. Thus, through this experiment I tested the hy-pothesis that the concomitant incidence of extreme hot days and heavy rainfall events would elicit larger effects on biomass and spatial distribution of EMPB compared to effects of individual extremes.

Finally, I focused on environmental drivers of phytoplankton distribution and abun-dance across the Mediterranean Sea, in order to predict the probability of occurrence of abrupt algal blooms (Chapter 6). I proposed that the environmental factors respon-sible for phytoplankton distribution and production (inferred from chlorophyll a con-centration) are sea surface temperature (SST) and patterns of superficial currents. SST directly influences cellular metabolism of phytoplankton organisms by enhancing en-zymes turnover rates and carbon dioxide assimilation. It has also an indirect effect by influencing water column stability, upwelling phenomena and mixed layer depth forma-tion, which in turn regulate nutrients supply. Superficial currents account for variation in chlorophyll a due to phytoplankton and zooplankton aggregation and dispersion phe-nomena. Nutrients availability is certainly an important factor influencing phytoplank-ton abundance and distribution, but the lack of long-term, broad-scale data records of these drivers prevented me from considering them in the analysis. I tested the hypoth-esis that exceptional phytoplankton blooms are compounded events, resulting from the chance alignment of environmental extremes leading to favorable conditions for phyto-plankton growth. Specifically, I used the environmental bootstrap method proposed by Denny and co-authors [60] to resample short-term environmental data to obtain an en-semble of hypothetical time series, which, together with models relating phytoplankton biomass to the selected environmental predictors, allowed me to analyze phytoplankton response to environmental extremes.

Overall, my thesis improves understanding of the causes and consequences of eco-logical extreme events involving changes in coastal primary productivity, which is im-portant to forecast the consequences of global change in marine ecosystems.

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CHAPTER

2

GENERAL METHODS

2.1

Data collection

2.1.1. Epilithic microphytobenthos

2.1.1.1. Microphytobenthos: from traditional techniques to field-based remote sensing Micro-algal biomass can be measured through both direct and indirect methods. The first imply counting the number or estimating the percentage cover of algal cells using light, scanning electron or confocal laser scanning microscopy. The latter de-termine the amount of chlorophyll a (as an index of biomass) extracted from samples of substratum using spectrophotometry or High Performance Liquid Chromatography (HPLC). Both techniques present several shortcomings. They are laborious, expensive and require the removal of microalgae from the substratum or the destructive sampling of the substratum itself, thus preventing repeated observation to be made. The estimate of microalgal biomass can be biased by loss or degradation of chlorophyll a during processing [216]. Since algae cannot be removed at very fine spatial scale from the rock-surface, the spatial scale of measurement is often determined by the physical con-straints of the method, rather than by requirements of the experiment. Moreover, since sampling of random point-locations is the only way to collect data, the contiguous small-scale measurements needed to reconstruct the complete picture of chlorophyll distribution over an intertidal area cannot be obtained.

The development of remote sensing techniques, which make use of cameras or sen-sors mounted either on aircrafts and on field-based platform, allowed to overcome some of these problems and greatly improved research on the ecology of epilithic microphy-tobenthos. Remote sensing techniques quantify benthic chlorophyll a by measuring the amount of reflected sunlight in the visible and infrared bands of the electromagnetic

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2.1. Data collection

spectrum. Airborne sensors proved to be useful in studies aiming at mapping epilithic microphytobenthos assemblages at large spatial scales (10s cm to m) (as in [37]), but the limited resolution power and other experimental and financial constraints [110] re-stricted their use. Conversely, remote sensing using cameras mounted on field-based platforms allows to obtain epilithic microphytobenthos biomass samples from specific areas and from independent replicates at a spatial resolution that fits with scales of variation of microalgae (mm - cm, [80]. Such image-based approaches have lots of ad-vantages over conventional methods: acquisition of images is quick and non-destructive (enabling repeated observations to be made of the same area without interfering with any experiment) and large areas can be sampled in a single image [110].

The first to employ a field-based imaging technique to quantify amounts of ben-thic microalgae were Jobson et al. [88]. Later on the use of these techniques has been limited due to the excessive costs of sensors. Only recently, improvements in CCD array technology allowed the commercialization of cost-effective imaging sen-sors suitable for use in intertidal areas. Murphy and co-authors ([107] developed a digital colour-infrared (CIR) camera, through which they examined the spatial distribu-tion of chlorophyll a (used as a proxy for microalgal biomass) on an emerged intertidal mudflat at very fine spatial scales (< 1mm). The same technique was later used to quantify amounts of chlorophyll in epilithic microalgal biofilms on rocky shores [109], to test hypotheses about grazing by herbivorous gastropods [166], [82], to detect fine spatial variability of biofilm biomass [110] and latitudinal and environmental patterns in abundance and composition of epilithic microphytobenthos [83].

Terrestrial vegetation and marine microalgae show distinctive spectral features in the visible and near-infrared (NIR) electromagnetic spectrum. With increasing amounts of chlorophyll a, there is a progressive increase in absorption at visible wavelengths, particularly in the blue and red, associated with an increase in reflectance in the NIR [107]. Since digital cameras can sense only three relatively broad spectral bands at green, red and NIR, microalgal biomass has been estimated on the bases of chloro-phyll a absorptive properties in these three bands. However, chlorochloro-phyll amount can-not be correlated to spectral reflectance in single bands because this relationship can be masked by differences in brightness of the substratum [27]. For this reason, spectral in-dices that allow to measure chlorophyll amount by quantify the difference in reflectance between visible (red or green) and NIR bands and to take into account substratum brightness variability have been developed. The ratio vegetational Index (RVI, [157]) and the Normalised Difference Vegetation Index (NDVI, [127]) use red and NIR bands and are commonly employed to quantify chlorophyll in terrestrial and aquatic vegeta-tion [175], [118] and intertidal microphytobenthic assemblages ([107] and subsequent papers). Quantitative measurements of chlorophyll a can be made using reflectance at red and NIR wavelengths because, with increasing amounts of chlorophyll, there is in-creasing absorption at red relative to NIR wavelengths. Since these indices are affected to some degree by background variation in the soil substratum, Huete [207] developed the Soil Adjusted Vegetation Index (SAVI), that partially compensate for this effect. In addition to these, spectral indices that use NIR and green bands have been proposed, e.g. the Infrared/Green Ratio (IRGVI, [96]) and the logarithm of this ratio (LIRGVI, [16]). The value assumed by all these indices augments as chlorophyll a amount in the substratum increases.

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In CIR imagery, chlorophyll a, which is used as a proxy for biofilm biomass, is estimated from the RVI index. The RVI detects the absorption of chlorophyll a using the reflectance at NIR wavelengths, where chlorophyll a does not absorb, normalized by the reflectance at red wavelengths (corresponding to the peak of chlorophyll a absorbance) [109]. A ratio is used because it removes variations due to the inherent spectral qualities of the rock substratum in addition to differences in brightness caused by small scale variation in surface topography [109]. This ratio is strongly related to the amount of chlorophyll a on the rock surface [108].

Despite the several advantages of remote sensing, there are some limitations that must be taken into account when acquiring CIR image data. For example, the NIR/red ratio is affected by small amounts of pooled water on the surface, even only few mil-limetres deep. This is because water is very absorptive at NIR wavelengths, thus pro-ducing a decrease in the NIR/red ratio, and because light has to pass through the air-water interface which may cause changes in the ratio which are unrelated to the amount of chlorophyll. For this reason, remote sensing in intertidal areas is presently limited to emerged surfaces. Another problem to be considered is that shading, caused by deep pits, crevices or burrows in the substratum, may also affect the NIR/red ratio. According to Murphy and co-authors [110], CIR imagery overestimates the amount of chlorophyll where there is deep shade, relative to adjacent areas where there is no shade. With respect to airborne remote sensing, these problems can be solved by specif-ically selecting areas without pits or crevices or pooled water, although one must then pay attention in drawing inferences from the data for a wider set of conditions [110]. In situations where it is not possible to do this for experimental or sampling reasons, data can be extracted from images in areas that do not contain these features-all of which are identifiable both during field-work and in raw CIR data. This method is also complicated by variable amounts of surface moisture. Surface moisture can affect the reflectance at each pixel in two ways. First, wetting a surface can reduce reflectance. Light reflected from the surface of the rock is “internally reflected” from the water-air interface back towards the substratum, thus increasing the chance that light will be further absorbed. Second, damp surfaces increase specular reflectance (sun-glint), where the direct solar beam is reflected back in a mirror-like fashion from the upper surface of the water on the rock to the observer. This reduces the amount of useable information in the image because specular reflectance gives no information about the substratum [166]. Areas where specular reflectance is dominant appear dark in NIR/red ratio images, compared to adjacent areas. Another problem is that the NIR/red ratio re-mains sensitive to changes in the amount of chlorophyll at concentrations at or below 10 µg/cm2_{. Red reflectance decreases with increasing amounts of chlorophyll up to}

10 µg/cm2_{, but, above this concentration, red reflectance becomes much less sensitive.}

However, amounts of microalgal chlorophyll on rocky shores are often reported to be between 0 and 12 µg/cm2 _{[166], [109], [110], [111], [83].}

2.1.1.2. Photographic image processing

Photos are taken by means of a IR-sensible camera (ADC c , Tetracam Inc), com-monly used in agricultural and vegetational studies. The ADC is a single sensor digital camera designed and optimized for the capture of visible light wavelengths longer than 520 nm and near-infrared wavelengths up to 920 nm. This camera uses a

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Bayern-2.1. Data collection

pattern filter to produce a 3-layered image comprising green, red and NIR layers which are analogous to the red, green and blue layers produced by conventional digital cam-eras. The ADC system writes lossless compressed image files or RAW files for ev-ery image. These images carry the extension∗.DCM or ∗.RAW. DCM and RAW files are greyscale images displaying “raw” pixel values; for this reason such files must be colour-processed prior to further use and saved in TIFF format, using PixelWrech2 pro-gram [1]. Images are 2560 by 1926 pixels in size and cover an area of ground of about 52 by 35 cm. The approximate spatial resolution of each pixel is 0.2 mm.

In order to get the best focus, photos were acquired using a stable platform 60 cm above and normal to the ground. Different exposure times for each photo were selected depending on ambient light conditions, in order to produce bright but not saturated photos. Photos were acquired in the range of high-angle solar conditions in order to minimize shading produced by pits and crevices.

To calibrate pixel values to the varying light conditions and different camera set-tings, a reflectance standard of 30% reflective Spectralon c , representing the range of brightness of Calafuria rock surfaces with microalgae, was always placed within the field of view of the camera (see [109]). Reflectance standards reflect light at differ-ent wavelengths according to their characteristics of absorbance; they are made from a spectrally flat material that has near-lambertian reflectance characteristics (i.e. they reflect light nearly equally in all directions).

The calibration of data to reflectance consists of the normalization of pixel values of each band to the brightness of pixels over the calibration panel. Pixel values (Digital Number, DN) over the calibration standard are averaged and the reflectance ρ for each band in each photo is calculate

ρ(panel) = DN (photo)ρ(panel)

DN (panel) (2.1)

where ρ(photo) is the reflectance at each pixel in the photo; ρ(panel) is the re-flectance of the calibration standard, which is a known constant; DN(photo) is DN at each pixel in the photo and DN(panel) is the average DN of the pixels over the cali-bration standard. Image calicali-bration is part of a java-routine on ImageJ program with which each ADC-image is processed.

2.1.1.3. In situ chlorophyll data

All methods of collecting remotely sensed data require calibration-validation by comparison with direct measurements [108]. In order to calibrate-validate estimates of chlorophyll a derived from the ADC data, 100 rock chips ∼2 cm in diameter were removed by cutting the rock with a diamond corer powered by a petrol driller and then photographed using the ADC camera. Rock chips were then taken to the laboratory for the determination of the amount of chlorophyll a, which was extracted in methanol as in [143]. During the transport to the laboratory, rock chips were kept in individual jars with lid filled with filtered sea-water, to ensure hydration, and maintained in the dark. Once in the lab, jars with lid and chips have been weighted and then a methanol has been added. Samples have been kept in the dark for 15 hours at room temperature

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(∼20◦C), then weighted again (the final volume of the methanol was hence calculated by subtraction). By means of a spectrophotometer, absorbance at Å665 and Å750 were measured. Finally, chlorophyll concentration (expressed per unit area in µg/cm2, [108]) is calculated following equation 2.2 presented in [143].

Chlorophyll a µg/mm2 = 13.0 × Ånet× v

d × a (2.2)

Where 13.0 is a constant for methanol, Ånetis the net absorbance of the chlorophyll

solution (Å665-Å750), v=final volume of solvent, d = path length of cell, a = surface area of sample (measured from the photos of rock chips by means of image analysis in ImageJ).

Results of calibration are presented in Chapter 3. 2.1.2. Phytoplankton

Modern ocean colour sensors, such as the Sea-viewing Wide Field-of-view Sen-sor (SeaWiFS) and more recently the Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua spacecraft, provide near real-time, long-term, synoptic, global estimates of chlorophyll a and other key physical variables (e.g. sea surface tempera-ture). Therefore, they give an opportunity to study the distribution of phytoplankton and primary productivity on spatial and temporal scales unattainable through conventional sampling methods [156]. Chlorophyll a (chl), being a distinguished constituent of phy-toplankton and having a universal distribution among all the photoautotrophic algae and cyanobacteria, is widely used as an index of phytoplankton biomass [46]. Although un-certainties in the computation of chl absolute values can arise primarily owing to the presence, in the water column, of optically active materials other than phytoplankton pigments but with partially overlapping spectral signature (i.e. dissolved organic matter and suspended inorganic particle), the recent technical advances in the computation of global algorithms of chl retrieval have greatly improved the sensitivity of satellite data to chl variation in the upper ocean [38]. Ocean colour satellites measure the upwelling radiance emitted from the top of the Earth’s atmosphere at discrete visible and infrared wavelengths. Many global algorithms that have been developed to estimate chl concen-trations from satellite ocean colour data typically take advantage of decreased radiance (or reflectance) in the blue (440 - 510 nm) and increased radiance (or reflectance) in the green (550 - 565 nm) by working in terms of the ratios in these two wavelength bands (e.g., the SeaWiFS four-band algorithm OC4v4 involving λ1 = 443, 490, and 510 nm, and λ2 = 555 nm and MODIS/Aqua Ocean Chlorophyll three-band algorithm OC3 involving λ1 = 443 and 488 nm, and λ2 = 551 nm) ([115]). In the Mediterranean Sea, the standard NASA algorithms lead to a significant overestimation of the chl con-centration compared to in situ data [48], [64], [152]. This observed bias can have a strong impact on primary production models for the Mediterranean. To reduce the difference between chl estimated by the remote sensed reflectance and the in situ mea-surements, an ocean color algorithm specifically designed for the Mediterranean Sea MODIS MedOC3 [131] is applied. In addition to this, digitization round-off and noise errors have been significantly reduced in MODIS imagery [79]. For these reasons, here

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2.2. Statistical analysis

we used chl concentration data extracted from MODIS AQUA oceanographic sensor images (http://oceancolor.gsfc.nasa.gov/ ) as a proxy for phytoplankton biomass.

2.2

Statistical analysis

2.2.1. Spectral analysis

1/f noise models and spectral analysis have been largely applied to describe fluctua-tions in spatial and temporal series of environmental and ecological variables (reviewed by [187]). Generally these analyses require a large number of observations collected continuously in time or space. Spectral analysis is a powerful tool that allows one to de-compose the overall variance of a temporal or spatial signal into its frequency-specific components [59]. Each component is a harmonic associated with a characteristic wave frequency and amplitude. Thus, a function can be written as a Fourier series through sine and cosine functions:

f (x) =

∞

X

n=0

(ancos 2πnx + bnsin 2πnx) (2.3)

The coefficients an and bn indicate the waves amplitudes, and their squares define

the Fourier coefficients on a function called “power spectrum” [186]. Therefore, any complex function can be written as a complex Fourier series, using the exponential function f (x) = +∞ X −∞ cnexp2πinx (2.4)

where cn is a complex number with real part an and imaginary part bn. These

coefficients can be calculated only with a finite sequence of data points by applying the Discrete Fourier Transform [4]. This function takes the form of power laws

f (x) = cxλ (2.5)

where c and λ are constants, and λ is called the spectral exponent. f(x) is a probabil-ity densprobabil-ity function, called “Spectral Densprobabil-ity”, which may represent the variance of the signal, expressed in the frequencies domain. When f depicts the frequency of harmonic components, namely the inverse of wave length, either spatial or temporal, we obtain the family of 1/f noise characterized by power-law spectra of the form

S(f ) = 1

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The observed variability can then be characterized by the relative importance of different wavelengths, the pattern of which defines a particular type of “noise” [140]. By analogy with light, a spectrum in which all frequencies are important is regarded as white. It can be interpreted as a completely uncorrelated signal. The value taken by a variable at any time or location does not depend on its value at any other instant or loca-tion. This produces a signal that stays most of the time close to its mean, with rare and punctual excursions to higher values [221]. Instead, if the power spectrum is dominated by low-frequencies (i.e. long-period or large-distance) cycles, as is typically the case in ecological data, it is considered reddened. In the time or space domain, this produces an increased probability of having long runs of above or below average conditions [12], which means that observations that are close in time or space are more correlated than it would be expected purely by chance. Similarly, when higher frequencies are more pronounced, the spectrum is blue [186]. This represents the case of a negatively au-tocorrelated signal, where variance increases at smaller scales [4]. In some cases the relationship between S(f ) and frequency takes the form S(f )_∝ _f1β, where 0 β 2

is the spectral coefficient. Spectral density is plotted on a double logarithmic scale, to produce a linear relation between variance (spectral density), on the y-axis, and fre-quency (spatial or temporal scale), on the x-axis. The estimated slope of this relation is the spectral coefficient, which determines how variance changes with scale [186]. For white noise, β is equal to zero (constant variance), while β is equal to 2 when the spectrum is generated by a signal doing a random walk (brown noise, from Brownian motion). For example Brownian motion perfectly describes the erratic displacement of a particle in a fluid which is created by the random impact of the liquid’s molecules on the immersed particle [221]. The position of the particle at any time or location is obtained by adding to its previous position a random number: the signal obtained is therefore strongly correlated in time or space so it is said that the particle “remembers” well where it was before. As its name suggest, pink noise occurs when β is close to 1 (S(f )_∝ _f1β), indicating that the spectral density is inversely related to frequency [186].

To understand its importance it is necessary to define the “spectral density per octave”, which is derived from spectral density by transformation using the formula:

F (φ) = df

dφ · S(f ) (2.7)

where φ = log₂(f ). The difference from spectral density is that it represents density per logarithm of frequency as distinct from density per unit frequency plotted against log(f ) [186]. This plot represents the relative influence of a signal associated with the various temporal or spatial scales of the signal. Thus, it is noticeable that white noise contains all frequencies, but assigns greater importance to shorter scales. Brown noise conversely emphasizes longer scales. Pink noise is special in that it contains equal amounts of fluctuations at all scales. For example, on a temporal scale fluctuations happening from about every year to once a decade (area under 1/f noise curve between 1 and 0.1) have, on average, as much influence on the present as events happening once a decade to once a century (area between 0.1 and 0.01). This demonstrates the special connection that pink noise has to the idea of fractals [186].

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2.2.2. Multifractal analysis

Fractal geometry is widely used in image analysis problems due to its ability to describe the irregular or fragmented shape of natural features as well as other complex objects that traditional Euclidean geometry fails to analyze.

Multifractal objects are defined by a spectrum of fractal dimensions: the spectrum of generalized dimensions Dqand the singularity spectrum f (α). Here I focused on the

generalized dimensions spectrum.

Generalized dimensions are exponents estimated by the box counting method: the image is covered with a grid of N (ε) squares of side ε and for each square a value of biomass µi(ε) is calculated. Then the partition function is computed as:

Zi(ε) = N (ε)

X

i

µi(ε))q (2.8)

Here q is called the moment order and can be considered an arbitrary exponent. The operation is performed for different values of ε and q, within a fixed range that includes negative and positive q. The generalized dimension is calculated as:

Dq =

1

q − 1limε→0

log(Zq(ε))

log(ε) (2.9)

This limit cannot be assessed. Hence the second term in Dq is calculated as the

slope of log(Zq) versus log(ε). Dq addresses how biomass varies with ε in an image,

telling how it behaves when the image is scaled to a series of ε-sized pieces that become “distorted” by q. The parameter q determines which squares have a greater contribution to the sum of Eq. 2.8 and therefore more influence on Eq. 2.9. When q is a relatively large positive number, the main contribution comes from higher µi. However, when

q is a negative number, large in absolute value, the highest contribution comes from smaller µi. Thus an image with large peaks surrounded by a relatively uniform values

of biomass will have higher Dqfor positive q and an image with sharp holes of biomass

will have higher Dq for negative q. An image with both will have the largest range of

Dq[132]. For q = 1, the denominator of the first term in Dqis undefined, so Eq. 2.9 is

replaced with:

limε→0

PN (ε)

i µi(ε)log(µi(ε))

log(ε) (2.10)

To see that Dq is actually an exponent, Eq. 2 can be rearranged to obtain:

Zq ≈ εDq(q−1) (2.11)

Eq. 2.11 determines Zqhow varies with the scale ε and it is evident that is a power

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confronted with a multifractal object, the spectrum of generalized dimensions Dqtakes

the shape of a sigmoid curve and it is a decreasing function of q [201]. Another as-sumption that must be verified in order to define an object as multifractal is that the relationship log(Zq) versus log(ε) should be linear for all q.

2.2.3. Mathematical methods and concepts for the analysis of extreme events Extreme value theory originates from the asymptotic study of maxima and min-ima of finite time series provided by random variables, assumed to be independent and identically distributed (i.i.d.).The main tenet of extreme value theory is that if (Xn)n∈N is a sequence of i.i.d. real-valued random variables, and if the maximum

Y ≡ max(X1, . . . , Xn) suitably standardized, has a limit distribution as n → ∞,

then this distribution belongs to one of the three standard types (Fréchet, Weibull and Gumbel). This distribution must satisfy the “max-stability property” [93]: namely, dis-tribution for which the operation of taking a maximum of a finite sequence of i.i.d. random variables leads to an identical distribution , except for differing location and scale parameters (defined afterwards). It recalls the central limit theorem for which the mean of normally distributed observations has exactly a normal distribution. The max stability property gives rise to a form of distribution named Generalized Extreme Value (GEV), with cumulative distribution

y(x; µ, σ, ε) =                      exp −h1 + ε(x−µ)_σ i −1 ε , 1 + ε(x−µ)_σ > 0 ε 6= 0 expn−exph−(x−µ)_σ io ε = 0 (2.12)

Here µ is termed “location” and specifies where the distribution is centered, σ > 0 “scale” and define its spread. ε is the “shape” parameter, determining the rate of tail decay, with

ε > 0 giving the heavy-tailed (Fréchet) case, ε = 0 giving the light-tailed (Gumbel) case and ε < 0 giving the short-tailed, bounded (Weibull) case.

The Gumbel type distribution has an unbounded upper tail which decreases at a relatively rapid (i.e. exponential rate (light tail). It is the domain of attraction for many common distributions (e.g. normal, lognormal, exponential, gamma). Also the Fréchet distribution has an unbounded upper tail, but it decreases at such a slow (power law) rate (heavy tailed) that its variance is infinite if ε > 0.5. it is of interest for precipitation, stream-flow and economic impacts. The Weibull type has a finite upper bound at x = µ −σ_ε and usually concerns temperature, wind speed and sea level values distributions.

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A topic of investigation of extreme value analysis are the extreme upper quantiles of the GEV distribution. In terms of quantiles, taking 0 < p < 1 and defining

xp = µ −

σ

ε 1 − [−log(1 − p)]

−ε

(2.13)

where f (xp) = 1 − p, allows to calculate the “return level” xp associated with

the “return period” 1/p. When modelling annual maxima, p = 0.01 corresponds to a 100-yr return period.

2.2.4. Environmental bootstrap method

The environmental bootstrap method [60] produces an ensemble of environmental realizations from the resampling of short time series of environmental predictors. These realizations are used as input for models relating the selected environmental predictors to the response variable to create a new record of response data, that are then analyzed for the occurrence of extreme events. The whole procedure consists of four steps. 2.2.4.1. Calculating the predictable signal of time series of environmental variables

The first step of the procedure is the identification of the predictable aspects of the time series of the selected environmental variables. The most thorny problem when dealing with ecological variables without well-known marked fluctuations (e.g. water temperature, wind speed, wave height), is that measurements records long enough to obtain reliable estimates of predictable signals are rarely available. However, taking advantage of the smoothly nature of mean patterns of temporal variation of these vari-ables, predictions can be obtained using an averaging sliding window. This means that in the average are included not only measurements taken on the same time (hour of the day/day/week) in separate years, but also measurements from nearby days or weeks within each year, depending on the temporal resolution of the record. In this way, suffi-ciently large samples from which to calculate a reliable set of means are obtained. Care must be taken in setting the width of the sliding window, which must be sufficiently wide to ensure that the predicted annual variation is smooth, but not as wide as the decorrelation time (this concept will be later explained), otherwise the record may be overly smooth. Using a sliding window, the best option is to consider the record circu-lar and allow the windows that fall outside the record to be filled with values preceding the beginning of the record in order from the end and vice versa.

Once the resampling scheme is determined, the mean annual pattern of each en-vironmental variable (¯xv(t)) and the predicted annual cycle of the standard deviation

(Sv(t)) are calculated for each point in the time series.

2.2.4.2. Separating out and arranging the stochastic remainder

Having identified the predictable aspects of time series of environmental variables, the next step is to isolate the stochastic signal and rearrange it so that segments of it are statistically interchangeable. This is true when the segments of the stochastic signals in which the time series is divided are independent and identically distributed and thus

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have the same: i) mean, ii) standard deviation and iii) autocorrelation function (ACF). To this end, we calculate the difference between the observed and the predicted value of the environmental variable for each sampling time:

4V (t) = V (t) − ¯xv (2.14)

and the standardized residual as:

4Vstd(t) =

4V (t) Sv(t)

(2.15) Finally, for each variable, the ACF is provided. Since it is possible only to em-pirically confirm the homogeneity among segments, one way to check for ACFs to be the same is to calculate the decorrelation time (d), that is the lag time at which the ACF settles to 0. The width of d defines also the length of segments that must be the same for all the included variables and it thus is determined by the variable that has the longest decorrelation time. Setting segments length to the longest observed d ensures that any relevant autocorrelation in the signal is included in the sampled segments of all variables.

2.2.4.3. Moving-block bootstrap

In virtue of the statistical similarity of the record, random segments of the 4Vn

series can be recombined with ¯xv to create a 10000yr-long bootstrapped series of

hy-pothetical environmental conditions; the procedure used is a moving-block bootstrap [26], [198],[199]). For the first variable, a segment is randomly chosen and the first 4Vstd(t1) value of this segment is multiplied by its corresponding Sstd(t1) and added

to the expected value for that point ¯xv(t1). The procedure is repeated for each point in

the segment and for each segment of the record until an entire new record, statistically similar to, but randomly rearranged from, the original, is created. The same procedure, with the same sampling scheme, is simultaneously applied to all the environmental variables that are included in the study. This ensures that any cross-correlation among them is maintained.

2.2.4.4. How many of the new hypothetical realizations would have caused an extreme ecological event?

The end point of this procedure is to calculate the probability with which the 10000 bootstrapped series would have caused an extreme ecological event. To do this, a model that properly relates the response variable to the selected environmental predictors must be found. Then, the 10000 bootstrapped series of hypothetical environmental condi-tions are played through the model in order to obtain a univariate time series of biolog-ically meaningful values of the response variable. Temporal patterns of extreme events were quantified in terms of return time, by fitting to the simulated time series of the response variable a GEV distribution.

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CHAPTER

3

MULTIFRACTAL SPATIAL DISTRIBUTION OF

EPILITHIC MICROPHYTOBENTHOS ON

INTERTIDAL ROCKY SHORES

3.1

Introduction

The measurement of variability in population abundance and distribution followed by the identification of the underlying causes are major goals in ecology [171], [59]. Hierarchical sampling designs, combined with variance components estimates, have been extensively employed to examine spatial patterns in abundance of animal and plant populations, showing how most of the variation is concentrated at small scales [114], [69], [10]. These methods focus on discrete spatial scales and require decisions to be made about the number, extent and spacing of the scales investigated. A possible limitation of this approach is that important scales of variation may be omitted from the study. The major strength of hierarchical sampling designs is that they enable the simultaneous analysis of a broad range of scales and they are the only possible approach to compare biogeographic or continental scales or when the habitat of interest (e.g., rocky shores) is interspersed among unfavourable habitats (e.g., sandy beaches). The alternative approach of sampling continuously in space is simply impractical in these circumstances.

Examining spatial variation in ecological variables continuously in space may, how-ever, capture patterns of variability that could go undetected otherwise. For example, Denny et al. [59] quantified spatial variation of physical and biological variables sam-pling continuously along three intertidal transects tens to hundreds of meters in length, on a wave-swept rocky shore at Hopkins Marine Station (CA). Results contradicted the expectation that variability is concentrated mostly at small spatial scales and the