TEMPERATURE EFFECTS < General, MARINE FISHERIES < General ... · Draft Predicting hatch time of American lobsters in nature 1 1 Using temperature-dependent embryonic growth models

Draft

Using temperature-dependent embryonic growth models to

predict time of hatch of American lobster, Homarus americanus, in nature

Journal: Canadian Journal of Fisheries and Aquatic Sciences

Manuscript ID cjfas-2015-0355.R1

Manuscript Type: Article

Date Submitted by the Author: 05-Feb-2016

Complete List of Authors: Miller, Erin; University of New Brunswick, Biology Haarr, Marthe; University of New Brunswick, Biology Rochette, Rémy; University of New Brunswick,

Keyword: TEMPERATURE EFFECTS < General, MARINE FISHERIES < General, LOBSTERS < Organisms, EMBRYOLOGY < General, MODELS < General

https://mc06.manuscriptcentral.com/cjfas-pubs

Canadian Journal of Fisheries and Aquatic Sciences

Draft

Predicting hatch time of American lobsters in nature 1

Using temperature-dependent embryonic growth models to predict time of hatch 1

of American lobster, Homarus americanus, in nature 2

3

4

Erin Miller, Marthe Larsen Haarr, and Rémy Rochette 5

6

Dept. of Biology, University of New Brunswick Saint John, 7

P.O. Box 5050, Saint John, NB, E2L 4L5 8

9

10

Corresponding Author – Erin Hope Miller 11

Email – [email protected] 12

13

Second Author – Marthe Larsen Haarr 14


16

Third Author – Rémy Rochette 17


19

20

21

Page 1 of 39



Draft


Abstract 22

Hatch time of American lobster, Homarus americanus, varies between years and 23

regions, which affects temperature experienced by the developing larvae and hence the 24

time and distance these drift before settling. Hatch time can be assessed by working 25

with fishermen and inspecting the brood of gravid females caught in their traps. 26

However, this would require frequent sampling as the hatch period is protracted (≈7-12 27

weeks), and would require dedicated sampling in many regions where hatching occurs 28

outside of the fishing season. To address these limitations, we tested the accuracy with 29

which hatch time can be predicted by taking egg samples during the fishing season and 30

estimating embryo development using embryonic eye size (Perkins Eye Index) and lab-31

derived temperature-dependent development functions. Using a linear development 32

function and observed variability in Perkins Eye Index at hatch, we successfully 33

predicted 100% of the observed 50-day hatch period, and 96% of predicted hatch dates 34

fell within this period. Our results suggest that samples can be obtained in collaboration 35

with fishermen to predict the timing and progression of hatch of American lobster 36

37

38

Keywords: Temperature effects, marine fisheries, lobsters, embryology, models 39

40

Page 2 of 39



Draft


Introduction 41

The American lobster, Homarus americanus (Milne Edwards 1837), is of 42

considerable economic importance to coastal communities in Atlantic Canada and the 43

northeastern United States (DFO 2014, NOAA 2014a). The fishery is managed through 44

45 separate Lobster Fishing Areas (LFAs) in Canada and 7 management areas in the 45

United States (DFO 2014, NOAA 2014b). Henceforth, the term Fishing Area (FA) will be 46

used to refer to both Canadian and American lobster management jurisdictions, the 47

boundaries of which are based primarily upon political and socioeconomic 48

considerations and generally do not reflect biological units or stocks (Miller 1995). As 49

management practices are not tailored to discrete biological stocks of lobsters and 50

recruits of one FA may be largely supplied by lobsters managed in a different 51

jurisdiction (Miller 1997, Xue et al. 2008, Chassé and Miller 2010), it is important to 52

understand connectivity among FAs, which is a function of dispersal by juveniles and 53

adults on the seafloor and pelagic larvae in the water column (Ennis 1995). 54

The larval phase has considerable dispersal potential and is generally assumed 55

to be the most important contributor to connectivity throughout the species’ range (Ennis 56

1986, Harding and Trites 1988). After a period of embryonic development that lasts up 57

to 12 months in Canadian waters (Templeman 1937), newly released larvae drift near 58

the surface of the water column for up to 8 weeks (MacKenzie 1988), undergoing three 59

molts prior to reaching the post-larval stage, which eventually becomes competent to 60

settle on the seafloor (Ennis 1995). The length of time these larvae drift with currents is 61

primarily a function of temperature, with warmer waters significantly accelerating 62

development (MacKenzie 1988). It is estimated that larvae may disperse up to several 63

Page 3 of 39



Draft


hundred kilometers from the location of hatch in certain conditions (Incze and Naime 64

2000, Xue et al. 2008). 65

Since the late 1980’s biophysical models have been developed to predict 66

dispersal of American lobster larvae, including for the Gulf of Maine (Harding and Trites 67

1988, Incze and Wahle 2006) and the Gulf of St Lawrence (Chassé and Miller 2010). 68

Using physical data of oceanographic conditions such as water temperature, ocean 69

currents, and wind-driven surface currents, these models predict the movement of 70

larvae from their point of origin to their settlement location. The accuracy of these 71

predictions is, however, dependent upon the accuracy of biological inputs such as the 72

location and quantity of larvae released as well as rates of larval development and 73

survival (Annis et al. 2007, Hudon and Fradette 1988). Another potentially important 74

input into these models is the time of hatching, as this will affect the currents and 75

temperature experienced by the larvae, which in turn will affect the direction, duration 76

and extent of their dispersal. 77

Timing-of-hatch can be determined through direct observation of females in the 78

process of hatching, as these can be easily discerned by reduced clutch volume and the 79

appearance of gluey “cement” on pleopods. However, it is logistically difficult to obtain 80

such information across a large geographic area. Collaborating with lobster fishermen 81

could in principle enable such direct observations of hatch. However, this would require 82

dedicated and expensive sampling in areas where much or all of the hatch period 83

occurs out of fishing season, such as in Atlantic Canada, where fishing is generally 84

closed during later summer months to protect reproductive females and to avoid 85

competition with peak U.S. landings and late summer molting (Miller 1995). 86

Page 4 of 39



Draft


Previous efforts have been made to determine the timing-of-hatch of American 87

lobster in nature (Templeman 1940; Fogarty 1983 and references therein; Harding and 88

Trites 1988; Miller et al. 2006). The majority of these studies used larval tows to infer 89

the timing and progression of hatch, based on the presence of stage I larvae in the 90

water, although Templeman made direct observations of clutches of ovigerous females 91

held in lobster pounds and in situ. The results of these studies, and of a recent analysis 92

of a long time-series of egg-bearing female data from the southern Gulf of Saint 93

Lawrence (M. Haarr, In preparation), indicate that hatching occurs from late spring to 94

late summer months, that the duration of hatch is variable (e.g., ≈9-12 weeks in Scarratt 95

1964, 7 weeks in this study) and that the timing and progression of hatch vary 96

considerably between years and regions. For example, the onset of hatch over the past 97

25 years has varied among regions of the southern Gulf of Saint Lawrence by as many 98

as 8 weeks in any given year, and by as many as 7-9 weeks in different years for a 99

same region (M. Haarr, In preparation). Similarly, the progression of hatching in a given 100

region also varies considerably from year to year, sometimes showing a marked peak 101

period of hatching and in other years showing more uniform hatching over time. For 102

example, using time series presented in Scarratt (1964) on the abundance of stage I 103

larvae in the Northumberland Strait we estimate that the inter-week variance in amount 104

of hatching ranged from 9 times less to almost 6 times more than the mean variance of 105

the 13-year data set (1949 to 1961). 106

Importantly, all studies conducted to assess hatch time of American lobster have 107

dependent on substantial sampling efforts and required extended time at sea. 108

Alternatively, if time of hatch can be predicted using eggs from ovigerous females 109

Page 5 of 39



Draft


sampled (a) at a single point in time and (b) during the fishing season, then hatch could 110

potentially be determined across the species’ range with minimal sampling effort and 111

cost if working in collaboration with lobster fishermen. 112

A method for predicting time of hatch based on water temperature and embryonic 113

development was first developed by Perkins in 1972. Ovigerous females from southeast 114

New England were held in the laboratory at either constant or fluctuating seasonal 115

temperatures and the development of embryos was monitored by measuring their eye 116

size (Perkins 1972). Perkins used embryo eye size to build a linear temperature-117

dependent function of embryonic development, and more recently a logarithmic variant 118

of this was proposed (Gendron and Ouellet 2009). By using these development 119

functions along with temperature data and eye size of embryos at hatch as an endpoint, 120

time to hatch can be estimated. Perkins (1972) concluded that hatch in southeast New 121

England occurred when the embryo’s eye reaches ≈560 µm in diameter, while Gendron 122

and Ouellet (2009) report a mean eye size at hatch of 550 µm in the Magdalen Islands 123

and Helluy and Beltz (1991) report an estimate of 570 ± 20 µm in Massachusetts. 124

Whereas these studies suggest relatively limited geographic variation in mean eye size 125

of lobster embryos at hatch, at least one study revealed considerable variation among 126

and within females of a same location (Gendron and Ouellet 2009), suggesting that 127

using a single mean eye-size-at-hatch value as an endpoint could reduce the accuracy 128

of hatch predictions made for a particular study site. 129

The primary objective of this study is to test the accuracy with which in situ hatch 130

time of ovigerous H. americanus can be predicted using embryonic eye size as a 131

measure of development, published temperature-dependent embryonic growth 132

Page 6 of 39



Draft


functions and both fixed and variable embryo eye sizes as development endpoints. Our 133

objective was not to develop new development models, but rather to determine whether 134

existing models, which had been developed in the lab, could actually be used to predict 135

hatch in nature. We estimate hatch dates of wild-caught embryos using site-specific 136

temperature data and both Perkins’ (1972) linear and Gendron and Ouellet’s (2009) 137

logarithmic embryonic growth functions, and compare these predictions to observed 138

hatch dates for the area obtained by sampling with fishermen. Specifically, we aim to 139

test (1) whether the timing of hatch can be accurately predicted based on egg samples 140

obtained from ovigerous females within the fishing season, but prior to the start of 141

hatching, (2) which embryonic growth function performs better, and (3) whether 142

consideration of inter- and intra-female variability of embryonic eye-size-at-hatch 143

improves predictions over a generalized eye-size-at-hatch obtained from the literature. 144

By attempting to validate this approach in nature we wish to determine whether regional 145

hatch times in American lobster can be accurately predicted by taking egg samples at a 146

single point in time during the fishing season, which would enhance our ability to predict 147

spatial connectivity via dispersal of lobster larvae over large geographic areas. 148

149

Methods 150

Sampling Location and Frequency 151

All sampling took place off Cheticamp, Nova Scotia, Canada over a 15-week 152

period from May 3rd to August 16th 2012, in an area covering ≈7.5 km2 and varying in 153

depth from 6 to 28 m. Sampling of ovigerous females was done in conjunction with 154

commercial fishing from May 3rd until June 23rd, and then with a vessel chartered out-of-155

Page 7 of 39



Draft


season until the end of the study, to capture the period over which female eggs hatched 156

at the study site. Two boats participated in the in-season sampling, each doing 1-3 trips 157

per week and hauling on average 240 traps per trip. The out-of-season sampling was 158

done by 1 boat making 3-4 trips per week and sampling on average 60 traps per trip. 159

Traps were always soaked for 24 hours before being surveyed, at which time the size 160

(carapace length) and developmental status (see below) of ovigerous females were 161

recorded. Carapace length (CL) was measured as the distance from the posterior edge 162

of the eye socket to the posterior edge of the cephalothorax, on a line parallel to the 163

centerline of the carapace. 164

165

Water temperature 166

Two HOBO Pro v2 Data Loggers (U22-00) were attached <1 m above the bottom 167

using a stationary mooring at a depth of ~18 m inside Cheticamp Harbour, within the 168

fishing ground, and programmed to record temperature at 30 minute intervals from June 169

to August. We estimated daily temperature values by taking the average of the 48 170

recordings made by each logger during a given day. Unfortunately, the time period over 171

which the loggers were deployed was not sufficient to predict the entire hatch period, 172

and we thus had to estimate the missing temperature data (August 16th – September 173

17th). We projected the missing data by fitting a second order polynomial to the existing 174

data (m = -0.0026x2 + 0.4539x, b = +0.7504) (Fig. 1), which provided a very strong fit 175

(R2 = 0.96) and mimicked the decrease in water temperature that is known to occur in 176

the region in late summer, a pattern that we confirmed using both historical SST data for 177

our study site (DFO 2013a) and 2012 bottom temperature data (DFO, pers. comm.) for 178

Page 8 of 39



Draft


Pleasant Bay, a fishing ground located ~10km from our study site. Note that we also 179

used a second approach to estimate the missing temperature data, based on difference 180

in bottom temperature between our study site and Pleasant Bay, and the two 181

approaches yielded similar temperature estimates and led to identical conclusions, 182

which is not surprising given that hatch time of samples collected within the fishing 183

season (the focus of this study) was almost entirely estimated using actual (rather than 184

estimated) temperature data from the study site. For example, using in-season samples 185

obtained 18 days before the beginning of hatch, the percentage of predicted hatch 186

dates that fell after August 15th, and hence required some reliance on estimates of 187

temperature, was ≤6% for the different models. 188

189

Observed Timing of Hatch 190

Timing of hatch in the field was observed by monitoring the progression of egg 191

development of ovigerous females. Each female’s clutch of eggs was categorized as 192

one of four developmental stages, based primarily on the colour and appearance of the 193

eggs in the clutch. Eggs in a stage I clutch have no visible “embryo eye”, are small, dark 194

green to black in colour and are tightly packed together. Eggs in a stage II clutch have 195

visible embryo eyes and they are dark–medium brown in colour. Eggs in a stage III 196

clutch are light brown to orange in colour, comprise fully developed embryos, are 197

loosely packed together and are close to hatching. A stage IV clutch comprises eggs 198

that are hatching and adhesive glue can be seen on the female’s abdomen along with 199

empty egg cases (MacKenzie et al. 2011). By observing the proportion of ovigerous 200

females with eggs in each of these stages over the course of the spring-summer we 201

Page 9 of 39



Draft


were able to monitor the temporal progression of embryonic development and obtain an 202

estimate of the period of time over which hatch occurred (henceforth the “hatch period”) 203

based on the presence of stage IV clutches. 204

205

Predicting Timing of Hatch 206

Timing of hatch in the field was predicted using small clusters of eggs removed 207

from a total of 227 ovigerous females with stage II or stage III clutches, 100 of which 208

were sampled prior to the hatch period (13th and 23rd of June; n=50 per trip) and 127 209

that were sampled during the hatch period (23 separate trips between July 4th and 210

August 16th). Fine tweezers were used to sample 8 small clumps of eggs spread 211

throughout the egg mass of each of these females. The eggs were placed in a 212

glycerine-ethanol solution (35:65%) in order to preserve the embryos and their size at 213

sampling. 214

The degree of embryonic development was measured by calculating the “Perkins 215

Eye Index” (henceforth PEI), which is the mean of the greatest width and length of an 216

embryo’s oval-shaped eye (Perkins 1972). We used a microscope (Leica S8AP0) at 80 217

X to measure the PEI on each of five eggs (preliminary tests with 4 females indicated 218

CV between 0.04 and 0.08, mean = 0.06) haphazardly selected from within each 219

female’s egg sample (eggs from 11 of the 227 females could not be processed due to 220

poor preservation). This measure of embryonic development (PEI) was then used in 221

conjunction with bottom temperature and Perkins’ (1972) and Gendron and Ouellet’s 222

(2009) embryonic development formulas to predict a future hatch date for each 223

individual embryo processed. Embryonic development (i.e., increase in PEI) was 224

Page 10 of 39



Draft


estimated on a daily basis and was added to the previous day’s PEI, beginning with the 225

initial PEI measurement and progressing until reaching PEI-at-hatch. This exercise was 226

carried out using two different embryonic growth formulas and different values of PEI-at-227

hatch. In terms of growth formulas, we used Perkins’ (1972) linear function: 228

229

� = −8.3151 + 2.6019(�)

230

where y is the embryonic growth rate expressed as change in PEI in microns per 231

week (we divided by 7 to obtain a daily rate), and x is water temperature, as well as 232

Gendron and Ouellet’s (2009) logarithmic function: 233

234

�� = 0.00002 ∗ ��.��

235

where PEIR is the change in PEI in mm per day, and t is water temperature. 236

237

We used two approaches for assigning values of PEI-at-hatch: (1) a fixed value 238

of 560 µm for all embryos, which is the mean of the three values reported in the 239

literature (Gendron and Ouellet 2009 (550 µm), Helluy and Beltz 1991 (570 µm), 240

Perkins 1972 (560 µm)), and (2) a frequency distribution of PEI-at-hatch values 241

observed during our study, which was obtained by measuring the PEI of newly hatched 242

prezoea that were found among egg samples taken from females in the process of 243

hatching larvae (60 prezoea from 7 females). The prezoea likely serves as an 244

appropriate indicator of PEI-at-hatch as it is a brief phase, thought to last only 24 hours, 245

Page 11 of 39



Draft


taken by a newly hatched lobster prior to its molt to larval stage I (Ennis 1975). As the 246

number of prezoea available to estimate PEI-at-hatch varied among females (n = 4 – 247

16), the proportion of each female’s prezoea that fell within each 1µm PEI interval 248

(460µm – 611µm) was calculated in order to avoid creating a frequency distribution 249

skewed by one or two females. A log-normal function was then fitted (R2 = 0.56, p = 250

0.0007) to this adjusted distribution of prezoea PEI and used to generate an estimate of 251

PEI-at-hatch for each embryo measured. This log-normal function was used to generate 252

PEI-at-hatch for all embryos with no consideration of maternal effects (e.g., female size) 253

as the majority of variability in prezoea PEI was found within clutches (64%) and there 254

was no significant relation between maternal size and PEI-at-hatch (R2 = 0.42, p > 255

0.10). 256

In total, therefore, four sets of predicted hatch dates were generated for five 257

embryos from each of 216 females through combinations of the linear and logarithmic 258

development functions and the two estimates of PEI-at-hatch. 259

260

Predicted versus Observed Timing of Hatch 261

To determine if, and how well, this approach can be used to predict hatch of 262

lobster in nature we addressed four questions: (1) do the predictions made by the four 263

models reflect the observed hatch period for Cheticamp?; (2) do the predictions made 264

by the four models reflect the observed progression of hatch in the hatch period?; (3) 265

does either of the two temperature-dependent embryonic development functions 266

perform better than the other?; (4) is the quality of the hatch predictions affected by the 267

estimate of PEI-at-hatch used? 268

Page 12 of 39



Draft


As the primary objective of this study is to determine whether the timing of larval 269

release can be predicted by sampling ovigerous females during the fishing season, all 270

main analyses are based on the two samples of females taken in-season, and prior to 271

the observed start of hatch (before July 1st). To assess the performance of different 272

models at predicting the hatch period (question 1) we compared the (a) number of 273

predicted hatches that fell within the hatch period, and (b) portion of the hatch period 274

that was covered by predicted hatch values. To assess the performance of different 275

models at predicting the progression of hatch (question 2) we compared predicted and 276

observed cumulative percentage of hatch on each of the 23 sampling dates (1-4 day 277

intervals) during the 50-day hatch period. To compare our four models’ ability to predict 278

the progression of hatch we used Akaike Information Criterion (AIC), where each 279

model’s residual sum of squares (RSS) was the sum of the squared differences 280

between observed and predicted cumulative hatch values for each of the 23 sampling 281

dates. We also included in this comparison a “null model”, which predicted a constant 282

proportion of hatch occurring on each of the 23 sampling dates (i.e., 4.3%). 283

284

Results 285

Water temperature at our study site was 6.9°C when we took our first sample of 286

eggs on June 13th, then it increased to a maximum of 20.3°C on August 8th, before 287

decreasing slightly to 19.0°C on September 17th, which is the latest day any of our 288

samples and models predicted hatching at our study site (Fig. 1). 289

290

Observed Timing of Hatch 291

Page 13 of 39



Draft


Ovigerous females with hatching (stage IV) clutches were observed on each 292

sampling date between July 4th and August 16th 2012 (Fig. 2). Hatching likely started 293

sometime between July 4th and June 23rd (the previous sample), given the abundance 294

of stage III females (close to hatching) in the June 23rd sample. Hatching ended on or 295

shortly after August 16th, our last date of sampling, because egg-bearing females 296

sampled on this day were either in the process of hatching (11% stage IVs) or had 297

newly extruded clutches that would not hatch until the following year (89% stage Is) 298

(Fig. 2). Due to the uncertainty around the exact day when hatch began (between June 299

23rd and July 4th) and ended (on or shortly after August 16th), the first and last observed 300

hatch dates plus 3 days was used to signify the beginning (July 1st) and end (August 301

19th) of hatch and create a 50-day hatch period. Whereas the addition of 3 days to the 302

first and last observed hatch dates was somewhat arbitrary, it likely resulted in a more 303

accurate description of the true hatch period. More importantly, all general conclusions 304

reached in this study were unchanged when we ran the analyses on a “non-modified” 305

hatch period or one that was further expanded (see examples in Discussion). 306

307

Predicted Timing of Hatch: 8-day versus 18-day samples 308

Using samples obtained 8 days prior to the beginning of hatch, hatch was 309

forecast 1–63 and 1-35 days in the future with the linear and logarithmic models, 310

respectively. Using samples obtained 18 days prior to hatch, these numbers increase to 311

11-75 and 9-46 days (Fig. 3). Predictions made with samples obtained 8 and 18 days 312

before the beginning of hatch were remarkably similar (Fig. 4) and we only present 313

Page 14 of 39



Draft


hereafter results pertaining to eggs sampled 18 days prior to the beginning of hatch, for 314

simplicity. 315

316

Predicted versus Observed Timing of Hatch: The Hatch Period 317

The vast majority (91-100% for different models) of predicted hatch dates of 318

individual embryos sampled 18 days prior to the beginning of hatch fell within the 319

observed hatch period, both for the linear (96 % using both the fixed and variable PEI-320

at-hatch values, respectively) and the logarithmic (91 % or 100 %) development 321

functions. However, the linear development functions did a better job at predicting the 322

entirety of the hatch period than the logarithmic functions (Fig. 5). For example, the 323

proportion of days of the 50-day observed hatch period that was forecast by the linear 324

temperature-dependent functions was very high (84 or 100% using the fixed and 325

variable PEI-at-hatch values, respectively) and markedly greater than that forecast by 326

the logarithmic temperature-dependent function (54 or 58%) (Fig. 5). In particular, and 327

in contrast to the linear temperature-dependent functions, the logarithmic temperature-328

dependent functions failed to capture later hatches, predicting no hatching during the 329

last 22 (fixed PEI-at-hatch) or 21 (variable PEI-at-hatch) days of the 50-day hatch 330

period. 331

Samples obtained out of season, after hatch had begun, predicted increasingly 332

later hatch dates on average (Fig. 5), likely because they comprised increasingly fewer 333

of the earlier hatching females as these would already have hatched their eggs and 334

been removed from the population. More surprisingly, however, predictions made from 335

Page 15 of 39



Draft


samples obtained after mid-July began predicting hatches extending beyond the 336

observed hatch period, and also beyond hatch dates predicted by in-season samples. 337

The predictive ability of the models was also affected by the PEI-at-hatch values 338

used as hatching endpoints, although this effect was less pronounced than that of the 339

temperature development functions (Fig. 5). Using PEI-at-hatch values observed during 340

this study produced a greater range of predicted hatch dates (17 and 11-day increase 341

for the linear and logarithmic temperature-dependent functions, respectively) compared 342

to using the mean PEI-at-hatch from the literature, and it increased the portion of the 343

observed hatch period that was predicted by 16% and 4% for the linear and logarithmic 344

development functions, respectively. 345

Overall, the hatch period was best predicted by the model that used the linear 346

temperature-dependent development function and the site-specific frequency 347

distribution of PEI-at-hatch. Using this model and samples obtained 18 days prior to the 348

beginning of hatch, 96% of predicted hatch dates of individual embryos fell within the 349

hatch period and 100% of the 50-day period of hatch was forecast. 350

351

Predicted versus Observed Timing of Hatch: Progression during the Hatch Period 352

In addition to predicting the timing and range of the hatch period with a high level 353

of accuracy, the models also tracked the cumulative progression of hatch within the 354

hatch period with relative success (Fig. 6). The observed hatch rate was fairly constant 355

over the hatch period, only showing a modest peak around days ≈15-20 of the 50-day 356

hatch period (Fig. 6). 357

Page 16 of 39



Draft


Of the 5 models compared, the linear development function with variable PEI-at-358

hatch and the null model based on “uniform hatch” best predicted cumulative hatch 359

throughout the 50-day hatch period. These two models performed similarly (Table 1), 360

yielding nearly identical AICc values and weights (Anderson 2008). Using the null 361

model, the average deviation between predicted and observed cumulative frequency of 362

hatch across the 23 timesteps was 8.6%, and the single greatest deviation was at 18 363

days into the hatch period, when the model predicted 39% of hatching to be completed 364

when in actuality 61% of hatch had been observed (22% deviation). Using the linear 365

model with variable PEI-at-hatch the average deviation between predicted and 366

observed cumulative frequency of hatch was 8.1%, and the single greatest deviation 367

was at 13 days into the hatch period, when the model predicted 26% of hatching to be 368

completed when in actuality 49% had been observed (23% deviation). The other three 369

models produced average deviations ranging from 14.2-24.1% and maximum deviations 370

between 31.7-51.4 %. 371

372

Discussion 373

Our study indicates that we can predict with accuracy hatch of American lobster 374

up to 67 days in the future using egg samples collected up to 18 days prior to the 375

beginning of hatch, temperature-dependent development functions developed in the lab 376

and development endpoints based on prezoea eye size. The strength and usefulness of 377

a best model in this context is a function of two complimentary and necessary 378

properties: (1) its predictions must fall within the observed hatch period, and (2) the 379

observed hatch period must be predicted in its entirely. If all predictions fell within a 380

Page 17 of 39



Draft


large hatch period but only captured a small proportion of this hatch period, then our 381

model would be weak, because predictions of hatch time and dispersal would only 382

cover a small portion of reality. Conversely, if our predictions covered all days of the 383

observed hatch period because they ranged widely and often extended beyond the true 384

hatch period, then our model would again be weak. A useful model in this context is one 385

that has both of these properties. 386

Of the two different temperature-dependent embryonic growth functions 387

proposed in the literature, Perkins’ (1972) linear function outperformed the logarithmic 388

function (Gendron and Ouellet 2009) in terms of forecasting hatch, based on the two 389

criteria outlined above. More specifically, using 250 eggs sampled 18 days prior to the 390

beginning of hatch, the linear temperature-dependent function successfully predicted 391

100% of the 50 days comprising the observed hatch period, and only 1% (variable PEI-392

at-hatch) of predicted hatch dates were more than five days before (max 6 days) or after 393

(max 8 days) this period. In contrast, the logarithmic temperature-dependent function 394

appeared to overestimate the rate of embryonic development, as with both the variable 395

and fixed PEI-at-hatch values the logarithmic models predicted hatching to end 21 or 22 396

days earlier than the end of the 50-day hatch period. 397

In addition to the error surrounding our predicted hatch dates, there was also 398

some uncertainty surrounding the true hatch period, caused in part by the fact that we 399

did not sample every day. However, this uncertainty is relatively small and it seemed to 400

have negligible impact on the accuracy of predictions. For example, if we had not semi-401

arbitrarily extended the tails of the hatch period by 3 days (44 days instead of 50 days) 402

relative to the dates when females with hatching eggs were actually sampled, the 403

Page 18 of 39



Draft


proportion of predicted hatch dates that would have fallen within the hatch period using 404

the linear model with variable PEI-at-hatch, which is the model with the greatest range 405

of predicted hatch dates (i.e., provides the most stringent comparison), would only have 406

dropped from 96% to 92%. Similarly, if we had extended the hatch period by 10 days 407

(instead of three) on both ends (64 days total instead of 50 days), we would still 408

successfully have predicted 100% of the hatch period and 100% of predictions would 409

have fallen in this period. In fact, the uncertainty surrounding the real hatch period likely 410

means that our results may to some degree understate the true accuracy of the 411

approach. Furthermore, that this uncertainty had such a small impact on the accuracy of 412

model predictions also means that our conclusion that the linear development function 413

with variable PEI at hatch best modeled the hatch period is unlikely to be compromised 414

by this error. The small adjustment we made to the “observed hatch period” almost 415

certainly decreased the error surrounding this estimate, but most importantly it did not 416

affect the main inferences of our study. 417

Another potential source of error surrounding our observed hatch data relates to 418

“catchability” of female lobsters with stage IV clutches, or more specifically whether the 419

propensity of these individuals to enter our baited traps changed over the course of the 420

study. The catch-per-unit-effort (CPUE) of adult lobsters has been shown to correlate 421

with their abundance on the bottom, although the match is not perfect due to density- 422

and environmentally-mediated changes in lobster behavior and trap saturation (e.g., 423

Watson and Jury 2013). Whereas we have no means of directly assessing such 424

potential errors, we made efforts to eliminate them and don’t believe they challenge our 425

main inferences. In particular, our traps were the only traps in the water during the 426

Page 19 of 39



Draft


hatching period and we maintained a relatively constant sampling effort in our ≈7.5 km2 427

study area during this period (3-4 boat trips/week, 60 traps/trip and a 24-hour soak 428

time). Also, water temperature during the hatch period varied between 13-20°C, a range 429

of temperatures over which movement rates and catchability of American lobsters do 430

not appear to vary (McLeese and Wilder 1958). Although not enabling a rigorous test of 431

the catchability bias hypothesis, our catch data of egg-bearing females do not raise any 432

concerns over the presence of such a bias as they clearly show the stage II-III clutches 433

gradually becoming stage IV clutches, and then these stage IV clutches being gradually 434

replaced by females with new clutches (stage I) that will hatch the following year. A 435

catchability bias is greatly limited here by the fact that we are using catch data to assess 436

changes in the abundance of a same type of lobster (females with stage IV clutches) 437

over a relatively small area and time period and under fairly constant sampling effort 438

and environmental conditions. 439

In addition to accurately predicting the overall hatch period, our four models also 440

did a reasonable job predicting the progression of hatch within this period, and here 441

again the best linear model (with variable PEI-at-hatch) outperformed the best 442

logarithmic model (with fixed PEI-at-hatch). For example, the average and maximum 443

deviations between observed and predicted cumulative hatch over the 23 sampling 444

dates were 8.1% and 23.1 % for the former versus 14.2% and 31.7% for the latter, and 445

these differences arose mainly because the log model predicted hatch to be completed 446

≈3 weeks earlier than was observed. The average (8.1%) and maximum (23.1%) 447

deviations between observed and predicted cumulative hatch for our best model (linear 448

with variable PEI at hatch) were comparable to deviations obtained with the null model 449

Page 20 of 39



Draft


of uniform hatch (8.6% and 22.2%, respectively), as were their respective AICc scores 450

and weights. We do not believe these results reflect failure of our best model, but rather 451

the fact that hatch did indeed progress relatively uniformly throughout the hatch period 452

during our study, given the small and similar deviations between observed and 453

predicted progression of hatch for our best model and the null model. The progression 454

of hatch in American lobster has been shown to vary markedly in different years and 455

locations (Fogarty 1983, Scarratt 1964), sometimes showing a marked peak period of 456

hatch and in other years showing more uniform hatching over time. We believe it is 457

likely that the temperature-dependent development functions will track to some extent 458

deviations from uniform hatch where and when that occurs, and are currently 459

undertaking further validations of these outcomes. 460

461

Considering Variability in PEI-at-Hatch Improves Model Predictions 462

The addition of a development endpoint based on variability of PEI-at-hatch of 463

prezoea observed within our samples increased the range of predictions made by both 464

temperature-dependent functions, relative to using a fixed mean value derived from the 465

literature, and it resulted in a better fit with the observed hatch period. For example, 466

when PEI-at-hatch was based on the size-frequency distribution of values found for 467

prezoea obtained in our samples, the proportion of the hatch period predicted increased 468

from 84% to 100%, and from 54% to 58%, for the linear and the logarithmic 469

development functions, respectively, and the mean deviation between observed and 470

predicted cumulative hatch frequency decreased from 18.1% to 8.1% for the linear 471

development function (see below for logarithmic function). 472

Page 21 of 39



Draft


This positive effect of including PEI-at-hatch in our predictions is not surprising, 473

given that it varied considerably among prezoea (460-611µm, n = 60). Interestingly, 474

64% of this variability was between prezoea of a same clutch, which is consistent with 475

the observation that a same female can hatch its embryos over a period of 2-4 weeks 476

(Ennis 1975). Within the clutch of a single female, the range of PEI-at-hatch was as high 477

as 492-611µm (n=16 prezoea), which is almost the entire range of PEI-at-hatch values 478

observed among the 60 prezoea we sampled from seven females. Between these 479

seven females, mean PEI-at-hatch varied by as much as 49µm. Somewhat surprisingly, 480

however, for the logarithmic model the mean deviation between observed and predicted 481

cumulative hatch values increased (not decreased) slightly from 14.2 % to 24.1 % with 482

inclusion of this variable endpoint. This small change may not be meaningful, 483

considering the errors associated with our different estimates, but it does support our 484

conclusion that the later stages of lobster embryo development may be better described 485

by the linear than the logarithmic function, given that the inclusion of observed variability 486

of PEI-at-hatch undoubtedly better approximates reality than using a mean value. 487

Although variability of PEI-at-hatch within or among females has not been 488

systematically quantified, it is evident from at least two studies (Helluy and Beltz 1991; 489

Fig. 1.1 in Gendron and Oulette 2009). Those findings, along with results of our study, 490

suggest that improved forecasting can likely be achieved by further characterization of 491

the variability in PEI-at-hatch. Interestingly, the mean PEI-at-hatch determined in this 492

study (520µm) was substantially smaller than that previously reported in the literature 493

(550µm -570µm), suggesting that future studies are also needed to more rigorously 494

contrast PEI-at-hatch among regions. 495

Page 22 of 39



Draft


496

Temporal Trends in Predicted Hatch Dates 497

There was a strong temporal trend in the hatch dates predicted, with samples 498

obtained after the beginning of hatch predicting increasingly later aggregated hatch 499

dates. This pattern is easily explained. As sampling progresses past the beginning of 500

hatch, early hatchers are lost, leading to later samples predicting later aggregated hatch 501

dates than the samples taken prior to the start of hatch, when all embryos to be hatched 502

in the coming season are still present. 503

There was, however, another temporal pattern in our data that is not as readily 504

explained, which is that females sampled mid-July onwards (well into the hatch period) 505

generated some predicted hatch dates beyond the observed hatch period, and also 506

beyond hatch dates predicted by in-season samples. One possible explanation for this 507

pattern is that later samples may have comprised females that migrated to the sampling 508

site from deeper waters after the fishing season, and hence were not present in pre-509

hatch samples. For example, in the Gulf of Maine larger ovigerous females migrate to 510

deeper offshore waters during the gestation period and then move inshore to release 511

their larvae (Cowan et al. 2007). If lobsters from our study area in the southern Gulf of 512

St Lawrence behave similarly, then such behavior may lead to a staggered regional 513

hatch period. However, if such offshore-inshore movements are displayed by female 514

lobsters in our study area they do not appear to be related to female size, as the 515

carapace length of sampled females did not change over the course of the study (N = 516

227, m = 0.077, R2 = 0.009, P = 0.16) and the mean carapace length of females with 517

embryos predicted to hatch within and outside the hatch period was similar (t214 = 1.97, 518

Page 23 of 39



Draft


p < 0.32). This does not, of course, preclude a change in the population of egg-bearing 519

females over the course of the sampling period unrelated to body size. 520

521

Application and Recommendations 522

In this study the first egg samples were collected during the fishing season 18 523

days prior to the start of hatch, which proved adequate to predict the entire hatch 524

period, up to 67 days in the future. Importantly, the fishing season is sufficiently close to 525

the beginning of hatch throughout much (but see below) of the species’ range for such 526

relatively short-term forecasting to be sufficient. 527

The method outlined in this paper may be most immediately applicable to the 528

development of bio-physical models of larva dispersal used to elucidate connectivity 529

amongst management areas. For example, larval release simulations made with a new 530

dispersal model for lobster larvae encompassing the species’ geographic range 531

(Brickman and Drozdowski 2012; Quinn 2014) indicate that hatches occurring 2 weeks 532

later than observed during our study would have resulted in drift distances increasing by 533

~40 km (B.K. Quinn, University of New Brunswick, pers. comm.). These findings 534

indicate that accurate estimates of hatch time will likely markedly improve connectivity 535

estimates made by bio-physical models of larva dispersal. 536

Although our findings unequivocally demonstrate the usefulness of the approach 537

to predict hatch time of lobster larvae in nature, and includes recommendations of 538

particular development functions and endpoints to use, more work should be done to 539

refine the method and better understand its limitations and context specificity. First, it 540

must be realized that our comparisons of development models are specific to the time 541

Page 24 of 39



Draft


period over which forecasting was done, which is short (≈60 days) relative to the 542

complete embryo development period (≈300 days). In other words, the models that 543

were successful at predicting development and hatch in this study may not do a good 544

job at predicting development from spawn to hatch. Whereas such long-term forecasting 545

was not the objective of this study, it would nevertheless be important to assess the 546

ability of the method to accommodate areas where there exists a larger disconnect 547

between the end of fishing season (and potential sampling) and the end of hatch (for 548

example, ≈90 days in LFA 33 and LFA 34 in Canada (DFO 2004, DFO 2013b)). 549

Second, over the time period investigated, the linear development function with 550

variable PEI-at-hatch was the best of the four models tested to predict the hatch period, 551

but none of the 4 study models outperformed the “null model” of uniform hatch to predict 552

the progression of hatch during the hatch period (the best “biological model” and the null 553

model appeared equally adequate). More work is needed to assess the generality of 554

this finding, and we expect that a biological model will in most natural scenarios better 555

predict the progression of hatch than the null model, despite the results found in this 556

study, where observed hatch rates did seem relatively uniform over the hatch period. 557

Third, it will similarly be important to repeat these tests in different regions, to ensure the 558

development functions perform well in different temperature conditions. Finally, it would 559

be worth doing additional tests in nature where egg-bearing females would be confined 560

and have their eggs monitored on a regular basis, which would enable a more direct 561

correlation between predicted and observed hatch of individual females instead of the 562

“aggregated relation” quantified in this study. 563

Page 25 of 39



Draft


564

Acknowledgments 565

Berried female data and egg samples were provided by Raja Wetuschat, Julie 566

Murdoch, Michel Comeau, Leonard Leblanc and the Gulf Nova Scotia Fishermen’s 567

Coalition. This project was funded by grants to R. Rochette from the Lobster Node of 568

the NSERC Canadian Fisheries Research Network (CFRN) and the NBIF Research 569

Innovation Fund, as well as a NSERC Discovery grant. E. Miller and M. Haarr were also 570

funded by the CFRN. 571

572

References 573

574

Anderson, D. R. 2008. Model based Inference in the Life Sciences. Springer, New York. 575

576

Annis, E.R., Incze, L.S., Wolff, N., and Steneck, R.S. 2007. Estimates of in situ larval 577

development time for the lobster, Homarus americanus. J. Crust. Biol. 27(3): 454-462. 578

doi: 10.1651/S-2758.1. 579

580

Brickman D., and Drozdowski, A. 2012. Development and Validation of a Regional Shelf 581

Model for Maritime Canada Based on the NEMO-OPA Circulation model. Can. Tech. 582

Rep. Hydror. Ocean Sci. 278: vii +57 p 583

584

Chassé, J., and Miller, R.J. 2010. Lobster larval transport in the southern Gulf of St. 585

Lawrence. Fish. Oceanogr. 19(5): 319-338. doi: 10.1111/j.1365-2419.2010.00548.x. 586

Page 26 of 39



Draft


587

Cowan, D.F., Watson, W.H., Solow, A.R., and Mountcastle, A.M. 2007. Thermal 588

histories of brooding lobsters, Homarus americanus, in the Gulf of Maine. Mar. Biol. 589

150(3): 463-470. doi: 10.1007/s00227-006-0358-5. 590

591

Department of Fisheries and Oceans Canada. 2004. South Shore Nova Scotia Lobster 592

(LFA 33). DFO Sci. Stock Stat. Rep. 2004/038. 593

594

Department of Fisheries and Oceans Canada. 2013a. The Sea-surface Temperature 595

(SST) Database: Satellite measurements of (nominally) weekly-averaged surface 596

temperature for the Northwest Atlantic. Department of Fisheries and Oceans, Canada. 597

http://www.bio.gc.ca/science/data-donnees/base/data-donnees/sst-en.php. Database 598

accessed on – 13 September 2013 599

600

Department of Fisheries and Oceans Canada. 2013b. Assessment of Lobster (Homarus 601

americanus) in Lobster Fishing Area (LFA) 34. DFO Can. Sci. Advis. Sec. Sci. Advis. 602

Rep. 2013/024 603

604

Department of Fisheries and Oceans Canada. 2014. Facts on Canadian Fisheries: 605

Lobster [online]. Available from http://www.dfo-mpo.gc.ca/fm-gp/sustainable-606

durable/fisheries-peches/lobster-homard-eng.htm [accessed 28 August 2014] 607

608

Page 27 of 39



Draft


Ennis, G.P. 1975. Observations on Hatching and Larval Release in the Lobster 609

Homarus americanus. J. Fish. Res. Board Can. 32(11): 2210-2213. doi: 10.1139/f75-610

260. 611

612

Ennis, G.P. 1986. Stock Definition, Recruitment Variability, and Larval Recruitment 613

Processes in the American Lobster, Homarus americanus: A Review. Can. J. Fish. 614

Aquat. Sci. 43(11): 2072- 2084. doi: 10.1139/f86-256. 615

616

Ennis, G.P. 1995. Larval and postlarval ecology. In Biology of the Lobster Homarus 617

americanus. Edited by R.J. Factor. Academic Press, Toronto. pp. 23-46. 618

619

Fogarty, M.J. 1983. Distribution and relative abundance of American lobster, Homarus 620

americanus, larvae: New England investigations during 1974-79. NOAA Tech. Rep. 621

NMFS SSRF-775, 64 p. 622

623

Gendron, L., and Ouellet, P. 2009. Egg development trajectories of early and late-624

spawner lobsters (Homarus americanus) in the Magdalen Islands, Québec. J. Crust. 625

Biol. 29(3): 356-363. doi: 10.1651/08-3098.1. 626

627

Harding, G.C., and Trites, R.W. 1988. Dispersal of Homarus americanus Larvae in the 628

Gulf of Maine from Browns Bank. Can. J. Fish. Aquat. Sci. 45(3):416-425. 629

doi:10.1139/f88-050. 630

631

Page 28 of 39



Draft


Helluy, S.M., and Beltz, B.S. 1991. Embryonic development of the American lobster 632

(Homarus americanus): Quantitative staging and characterization of an embryonic molt 633

cycle. Biol. Bull. 180(3): 355-371. 634

635

Hudon, C., and Fradette, P. 1988. Planktonic Growth of Larval Lobster (Homarus 636

americanus) off îles de la Madeleine (Quebec), Gulf of St. Lawrence. Can. J. Fish. 637

Aquat. Sci. 45(5): 868-878. doi: 10.1139/f88-105. 638

639

Incze, L., and Naime, C.E. 2000. Modelling the transport of lobster (Homarus 640

americanus) larvae and postlarvae in the Gulf of Maine. Fish. Oceanogr. 9: 99-113. doi: 641

10.1046/j.1365-2419.2000.00125.x. 642

643

Incze, L.S., Wahle, R.A., Wolff, N., Wilson, C., Steneck, R., Annis, E., Lawton, P., Xue, 644

H., and Chen, Y. 2006. Early Life History and a Modeling Framework for Lobster 645

(Homarus americanus) Populations in the Gulf of Maine. J. Crust. Biol. 26(4): 555-564. 646

doi: 10.1651/S-2764.1. 647

648

MacKenzie, B.R. 1988. Assessment of temperature effects on interrelationships 649

between stage durations, mortality, and growth in laboratory-reared Homarus 650

americanus Milne Edwards larvae. J. Exp. Mar. Biol. Ecol. 116: 87-98. doi: 651

10.1016/0022-0981(88)90248-1. 652

653

Page 29 of 39



Draft


MacKenzie, C., King, P., King, M. 2011. Canadian Capture Fisheries Research Network 654

Lobster Science Training Manual. Available from http://www.cfrn-rcrp.ca/Public-655

Products-EN [accessed 29 September 2014] 656

657

McLeese, D. W., Wilder, D.G. 1958. The Activity and Catchability of the Lobster 658

(Homarus americanus) in Relation to Temperature. J. Fish. Res. Board Can. 15(6): 659

1345-1354. doi: 10.1139/f58-073 660

661

Miller, R.J. 1995. Fisheries Regulations and Methods. In Biology of the Lobster 662

Homarus americanus. Edited by R.J. Factor. Academic Press, Toronto. pp. 89-108. 663

664

Miller, R.J. 1997. Spatial differences in the productivity of American lobster in Nova 665

Scotia. Can. J. fish. Aquat. Sci. 54(7): 1613-1618. doi: 10.1139/f97-068. 666

667

Miller, R.J., Mallet, M., Lanteigne, M., MacMillan, Robert. 2006. Bottlenecks to Fishery 668

Yield for American Lobster in a Portion of the Gulf of St. Lawrence. N. Am. J. Fish 669

Manage. 26(3): 765-776. doi: 10.1577/M05-001.1 670

671

Milne Edwards, H. 1837. Histoire naturelle des Crustacés, comprenant l'anatomie, la 672

physiologie et la classification de ces animaux. Volume 2. Librairie encyclopédique de 673

Roret, Paris, Fr. 674

675

Page 30 of 39



Draft


National Oceanic and Atmospheric Administration. 2014a. Imports and Exports of 676

Fishery Products, Annual Summary, 2012 [online]. Available from 677

http://www.st.nmfs.noaa.gov/st1/trade/documents/TRADE2012.pdf [accessed 28 678

August 2014] 679

680

National Oceanic and Atmospheric Administration. 2014b. American Lobster 681

Information Sheet [online]. Available from 682

http://www.greateratlantic.fisheries.noaa.gov/nr/2014/February/american_lobster_info_s683

heet_2.12.14.pdf [accessed 28 August 2014] 684

685

Perkins, H.C. 1972. Developmental Rates at Various Temperatures of Embryos of the 686

Northern Lobster (Homarus Americanus Milne-Edwards). Fish. Bull. 70(1): 95-99. 687

688

Quinn, B.K. 2014. Assessing potential influence of larval development time and drift on 689

large-scale spatial connectivity of American lobster (Homarus americanus). MSc thesis, 690

University of New Brunswick, Saint John, NB. 691

692

Scarratt, D. J. 1964. Abundance and distribution of lobster larvae (Homarus 693

americanus) in Northumberland Strait. J. Fish. Board Can. 21(4): 661-680. doi: 694

10.1139/f64-060 695

696

Templeman, W. 1937. Egg-laying and hatching postures and habits of the American 697

lobster (Homarus americanus). J Biol. Board Can. 3(4): 339-342. doi: 10.1139/f37-017 698

Page 31 of 39



Draft


699

Templeman, W. 1940. Embryonic Developmental Rates and Egg laying 700

of Canadian Lobsters. J. Fish. Res. Bd. Can. 5a(1): 71-83. doi: 10.1139/f40-009 701

702

Watson III, W.H., Jury, S.H., 2013. The relationship between American lobster catch, 703

entry rate into traps and density. Mar. Biol. Res. 9(1): 59–68. doi: 10.1139/cjfas-2013-704

0061 705

706

Xue, H., Incze, L., Xu, D., Wolff, N., and Pettigrew, N. 2008 Connectivity of lobster 707

populations in the coastal Gulf of Maine: Part I: Circulation and larval transport potential. 708

Ecol. Model. 210(1-2):193-21. doi: 10.1016/j.ecolmodel.2007.07.024 709

710

711

712

713

714

715

716

717

718

719

Page 32 of 39



Draft


Table 1. Comparison by Akaike’s information criterion (corrected for small sample size) 720

of accuracy of predictions of cumulative hatch made by five models based on egg 721

samples obtained 18 days prior to the beginning of hatch. 722

Model

a

RSS

b AICc

c ∆AICc

d wie

Null 0.271995 -42.32483

0.248596 0.467843

Linear Fixed 1.590994 -24.68137

17.89206

6.9E-05

Logarithmic Fixed 0.791062 -31.6609

10.91252

0.002262

Linear Variable 0.26531 -42.57342

0

0.529764

Logarithmic

Variable

1.624387 -24.47388

18.09954

6.22E-05

aThe five models compared are a null model of constant hatch throughout the hatch period and four

different temperature-dependent models of embryo development and hatch: linear formula of embryo

development with fixed PEI-at-hatch; logarithmic formula of embryo development with fixed PEI-at-hatch;

linear formula of embryo development with variable PEI-at-hatch; and logarithmic formula of embryo

development with fixed PEI-at-hatch.

bRSS is residual sum of squares

cAICc is Akaike’s information criterion (corrected for small sample size)

d∆AICc is the difference between the AICc score of each model and the score of the best model

ewi is Akaike weight.

Page 33 of 39



DraftDate

01/6/12 01/7/12 01/8/12 01/9/12 01/10/12

Tem

per

atu

re (

deg

rees

C)

4

6

8

10

12

14

16

18

20

22

Observed temperature

Estimated temperature

Figure 1: Observed (black circles) and estimated (white circles) temperature in the lobster fishing grounds

in Cheticamp, Nova Scotia, between June 1st and September 30th 2012. Observed temperatures were

based on the average daily temperature recorded by 3 temperature loggers. Temperature data extending

beyond the sampling period (August 16th – September 30th) was estimated by fitting a second order

polynomial to the existing data (m = -0.0026x2 + 0.4539x, b = +0.7504) (R2 = 0.96). The dashed line

marks the latest date at which a lobster embryo was predicted to hatch based on samples collected

during the fishing season.

Page 34 of 39



Draft

Sampling date

07/5 21/5 04/6 18/6 02/7 16/7 30/7 13/8

Pro

po

rtio

n o

f o

vige

rou

s fe

mal

es

0.0

0.2

0.4

0.6

0.8

1.0

Stage I

Stage II

Stage III

Stage IV

Figure 2: The observed hatch window indicated by the proportion of ovigerous females sampled from

early-May to mid-August 2012 in Cheticamp, NS, with eggs at different stages of development. Each

female’s clutch of eggs was categorized as one of four developmental stages, based primarily on the

colour and appearance of the eggs in the clutch. Eggs in a stage I clutch have no visible “embryo eye”,

are small, dark green to black in colour and are tightly packed together. Eggs in a stage II clutch have

visible embryo eyes and they are dark–medium brown in colour. Eggs in a stage III clutch are light brown

to orange in colour, comprised of fully developed embryos, are loosely packed together and are close to

hatching. A stage IV clutch has begun hatching and adhesive glue can be seen on the female’s abdomen

along with empty egg cases.

Page 35 of 39



Draft

Embryo development and hatch model

Hat

ch f

ore

cast

(d

ays)

0

20

40

60

80

100

LINF LOGF LINV LOGV

Figure 3: Number of days after sampling that hatch was predicted to occur using samples collected 8

(white box) and 18 (shaded box) days prior to hatch in 2012 in Cheticamp, Nova Scotia, based on our

four different temperature-dependent models of embryo development and hatch: linear function of embryo

development with fixed PEI-at-hatch (LINF); logarithmic function of embryo development with fixed PEI-

at-hatch (LOGF); linear function of embryo development with variable PEI-at-hatch (LINV); and

logarithmic function of embryo development with fixed PEI-at-hatch (LOGV). Boxes show 25th, 50th, and

75th percentile, whiskers represent 10th and 90th percentiles and black circles represent the 5th and 95th

percentiles.

Page 36 of 39



Draft

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sam

ple

d 8

day

s p

rio

r to

th

e b

egin

nin

g o

f h

atch

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Sampled 18 days prior to the beginning of hatch

A B

C D

Figure 4: Relation between cumulative timing of hatch predicted using eggs samples obtained 18 and 8

days prior to the beginning of hatch in 2012 in Cheticamp, Nova Scotia, using four models: linear formula

with fixed PEI-at-hatch (A); logarithmic formula with fixed PEI-at-hatch (B); linear formula with variable

PEI-at-hatch (C); and logarithmic formula with fixed PEI-at-hatch (D). Each point represents one of 23

sampling days during the 50-day hatch period.

Page 37 of 39



Draft

Sampling date

13/6/12 27/6/12 11/7/12 25/7/12 08/8/12

Hat

ch d

ate

17/6/12

01/7/12

15/7/12

29/7/12

12/8/12

26/8/12

09/9/12

23/9/12

13/6/12 27/6/12 11/7/12 25/7/12 08/8/12

17/6/12

01/7/12

15/7/12

29/7/12

12/8/12

26/8/12

09/9/12

23/9/12

A B

C D

Figure 5: Relation between predicted (circles) and observed (gray area) time of hatch in 2012 in

Cheticamp, Nova Scotia. Hatch time was predicted by measuring eye size of embryos in eggs of

ovigerous females sampled prior to hatch (gray circles) and after hatching had begun (black circles), and

projecting embryo development using different combinations (four panels) of two temperature-dependent

development functions: linear function with fixed PEI-at-hatch (A); logarithmic function with fixed PEI-at-

hatch (B); linear function with variable PEI-at-hatch (C); logarithmic function with variable PEI-at-hatch (D)

(see Methods). The observed hatch period is based on the presence of ovigerous females with recently

hatched eggs (see Fig. 2) in samples obtained by sampling out-of-season with fishermen.

Page 38 of 39



DraftSampling day

3 6 9 12 15 18 21 24

Pro

po

rtio

n o

f h

atch

co

mp

lete

d

0.0

0.2

0.4

0.6

0.8

1.0 LINF

LOGF

LINV

LOGV

NULL

OBSERVED

Figure 6: Observed (X), null (black circles) and predicted (4 other symbols) cumulative timing of hatch in

2012 in Cheticamp, Nova Scotia. The observed progression of hatch is based on the presence of

ovigerous females with recently hatched eggs (see Fig. 2) (see Methods), whereas predictions are based

on egg samples obtained 18 days prior to the beginning of hatch and four different temperature-

dependent models of embryo development and hatch: linear function of embryo development with fixed

PEI-at-hatch (LINF); logarithmic function of embryo development with fixed PEI-at-hatch (LOGF); linear

function of embryo development with variable PEI-at-hatch (LINV); and logarithmic function of embryo

development with fixed PEI-at-hatch (LOGV). Each point represents one of 23 sampling days during the

observed 50-day hatch period.

Page 39 of 39



Documents

TEMPERATURE EFFECTS < General, MARINE FISHERIES < General ... · Draft Predicting hatch time of American lobsters in nature 1 1 Using temperature-dependent embryonic growth models