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SPATIAL ANALYSIS OF OCTOPUS DENS AND PREDATION BY ELIZABETH ALENE HAMMAN A Thesis Submitted to the Division of Natural Sciences New College of Florida In partial fulfillment of the requirements for the degree Bachelor of Arts Under the sponsorship of Dr. Sandra Gilchrist Sarasota, Florida May, 2010
ii Acknowledgements The research for this thesis was funded by the Explorers Club, the New College Research and Travel Grant, and the Council of Academic Affairs. I would also like to thank my sponsor, Dr. Sandra Gilchrist, and committee members Dr. Meg Lowman, Dr. Necmettin Yildirim, and Dr. Leon Kaganovskiy, fo r all of their encouragement, criticism, and support. I could not have done the field work without th e help of Caitlin Petro, who was an amazing field work companion. I would also like to thank my parents, Ann and John, for all of their support, Catherine for being the best sister anyone could ask fo r, Grandma for being the perfect haven when I needed an escape, Jesse for always being there, and all of the wonderful friends and professors that have made New College the best four years of my life.
iii Table of Contents Acknowledgements ii Table of Contents . iii List of Tables and Figures iv Abstract . vii 1. Introduction .. 1 1.1 Foraging 1 1.2 Hunting . 4 1.3 Prey Preference . 8 1.4 Growth .. 12 1.5 Octopus Den Location .. 14 1.6 Octopus Den Construction 15 1.7 Octopus Middens .......... 17 1.8 Eels as Predators 19 2. Methods 21 2.1 Field Research .. 21 2.2 Computer Modeling and Simulation . 25 3. Results .. 31 3.1 Field Results ..31 3.1.1 Midden Contents ... 31 3.1.2 Octopus Dens 37 3.1.3 Spatial Distribution in Relation to Predators 49 3.1.4 Spatial Distribution in Relation to Prey 51 3.2 Model Results 52 3.2.1 Varying Initial Con centrations with Random Distributions .. 52 3.2.2 Exploration of Vari ous Foraging Radii . 60 3.2.3 Exploration of Additiona l Spatial Configurations .69 4. Discussion 73 4.1 Prey Preference .. 73 4.2 Octopus Dens 75 4.3 Eels . 76 4.4 Model . 77 4.5 Conservative Implications and Conclusion 77 5. References 78 Appendices 83 Appendix A: Field Data .. 83 Appendix B: Matlab Codes 91
iv List of Figures and Tables Table 1.1.1 Foraging and Hun ting Patterns Observed by Various Researchers .. 4 Table 1.3.1 . Summary of Preferred Pr ey Items Across Different Studies 10 Table 18.104.22.168 . Key for the Identifi cation of Prey Items Found in Middens 31 Table 22.214.171.124 . Distances between Dens and Predators in Meters . 49 Table 126.96.36.199 . Distances between Dens and Prey Items in Meters ...51 Table 188.8.131.52 . Order in Which Steady State is reached as Den Availability Changes . 57 Table 184.108.40.206 . Rank in Decrease of Percentage of Prey Population with Changing Initial Percent of Prey in the first 10 days 59 Figure 1.1.1 Important Asp ects of Octopus Anatomy 3 Figure 1.2.1 Bivalve Anatomy .. 5 Figure 1.2.2 Mouth Parts of An Octopus 6 Figure 1.2.3 Internal Octopus Anatomy 7 Figure 1.7.1 .. Smaller Midden in front of Den 3 . 18 Figure 1.7.2 .. Larger Midden in front of Den 9 .. 18 Figure 2.1.1 .. Cayos Cochinos Islands . 21 Figure 2.1.2 .. Study site on Cayos Mejor 22 Figure 2.1.3 .. Den marked with Red Numbered Flag . 23 Figure 2.1.4 .. Diagram of meas urements to Den 4 . 24 Figure 2.1.5 .. Plot of Den 4 . 25 Figure 2.2.1 .. Flowchart of Code .26 Figure 2.2.2 .. Path of Movement with Mod Function . 27 Figure 2.2.3 .. Combination of Matrices .. 27 Figure 2.2.4 .. Sample of Run wit hout Behavioral Adjustments And Modifications .29 Figure 2.2.5 .. Representation of Natural System in Matlab Matrix 30 Figure 220.127.116.11 Overall Midden Content Totals by Prey Type as Identified in Table 18.104.22.168 . 32 Figure 22.214.171.124 The Midden Surrounding Den 4 ... 33 Figure 126.96.36.199 ... Analysis of Midden Content by Percentage within Each Individual Midden 34 Figure 188.8.131.52 Amount of prey found in each midden over the Sampling period of 8 days .35 Figure 184.108.40.206 Octopus in Den 7 holding onto Prey Fragments 36 Figure 220.127.116.11 Map of the Lo cation of the Dens .. 38
v Figure 18.104.22.168 Den 1 . 39 Figure 22.214.171.124 Den 2 . 40 Figure 126.96.36.199 Den 3 41 Figure 188.8.131.52 Den 4 . 42 Figure 184.108.40.206 Den 5 . 43 Figure 220.127.116.11 Den 6 . 44 Figure 18.104.22.168 ... Den 7 . 45 Figure 22.214.171.124 Den 8 . 46 Figure 126.96.36.199 .. Den 9 . 47 Figure 188.8.131.52 .. Den 10 ... 48 Figure 184.108.40.206 . Map of Predator and Prey Locations 50 Figure 220.127.116.11 . Initial Random Spatial Distribution .. 53 Figure 18.104.22.168 Spatial Results after Simulation 53 Figure 22.214.171.124 . Effect of Octopus Concentration on Prey .... 54 Figure 126.96.36.199 Percentage of Prey at Steady State with Variation in Initial Octopus Concentration 54 Figure 188.8.131.52 Percentage of Prey over Time with Variation in Available Dens .. 56 Figure 184.108.40.206 Percentage of Prey at Steady State with Variation in Den Availability 57 Figure 220.127.116.11 Percentage of Prey over Time with Variation in Concentration of Prey ....58 Figure 18.104.22.168 Percentage of Prey at a Steady State with variation In Initial Concen tration of Prey 59 Figure 22.214.171.124 Second Initial Distribution 61 Figure 126.96.36.199 ... Spatial Distributi on after the Running of the Simulation Shown in Figure 188.8.131.52 with the Radius of Search Based on Hunger Levels ... 61 Figure 184.108.40.206 . Radius Increasing by the Hill Equation 62 Figure 220.127.116.11 Spatial Results with Radius Varying by Equation (1) .. 63 Figure 18.104.22.168 . Temporal Results with Radius Varying by Equation (1) (Km=50) .. 64 Figure 22.214.171.124 Radius Changing by Equation (1) (Km=50) . 64 Figure 126.96.36.199 Percentage of Prey with Decreased (Km=10) .. 65 Figure 188.8.131.52 Radius with Decreased (Km=10) .. 66 Figure 184.108.40.206 Third Initial Spatial Distribution ... 67 Figure 220.127.116.11 Percentage of Prey ove r Time in Simulation Three .. 6 Figure 18.104.22.168 .. Spatial Distribution of Third Simulation ...69 Figure 22.214.171.124 Initial Spatial Distribu tion with Octopuses Closer to Habitat with Prey and Available Dens .. 69 Figure 126.96.36.199 Percentage of Prey with Octopuses Located Closer to One Area 70
vi Figure 188.8.131.52 Initial Concentra tion for Recreation of Cayos Cochinos Reef 71 Figure 184.108.40.206 Spatial Results after Simulation of Cayos Cochinos Reef 72
vii Spatial Analysis of Octopus Dens and Predation Elizabeth Hamman New College of Florida, 2010 Abstract Octopuses build dens based on a variety of factors, possibly including the location of predators, prey, and available den mate rials. Through field work and computer modeling, this thesis examines these factors and their effect on den location and the local prey population. Field work was conducted in Cayos Cochinos, Honduras and studied the location of 10 octopus dens, eels as major pr edators, and two bivalv e species as prey. Major prey items were determined based on midden contents and measurements of distances and angles were used to create a map of the locations of predators, prey, and octopus dens. A computer model was create d to simulate the dynamics of the system. The model allowed for movement of octopus es among a matrix incl uding the occupying of dens and consuming of prey. Initial cond itions such as octopus concentration, prey concentration, and available den concentration were explored w ith changes in search radii and variations in spat ial arrangements of prey and av ailable dens. Through both field work and simulations, octopuses were found to choose dens on borders between areas of prey (such as a sea grass bed) and areas of available dens (coral reef). Dr. Sandra Gilchrist Division of Natural Sciences
1 Chapter 1: Introduction 1.1 Foraging The way an animal forages is important to determining the maximum fitness or rate of energy intake (McQuaid, 1994). Oct opuses are usually classified as searching predators. They have been found to modi fy their foraging behavior based on chance encounters with prey, and have been found to exploit certain areas wh ere patches of prey occur. The area over which an octopus forage s is not consistent across the literature. Octopuses have been found to search 15 m aw ay from the den (Mather, 1991) or up to 120 m (Forsythe and Hanlon, 1997). Foraging to ok place for between an hour and a half and two hours (Forsythe and Hanlon, 1997). The foraging patterns of O. insularis were found to minimize time, rather than rate (Leite et al., 2009). Two major types of movement have been observed during foraging: slow forward swimming involving hops and jumps to cove r short distances and fast backward swimming (Forsythe and Hanlon, 1997). Juvenile Octopus vulgaris were found to have an oval pattern where they sear ched, exploring rocks, crevices and pulling at sessile prey (Mather, 1991). The patterns of foraging depend on the location and availability of prey (Mather and ODor, 1991). This confirms that octopuses forage with knowledge of the prey distribution and actively change their methods based on this knowledge (Leite et al., 2009), as well as return to home dens ba sed on memory (Boal et al., 2000). These foraging patterns use visual cues (Alves et al., 2008). Foraging over soft sediment was al so noted (Anderson, 1997), although it was found in one study to occur mainly at ni ght (Katsanevakis a nd Verriopoulos, 2004). Foraging was observed during both day and night (Gilchrist, 2003) for O. vulgaris This
2 behavior is difficult to test in lab conditions because natu ral foraging behavior does not always typically occur in small scale la boratory experiments (McQuaid, 1994). Forsyth and Hanlon (1997) found that ma ny activities during foraging do not rely on sight, but rather fall into two categorie s: pouncing and groping. Pouncing involves food caught in the web shown in Figure 1.1.1, while groping occurs when octopus extend their arms into crevices and force food out. A similar technique has been described as more of a poki ng method (Mather, 1991). Octopus vulgaris and Octopus briareus at Baileys Cay, Roatan were observe d using 9 different movements while foraging: crawl, poke, crawl and poke, tuck-old tuck-hold and poke, web over, pause, jet, and pull (Rosebrock, 2000). The majority of the time was spent crawling, poking, and tuck-hold. Behaviors did not differ greatly be tween reef and sea grass environments as the only difference was seen in the web-ove r method of hunting. Leite and colleagues (2009) used video recordings to docum ent and examine poking and crawling done by O. insularis noting that behaviors were associated with environmental conditions as well as body size. As octopuses forage, predictions can be made about prey preference and availability. The patterns of hunting behaviors and foraging for various octopus species are summarized in table 1.1.1.
3 Figure 1.1.1: Important Aspects of Octopus Anatomy Web Mantle Arm
4 Table 1.1.1 Foraging and Hunting Pattern s Observed by various researchers 1.2 Hunting The hunting methods of an octopus vary by species. One method of hunting is the poke-web over-pull approach, where an area of coral is covered by the large web, and the arms are used to poke to encourage any prey to exit the coral, and be caught by the web (Mather, 1991). The arms and suckers of an octopus are used in coordination to extract prey from cracks and burrows (Grasso, 2008) After the initial web over approach, changes in the octopuses coloration have been noted, described as a passing cloud Species Location Habitat Pattern of Foraging Author Octopus vulgaris South Africa Reef McQuaid, 1994 Octopus vulgaris (juvenile) Bermuda Rocky substrate Circular area 15m in diameter Mather and ODor 1991 Octopus vulgaris (juvenile) Bermuda Rocky substrate Oval pattern to examine rock crevices Mather, 1991 Octopus cyanea French Polynesia Multiple substrata Stop and go patterns, methods change based on substratum (primarily pounce and grope) Forsythe and Hanlon, 1997 Octopus insularis Northern Brazil Rock and Rubble Web over Leite et al, 2009 Octopus vulgaris Honduras Rocky Web over Rosebrock, 2000 Octopus insularis Northern Brazil Bedrock with Sand Poke Leite et al, 2009
5 (Mather and Mather, 2006). This method ha s been found to be more common on rocky substrates than soft substr ates (Rosebrock, 2000) for at least two octopus species. Octopuses have been found to use at least one, and often multiple methods of hunting under the web to penetrate bivalve shells (Anderson and Mather, 2007). In the opening of the bivalve, there are two main methods, pulling and drilling (McQuaid, 1994). Pulling occurs with tension in the arms and ends with the rel ease of tension as the mussel opens. To pull the mollusc apart, the bivalve (shown in Figure 1.2.2) is held close to the mouth with the apex poi nting away and the dorsal ligament vertical. The pull lasts approximately five seconds. Regardless of size, pulling is the first attempt of the octopus when handling prey (Fiorito a nd Gherardi, 1999; Steer and Semmens, 2003). Arms and suckers are used within functiona l groups with a large amount of variety, focusing on suckers in the middle of the ar m for most effective pulling (Grasso, 2008). Figure 1.2.1 Bivalve Anatomy Image from Wallace and Taylor, 2003
6 Through observation, drilling appears to begin after the mussel is rearranged under the web, the octopus appears to sit motio nless, and is terminated as the octopus pulls the bivalve apart. The octopus drills with the salivary papi lla shown in Figure 1.2.2, with general internal anatomy in 1.2.3), and the holes are described as irregular slits with sharply tapering sides (McQuaid, 1994). Figure 1.2.2 Mouth Parts of an Octopus Image from: http://static.howst uffworks.com/gif/octopus-2.jpg
7 Figure 1.2.3 Internal Octopus Anatomy Image from Wallace and Taylor, 2003 In a study of O. vulgaris in the Caribbean, approximately 60 % of the gastropods found in middens at the den in the study were drilled. However, there was no relation to size or weight of the shell and whether drilli ng occurred. Holes are usually drilled to inject venom to paralyze the adductor musc les (Anderson et al, 2008). Small octopuses have been found to drill more than one hol e, while others drill incomplete holes (McQuaid, 1994). For a study conducted in the Mediterranean, Ambrose and Nelson (2008) found that drilling holes in two types of bivalves was non-random, while the holes in abalone shells were not distinguishable from random. Handling time has been found to be related to the length of the bivalve and size of the octopus, with larger octopuses usually being able to pull musse ls apart. Drilling, however, is not affected by size (McQuaid, 1994). In anot her laboratory experiment, Fiorito and Gherardi (1999) not ed that handling time was fo und to be consistent across
8 the group of octopuses, but to vary by the spec ies of bivalve. Handling time is of a large concern to the octopus. Octopus Enteroctopus dofleini was observed choosing prey with the least amount of handling time to cons ume first (Anderson et al, 2007), as was O. dierythraeus (Steer and Semmens, 2003). 1.3 Prey Preference In an octopus diet, the most abundant preferred species is the most dominant, with small portions of common species of lo w preference and preferred species that are rare based on data collected from a midden (Ambrose, 1984). Octopus vulgaris juveniles were found to prefer crabs and clams in both captivity and through field observation (Mather, 1991), but in another study, bivalv es were the most popular (Ambrose and Nelson, 1983). While foraging, the prey is either consumed when encountered or taken back to the den fo r consumption. Mather found no connection between the size of the prey and the likelihood th at the octopus would take the prey to the den or consume it when captured (1991), sugges ting other factors dictate this decision. Another study found that when an octopus cam e across a bivalve prey item it recognized as being difficult to open, it would bring the bivalve to its den rather than to consume it on location (Fiorito and Gherardi 1999), which was also found in Octopus dierythraeus by Steer and Simmons (2003). Octopuses have been found to eat a larg e variety of species. Field research involving the middens of Octopus bimaculatus found that 25 species were common enough in the diets of the octopus to be qua ntified, with individual organisms consuming at least 5 different species (Ambrose, 1984). Octopus vulgaris which hunts across
9 intertidal and shallow subtidal zones, has also been observed to consume many species (McQuaid, 1994), with larger O. vulgaris taking a larger distribution of prey species (Smale and Buchan, 1981 phide in McQuaid, 1994). In the Caribbean, it was found that while among a species there is wide dist ribution between gastropods, bivalves, and crustaceans, each individual octopus showed strong preference for a certain prey items brought back to middens (Anderson et al., 2008). Species appeared to be selected based on size and nutritional va lues, in addition to preferences specific to an indi vidual octopus. Ambrose (1984) found that five major prey groups existed in middens for O. bimaculatus : crustaceans, snails (primarily archaeogastropods), sedentary grazers, unattach ed bivalves and hermit crabs. These groups appear to also be representative of the food choices of other octopus species. However, some studies are limited in accurate ly analyzing what an octopus has eaten, as octopuses normally ingest a small amount of soft tissue that is useful in determining diet in gut analysis (Grisley and Boyle, 1988). Many studies have detailed the diet of various species of octopus. Table 1.3.1 gives as summary of some of these findings.
10 Species Geographical Location Habitat Type Method of Study Bivalves Gastropods CrustaceansOther Author Year Octopus vulgaris South Africa Reef Midden contents Mussel None None None Smale and Buchan 1981 Octopus vulgaris South Africa Reef Laboratory observations Mussels None None None McQuaid 1994 Octopus vulgaris South Africa Reef Stomach Contents 0% 28.6% 51.6% 19.7% Smith 2003 Octopus vulgaris South Africa Reef Midden Contents 12.8% 71.5% 12.8% 3.6% Smith 2003 Octopus vulgaris South Africa Reef Daytime Observations N/A 77.8% 11.1% 11.1% Smith 2003 Octopus vulgaris Northwest Spain Sand and algae Midden Contents Yes Yes Yes N/A Guerra and Nixon 1987 Octopus vulgaris Mediterranean Rocky substrates Midden Contents 37.6% 42.4% <20% minimal Ambrose and Nelson 1983 Octopus vulgaris Mediterranean Shallow, no substrate information Midden Contents 51% 19% 30% N/A Anderson, et al 2008 Octopus dofleini Alaska Kelp, rocky Midden Contents 19% <5% 77% <5% Vincent, et al 1998 Octopus insularis Brazil Rock, barrier reef Midden Contents 12.5% 17.5% 70% N/A Leite et al 2009 Octopus vulgaris Honduras Reef Rocky Midden Contents 25-55% N/A 40-70% <5% Rosebrock 2000 Octopus vulgaris Honduras Grass flats Midden Contents 5-10% N/A 90-100% <5% Rosebrock 2000 Table 1.3.1: Summary of pr eferred prey items across different studies
11 The prey preference is specific to an octopus There was variation within each of these prey collections. Some had only a few species in each group, such as 3 snail species that compose the gastropod category (Smith, 2003), while others had greater variety. For example, the study of O. insularis had over 55 species returned to the middens, with only four composing a significant portion of the overall diet (L eite et al., 2009). When comparing numbers, though, it is important to note time scale. The Smith study spanned 13 months, while the Leite observed for an unknow n period of time. It is possible that this discrepancy is due to the timescale, vari ations in surrounding ha bitats, or differences between species, as Smith observed O. vulgaris and Leite studied O. insularis Preferences based on size appeared to i nvolve larger octopuses selecting mussels larger in size, while the middens of smalle r octopuses contained mussels of a smaller size. Both of these observations maximized the E/H value, or the energetic return, found by dividing the energetic value of the prey by the handling time, with larger mussels generally having a slightly hi gher value (McQuaid, 1994). Nutr itional values also appear to play a role in prey selection, as sh own through the choice between bogue (fish) and crabs. Even though the feeding efficiency is higher with bogue than crabs, the nutritional value of crabs as expressed throughout the P/ E (protein to energy) ratio is higher, and crabs are the preferred food (Garcia and Gimenez, 2002). No link was found to exist between prey selection and the mortality rate of the octopus. In a study with O. vulgaris hermit crabs were not found to be a preferred food, instead Carcinus was chosen first, so to ensure both were eaten, the hermit crab was offered first (Grisl ey and Boyle, 1988). Ambrose (1984) found that in middens of O. bimaculatus bivalves and sedentary grazers were found more often, followed by snails. Preferences involving gastropods showed
12 selection on the species level, and abundant species that we re not preferred were not eaten. However, with all pref erence studies, it is important to note that an octopus will specialize in the sense that they have preferred prey, but will often select the first familiar prey item shown. Ambrose (1984) not ed that while in theory predators rank prey, it is often hard to support this with findings in the field. Mather (1991) showed how simply analyzing midden contents does not always give an accurate description of the octopus diet. In addition, stomach anal ysis underestimates th e amount of mollusk prey, while middens underestimate the cr ustacean component of an octopus diet (Ambrose and Nelson, 1983). The amount of prey consumed varies due to different factors. Gimenez and Garcia (2002) found in a mariculture study th at the amount consumed was influenced the most by temperature and body weight. The ideal temperature f ound in this study for feeding in O. vulgaris was between 16 and 21 degrees Celsius, and the optimum temperature is also inversely related to body size. In addi tion, higher water temperatures result in higher digestion rates (Grisley a nd Boyle, 1988). However, models were often inaccurate because of cannibalism. 1.4 Growth Octopuses have a high capacity to convert energy obtained from their diet into body weight. They grow extremely fast desp ite diet consumption, but their ability to consume large amounts of food assists the exponen tial growth rate. This growth rate is due to several factors, includi ng the lack of a complex skel etal system, high food intake,
13 efficient digestion and assim ilation, and direct embryonic deve lopment. The nature of the reproductive cycle also demands rapi d growth (Gimenez and Garcia, 2002). Growth rate and feeding rate do not ha ve a consistent relationship across the literature. In O. pallidus hatchlings, growth rate was found to be unrelated to feeding rate (Andre et al., 2007), though when groups of O. vulgaris were fed formulated moist diets, one sample group showed a significant connect ion between growth rate, feeding rate, and feeding efficiency (Valverde et al., 2008). Lipi ds in particular were found to be crucial to a positive correlation between feed ing rate and growth rate. Mathematical relationships have been f ound between food intake and growth rate. The absolute growth rate, specific growth rate absolute feeding rate and specific feeding rate are all connected to the initial and final weights, av erage weight between sampling, and the amount of ingested food. A natural l ogarithmic relationship also exists between body weight, growth, and food intake, but thes e models are not good for negative growth (absolute value must be used) and are limited to situations where octopuses consumed a healthy amount of prey (Gimenez and Garcia 2002). Meal recove ry contained a large range, from 18-81% of the energy being used by the octopus (Grisley and Boyle, 1988). However, handling of the specimens influenced the results, and only half of the animals in the study could be tested for distinguishable crab species. Another important factor, in addition to feeding rate, is temperature. A temperature change as small as 1 degree Celsius might have an effect on the growth ra te of an octopus in captivity (Andre et al., 2009). While the connection between the food in take needed to maintain high growth rates in octopuses is impo rtant to understanding hunti ng and foraging, laboratory
14 experiments have shown a variety of results. It is therefore impractical at this time to conclude a universal relationship and specifi c motive for feeding rates and associated hunting and foraging. Without increased consis tency in data, as well as information on how the age and experience of the octopus, pr edation pressure, and density pressure, a clear relationship cannot be determined. 1.5 Octopus Den Location Octopus dens have been found in a variet y of habitats, as long as something is available to provide shelter for the octopus. They have been found in various depths, with smaller, juvenile octopuses typically occurring in shallow waters and larger octopuses typically occurring at greater depths (Katsane vakis and Verriopoulos, 2004; Leite et al, 2009). Soft sediment has also been shown to be a factor in the location of dens for some octopus species. In a study in New Zeala nd, Anderson (1997) show ed that increasing soft sediment limited prey availability and increased the presence of large predators, resulting in dens being moved shoreward, while Katsanevakis and Veriopoulos (2004) noted that while no dens occurred on soft sediment, soft sediment was often a limiting factor in the placement of dens in coastal waters around Greece. Areas with rock and sand are often popular and Leite a nd colleagues (2009) in Brazil found Octopus insularis preferred to inhabit areas under rocks in soft sediment as well as dens in horizontal crevices. Many octopus dens are found around more stru ctured areas, such as backreefs. In French Polynesia, Octopus cyanea was found only in intertidal areas of the backreefs
15 (Forsythe and Hanlon, 1997). It was noted that the calmer backreef was preferred over the forereef and topreef. Octopus dens have also been found in highest concentrations on the backreefs edge, with numbers decrea sing towards shore (Anderson, 1997), as well as on areas designated patch reef. Octopus bimaculatus is frequently found in areas of bedrock and boulders off the coast of Ca lifornia (Ambrose, 1982). Abundance across habitats can vary temporally. Octopus tetricus were found to be abundant during the summer, but were found infrequently duri ng winter months (Anderson, 1997). This observation could be a result of seasonal ch anges, such as weather, turbulence, temperature and spawning. Density of O. vulgaris has been found with population peaks during the summer and late autumn (Katsane vakis and Verriopoulos, 2006). At Baileys Cay in Roatan, octopus dens belonging to O. briareus and O. vulgaris were found in rubble and in grass flats close within a mete r of the sea floor (Rosebrock, 2000). Many of the O. vulgaris dens were excavated under coral head s. All were spaced at least 6 m from the nearest den, with up to distances of 25m between dens. Dens in grass flats for the current study were found beneath excavated coral heads as well as in and under large shells, often as near as 1 m apart (personal observation). 1.6 Octopus Den Construction Shelters can be constructed out of a va riety of items and are commonly altered to suit an individual octopus needs or pref erences. When studying the den ecology of Octopus vulgaris Katsanevakis and Verriopoluous (2004) classified each den as a well, shell, human origin, or rock. For this particular study, a well was den dug into the sediment, while a rock was used to descri be a crevice dug underneath a rock. Rock
16 crevices have been particularly common among juvenile Octopus vulgaris (Mather, 1991) and O. bimaculatus (Ambrose, 1982). Dens are also frequently of biological origin, as Octopus joubini use bivalve shells, and frequently block the aperture (Mather, 1991), and O. tehuelchus frequents oyster and gastr opod shells (Iribarne, 1990). Dens are frequently modified to suit th e needs and preferences of an individual octopus. Juvenile O. vulgaris have been found to block larg er home apertures with items such as bivalve shells, gastropod shells, a nd crab carapaces and chelipeds. Abiotic materials such as broken glass, rocks, and s oda cans were also found at the entrances to dens (Mather, 1991). Anderson (1997) found that female O. tetricus were never found in an unmodified or unexcavated den. Excavation was also found to be an important aspect in den construction in the Mediterranean, es pecially by small and medium sized octopus which may modify the shelter as they gr ow (Katsanevakis an d Verriopoulos, 2004). Octopus cyanea in French Polynesia was observed pu lling rocks or other debris over the entrance to the den during day light hours (Forsythe and Hanlon, 1997). This species was only spotted excavating once. Octopus bimaculatus frequently attempted to dig or blow out holes in shelters with je ts of water, and frequently moved around stones and other debris (Ambrose, 1982). The length of time that an octopus occupies a den varies. Juvenile Octopus vulgaris stayed in each den for fewer than 2 we eks in one study (Mather and ODor, 1991). Octopus dofleini stayed in a den anywhere from 1 day to 5 months (Hartwick et al., 1984). Not only is the amount of time spent in a den variable, but also the number of dens occupied at one time. A study of male Octopus vulgaris in a large seawater tank found that none occupied one den exclusively, and often had multiple dens (Boyle, 1980).
17 A study of a fishery in Tanzan ia indicated that larger Octopus cyanea reside in dens for a longer duration than those of a smaller size (Guard and Mgaya, 2002), which is likely due to need for increased size beyond the capacity obtained by modifying the den. It may also be that larger animals are able to defe nd the den from competitors or predators. 1.7 Octopus Middens In addition to items brought back or us ed around the midden in construction such as rocks and human debris, piles of shells and other prey discar ds are also commonly found around dens. These piles are referred to as middens. Two example middens are shown in Figures 1.7.1 and 1.7.2. The first midden has a few shells spread around a rock pile, while the second has a smaller ar ea, but with many more shells.
18 Figure 1.7.1 Smaller Midden in front of Den 3 Octopus is indicated by white arrow Figure 1.7.2 Larger Midden in front of Den 9 Octopus is indicated by white arrow 2.5cm 2.5cm
19 A lack of a midden can make an octopus de n difficult to find (Ambrose, 1983). Midden contents are often used to study the diet of an octopus (Ambrose, 1983; Smith, 2003). Ambrose and Nelson (1983) observed middens of Octopus vulgaris as well as other species. Middens often contain pieces of bi valve and gastropod shells, as well as pieces of crab carapaces. The presence of a midden can be determined by several factors, both biotic and abiotic. In terms of biotic f actors, hermit crabs have been found to remove gastropod shells (Ambrose, 1983); often carry ing them away before changing shells (Gilchrist, 2003). Gastropod sh ells were found to disappear faster than bivalves, which were removed by high surf (Ambrose, 1983). At Baileys Cay in Roatan, middens were found only outside the dens of O. vulgaris (Rosebrock, 2000), though Gilchrist (personal communication) has observed middens for both O. vulgaris and O. briareus Gilchrist indicated that middens of O. briareus sometimes occur about a half meter from the den. Octopus middens are most often used in studies to determine diet, although the studies of middens of other species provide a variety of other clues. Remnants of human debris are often used to examine diet of pe ople living in the area, as well as providing insight into the artisan and cultural aspects of the community living in the area (Aizpurua and McAnany, 1999). Other animals middens have also been used to determine similar information, both about habits and diets. Pack rats ( Neotoma ) use middens as urinary perches, which serves to harden and preser ve the specimens, allowing for later study on climate change, vegetation, a nd grazers (Cole, 1990). Octopus middens are the most widely studied for various habitats, with many studies utilizing them for diet analysis as seen above.
20 1.8 Eels as predators Eels are frequently described as the majo r predators of octopuses, especially in reef environments. Moray eels of the genera Gymnothorax and Lycodontis are frequently found in areas with rock and coral substrat e (Fishelson, 1997). An interaction between and octopus and an eel is de scribed by Forsythe and Hanlon (1997). A small eel bit the arm of an octopus hunting, after which the oc topus quickly retreated, changed body color, and released a large amount of ink. Gilchr ist (2003) notes that at least one octopus during her observation time each year was eaten or injured by an eel. Eels move across the reef at night usi ng a variety of senses, particularly smell (Winn and Bardach, 1959). Touch and taste ar e also used. Eels that are found on reefs use vision more than those on sandy habitats which are more likely to use olfactory methods (Fishelson, 1997). These changes likely reflect niche differences. Dubin (1982) notes that some prey of eel s rub against the eel and swim with them during hunting, either for scent protection and/or to benefit from prey scared by the eel. While the eel is usually nocturnal, Chave and Randall (1971) sight ed them moving about during the day, but not during the full moon. Eels had been observed moving among the reef as far as 50m from their burrow. Much about the nature of their burrow and predation, however, is unreported.
21 Chapter 2: Methods 2.1 Field Research The study was conducted from June 30, 2009 through July 17, 2009. The area studied included the back reef off of the Plantation Beach Resort on Cayos Mejor, Honduras. This area is part of the Ca yos Cochinos Archipelago Natural Marine Monument. This preserved area is shown below in Figure 2.1.1, with the study site shown in Figure 2.1.2. Figure 2.1.1: Cayos Cochinos Islands Image from: http://www.moon.com/files/map-images/hond_03_Cayos-Cochinos-HogIslands.jpg
22 Figure 2.1.2: View overlooking study site on Cayos Mejor. Note the dock near the arrow as this structure served as an importa nt locator for mapping the area. Arrow points north The area studied was approximately 400 m by 90 m, and depth up to 3m. The area was surveyed by snorkeling in a pattern fr om north to south along the reef. Piles of shells and other debris (middens) that woul d indicate the presence of an octopus were located. When found, the area was searched cl osely for the actual den. Octopus middens were marked with a numbered red flag as shown in Figure 2.1.3.
23 Figure 2.1.3: Den marked w ith Red Numbered Flag Octopus is indicated by white arrow. Eight dens were initially marked. Two de ns were later found underneath a boat mooring area that was previously obscure d. Each of the first eight dens found were visited eight times to monitor contents of the middens. A ll dens were also visited as needed to make measurements between den, predators and pre y. Abiotic data were collected, including temperature and cloud cover. The approximate depth of the dens was also noted. The diet was analyzed by collecting the midden contents of each den each afternoon for a week and analyzing and meas uring each piece brought by the octopus to its den. Materials were th en discarded away from the den. Among the prey items recovered, two major prey returned to the de ns were identified as being prominent among the samples and their location determined and marked within the same research site. The
24 location of flame scallops, Lima scabra were marked with a yellow flag among crevices, and the ark clam ( Anadara brasiliana ), marked by yellow flags outlining the submerged aquatic vegetation, where ark clams were found rather than disturbi ng the entire bed to mark individual bivalves. All prey items we re found and marked from late morning to early afternoon. The burrows of the eels (octopus predators) were marked with a blue flag. Eels were searched for around dusk. A map including the locations of the oct opus, their predators, and their prey was created. All points were measur ed in relation to the end post of the dock. An example of this measurement is shown in Figure 2.1.4. Figure 2.1.4: Diagram of measurements to Den 4 Brown rectangle represents the end of the dock and the red circle the den These values were noted and later converted to Cartesian coordinate vectors using Excel. Vector addition was used to construct vector s from the origin (end post of the dock), and
25 the final coordinates plotted in Matlab. Th e plot of den 4, whose measurement is shown in Figure 2.1.4, is shown in Figure 2.1.5. -4 -3 -2 -1 0 1 2 -2 -1 0 1 2 Example Plot of Den 3 Figure 2.1.5: Plot of Den 4 Red circle represents den, Bl ack circles represent dock posts 2.2 Computer Modeling and Simulation Initial simulations created in Matlab cons isted of matrix movements. A flowchart of the code is shown in Figure 2.2.1. First, one matrix was created with ones and zeros. Ones indicated the presence of an octopus, and movement to the eight surrounding cells was created by generating a random number assi gned to the range of a specific movement and a plot created of each st ep. To move the octopus, a surrounding cell of the desired coordinates (such as i+1,j), wa s filled with a one and the or iginal cell given a zero. The original code resulted in bu ildup along the edges of the matrix as the coordinates became
26 non-existent, or an error code as it attempte d to reach a cell with a coordinate of zero. The mod function was used to allow unhindered movement, which is illustrated in Figure 2.2.2. To eliminate problems related to the teleportation of oc topus during movement, the matrix of interest was placed in a larger matrix so that the octopus would not move from one side of the matrix to the other side immediately. This co mbination of matrices is illustrated in Figure 2.2.3. Figure 2.2.1: Flowchart of Code
27 Figure 2.2.2: Path of Movement with Mod Function Arrows indicate the cy cling of coordinates Image courtesy of N. Yildirim and A. Salisbury 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500 Figure 2.2.3: Combination of Matrices
28 After movement was created, prey items were added and consumed. Finally, to allow empty dens and octopus movement between them, a third designation in the matrix was created as an empty den for which th e octopus searches after finding food. To accomplish this, the coordinate where the food wa s found is stored and used as the initial searching point for another available den, wh ich takes place in a similar manner as the search for food. The output of a sample run wi th these specifications is shown in Figure 2.2.4. Red boxes indicate an available den, ye llow an octopus, and lig ht blue prey. As evident by the example, the octopus were quick ly consuming all prey available, and their movement was unrealistic as they continued to search in identical patterns dictated by order of matrix coordinate and proceed with a large radius regardless of their hunger level. To make the simulation more realistic, each octopus was called in a random pattern and given unique search ing behavior. An array was created of each coordinate available to search in relation to the initial coordinate and the radius. Each octopus was then assigned a direction number correspondi ng to a starting point in the array. The octopus then proceeds in a se t pattern to search for food and other available dens. To vary the octopus radius of search, a second matrix was created to store values relative to an octopuss hunger level. Anot her function was programmed to calculate a radius based on the hunger level. For each time step, the level decreased by 1, and if food was found, increased again. An alternat ive function was also created to increase the octopus radius gradually by days through a variation of the stair step function. Both methods of radius variation are co mpared in the final analysis.
29 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Figure 2.2.4: Sample of R un without behavioral adju stments and modifications Legend: Dark blue: Open Space Light blue: Prey Item Yellow: Octopus Red: Available Den
30 After working on randomly generated matrices, one was created relatively similar to the study site at Cayos Cochi nos, as shown in Figure 2.2.5. 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Figure 2.2.5: Representation of natu ral system in Matlab matrix Light blue represents prey, re d represents available dens Approximate areas of reef were used as available dens, and approximate areas of sea grass beds were used as areas of prey. Oct opus were then randomly distributed and able to choose dens. Predators are excluded from the system based on field data lending no relation to their location and information in the literature about foraging methods. After the simulation was completed, values such as matrix size and amount of octopuses prey and empty dens were altered a nd the effect observed. Spatial, as well as temporal observations were made from the model to predict dist ribution and abundance.
31 Chapter 3: Results 3.1 Field Results 3.1.1 Midden Contents Each of the octopuses showed unique habi ts and patterns of returning prey to the dens. Each of the biotic remnants collected from the middens was given a coded letter, shown below in Table 220.127.116.11. Letter Designation for Midden Contents Letter Designation Midden Item A Laevicandium laevigatum B Parvilucina crenella C Chione cancellata D Saxidomus giganteus E Modiolus modiolus F Petricola pholadiformis G Tellina radiate H Cittarium pica I Lima lima J Archidae barbatia K Lucinidae sp. L Cittarium pica M Cerithium stercusmuscarum N Atrina rigida O Chione cancellata P Trachycardium egmontianum Table 18.104.22.168: Key for the Identificati on of Prey Items Found in Middens Overall, 17 different types of prey were discovered in 8 middens. The frequency ranged from samples in small quantities, such as in A, K, and L, to large quantities sometimes encompassing entire samples for the day, such as E, H, and J. The overall consumption of each prey type is shown in the Figure 22.214.171.124, and an example of a
32 midden is shown in Figure 126.96.36.199. The individual makeup of each midden is shown in Figure 188.8.131.52. Overall Midden Content Totals by Prey Type0 5 10 15 20 25 30 ABCDEFGHIJKLMNOP Prey TypeNumber of Items Collected Figure 184.108.40.206: Overall Midden Content Totals of 8 middens in 8 days by Prey Type as Identified in Table 220.127.116.11
33 Figure 18.104.22.168: The Midden Surrounding Den 4. The octopus is indicated by the white arrow, and has a mantle of approximately 5cm.
34 Figure 22.214.171.124: Analysis of Midden Conten t by Percentage within Each Individual Midden
35 Each midden demonstrated a personal diet, with some middens showing high consumption of certain prey items at the de n, perhaps based on availability. Each den did not produce the same amount of prey, how ever. Figure 126.96.36.199 shows the relative amounts of prey found in each midden. The median average midden produced 10.5 prey items over the course of the observation, or an average of 1.0 .25 prey items per day returned to the den af ter the first collection. Amount of Prey in Each Midden over 1 Week0 2 4 6 8 10 12 14 16 Midden 1 Midden 2 Midden 3 Midden 4 Midden 5 Midden 6 Midden 7 Midden 8 MiddenNumber of Prey Items Figure 188.8.131.52: Amount of prey found in each midden over the sampling period of 8 days Some of the dens were not always occ upied. Dens 6, 7 and 8 frequently were empty, but prey remnants were also frequently found. No data were recorded for den 7;
36 the octopus was eating and rather than casting it s remnants into a pile, instead held onto them as shown in Figure 184.108.40.206. Figure 220.127.116.11: Octopus in Den 7 holding onto Prey Fragments Other octopuses made it difficult to collect the midden contents. For example, the octopus in Den 4 shoved bivalve shells unde r rocks after we bega n collecting, clearly responding to the presence of researchers. The octopus in Den 2 also brought back old shells that had not been recently consumed a nd added the shells to its entry way. Only shells that appeared to be recently consumed were sampled.
37 Based on the results of prey returned to the midden and the ease of habitat location, the two prey items chosen to be loca ted were the ark clam and the flame scallop. Flame scallops were found among crevices in many parts of the reef, and ark clams were found in the sea grass beds at the edges of the reef. 3.1.2 Octopus Dens Figures 18.104.22.168 22.214.171.124 show the dens examined for this study. Ten dens were tagged, and fell into 3 major categories: a cr evice within the major reef structure, a submerged shell or other object, human created rock piles, or areas of patch reef. An overall map is given in Figure 126.96.36.199. Dens 1, 6, and 7 were all locat ed within crevices on the major backbone of the back reef. The wa ter depth in this area was less than 1.5m. Dens 2 and 10 were located in patch reef, and dens 3 and 4 were located in a human created rock pile at the end of a dock where the water dept h was about 3m on average. Dens 5, 8, and 9 were located in submerge d objects surrounded by sea grass in water approximately 2 m deep.
38 Figure 188.8.131.52: Map of the location of dens
39 Figure 184.108.40.206: Den 1. Octopus location is marked with a white arrow. This den wa s located in a reef wall near the surface of the water.
40 Figure 220.127.116.11: Den 2 This den (location marked with white arro w) was located in a coral h ead surrounded by sea grass and approximately 2.5m from the nearest reef.
41 Figure 18.104.22.168: Den 3 This den (marked with white arrow) was loca ted at the base of the rock pile at the end of the dock. It was at approximately 3m depth and surrounded by sea grass. The octopus is not in the den when this picture was ta ken, occupying a nearby conch shell instead
42 Figure 22.214.171.124: Den 4 Octopus location marked with a white arrow. This den was locat ed in the same rock pile as Den 3, although at a depth of 2m.
43 Figure 126.96.36.199: Den 5 This den (indicated by the white arrow), was rarely occupied when visited by researchers, and loca ted in the center of the sea grass bed.
44 Figure 188.8.131.52: Den 6 Octopus location is marked with a white arrow. This den was lo cated near the rocky shoreline and was at approximately 1 m dept h.
45 Figure 184.108.40.206: Den 7 This octopus (marked with a white arrow) utilized a crev ice near the shoreline in le ss than 1m of water.
46 Figure 220.127.116.11: Den 8 This den was never occupied when visited by researchers. Like den 5, it was located in an area surrounded by sea grass and wou ld not be noticeable without a midden.
47 Figure 18.104.22.168: Den 9 This den (marked with a white arrow), was loca ted in a conch shell su rrounded by sea grass.
48 Figure 22.214.171.124: Den 10 This den (marked with a white arrow), was located in a head of coral surrounde d by sea grass near den 9.
49 3.1.3 Spatial Distribution in Relation to Predators Ten octopus dens, four eels and numerous sites of octopus prey were located for the present study. The map of the back reef and sea grass beds of Cayos Cochinos in figure 17 shows the general location of the organi sms in the area. Of course, some of the prey and the eels were mobile. However, eels were observed foraging in the same general areas on several days. The distances from each den to its pred ators in the vicinity are given in the following table. Den Eel #1 Eel #2 Eel #3 Eel #4 1 4 62 197 243 2 12 47 182 228 3 57 4 136 182 4 60 2 134 179 5 216 160 37 38 6 309 251 116 70 7 323 265 130 84 8 24 37 170 216 9 77 26 119 164 10 105 48 89 135 Table 126.96.36.199: Distances between de ns and predators in meters There was large variation between the di fferent dens and the distance to the closest predator. The averag e was 31.79 9.57m. The closest were Dens 1, 3, and 4, all of which were in crevices of the major reef or in human created ro ck piles with multiple hiding places with multiple crevices. While no dens had objects completely covering the den entrance, large piles of rocks or shells were located at dens 2 and 6.
51 3.1.4 Spatial Distribution in Relation to Prey The overall relationship betw een predators and prey is shown in the map in Figure 188.8.131.52. The results for the distance between th e octopus den and the nearest four prey items are shown below in Table 184.108.40.206. Some of the octopus dens were located in the middle of a sea grass bed, in which case all of the correspon ding prey items are given a 0m, as the den was bordered by prey ha bitat in the case of the ark clam. Den Prey #1 Prey #2 Prey #3 Prey #4 1 6 7 11 14 2 3 8. 11 12 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 6 8. 10 10 15 7 11 16 20 23 8 0 0 0 0 9 0 0 0 0 10 0 0 0 0 Table 220.127.116.11: Distances between De ns and Prey Items in Meters Many of the dens were surrounded by habitat for the ark clam. The dens that were found among the reef were an average of 7.05 1.76 m from their nearest prey item.
52 3.2 Model Results 3.2.1 Varying Initial Concentrations with Random Distributions The first analysis conducted examined th e percentage of prey over time and its comparison to various initial starting conditi ons. Random distributi ons were used, with example spatial outputs shown in Figures 18.104.22.168 and 22.214.171.124. The radius of search was generated by the hunger level of each octopus. The first variable tested was the amount of octopus in the area. The results of varying octopus concentration are shown in Figure 126.96.36.199.
53 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Figure 188.8.131.52: Initial Rando m Spatial Distribution Red Indicates Available Dens, Yellow Indicates the Presence of an Octopus (Occupied Den), and Light Blue Prey Conditions are 30% Prey, 1% Octopus, 10% Available Dens 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Figure 184.108.40.206: Spatial Results after Simulation Initial conditions as shown in Figure 220.127.116.11
54 Figure 18.104.22.168: Percentage of Prey with Variation in Oct opus Concentration Prey = 50%, Available Dens = 10% Effect of Octopus Concentration on Percentage of Prey Steady State-5 0 5 10 15 20 25 30 35 0510152025 Octopus Concentration (Percentage)Percentage of Prey at Steady State Figure 22.214.171.124: Percentage of Prey at Steady State with Va riation in Initial Octopus Concentration
55 As evident in the graph, slightly cha nging the initial concen tration has drastic effects on the prey population. A higher population of octopus makes the prey population drop quicker and reaches a lower steady state. These steady states are displayed in Figure 126.96.36.199. The second scenario simulate d the variation of den avai lability. The radius of search was based on hunger of each individual octopus, and the simulation run for 20 days. The initial conditions were 1% oct opus and 30% prey. The results are shown in Figure 188.8.131.52.
56 Figure 184.108.40.206: Percentage of Prey over Ti me with Variation in Available Dens Prey: 30%, Octopus: 1% This graph indicates that there are variations in how quickly the prey population reaches a steady state as well as what the st eady states are that come with changing den availability. Steady state is correlated to the percent of den availability. Table 220.127.116.11 below gives the order in which the graphs reach a steady state.
57 Rank Den Availability 1 0% 2 1% 3 2.5% 4 5% 5 7.5% 6 10% Table 18.104.22.168: Order in Which Steady State is reached as Den Availability Changes Overall, the trend shows that increasing den availability decreases the time needed to reach a steady state. This trend was conf irmed by the running of extreme conditions of 50% and 60%. The steady state reache d, however, is shown in Figure 22.214.171.124. Effect of Dens on Percentage of Prey on Steady State0 10 20 30 40 50 60 70 051015202530 Den Availability (Percentage)Percentage of Prey Figure 126.96.36.199: Percentage of Prey at Steady State with Va riation in Den Availability
58 As indicated by the trend, it is not always a dvantageous for the octopus to have additional dens in the area for increased consumption of pr ey as the steady state for prey rises as the available dens increase. There appears to be an optimal initial percentage, in this model around 7-8% for the octopus to consume th e maximum amount of prey. Beyond this point, moving from den to den provides a di straction from the prey, and fewer amounts are consumed. Altering the concentrations of prey also has an effect on the patterns of the graph of percentage of prey over time. This gr aph is shown below in Figure 188.8.131.52 when the simulation is run for 60 days. Figure 184.108.40.206: Percentage of Prey over Time with Variation in Concentration of Prey N=100, Octopus=1%, Available Dens=10%
59 The order of rate of the decrease for the fi rst 10 days in the prey population according to initial the concentr ation of prey is shown in Table 220.127.116.11. Rank Initial Percent Prey 1 1% 2 5% 3 10% 4 20% 5 30% 6 40% Table 18.104.22.168: Rank in Decrease of Percentage of Prey Popul ation with Changing Initial Percent of Prey in the first 10 days The steady state percentage also differs with va riation in initial prey concentration and is shown in Figure 22.214.171.124 Effect of Initial Prey on Percentage of Prey Steady State0 10 20 30 40 50 60 70 80 051015202530354045 Initial Prey Population (Percentage)Percentage of Prey at Steady State Figure 126.96.36.199: Percentage of Prey at a Steady State with variation in Initial Concentration of Prey `
60 It is interesting to note that increasing the in itial concentration of prey results in a lower steady state for the percentage of prey. This could be due to increased mobility of the octopus with a larger amount of prey to use to move around the matrix. 3.2.2 Exploration of Various Foraging Radii After the initial concentrations are investigated, spatial configurations are examined. The first simulation involves two ba rs of available dens and a central area of prey. The octopuses are randomly distributed in the area. This initial distribution is shown in Figure 188.8.131.52. The first simulation is run with the radi us based on the octopuses hunger levels. This does not allow for a large enough radii for most of the oc topuses to reach the prey or any to look for available dens. The final spatial distribution is shown in Figure 184.108.40.206. Because of the lack of ability to reach the prey, the radius was changed to an increasing function. When run with the radius varying by equation (1) to allow for alterations that result in changes of the shape of the search radius. n m nt K t V r t r ) ( ) ( ) (max min (1) For this simulation, Vmax is equal to the number of days th e simulation is run, t is the time (in this run is equal to 50). This is the Hill equation, which is a sigmoidal equation illustrated in Figure 220.127.116.11.
61 180 200 220 240 260 280 300 320 160 180 200 220 240 260 280 300 320 340 360 Figure 18.104.22.168: Second Initial Distribu tion (Zoomed to area of interest) Red Represents Available Dens, Light Bl ue Prey, and Octopuses (.1%) by Yellow 200 220 240 260 280 300 200 220 240 260 280 300 320 Figure 22.214.171.124 Spatial Distributi on after the Running of the Simulation Shown in Figure 126.96.36.199 with the Radius of Search Based on Hunger Levels
62 Figure 188.8.131.52: Radius increasing by the Hill Equation (Equation (1)) The spatial results are shown in Figure 184.108.40.206, and the temporal in Figure 220.127.116.11. The radius is shown in Figure 18.104.22.168. Vmax rmin
63 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500 Figure 22.214.171.124: Spatial Results with Radius Varying by Equation (1) 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100Percentage of Prey Over Time With Radius Increasing by Equation (1) DaysPercentage of Prey Figure 126.96.36.199: Temporal Results wi th Radius Varying by Equation (1)
64 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Radius Changing by Equation (1) Over Time DaysRadius Length Figure 188.8.131.52: Radius Cha nging by Equation (1) (Km=50) While the radius is increasing, once the oc topuses come within range of the prey, the prey source is quickly eliminated in a lin ear fashion. By altering the steepness of the curve of the radius, the prey population will be altered accordingly. This is shown below in Figures 184.108.40.206 and 220.127.116.11
65 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100Percentage of Prey with decreased Km DaysPercentage of Prey Figure 18.104.22.168: Percentage of Pr ey with Decreased Km (=10) 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Radius with Decreased Km DaysRadius Figure 22.214.171.124: Radius with Decreased Km (=10)
66 These results are expected, as the prey is completely consumed by day 55 with a high Km, and 42 with a low Km. The spatia l results in Figure 126.96.36.199 show the octopuses eventually selecting dens near the perimeter of the area that previously held prey as they migrated in from the init ial random distribution. To look further at the spa tial relationships, another initi al distribution was used as shown in Figure 188.8.131.52. 180 200 220 240 260 280 300 320 200 220 240 260 280 300 320 Figure 184.108.40.206: Third Initial Spatial Distribution (zoomed into area of interest) This initial distribution has two area s with concentrated prey surrounded by available dens. When presented with the ra dius increasing with equation (1) with the conditions of Figure 220.127.116.11, the octopuses in turn reach the areas of prey and settle in the surrounding available dens. This is i llustrated in Figure 18.104.22.168 and Figure 22.214.171.124.
67 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 100Percentage of Prey Over Time with Simulation Three DaysPercentage of Prey Figure 126.96.36.199: Percentage of Prey over Time in Simulation Three The stair-like pattern observed once th e octopus reaches prey (around t = 28), indicates that with every few days, additiona l octopuses are reaching the areas of prey, with slight steps in between. The spatial distribution illustrate s this in Figure 188.8.131.52. As the octopuses nearer to the prey consume the prey, the change in spatial distribution extends the radius needed to reach the food of the octopuses further from the prey. The octopuses continue to settle at the edges of the area that previously, or continue, to hold prey.
68 3.2.3 Exploration of Additional Spatial Configurations The next simulation is similar, only the grouping of octopus is positioned slightly nearer to one area of habitat and available dens than the other as shown in Figure 184.108.40.206. 180 200 220 240 260 280 300 160 180 200 220 240 260 280 300 320 340 360 Figure 220.127.116.11: Initial Sp atial Distribution with Octopuses Closer to Habitat with Prey and Available Dens (Zoomed into Area of Interest) This simulation was run for 100 days with the same radius parameters as the previous simulation. The results for the pe rcentage of prey remaining are shown in Figure 18.104.22.168.
69 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 DaysPercentage of PreyPercentage of Prey With Initial Octopus Concentration Nearer to One Habitat Figure 22.214.171.124: Percentage of Prey with Octopuses Located Closer to One Area There is a slight deviation in the linear nature of this graph around t=30. This is explained by the octopus consuming most of th e prey within the first habitat and the time it takes them to move to the second to consume all that is there. Spatial results continue to involve the octopus choosing dens that are surrounding the area where prey was found. The final simulation involves a habitat design similar to the reef in Honduras. Octopuses were distributed randomly in th e area and the simulation was run with increasing radius by equation (1) with the same parameters as the la st two simulations. The initial spatial distribution is show n in Figure 126.96.36.199 with an initial octopus concentration.
70 180 200 220 240 260 280 300 320 340 180 200 220 240 260 280 300 320 340 Figure 188.8.131.52: Initial Concentration for Recreation of Cayos Cochinos Reef After running the simulation, the spatial distribution was as expected from the previous results. The octopuses ate in their general area, and then began to occupy dens along the edge of available de ns and the area where prey was located as shown in Figure 184.108.40.206.
71 Figure 220.127.116.11: Spatial Results after Simulation of Cayos Cochinos Reef These results are fairly similar to the field results in that some had dens in the middle of the prey areas, while others bor dered on the reef. Without long term projections and conditions such as birth and death, the exact na ture of the relationship is hard to predict. Spatially though, the simulati on results seem to confirm predictions that octopuses choose dens in close proximity to pr ey. This was also seen at Cayos Cochinos, as octopus dens often were found near prey (l ocated in the seagrass as well as available dens on the edge of the backreef.
72 Chapter 4: Discussion This study provided insight into spatia l distributions of octopus and their predators and prey, as well as components su ch as prey preference and den construction. Overall findings suggest that octopuses build dens at barriers betw een prey habitat and habitat most useful for den building. This is supported in the literatu re as octopuses have been noted to build dens in areas of patc h reef (Anderson, 1997) a nd near large, solid areas such as rock, shells, and submer ged human discards (Katsanevakis and Verriopoulos, 2004). Conclusions are limite d, however, by the nature of the data collected and parameters of the model. Ba sed on midden collections, octopuses exhibit prey preference and often occupy dens loca ted near the most common prey items as determined by the examination of midden conten t. While prey preference varies across populations and individual oc topuses (see Table 1.3.1), the prevalence of bivalves has been observed in Octopus vulgaris in the Mediterranean (Ambrose and Nelson, 1983; Anderson et al., 2008) as well as rocky reef areas and grass flats of Honduras (Rosebrock, 2000) and reef areas of South Africa (Smith, 2003). The dens of Cayos Cochinos are often located within crevices and other objects and sometimes altered to fit the needs of the octopus occupying the den. 4.1 Prey Preference Many investigators have studied prey preference in the past (Table 1.3.1) and many observations were made for the current study as well. Each octopus had a diet unlike the others based on midden contents, but with varying degr ees of specialization and favorite foods. Bivalves were by far the most popular overall but this could be
73 due to the type of sampling. Among eight ot her studies using midden contents (Table 1.3.1), only one named bivalves as the top choi ce, while seven named gastropods. It is therefore possible that crustaceans and small fi sh made up a larger portion of the diet but were not recovered at the midden. Because ga stropods and bivalves are equally favored by the sampling method though, it is likely that bivalves composed a larger portion of the diet than gastropods. Rosebrock (2000) found in a similar area that crustaceans were the largest portion of prey, so po ssible explanations could be either annual variation in bivalve, gastropod, and crustacean populations, or preference of the j uvenile octopuses in the area each year in regards to ob jects returned to the den. Obtaining a more accurate picture will invo lve several different things. First, it will be important to control availability and location to determine if an octopus has a favorite prey, or rather one that is just more convenient. Is sues that arise are familiarity, when an octopus chooses a food it is familiar with rather than trying new ones, especially in captivity, and the ability to control these factors in a natural e nvironment, as Mather (1991) found prey preference differs significantl y between the laboratory and the field. The results of prey preference also differ by collecting method (Smith, 2003), so multiple methods would provide a more accurate pictur e of the diet of an octopus. Combining knowledge about differences between lab and fi eld and data collection would indicate the necessity of a more rounded study. Within the same study group of octopuses, a combination of midden contents and fo raging observations would be necessary, preferably with limited researcher/octopus inte raction to determine th e exact nature of the diet of an octopus.
74 4.2 Octopus Dens The dens in the current study were all located on the back re ef or in surrounding sea grass, where one of the major prey items, ark clams ( Archidae barbatia) was found. Many made use of crevices in rocks and submerged objects and were often near open areas of soft sediment. Within the reef, another common prey item, the flame scallop ( Lima lima) was found in crevices. All octopus dens were found within 11 m of the nearest prey item, often surrounded by its hab itat. Whether the oct opus chose a den close to the prey or simply brought back prey to the midden that was nearest is unknown. The octopus also could have chos en dens with optimal protection from predators. The octopus dens were located close to one another (figure 18.104.22.168), indicating little territorial behavior among these octopuses. This is cons istent with observations by Katsanevakis and Verriopoulos (2004) and Le ite and colleagues (2009). The fact that these concentrations were on the back reef is consistent with Ande rsons findings as well (1997). The dens were often unoccupied dur ing the day, while newly discarded prey items continued to appear, indicating multiple dens in use. Further studies might examine the behavior of octopus involving mu ltiple dens, as some of the diet results could be skewed if two dens belonged to th e same octopus, as well as patterns of den location and construction found within multiple dens belonging to the same octopus. Den construction varied greatly among th e different dens. Some octopuses had manipulated areas around them significantly, while others simply used what was already present in the habitat in terms of crevi ces and shells, both submerged beneath the sediment and on top of sediments. The mo st common modifications were additions to the entry way to make it smaller. This occu rred in two dens, one with shells, and the
75 other with small pieces of rocky rubble. In one instance, the presence of researchers resulted in the closing off of a den. Add itional investigations would be needed to determine the effects of mobile predators on the size of entrie s to dens, and possibly their locations. The middens outside each den were critic al for original location of the den. Middens varied in contents and size, as noted in the results for prey preference. Midden contents sometimes appeared to be incorporat ed into den construction, as a shell fragment was used to close off den two in the presence of researchers, and the octopus in den seven held onto pieces in the presence of a research er. Perhaps midden contents are useful in hiding from or fending off mobile predators, and could be inve stigated by future studies. Another possible purpose for the middens w ould be visual clues while foraging, or attracting hermit crabs as suggested by Gilchr ist (2003) and other prey. Overall, there has been very little work done on the purpose of middens in general other than using discards to determine characteristics about a population and the urinary perches of pack rats. This would be another pot ential area of future study. 4.3 Eels Perhaps the area that needs the most study is that of eels. Very little literature is available for the hunting patterns and behavior s of eels. Nothing definitive came out of this study about eels, other than they can be located either very near or far from an octopus den. The presence of the eel ( Gymnothorax moringa ) and its apparent hunting grounds did not seem to affect the location of the octopus dens. The eel, which appeared to be around 1 1.5 m long (the full length of the eel was never visible), was seen
76 repeatedly, though no specific interactions wi th the octopuses were observed. Because the octopus foraging range has been docum ented as 50 m, it is possible that any interactions that occur while foraging over su ch a large area are pos sibly more important than den locations. Before any conclusions can be drawn about the spatial relationships between octopuses and eels, more informa tion, including diet, foraging patterns, hunting and burrow habits must be obtained. 4.4 Model The model provides a simple simulation of the dynamics that occur between the octopus and their prey within both spatial and temporal domains. Eels are excluded because of the aforementioned lack of conclu sive evidence to their role. In addition, births and deaths are not included, which ma kes the model useful only for determining patterns in terms of days, not long term projections. Within these confines, the model produced results similar to what was seen in the field as octopus accumulated in reef areas bordering open sediment where prey was located. Several factors influenced the preda tion rates, including ra dius of search and initial concentrations. To determine the ex act nature of these parameters, more study on octopus behavior, especially under conditi ons where food becomes limited, would be needed. Introducing octopus death by pred ation and starvation would also make the model more realistic. The issu es of complexity would have to be examined at that point to decide how many additions would still provide for worthwhile and understandable outputs.
77 4.5 Conservation Implications and Conclusion Both the model and field observation s support the conclusion that octopuses frequently construct and inhabit dens in an area bordering both available den materials and prey habitat. This could be a behavi oral adaptation to optimize foraging and den materials, but more study would be needed to draw any more conclusions. Octopuses are an important fishery in various parts of the world, such as the Mediterranean (Katsanevakis and Verriopoulos, 2004) and Brazil (Leite et al ., 2009) as well as critical players in ecosystems protected by M.P.A. s and other areas important to ecosystem tourism. This study shows the importance not only of reef environments, but areas of soft sediment around them. It al so demonstrates the role the border area plays in the life history of an octopus, particularly juvenile Octopus vulgaris These are essential areas to protect in addition to the coral reef itself.
78 References Aizpura, I. I. I., and P. A. McAna ny. 1999. Adornment and identity. Ancient Mesoamerica 10, (01): 117-27. Alves, C., J. G. Boal, and L. Dickel. 2008. Short-distance navigation in cephalopods: A review and synthesis. Cognitive Processing 9, (4): 239-47. Ambrose, R. F. 1982. Octopus bimaculatus. Marine Ecology-Progress Series 7, : 67-73. Ambrose, RF. 1983. Midden formation by octopuses: The role of biotic and abiotic factors. Marine Behaviour and Physiology 10, (2): 134-44. Ambrose, RF, and BV Nelson. 1983. Predation by Octopus vulgaris in the Mediterranean. Marine Ecology (Berlin) 4, (3): 251-61. Anderson, R. C., J. B. Wood, and J. A. Mather. 2008. Octopus vulgaris in the Caribbean is a specializing generalist. Marine Ecology Progress Series 371 : 199-202. Anderson, RC, DL Sinn, and JA Mather. 2008. Dr illing localization on bivalve prey by O ctopus rubescens bery 1953 (cephalopoda: Octopodidae). The Veliger 50, (4): 326-8. Anderson, T. J. 1997. Habitat selection and shelter use by O ctopus tetricus Marine Ecology Progress Series 150, (1): 137-48. Andr, J., E. P. M. Grist, J. M. Semmens, G. T. Pecl, and S. Segawa. 2008. Effects of temperature on energetics and the grow th pattern of benthic octopuses. Marine Ecology Progress Series 374, : 167-79. Andr, J., G. T. Pecl, J. M. Semmens, and E. P. M. Grist. 2008. Early life-history processes in benthic octopus : Relationships between temperature, feeding, food conversion, and growth in juvenile Octopus pallidus Journal of Experimental Marine Biology and Ecology 354, (1): 81-92. Berger, D. K., and M. J. Butler. 2001. Oct opuses influence den selection by juvenile caribbean spiny lobster. Marine and Freshwater Research 52, (8): 1049-54. Boal, J. G., A. W. Dunham, K. T. Will iams, and R. T. Hanlon. 2000. Experimental evidence for spatial learning in octopuses (octopus bimaculoides). Journal of Comparative Psychology 114, (3): 246-52. Cerezo Valverde, J., M. D. Hernndez, F. Aguado-Gimnez, and B. Garca Garca. 2008. Growth, feed efficiency and condition of common octopus (octopus vulgaris) fed on two formulated moist diets. Aquaculture 275 (1-4): 266-73.
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82 Appendix A: Field Data Locations of Lima lima Dist. (m) Angle (deg) Angle (Rad) Adj. Angle X Coord Y Coord X Origin Y Origin Final X Final Y R8 to I 3.95 60.00 1.05 2.09 -1.97 3. 42 30.67 -17.71 28.70 -14.29 5.66 0.00 0.00 3.14 -5.66 0.01 30.67 -17.71 25.01 -17.70 5.84 340.00 5.93 -2.79 -5. 48 -2.01 30.67 -17.71 25.19 -19.72 8.50 350.00 6.11 -2.97 -8. 37 -1.49 30.67 -17.71 22.30 -19.20 14.63 30.00 0.52 2.62 -12.66 7.33 30.67 -17.71 18.01 -10.38 11.40 40.00 0.70 2.44 -8.72 7.34 30.67 -17.71 21.95 -10.37 R2 to I 2.65 130.00 2.27 0.87 1. 70 2.03 45.08 -10.99 46.78 -8.96 8.07 165.00 2.88 0.26 7.80 2.09 45.08 -10.99 52.88 -8.90 11.41 170.00 2.97 0.17 11.24 1.98 45.08 -10.99 56.32 -9.01 12.32 155.00 2.70 0.44 11.17 5.20 45.08 -10.99 56.25 -5.79 12.19 140.00 2.44 0.70 9.34 7.83 45.08 -10.99 54.42 -3.16 10.93 115.00 2.01 1.13 4.62 9.90 45.08 -10.99 49.70 -1.09 8.56 315.00 5.50 -2.36 -6. 05 -6.06 45.08 -10.99 39.03 -17.05 12.75 10.00 0.17 2.97 -12.55 2.23 45.08 -10.99 32.53 -8.76 13.16 5.00 0.09 3.05 -13.11 1.17 45.08 -10.99 31.97 -9.82 R1 to I 6.24 260.00 4.54 -1.40 1. 09 -6.14 57.77 -19.88 58.86 -26.02 7.35 265.00 4.62 -1.48 0.65 -7.32 57.77 -19.88 58.42 -27.20 10.97 240.00 4.19 -1.05 5.49 -9.50 57.77 -19.88 63.26 -29.38 14.10 290.00 5.06 -1.92 -4.81 13.25 57.77 -19.88 52.96 -33.13 15.40 215.00 3.75 -0.61 12.62 -8.83 57.77 -19.88 70.39 -28.71 DR to I 1.87 195.00 3.40 -0.26 1.81 -0.48 0.00 0.00 1.81 -0.48 R3 to I 5.13 245.00 4.27 -1.13 2. 17 -4.65 0.00 -1.87 2.17 -6.52 R4 to I 3.74 305.00 5.32 -2.18 -2.14 -3 .07 -2.25 1.30 -4.39 -1.77 R6 to I 8.32 240.00 4.19 -1.05 4.16 -7.20 244.9958.15 240.8350.95 R7 to I 8.16 20.00 0.35 2.79 -7.66 2.80 256.60 67.89 264.26 70.69 11.00 260.00 4.54 -1.40 1.92 10.83 256.6067.89 254.6857.06
83R7 to I Dist. (m) Angle (deg) Angle (Rad) Adj. Angle X Coord Y Coord X Origin Y Origin Final X Final Y 15.67 280.00 4.88 -1.74 -2.71 15.43 256.60 67.89 259.31 52.46 20.22 250.00 4.36 -1.22 6.93 19.00 256.6067.89 249.6748.89 20.16 255.00 4.45 -1.31 5.23 19.47 256.6067.89 251.3748.42 29.43 245.00 4.27 -1.13 12.45 26.67 256.60 67.89 244.15 41.22 Locations of Sea Grass Dist. (m) Angle (deg) Angle (Rad) Adj. Angle X Coord Y Coord X Origin Y Origin Final X Final Y Dock Left 8.50 90.00 1.57 2.09 -4.24 7.37 -2.00 0.00 -6.24 7.37 14.85 145.00 2.53 3.14 14.85 0.02 -6.24 7.37 -21.09 7.39 14.90 200.00 3.49 -2.79 13.99 -5.12 -21.09 7.39 -35.09 2.27 10.77 300.00 5.23 -2.97 10.60 -1.89 -35.09 2.27 -45.69 0.39 12.57 195.00 3.40 2.62 10.88 6.30 -45.69 0.39 -56.57 6.69 7.43 190.00 3.31 2.44 -5. 69 4.78 -56.57 6.69 -62.25 11.47 13.66 85.00 13.66 0.00 -62.25 11.47 -48.59 11.47 14.95 210.00 3.66 0.87 9.61 11.45 -48.59 11.47 -38.98 22.92 11.45 155.00 2.70 0.26 11.06 2.96 -38.98 22.92 -27.92 25.88 21.40 205.00 3.58 0.17 21.08 3.71 -27.92 25.88 -6.84 29.59 13.80 80.00 1.40 0.44 12.51 5.83 -6.84 29.59 5.67 35.42 going out 235.00 4.10 0.70 0.00 1.13 Dock Right 8.00 90.00 1.57 -2.36 -5.65 -5 .66 0.00 0.00 -5.65 -5.66 6.20 0.00 0.00 2.97 -6.10 1. 09 -5.65 -5.66 -11.75 -4.58 15.60 335.00 5.84 3.05 15.54 1.38 -11.75 -4.58 -27.29 -3.19 11.70 65.00 11.70 0. 00 -27.29 -3.19 -15.59 -3.19 8.80 145.00 2.53 -1.40 1.53 -8 .67 -15.59 -3.19 -14.06 -11.86 12.50 40.00 0.70 -1.48 1.10 12.45 -14.06 -11.86 -12.96 -24.31 18.60 270.00 4.71 -1.05 9.31 16.10 -12.96 -24.31 -3.65 -40.41 23.60 345.00 6.02 -1.92 -8.05 22.18 -3.65 -40.41 -11.70 -62.60 going out 20.00 0.35 -0.61 R5 16.60 105.00 16.60 0.00 160.209.41 143.60 9.41
84 Dist. (m) Angle (deg) Angle (Rad) Adj. Angle X Coord Y Coord X Origin Y Origin Final X Final Y 41.07 210.00 3.66 -0.26 39.67 10.62 143.609.41 103.93 -1.21 22.00 10.00 22.00 0.00 103.93 -1.21 -81.93 -1.21 34.20 275.00 4.80 -1.13 14.47 30.99 -81.93 -1.21 -67.46 -32.20 40.15 0.00 40.15 0. 00 -67.46 -32.20 -27.31 -32.20 47.90 100.00 1.74 -2.18 27.43 39.27 -27.31 -32.20 -54.74 -71.47 17.80 65.00 17.80 0. 00 -54.74 -71.47 -36.94 -71.47 47.60 195.00 3.40 -1.05 23.82 41.21 -36.94 -71.47 -13.12 112.68 Locations of Eels Dist. (m) Angle (deg) Angle (Rad) Adj. Angle X Coord Y Coord X Origin Y Origin Final X Final Y R3 to B 3.74 265.00 4.62 -1.48 0.33 -3.73 0.00 -1.87 0.33 5.60 R1 to B 3.91 215.00 3.75 -0.61 3. 20 -2.24 57.77 -19.88 60.97 -22.12 R5 to B 36.95 320.00 5.58 -2.44 28.28 23.79 160.209.41 188.48 -14.38 38.36 245.00 4.27 -1.13 16.23 34.76 160.209.41 143.97 -25.35
85 Location of Octopus Dens Distance (m) Angle (degrees) Final X Final Y R1 57.77 -19.88 R8 to R2 15.90 335.00 R2 45.08 -10.99 R3 0.00 -1.87 R2 to R1 15.50 35.00 R4 -2.25 1.30 R5 -160.20 9.41 Dock Right to R3 1.87 90.00 R6 -244.99 58.15 R7 -256.60 67.89 Dock Right to R4 2.60 210.00 R8 30.67 -17.71 R9 -22.26 -12.85 R4 to R3 3.80 45.00 R10 -48.24 2.15 R6 to R7 15.16 220.00 Dock Right To R8 35.41 30.00 Dock Right to R9 25.70 150.00 R9 to R10 30.00 210.00 R10 to reference 42.63 185.00 20.40 190.00 Reference Flag to R5 49.40 180.00 Dock R to Dock L 2.00 180.00 R5 to R6 50.16 205.00 48.02 215.00
86 Midden Contents Day 1 1 2 3 4 5 6 7 8 Totals A 0 B 0 C 0 D 0 E 2 2 F 1 1 2 G 1 1 H 1 1 2 4 I 1 1 2 J 1 3 4 K 0 L 1 1 M 0 N 0 O 0 P 0 Totals 0 2 2 3 5 2 2 0 Day 2 Totals A 0 B 1 1 C 0 D 0 E 1 1 2 F 0 G 0 H 1 1 I 0 J 1 1 2 K 0 L 0 M 0 N 0 O 0 P 0 Totals 0 1 1 1 1 0 0 2
87Day 3 Totals A 1 1 B 1 1 C 0 D 0 E 1 1 F 0 G 0 H 1 1 2 I 1 1 J 1 1 K 1 1 L 0 M 1 1 N 0 O 0 P 0 Totals 1 1 0 0 0 0 1 6 Day 4 Totals A 0 B 1 1 C 0 D 0 E 4 1 5 F 1 1 G 0 H 1 1 I 0 J 1 2 3 K 0 L 0 M 1 1 N 1 1 O 1 1 P 0 Totals 0 1 1 2 7 1 0 18
88Day 5 1 2 34567 8 Totals A 0 B 0 C 0 D 0 E 0 F 0 G 0 H 0 I 0 J 31 4 K 0 L 0 M 1 1 N 0 O 0 P 0 Totals 0 0 31000 1 Day 6 Totals A 0 B 0 C 0 D 0 E 0 F 0 G 0 H 1 1 I 0 J 1 21 4 K 0 L 0 M 0 N 0 O 0 P 1 1 Totals 0 2 21000 0
89Day 7 Totals A 0 B 0 C 0 D 0 E 1 1 F 0 G 0 H 1 1 2 I 0 J 1 21 4 K 0 L 0 M 0 N 0 O 0 P 1 1 Totals 0 2 21200 0 Day 8 Totals A 0 B 0 C 0 D 0 E 1 1 F 0 G 0 H 0 I 0 J 1 1 2 K 0 L 0 M 0 N 0 O 0 P 0 Totals 0 1 11000 0
90 Appendix B: Matlab Code Main Code clc clear all figure(1),clf figure(2),clf figure(3),clf figure(4),clf N=500; N1=100; NumDays=100; cc='b-'; FoodVal=1; ShelterVal=3; %% Define Xout Xout=zeros(N,N); Xout1=zeros(N1,N1); % %random distribution % %prey % pA = 50/100; % Val=1; % [Xout1]=InitialDistribution(N1,Xout1,pA,Val); % %octopus % pB=.1/100; % Val=2; % [Xout1]=InitialDistribution(N1,Xout1,pB,Val); % % %unoccupied den % pC=10/100; % Val=3; % [Xout1]=InitialDistribution(N1,Xout1,pC,Val); % %two bars of dens and square of prey % Xout1(40:59,40:59)=ones(20); % % Xout1(30:39,30:69)=3*ones(10,40); % Xout1(60:69,30:69)=3*ones(10,40); % %octopus % pB=.1/100; % Val=2; % [Xout1]=InitialDistribution(N1,Xout1,pB,Val);
91 % %Two habitats in corners % %lower left % Xout1(71:100,1:5)=3; % Xout1(71:100,26:30)=3; % Xout1(71:75,6:25)=3; % Xout1(96:100,6:25)=3; % Xout1(76:95,6:25)=1; % % Xout1(61:65,41:45)=2; % % %upper right % Xout1(1:30,71:75)=3; % Xout1(1:30,96:100)=3; % Xout1(1:5,76:95)=3; % Xout1(26:30,76:95)=3; % Xout1(6:25,76:95)=1; % %recreation of habitat in Honduras (needs random distribution of octopus as % %well) % Xout1(31:100,1:5) = 3*ones(70,5); % Xout1(96:100,6:100) = 3*ones(5,95); % Xout1(61:100,96:100)= 3*ones(40,5); % Xout1(51:60,66:75)= 3*ones(10,10); % % Xout1(20:95,6:65) = ones(76,60); % Xout1(40:95,76:95) = ones(56,20); % % %octopus % pB=.1/100; % Val=2; % [Xout1]=InitialDistribution(N1,Xout1,pB,Val); Xout(201:300,201:300)=Xout1; %% Generate and plot initial distributions figure(1),imagesc(Xout) %plots initial distributions figure(2), imh = imagesc(Xout); %plots initial distributions and for updating the image set(imh, 'erasemode', 'none') axis equal axis tight drawnow; [I J]=find(Xout==2); %finds octopuses and creates array of locations
92[Hungerout]=Xout; %assigns a matrix to meausure the "hunger" of each octopus %find initial numbers preyTot(1)=length(find(Xout==1)); octTot(1)=length(find(Xout==2)); emptyTot(1)=length(find(Xout==3)); % Creating A Radius of Search %always increasing rmin = 1; Vmax = NumDays; Km = 50; mm = 1; kq2=1:NumDays; %rad=round(rmin+Vmax*kq2.^mm./(Km^mm+kq2.^mm)); %figure(4),plot(kq2,rad) %% Foraging Patterns for kq=1:NumDays %determine radius based on increasing formula rad=round(rmin+Vmax*kq^mm/(Km^mm+kq^mm)); figure(4),plot(kq,rad,'o'),hold on axis([0 NumDays 0 rmin+Vmax]) %determine random direction of movement OrMov = randperm(numel(I)); Direction = 1+floor(8*rand(1,numel(J))); for counter=1:numel(I) %determine starting position of the octopus i = I(OrMov(counter)); j = J(OrMov(counter)); % %determine radius based on hunger of the octopus % OctVal = Hungerout(i,j)-1; % rad = radius(OctVal); % r = rad; DirectionNow = Direction(counter); %assigns random starting direction to each octopus %looking for food for r = 1:rad [Xout,iout,jout,flagF] = LookforFood(i,j,r,N,Xout,FoodVal,DirectionNow); if flagF==2 break end end
93 %looking for another shelter if food is found for r = 1:rad if flagF==2 [Xout,ff]=LookforShelter(iout,jout,r,N,Xout,ShelterVal,DirectionNow); if ff==10 Xout(i,j) = 3; ff = 1; break end flagF=1; end end end %update new numbers of each type of location preyTot(kq+1) = length(find(Xout==1)); octTot(kq+1) = length(find(Xout==2)); emptyTot(kq+1) = length(find(Xout==3)); %update spatial distribution image figure(2), imh = imagesc(Xout); set(imh, 'erasemode', 'none') drawnow; end %clear variables and find the new locations of the octopuses clear I clear J clear OrMov [I J]=find(Xout==2); %plot the percentage of prey over time figure(3),hold on,plot([0:NumDays],preyTot(1:NumDays+1)/preyTot(1)*100,cc); hold on axis([0 NumDays 0 101]) %figure(3),hold on,plot([0:NumDays],preyTot(1:NumDays+1)/preyTot(1)*100,cc); hold on
94 Initial Distribution Code function [Xout]=InitialDistribution(N,Xin,pX,Val) for i=1:N for j=1:N if rand
95 Look for Food Codefunction [Xout ff]=LookforShelter(i0,j0,r,N,Xout,ShelterVal,Direction2) %set initial conditions for if food is not found ff=1; %array for one of 8 starting points per radius Or0=[1+mod(i0-1-r,N) 1+mod(i0-1-r,N) 1+mod(i0-1-r,N) 1+mod(i01,N) 1+mod(i0-1+r,N) 1+mod(i0-1+r,N) 1+mod(i0-1+r,N) 1+mod(i0-1,N); 1+mod(j0-1-r,N) 1+mod(j0-1,N) 1+mod(j0-1+r,N) 1+mod(j01+r,N) 1+mod(j0-1+r,N) 1+mod(j0-1,N) 1+mod(j0-1-r,N) 1+mod(j0-1-r,N)]; %choose a random number to choose Clockwise or Counterclockwise rr=rand; %Set initial foraging position based on array above Positioni=Or0(1,1+mod(Direction2,8)); Positionj=Or0(2,1+mod(Direction2,8)); if rr<=.5 %Clockwise for k=1:8*r-1 %check for shelter if Xout(Positioni,Positionj)==3; ff=10; Xout(Positioni,Positionj)=2; %Xout(i0,j0)=3; return end %move in box-shaped pattern if Positioni==1+mod(i0-r-1,N) & Positionj< 1+mod(j0+r-1,N) Positionj=1+mod(Positionj+1-1,N); elseif Positionj==1+mod(j0+r-1,N) & Positioni < 1+mod(i0+r-1,N) Positioni=1+mod(Positioni+1-1,N); elseif Positioni==1+mod(i0+r-1,N) & Positionj > 1+mod(j0-r-1,N) Positionj=1+mod(Positionj-1-1,N); elseif Positionj==1+mod(j0-r-1,N) & Positioni > 1+mod(i0-r-1,N) Positioni=1+mod(Positioni-1-1,N); end end else %Counterclockwise for k=1:8*r-1 %check for shelter if Xout(Positioni,Positionj)==3; ff=10; Xout(Positioni,Positionj)=2; %Xout(i0,j0)=3; return
96 end %move in box-shaped pattern if Positioni==1+mod(i0-r-1,N) & Positionj > 1+mod(j0-r-1,N) Positionj=1+mod(Positionj-1-1,N); elseif Positionj==1+mod(j0+r-1,N) & Positioni > 1+mod(i0-r-1,N) Positioni=1+mod(Positioni-1-1,N); elseif Positioni==1+mod(i0+r-1,N) & Positionj < 1+mod(j0+r-1,N) Positionj=1+mod(Positionj+1-1,N); elseif Positionj==1+mod(j0-r-1,N) & Positioni < 1+mod(i0+r-1,N) Positioni=1+mod(Positioni+1-1,N); end end end
97 Look for Shelter Code function [Xout,iout,jout,flagF]=LookforFood(i0,j0,r,N,Xout,Val,Direction2) %set initial conditions for if food is not found iout=i0; jout=j0; flagF=1; %array for one of 8 starting points per radius Or0=[1+mod(i0-1-r,N) 1+mod(i0-1-r,N) 1+mod(i0-1-r,N) 1+mod(i01,N) 1+mod(i0-1+r,N) 1+mod(i0-1+r,N) 1+mod(i0-1+r,N) 1+mod(i0-1,N); 1+mod(j0-1-r,N) 1+mod(j0-1,N) 1+mod(j0-1+r,N) 1+mod(j01+r,N) 1+mod(j0-1+r,N) 1+mod(j0-1,N) 1+mod(j0-1-r,N) 1+mod(j0-1-r,N)]; %choose a random number to choose Clockwise or Counterclockwise rr=rand; %Set initial foraging position based on array above Positioni=Or0(1,1+mod(Direction2,8)); Positionj=Or0(2,1+mod(Direction2,8)); %Movement Patterns if rr<=.5 %Clockwise for k=1:8*r-1 %check for food if Xout(Positioni,Positionj)==Val Xout(Positioni,Positionj)=0; flagF = 2; iout = Positioni; jout = Positionj; return end %move in box-shaped pattern if Positioni==1+mod(i0-r-1,N) & Positionj< 1+mod(j0+r-1,N) Positionj=1+mod(Positionj+1-1,N); elseif Positionj==1+mod(j0+r-1,N) & Positioni < 1+mod(i0+r-1,N) Positioni=1+mod(Positioni+1-1,N); elseif Positioni==1+mod(i0+r-1,N) & Positionj > 1+mod(j0-r-1,N) Positionj=1+mod(Positionj-1-1,N); elseif Positionj==1+mod(j0-r-1,N) & Positioni > 1+mod(i0-r-1,N) Positioni=1+mod(Positioni-1-1,N); end end else %Counterclockwise for k=1:8*r-1 %check for food if Xout(Positioni,Positionj)==Val
98 Xout(Positioni,Positionj)=0; flagF = 2; iout = Positioni; jout = Positionj; return end %move in box-shaped pattern if Positioni==1+mod(i0-r-1,N) & Positionj > 1+mod(j0-r-1,N) Positionj=1+mod(Positionj-1-1,N); elseif Positionj==1+mod(j0+r-1,N) & Positioni > 1+mod(i0-r-1,N) Positioni=1+mod(Positioni-1-1,N); elseif Positioni==1+mod(i0+r-1,N) & Positionj < 1+mod(j0+r-1,N) Positionj=1+mod(Positionj+1-1,N); elseif Positionj==1+mod(j0-r-1,N) & Positioni < 1+mod(i0+r-1,N) Positioni=1+mod(Positioni+1-1,N); end end end