1

ESTIMATE OF TOTAL INJURY TO DIAMONDBACK 

TERRAPINS FROM THE CHALK POINT OIL SPILL 

By Heath Byrd, Eric English, Richard Greer, Heidi Hinkelday, Wayne Kicklighter, 

Norman Meade, Jacqueline Michel, Ted Tomasi and Roger Wood1

February 25, 2002 

I. INTRODUCTION

This report was prepared by a subgroup of the Wildlife Injury Workgroup, which was established 

by the Natural Resource Trustee Council conducting the natural resource damage assessment of the April 

7, 2000 oil spill at Chalk Point, Maryland. The report presents a comprehensive estimate of injuries to 

diamondback terrapins (Malaclemys terrapin) inclusive of acute mortality, reduced survivability of 

hatchlings due to the oil and the loss of production in the next generation of terrapins following the spill.

Quantification of these injuries is presented in terms of terrapin years foregone. The trustees have found 

this to be a useful metric for purposes of identifying and evaluating restoration projects. These calculations 

are based in part on injury estimates found in the reports entitled: Acute Mortality of Diamondback 

Terrapins from the PEPCO Oil Spill, Patuxent River (Michel, et al., 2001) and Comparison of northern 

diamondback terrapin (Malaclemys terrapin terrapin) hatching success among variably oiled nesting sites 

along the Patuxent River following the Chalk Point Oil Spill of April 7, 2000 (Wood, et al., 2001). 

Estimates of the number of terrapin-years lost from acute mortality and next-generation production 

foregone were obtained using methods similar in concept to those found in the bird injury quantification 

report prepared for the North Cape oil spill natural resource damage assessment (Sperduto et al., 1999). 

The additional loss of terrapin years due to an increase in hatchling mortality in 2000 because of the oil spill 

is estimated by reducing survival of this life stage by 10% below normal (without oil) baseline. 

The diamondback terrapin ranges from the Gulf Coast of Texas to Cape Cod, Massachusetts, 

however, little information is available on the life history of this species. Thus, some data reported for 

several turtles belonging to the family Emydidae were used in the calculations. The average age of the 

population and the annual survival of terrapins in the absence of the oil spill were used to determine the 

injury in terrapin-years lost for the juveniles and adults killed by the spill (i.e., direct terrapin-years). 

Production foregone (i.e., the terrapin-years lost from the next generation that would have otherwise been 

produced by the terrapins that were killed directly by the oil) was estimated using the number of years an 

average-aged terrapin would have produced hatchlings and the number of terrapin-years the hatchlings 

would have been expected to live. The loss of hatchlings due to the oil was based on the field work of 

Wood, et al. (2001) and their best professional judgement (Wood, et al. 200-2002). In cases where a range 

of choices was available, a balance was sought between choosing parameter values that were either 

extremely high or extremely low. 

The analysis results in an estimate of 615.6 lost discounted terrapin-years from the direct mortality 

of 122 adults and juveniles. An additional 3,792.7 discounted terrapin-years were lost due to production 

foregone in the next generation. And an additional 836.3 discounted terrapin years were lost due to the 

10% increase in mortality of hatchlings in 2000. The total estimated injury is 5,244.6 lost discounted 

terrapin-years. 

 

1

 Hinkeldey and Michel: Research Planning, Inc.; Tomasi, Greer, Byrd, and Kicklighter: ENTRIX, Inc.; Wood: 

Richard Stockton College; English and Meade: NOAA. 
2

II. METHODS 

A. Direct Terrapin-Years Lost 

 The direct terrapin-years lost is estimated in three steps. First, the average age of a Patuxent River 

terrapin is estimated. It is assumed that all terrapins killed due to the oil spill were the average age. Second, 

it is recognized that there is less than a 100% probability that all terrapins alive in a given year survive to the 

next age class. The expected value of terrapin-years lost is estimated each year. The average survival rate is 

applied, and those expected to live to the next age class contribute one terrapin-year, while those who die 

sometime during the year are assumed to contribute 1⁄2 terrapin-year. Third, the terrapin years are discounted, 

and summed over future potential years of life --- from the average age through the maximum age. 

1. Age-Class Distribution and Average Age of the Population 

An age-class distribution for diamondback terrapins was created using survival rates from terrapin studies 

as well as other turtle species in the emydid family. Roosenburg (1990a), Wood, et al. (2000-2002) and 

others report that terrapin egg-to-hatchling survival rates range between 1% and approximately 30% in the 

wild. A survival rate of 20% was assumed for purposes of this study (Table 1). Survival rates for hatchling 

to year one, juvenile, and adult age classes for terrapins are unknown, however. Therefore, these rates were 

gathered for other emydid species from Heppell (1998) and Natureserve (2001) and applied to the Patuxent 

River terrapin population (Table 2). An annual survival rate was calculated for each age group: hatchlings 

(0-1 yrs), juveniles (1-4 yrs), subadults (4-7 yrs), and adults (> 7 yrs). These age groups were chosen based 

on Heppell's compilation of age group lengths for representatives of the emydid family (1998) and data 

from Roosenburg (1990a). 

Table 1. Population parameters for Patuxent River diamondback terrapins 

POPULATION PARAMETERS VALUES 

Population size 4,698 individualsa

Max attainable age 50 years 

Survivorship 

 Eggs to hatchling 0.20 

 Hatchlings to year 1 0.415b

 Hatchlings (0-1 yr: combined eggs 

 to hatchling + hatchling 

 survival to year 1) 

0.083b

 Juveniles (1-3 years) 0.662 annuallyb

 Subadults (4-6 yr) 0.862 annuallyb

 Adults (7+) 0.847 annuallyb

Age at 1st reproduction- males 4-7 yrs 

Age at 1st reproduction- females 8-13 yrs 

Ratio of Females: Males 3:1 

Clutch Frequency/yr 2 (range 1-3) 

Clutch size 13 (range 7-22) 

Expected No. of Eggs/Female per yr 26 

 a Michel, et al., 2001 

 bdenotes values extrapolated from several species in emydid family 

The overall hatchling survival rate was defined as the survival of the egg to hatchling multiplied by the 

survival of hatchlings to year one age classes. The probability of hatchling survival to year one was 

calculated by multiplying the egg to hatchling survival rate, 20% (Woods et. al., 2000-2002), by the average 
3

survival rate to year one and year one to year two from slider and painted turtles (.415, from juvenile 

category). Slider and painted turtle hatchling survival rates from Heppell (1998) were not used because they 

combined the egg to hatchling survival and survival to year one age classes, while egg to hatchling 

survivorship for terrapins was already available. It was not possible, given available information, to separate 

the two values (egg to hatchling survival and survival to year one) from the Heppell study data, so the slider 

turtle juvenile survival rates to year one and the painted turtle survival rates from year 1 to year 2 were used 

as surrogates for the terrapin hatchling survival rate. This gave a survival probability of 0.083 (0.415 * .20), 

the probability that a terrapin would survive to become a one year old juvenile once the egg was laid. These 

values appear to be reasonable estimates, given that the worst-case scenario for hatchling survival rates for 

the slider turtle was reported as .010 (Table 2). 

Juvenile terrapin survivorship was obtained by taking the average of all survivor rates from juvenile slider 

and painted turtles (.662). The survival rate for terrapin subadults and adults was calculated by taking an 

average of all rates given for slider, painted, and eastern box turtles (.862 and .847), respectively for 

subadults and adults. 

Table 2. Annual survival rates for emydidae turtles (Heppell 1998). 

 Hatchlingsa Juvenilesb Subadults Adults 

 (0-1yrs) (1-3 yrs) (4-6 yrs) (7+) 

Slider Turtle (Heppell 

1998) 

 

worst case 0.010 0.248(yr 1), .774 (yrs 

2-3) 

0.774 0.774 

medium case 0.105 0.539 (yr 1), .829 (yrs 

2-3) 

0.814 0.814 

best case 0.275 0.829 (yrs 2-3) 0.854 0.854 

mean 0.130 0.6438 0.814 0.814 

Painted Turtle 

Wilbur 1975 0.080 0.82 (yr 1-3) 0.82 

Tinkle et al. 1981 0.670 0.76 (yr 1-3) 0.76 0.76 

Mitchell 1988 0.193 0.457 (yr 1-2) 0.944 (yr 3-7) 0.96 

mean 0.314 0.679 0.841 0.846 

Eastern Box Turtle 

Natureserve 2001 0.93 .93-.94 

 74-.92 

 

Average .222 0.662 0.862 0.847 

 a Hatchling rates represent egg to hatchling survival plus hatchling to year one. 

 b Bold-faced juvenile survival rates were used for terrapin hatchling to year one survival rates (0.248, 0.539, 0.457, with a 

mean of 0.415). For years two and three, a .662 average survival rate is used . For years four, five and six, a .862 

average survival rate is used. And for years seven through fifty, a .847 average survival rate is used. 

Using the estimated survival rates for each age group, and a maximum attainable age of 50 years 

(Roosenburg, 1990a), an age-class table was created (Table 3). It was determined that terrapin hatchlings 

have an 8.3% probability of surviving to age one. To obtain the probabilities of surviving to the second 

year, the average survival rate of the second year (.662) is multiplied by the survival probability from the 

previous year (.083), and so on, for a total of 50 years. The third column is the probability that a hatchling 

lives to the associated age. 

To obtain the average age of the population requires two steps. First, the probability that a 

randomly chosen terrapin is a given age is computed (this is shown in Table 3, column 4). This equals the 

probability that a hatchling lives to that age (Table 3, column 3) divided by the sum of these probabilities 

(the sum of column 3). Then, the average age is computed. This is done by multiplying each age class 
4

(column 1) by the probability that an individual is that many years old (column 4), the result of which is 

shown in column 5, and adding up all the possible ages.2

 

The resulting average age of the Patuxent River diamondback terrapin population, based on the data in 

Table 3, is estimated to be 6.01 years. It is assumed that all terrapins killed as a result of the oil spill are 6 

years old. 

 

2

 More formally, let prx-1,x be the conditional probability that a hatchling survives to age x, given that it has survived to 

age x-1. Then the probability that a hatchling survives to age x is prx = prx-1(prx-1,x) with pr0 = 1. If P = Σx prx, then the 

probability that an individual chosen at random is age x is fx = prx/P. The average age in the population is then the 

usual expected value E(x) = Σx xfx. 
5

Table 3. Average age of juvenile and adult terrapins 

1 2 3 4 5 

Age Annual Survival 

Rate P(age) f(age) f(age)*Age 

1 0.083 0.083000 0.215646 0.215646 

2 0.662 0.054946 0.142758 0.285516 

3 0.662 0.036374 0.094506 0.283517 

4 0.862 0.031355 0.081464 0.325856 

5 0.862 0.027028 0.070222 0.351109 

6 0.862 0.023298 0.060531 0.363188 

7 0.847 0.019733 0.051270 0.358890 

8 0.847 0.016714 0.043426 0.347405 

9 0.847 0.014157 0.036782 0.331034 

10 0.847 0.011991 0.031154 0.311540 

11 0.847 0.010156 0.026387 0.290262 

12 0.847 0.008602 0.022350 0.268202 

13 0.847 0.007286 0.018931 0.246097 

14 0.847 0.006171 0.016034 0.224479 

15 0.847 0.005227 0.013581 0.203714 

16 0.847 0.004427 0.011503 0.184049 

17 0.847 0.003750 0.009743 0.165633 

18 0.847 0.003176 0.008252 0.148543 

19 0.847 0.002690 0.006990 0.132806 

20 0.847 0.002279 0.005920 0.118407 

21 0.847 0.001930 0.005015 0.105305 

22 0.847 0.001635 0.004247 0.093441 

23 0.847 0.001385 0.003597 0.082742 

24 0.847 0.001173 0.003047 0.073129 

25 0.847 0.000993 0.002581 0.064522 

26 0.847 0.000841 0.002186 0.056836 

27 0.847 0.000713 0.001852 0.049991 

28 0.847 0.000604 0.001568 0.043911 

29 0.847 0.000511 0.001328 0.038521 

30 0.847 0.000433 0.001125 0.033752 

31 0.847 0.000367 0.000953 0.029541 

32 0.847 0.000311 0.000807 0.025828 

33 0.847 0.000263 0.000684 0.022560 

34 0.847 0.000223 0.000579 0.019688 

35 0.847 0.000189 0.000490 0.017166 

36 0.847 0.000160 0.000415 0.014955 

37 0.847 0.000135 0.000352 0.013019 

38 0.847 0.000115 0.000298 0.011325 

39 0.847 0.000097 0.000252 0.009845 

40 0.847 0.000082 0.000214 0.008552 

41 0.847 0.000070 0.000181 0.007425 

42 0.847 0.000059 0.000153 0.006442 

43 0.847 0.000050 0.000130 0.005586 

44 0.847 0.000042 0.000110 0.004842 

45 0.847 0.000036 0.000093 0.004194 

46 0.847 0.000030 0.000079 0.003631 

47 0.847 0.000026 0.000067 0.003143 

48 0.847 0.000022 0.000057 0.002718 

49 0.847 0.000018 0.000048 0.002351 

50 0.847 0.000016 0.000041 0.002032 

sum 0.384889 1.000000 6.012886 
6

2. Estimated Lost Direct Discounted Terrapin-Years 

In this section the expected number of lost discounted terrapin-years for the juvenile and adult 

turtles killed by the spill is estimated. The adult survival rate is incorporated into the discounted survival 

rate formula for each year that an adult terrapin could have lived in the absence of the spill. Each year 

there are two possibilities; either the terrapin lives one more year or it dies sometime during the year. If 

the terrapin lives (with a survival probability of 0.847), then it provides one terrapin-year. If a terrapin dies 

(with probability equal to 1-0.847 = 0.153), it is assumed that it dies mid-way through the year, and so 

provides 1⁄2 a terrapin-year. These terrapin-years are then discounted at the appropriate discount rate (3%).3

 

It was previously estimated that the average aged turtle in this spill was 6.012886 years of age and will be 

7 the first year following the spill, therefore having the possibility to live 44 more years of his maximum 

attainable age after the spill. Summing over all years results in the discounted terrapin-years (DTYs) per 

adult killed.4

 

This calculation is shown in Table 4. The first column is the number of years after the spill, and 

runs from zero to 44; the second column is the age of the terrapin. The third column is the annual survival 

probability. The fourth column is the terrapin-years added by those who survive from one age to the next. 

This is the probability of surviving to an age (called P(Age) in Table 3), times the number of terrapin-years 

added (equal to one for survivors). The fifth column is the terrapin-years contributed by those who die 

during the year. This is the probability of surviving to the prior age (i.e. P(age-1)) times the probability of 

dying (0.153) times the terrapin-years added (1/2 for those who die). The sixth column is the discount 

factor. The seventh column multiplies the discount factor times the sum of entries in columns four and 

five. Adding up column seven gives the lost DTYs per adult killed, equal to 5.046. The lost DTYs is then 

multiplied by 122, total direct terrapin mortality (acute injury) from the spill (Michel, et al., 2001). Using 

these values, the number of direct discounted terrapin-years lost is estimated to be 615.6. 

To illustrate how the calculation of direct injury works, absent the spill there would have been 122 

terrapins that were six years old. In the first year after the spill, 122 × 0.847 = 103 would have lived and 

122 × 0.153 = 19 would have died. So, in this year there would have been 103 + (1/2)19 = 112.5 terrapinsyears, which equates to 109.2 discounted terrapin-years. In the second year, 122 × 0.8474 × 0.847 = 87 

terrapins would have lived to provide one additional terrapin-year, while 122 × 0.847 × 0.153 = 16 would 

have died and provided 1⁄2 terrapin-year. This equates to 87 + (1/2)16 = 95 current terrapin-years, or 90 

discounted terrapin-years. These numbers can be obtained (except for small differences due to rounding) 

by multiplying the entries in column seven by 122. Doing this calculation for each year and adding up the 

years from age six to fifty yields the estimated direct injury to terrapins. 

 

3

 NOAA's "Scaling Compensatory Restoration Actions: Guidance Document for Natural 

Resource Damage Assessment Under the Oil Pollution Act of 1990" recommends the use of anannual discount rate of 

3% to approximate today's value of future terrapin-years lost; this will be the discount rate used for the calculations 

found in this report. 

4

 For adults, the surrvial probability is a constant, pr (equal to 0.847). If the annual percentage discount rate is r, the 

lost discounted terrapin-years per adult killed is given by L = Σt∈[1,44] (1+r)-t {prt

 + prt-1(1 – pr)(1/2)}. The first term is 

the discount factor. The second term is the sum of the terrapin years contributed by those who live from age t-1 to age 

t and by those who live to t but die before t+1 and so only contribute 1⁄2 a terrapin-year. 
7

Table 4. Lost direct discounted terrapin-years 

1 2 3 4 5 6 7 

Year 

After 

Spill 

Age 

Annual 

Survival 

Rate 

Terrapin 

Years 

per 

Survivor

Terrapin 

Years per 

Deceased

Discount 

Factor DTY 

0 6 

1 7 0.847 0.847000 0.076500 0.970874 0.896602 

2 8 0.847 0.717409 0.064796 0.942596 0.737303 

3 9 0.847 0.607645 0.054882 0.915142 0.606306 

4 10 0.847 0.514676 0.046485 0.888487 0.498584 

5 11 0.847 0.435930 0.039373 0.862609 0.410001 

6 12 0.847 0.369233 0.033349 0.837484 0.337156 

7 13 0.847 0.312740 0.028246 0.813092 0.277253 

8 14 0.847 0.264891 0.023925 0.789409 0.227994 

9 15 0.847 0.224363 0.020264 0.766417 0.187486 

10 16 0.847 0.190035 0.017164 0.744094 0.154175 

11 17 0.847 0.160960 0.014538 0.722421 0.126783 

12 18 0.847 0.136333 0.012313 0.701380 0.104258 

13 19 0.847 0.115474 0.010429 0.680951 0.085734 

14 20 0.847 0.097807 0.008834 0.661118 0.070502 

15 21 0.847 0.082842 0.007482 0.641862 0.057976 

16 22 0.847 0.070167 0.006337 0.623167 0.047675 

17 23 0.847 0.059432 0.005368 0.605016 0.039205 

18 24 0.847 0.050339 0.004547 0.587395 0.032239 

19 25 0.847 0.042637 0.003851 0.570286 0.026511 

20 26 0.847 0.036113 0.003262 0.553676 0.021801 

21 27 0.847 0.030588 0.002763 0.537549 0.017928 

22 28 0.847 0.025908 0.002340 0.521893 0.014742 

23 29 0.847 0.021944 0.001982 0.506692 0.012123 

24 30 0.847 0.018587 0.001679 0.491934 0.009969 

25 31 0.847 0.015743 0.001422 0.477606 0.008198 

26 32 0.847 0.013334 0.001204 0.463695 0.006741 

27 33 0.847 0.011294 0.001020 0.450189 0.005544 

28 34 0.847 0.009566 0.000864 0.437077 0.004559 

29 35 0.847 0.008102 0.000732 0.424346 0.003749 

30 36 0.847 0.006863 0.000620 0.411987 0.003083 

31 37 0.847 0.005813 0.000525 0.399987 0.002535 

32 38 0.847 0.004923 0.000445 0.388337 0.002085 

33 39 0.847 0.004170 0.000377 0.377026 0.001714 

34 40 0.847 0.003532 0.000319 0.366045 0.001410 

35 41 0.847 0.002992 0.000270 0.355383 0.001159 

36 42 0.847 0.002534 0.000229 0.345032 0.000953 

37 43 0.847 0.002146 0.000194 0.334983 0.000784 

38 44 0.847 0.001818 0.000164 0.325226 0.000645 

39 45 0.847 0.001540 0.000139 0.315754 0.000530 

40 46 0.847 0.001304 0.000118 0.306557 0.000436 

41 47 0.847 0.001105 0.000100 0.297628 0.000358 

42 48 0.847 0.000936 0.000085 0.288959 0.000295 

43 49 0.847 0.000792 0.000072 0.280543 0.000242 

44 50 0.847 0.000671 0.000061 0.272372 0.000199 

sum 5.045525 
8

B. Production Foregone 

For the next component of turtle injury quantification, production foregone must be evaluated. This 

is accomplished in several steps. First, if a female survives to sexual maturity, it is assumed that she 

produces young.5

 Data from Table 1 are used to compute the expected number of hatchlings per female. 

Second, the expected DTYs provided by a hatchling from a female of any age is computed. This is the 

DTY per member of a cohort of hatchlings born of an average female who survives to a given age. 

Multiplying the expected number of hatchlings per female by the DTYs contributed by a hatchling gives 

the terrapin-years foregone from a female that survives to a given age. Third, using the annual survivorship 

for females, the expected number of females each year is computed. Finally, adding across years and 

discounting yields the lost DTYs from the production forgone. 

1. Expected Hatchlings per Female 

Using information in Table 1, each fecund female is assumed to produce 2 clutches per year (the 

midpoint of the range reported in Roosenburg (1990a)), with an average clutch size of 13 eggs. Thus, each 

female is expected to produce 26 eggs in a year. The probability of an egg producing a hatchling is 0.20. 

The expected number of hatchlings produced by a fecund female is 0.2 × 26 = 5.2. Fecundity is assumed to 

begin at age 8. 

2. Discounted Terrapin-Years per Cohort Member 

 The DTYs contributed by a hatchling that is a member of a cohort born at a given time is computed 

by multiplying the probability of survival to a given age times the terrapin-years at that age (one for those 

that survive, and 1⁄2 for those that die), times the discount factor, summed over the potential ages of a 

hatchling (1 to 50). This is shown in Table 5. The first column is the age of a hatchling. The second 

column is the annual survival rate, i.e. the probability of surviving from one age to the next. The third 

column gives the probability of surviving to the associated age. This is the product of the annual survival 

rates for the previous years; for example, for the second year, 0.275 = 0.415 × 0.662, and so on for the other 

years. The fourth column is the terrapin-years added at the associated age. Just as with the adults, this is 

one terrapin year for each terrapin that survives and 1⁄2 terrapin-year for each one that dies. The fifth column 

is the discounted terrapin-years at that age; this multiplies the discount factor times the fourth column. 

Summing the fifth column yields the number of DTYs provided by a hatchling born into a cohort at any 

given time. This equals 2.095. 

 Note that this is essentially the same calculation as was carried out for the adult discounted terrapinyears lost, but incorporates the ages before age six. Since young terrapins are more likely to die in a given 

year than older ones, the DTY for a hatchling is less than for a terrapin that is known to have lived to age 

six. 

 

5

 It is assumed that those who do not survive to the next age class produce young before they die. 

7

 Formally, the computation is that DTY per hatchling, H, is given by : 
9

Table 5. Discounted terrapin-years per hatchling

1 2 3 4 5 

Age Annual 

Surv Rate P(age) Terrapin Years DTY per Hatchling 

1 0.415 0.415000 0.707500 0.686893 

2 0.662 0.274730 0.637365 0.325068 

3 0.662 0.181871 0.590936 0.208927 

4 0.862 0.156773 0.578387 0.150441 

5 0.862 0.135138 0.567569 0.125903 

6 0.862 0.116489 0.558245 0.105367 

7 0.847 0.098666 0.549333 0.087471 

8 0.847 0.083570 0.541785 0.071930 

9 0.847 0.070784 0.535392 0.059150 

10 0.847 0.059954 0.529977 0.048641 

11 0.847 0.050781 0.525391 0.039999 

12 0.847 0.043012 0.521506 0.032892 

13 0.847 0.036431 0.518215 0.027048 

14 0.847 0.030857 0.515428 0.022243 

15 0.847 0.026136 0.513068 0.018291 

16 0.847 0.022137 0.511069 0.015041 

17 0.847 0.018750 0.509375 0.012369 

18 0.847 0.015881 0.507941 0.010171 

19 0.847 0.013451 0.506726 0.008364 

20 0.847 0.011393 0.505697 0.006878 

21 0.847 0.009650 0.504825 0.005656 

22 0.847 0.008174 0.504087 0.004651 

23 0.847 0.006923 0.503462 0.003825 

24 0.847 0.005864 0.502932 0.003145 

25 0.847 0.004967 0.502483 0.002586 

26 0.847 0.004207 0.502103 0.002127 

27 0.847 0.003563 0.501782 0.001749 

28 0.847 0.003018 0.501509 0.001438 

29 0.847 0.002556 0.501278 0.001183 

30 0.847 0.002165 0.501083 0.000973 

31 0.847 0.001834 0.500917 0.000800 

32 0.847 0.001553 0.500777 0.000658 

33 0.847 0.001316 0.500658 0.000541 

34 0.847 0.001114 0.500557 0.000445 

35 0.847 0.000944 0.500472 0.000366 

36 0.847 0.000799 0.500400 0.000301 

37 0.847 0.000677 0.500339 0.000247 

38 0.847 0.000574 0.500287 0.000203 

39 0.847 0.000486 0.500243 0.000167 

40 0.847 0.000411 0.500206 0.000138 

41 0.847 0.000349 0.500174 0.000113 

42 0.847 0.000295 0.500148 0.000093 

43 0.847 0.000250 0.500125 0.000076 

44 0.847 0.000212 0.500106 0.000063 

45 0.847 0.000179 0.500090 0.000052 

46 0.847 0.000152 0.500076 0.000043 

47 0.847 0.000129 0.500064 0.000035 

48 0.847 0.000109 0.500054 0.000029 

49 0.847 0.000092 0.500046 0.000024 

50 0.847 0.000078 0.500039 0.000019 

sum 2.094830 
10

3. Lost Discounted Terrapin- Years from Production Foregone 

Several steps are used to compute the number of terrapin-years produced from each hatchling that 

would have been born in absence of the spill. First, the expected number of females that would have lived to 

a given age but for the spill is estimated. This is given by the estimated direct terrapins mortality (122) 

times the ratio of females to total terrapins (0.75, from Table 1), times the probability that a female survives 

to that age (column 3). This calculation is shown in column 4 of Table 6. Second, multiplying by the 

expected number of hatchlings per female (26 ∗ 0.2 = 5.8) times the number of females of that age (column 

4) gives the size of a cohort of hatchlings born at that date in column 5. Note that there will be no hatchling 

years lost in the first two years following the spill, as the terrapins would be in age classes 6 and 7 and 

would not yet be able to reproduce. In the previous section it was calculated that a hatchling born at a given 

date provides 2.095 (rounded) DTYs, where these terrapin-years are realized in years after the date of birth, 

discounted back to the date of birth. This 2.095 DTYs per hatchling is a constant, irrespective of the date of 

birth. Multiplying the size of the hatchling cohort by the 2.095 DTYs per hatchling (shown in Table 6, 

column 6) results in DTYs for a given cohort (column 7), as of the date of birth of this cohort. For example, 

for the cohort born in the second year after the spill, 715.1 discounted terrapin-years are produced. This 

then needs to be discounted from the date of birth (year two following the spill) back to the spill date. This 

final discounting step is shown in column 8. Summing over all the future cohorts through the maximum 

age (i.e. the sum of column 7) yields the DTYs from the production foregone.7

 The number of DTYs from 

hatchlings lost due to acute injury to adults for the Patuxent River population after the spill is estimated to 

be 3,792.8. 

Table 6. Lost discounted terrapin-years for production foregone 
11

1 2 3 4 5 6 7 8 

Year 

After 

Spill 

Age of 

Adults 

Adult 

P(age) 

Expected 

Number of 

Females 

Offspring 

Cohort 

Size 

DTY per 

Cohort 

Member 

DTY per 

Cohort 

Discounted 

DTY per 

Cohort 

0 6 91.500 

1 7 0.847 77.501 

2 8 0.717 65.643 341.343 2.095 715.056 674.009 

3 9 0.608 55.600 289.118 2.095 605.652 554.258 

4 10 0.515 47.093 244.883 2.095 512.988 455.783 

5 11 0.436 39.888 207.416 2.095 434.501 374.804 

6 12 0.369 33.785 175.681 2.095 368.022 308.213 

7 13 0.313 28.616 148.802 2.095 311.715 253.452 

8 14 0.265 24.238 126.035 2.095 264.022 208.422 

9 15 0.224 20.529 106.752 2.095 223.627 171.391 

10 16 0.190 17.388 90.419 2.095 189.412 140.940 

11 17 0.161 14.728 76.585 2.095 160.432 115.899 

12 18 0.136 12.474 64.867 2.095 135.886 95.308 

13 19 0.115 10.566 54.943 2.095 115.095 78.374 

14 20 0.098 8.949 46.536 2.095 97.486 64.450 

15 21 0.083 7.580 39.416 2.095 82.570 52.999 

16 22 0.070 6.420 33.386 2.095 69.937 43.583 

17 23 0.059 5.438 28.278 2.095 59.237 35.839 

18 24 0.050 4.606 23.951 2.095 50.174 29.472 

19 25 0.043 3.901 20.287 2.095 42.497 24.235 

20 26 0.036 3.304 17.183 2.095 35.995 19.930 

21 27 0.031 2.799 14.554 2.095 30.488 16.389 

22 28 0.026 2.371 12.327 2.095 25.823 13.477 

23 29 0.022 2.008 10.441 2.095 21.872 11.082 

24 30 0.019 1.701 8.844 2.095 18.526 9.113 

25 31 0.016 1.440 7.490 2.095 15.691 7.494 

26 32 0.013 1.220 6.344 2.095 13.291 6.163 

27 33 0.011 1.033 5.374 2.095 11.257 5.068 

28 34 0.010 0.875 4.552 2.095 9.535 4.167 

29 35 0.008 0.741 3.855 2.095 8.076 3.427 

30 36 0.007 0.628 3.265 2.095 6.840 2.818 

31 37 0.006 0.532 2.766 2.095 5.794 2.317 

32 38 0.005 0.450 2.343 2.095 4.907 1.906 

33 39 0.004 0.382 1.984 2.095 4.156 1.567 

34 40 0.004 0.323 1.681 2.095 3.521 1.289 

35 41 0.003 0.274 1.423 2.095 2.982 1.060 

36 42 0.003 0.232 1.206 2.095 2.526 0.871 

37 43 0.002 0.196 1.021 2.095 2.139 0.717 

38 44 0.002 0.166 0.865 2.095 1.812 0.589 

39 45 0.002 0.141 0.733 2.095 1.535 0.485 

40 46 0.001 0.119 0.621 2.095 1.300 0.398 

41 47 0.001 0.101 0.526 2.095 1.101 0.328 

42 48 0.001 0.086 0.445 2.095 0.933 0.269 

43 49 0.001 0.073 0.377 2.095 0.790 0.222 

44 50 0.001 0.061 0.319 2.095 0.669 0.182 

sum 3792.759 
12

C. Increased Hatchling Mortality 

 Another component of injury is increased hatchling mortality during the 2000 nesting season. It 

was assumed that the oil had no effect on hatchling mortality in other years. This component incorporates 

the reduction of the likelihood that an egg laid in the 2000 nesting season will produce a viable hatchling 

which survives to the following year. The injury is measured as the estimated discounted terrapin years 

provided by the 2000 hatchling cohort in baseline conditions minus the estimated discounted terrapin years 

provided by the 2000 hatchling cohort, including an oil effect on hatchling success relative to baseline. The 

oil effect was assumed to be a 10% reduction in the first-year hatchling survival rate. 

1. Baseline Discounted Terrapin-Years of 2000 Hatchlings 

 Baseline discounted terrapin years that would have been provided by the 2000 cohort is estimated 

in three steps: (1) the number of eggs that would have been laid is estimated based on baseline population 

parameters; (2) the number of expected hatchlings from those eggs is estimated; and (3) the number of 

expected hatchlings is multiplied by the discounted terrapin years per hatchlings under baseline conditions. 

 The terrapin population in the area affected by the spill was estimated to be 4,698 (Michel et. al., 

2001). Based on the age-class distribution in Table 3, approximately 28% of the population are fecund (age 

class eight or older). Using the baseline parameters that 75% of the population is female, each female 

produces 26 eggs per year, and the egg to hatchling success rate is 20%, the estimated baseline number of 

hatchlings produced in 2000 is (4,698 ∗ 0.75 ∗ 0.2836 ∗ 26 ∗ 0.2) = 5,196.2. From Table 5, the baseline 

discounted terrapin years per hatchling is 2.095. The baseline discounted terrapin years for the 2000 

hatchling cohort is 5,196.2 ∗ 2.095 = 10,885.2. 

2. Discounted Terrapin-Years of 2000 Hatchlings under the Effects of Oil 

 It was assumed that the effect of the oil spill on hatchling success was a 10% reduction in the firstyear survivorship, from 41.5% to 37.4%. The expected number of hatchlings is the same as under baseline 

conditions, 5,196.2. With the reduced first-year survivorship of 37.4%, the discounted terrapin years per 

hatchling is 1.934, as depicted in Table 7. The estimated discounted terrapin years produced by the 2000 

cohort is 5,196.2 ∗ 1.934 = 10,048.9. 
13

Table 7: Discounted Terrapin Years per Hatchling in 2000 

1 2 3 4 

Age Annual 

Surv Rate P(age) DTY per Hatchling 

1 0.374 0.373500 0.666748 

2 0.662 0.247257 0.292562 

3 0.662 0.163684 0.188035 

4 0.862 0.141096 0.135396 

5 0.862 0.121625 0.113312 

6 0.862 0.104840 0.094830 

7 0.847 0.088800 0.078724 

8 0.847 0.075213 0.064737 

9 0.847 0.063706 0.053235 

10 0.847 0.053959 0.043777 

11 0.847 0.045703 0.035999 

12 0.847 0.038711 0.029603 

13 0.847 0.032788 0.024343 

14 0.847 0.027771 0.020018 

15 0.847 0.023522 0.016462 

16 0.847 0.019923 0.013537 

17 0.847 0.016875 0.011132 

18 0.847 0.014293 0.009154 

19 0.847 0.012106 0.007528 

20 0.847 0.010254 0.006190 

21 0.847 0.008685 0.005090 

22 0.847 0.007356 0.004186 

23 0.847 0.006231 0.003442 

24 0.847 0.005278 0.002831 

25 0.847 0.004470 0.002328 

26 0.847 0.003786 0.001914 

27 0.847 0.003207 0.001574 

28 0.847 0.002716 0.001294 

29 0.847 0.002301 0.001064 

30 0.847 0.001949 0.000875 

31 0.847 0.001650 0.000720 

32 0.847 0.001398 0.000592 

33 0.847 0.001184 0.000487 

34 0.847 0.001003 0.000400 

35 0.847 0.000849 0.000329 

36 0.847 0.000719 0.000271 

37 0.847 0.000609 0.000223 

38 0.847 0.000516 0.000183 

39 0.847 0.000437 0.000151 

40 0.847 0.000370 0.000124 

41 0.847 0.000314 0.000102 

42 0.847 0.000266 0.000084 

43 0.847 0.000225 0.000069 

44 0.847 0.000191 0.000057 

45 0.847 0.000161 0.000047 

46 0.847 0.000137 0.000038 

47 0.847 0.000116 0.000031 

48 0.847 0.000098 0.000026 

49 0.847 0.000083 0.000021 

50 0.847 0.000070 0.000018 

sum 1.933891 
14

3. Lost Discounted Terrapin-Years due to Increased Hatchling Mortality 

 The lost discounted terrapin years due to the increased mortality of hatchlings is the difference 

between the discounted terrapin years provided under baseline conditions and the conditions found during 

the oil spill. The injury is 10,885.2 – 10,048.9 = 836.3 discounted terrapin years. 

III. SUMMARY 

Based on the survival rates from the diamondback terrapin and several other species in the emydid 

family, the average age of the Patuxent River population of diamondback terrapins is estimated to be 6 

years. Roosenburg (1990a) stated that the maximum attainable age could be as long as 50 years. Using 

estimated survival rates and discounting the lost terrapin-years results in an estimated 615.6 of direct 

discounted terrapin-years lost. 

From Table 1, it is expected that a female terrapin will produce 26 eggs per year. Based on 

survivorship over their lifetime, each hatchling born into a cohort was estimated to contribute 2.095 

discounted terrapin-years. Taking account of the survivorship of females and the age of fecundity, the total 

hatchling discounted terrapin-years lost (adult equivalent) is estimated to equal 3,792.7. 

 It was assumed that the oil spill caused a 10% reduction in the survivorship of hatchlings for the 

2000 nesting season. This effect reduced the discounted terrapin-years for the 2000 cohort to 1.934 from the 

baseline level of 2.095. This is a loss of 0.161 discounted terrapin years per hatchling. The 2000 hatchling 

cohort size is estimated to be 5,196. The loss due to increased hatchling mortality is 836.3 discounted 

terrapin-years. 

The sum of the direct terrapin-years lost, production foregone, and the loss from increased hatchling 

mortality is the total terrapin-years lost for the Chalk Point oil spill event. Based on these calculations, the 

total injury for the Patuxent River population of diamondback terrapins is estimated to be 5,244.6 

discounted terrapin-years (Table 8). 
15

Table 8: Summary of the Lost Discounted Terrapin Years 

Diirect Lost Terrapin Years Production Foregone Increased 2000 Hatchling Mortality 

Year After 

Spill 

Age of Adults 

Annual 

Survival Rate P(year) Expected Adults Terrapin Years (Survivors) Terrapin Years (Deceased) Expected Females Expected Hatchlings DTY per Hatchling Terrapin Years (Hatchlings) Expected Hatchlings DTY per Hatchling (Basline) DTY per Hatchling (With Spill) Lo

Ha

0 6 122 91.5 5,196.232 2.095 1.934 81 7 0.847 0.847 103.334 103.334 9.333 77.501 2 8 0.847 0.717 87.524 87.524 7.905 65.643 341.343 2.095 715.056 3 9 0.847 0.608 74.133 74.133 6.696 55.600 289.118 2.095 605.652 4 10 0.847 0.515 62.790 62.790 5.671 47.093 244.883 2.095 512.988 5 11 0.847 0.436 53.183 53.183 4.803 39.888 207.416 2.095 434.501 6 12 0.847 0.369 45.046 45.046 4.069 33.785 175.681 2.095 368.022 7 13 0.847 0.313 38.154 38.154 3.446 28.616 148.802 2.095 311.715 8 14 0.847 0.265 32.317 32.317 2.919 24.238 126.035 2.095 264.022 9 15 0.847 0.224 27.372 27.372 2.472 20.529 106.752 2.095 223.627 

10 16 0.847 0.190 23.184 23.184 2.094 17.388 90.419 2.095 189.412 11 17 0.847 0.161 19.637 19.637 1.774 14.728 76.585 2.095 160.432 12 18 0.847 0.136 16.633 16.633 1.502 12.474 64.867 2.095 135.886 13 19 0.847 0.115 14.088 14.088 1.272 10.566 54.943 2.095 115.095 14 20 0.847 0.098 11.932 11.932 1.078 8.949 46.536 2.095 97.486 15 21 0.847 0.083 10.107 10.107 0.913 7.580 39.416 2.095 82.570 16 22 0.847 0.070 8.560 8.560 0.773 6.420 33.386 2.095 69.937 17 23 0.847 0.059 7.251 7.251 0.655 5.438 28.278 2.095 59.237 18 24 0.847 0.050 6.141 6.141 0.555 4.606 23.951 2.095 50.174 19 25 0.847 0.043 5.202 5.202 0.470 3.901 20.287 2.095 42.497 20 26 0.847 0.036 4.406 4.406 0.398 3.304 17.183 2.095 35.995 21 27 0.847 0.031 3.732 3.732 0.337 2.799 14.554 2.095 30.488 22 28 0.847 0.026 3.161 3.161 0.285 2.371 12.327 2.095 25.823 23 29 0.847 0.022 2.677 2.677 0.242 2.008 10.441 2.095 21.872 24 30 0.847 0.019 2.268 2.268 0.205 1.701 8.844 2.095 18.526 25 31 0.847 0.016 1.921 1.921 0.173 1.440 7.490 2.095 15.691 26 32 0.847 0.013 1.627 1.627 0.147 1.220 6.344 2.095 13.291 27 33 0.847 0.011 1.378 1.378 0.124 1.033 5.374 2.095 11.257 28 34 0.847 0.010 1.167 1.167 0.105 0.875 4.552 2.095 9.535 29 35 0.847 0.008 0.989 0.989 0.089 0.741 3.855 2.095 8.076 30 36 0.847 0.007 0.837 0.837 0.076 0.628 3.265 2.095 6.840 31 37 0.847 0.006 0.709 0.709 0.064 0.532 2.766 2.095 5.794 32 38 0.847 0.005 0.601 0.601 0.054 0.450 2.343 2.095 4.907 33 39 0.847 0.004 0.509 0.509 0.046 0.382 1.984 2.095 4.156 34 40 0.847 0.004 0.431 0.431 0.039 0.323 1.681 2.095 3.521 35 41 0.847 0.003 0.365 0.365 0.033 0.274 1.423 2.095 2.982 36 42 0.847 0.003 0.309 0.309 0.028 0.232 1.206 2.095 2.526 37 43 0.847 0.002 0.262 0.262 0.024 0.196 1.021 2.095 2.139 38 44 0.847 0.002 0.222 0.222 0.020 0.166 0.865 2.095 1.812 39 45 0.847 0.002 0.188 0.188 0.017 0.141 0.733 2.095 1.535 40 46 0.847 0.001 0.159 0.159 0.014 0.119 0.621 2.095 1.300 41 47 0.847 0.001 0.135 0.135 0.012 0.101 0.526 2.095 1.101 42 48 0.847 0.001 0.114 0.114 0.010 0.086 0.445 2.095 0.933 43 49 0.847 0.001 0.097 0.097 0.009 0.073 0.377 2.095 0.790 44 50 0.847 0.001 0.082 0.082 0.007 0.061 0.319 2.095 0.669 

sum 
Oct. 11, 2001

16

References 

Bishop, J. M. 1983. Incidental capture of diamondback terrapins by crap pots. Estuaries: Vol. 6: 426-430. 

Heppell, S.S. 1998. Application of life-history theory and population model analysis to turtle conservation. 

Copeia. Vol. 2: 367-375. 

Michel, J., R. Greer, M. Hoffman, P. McGowan, and R. Wood. 2001. Acute Mortality of Diamondback 

Terrapins from the Chalk Point Oil Spill. Report by the Wildlife Injury Workgroup to the Chalk 

Point Oil Spill Natural Resource Trustee Council. October, 2001, 7 pp. 

Mitchell, J.C. 1988. Population ecology and life histories of the freshwater turtles Chrysemys picta and 

Sternotherus odoratus in an urban lake. Herp. Monogr. 2: 40-61. 

NatureServe: An online encyclopedia of life [web application]. 2001. Version 1.4. Arlington, Virginia, 

USA: Association for Biodiversity Information. Available at: 

http://www.natureserve.org/. (Accessed: July 9, 2001). 

Roosenburg, W.M. 1990a. The diamondback terrapin: population dynamics, habitat requirements, 

opportunities for conservation. In Proceedings of a Conference: New Perspectives in the 

Chesapeake System: A Research and Management Partnership. Baltimore, Maryland. Pages 227-

234. 

Roosenburg, W.M. 1990b. Final Report: Chesapeake diamondback terrapin investigations for the period 

1987, 1988, and 1989. Chesapeake Research Consortium. Solomons, Maryland. 84pp. 

Roosenburg, W.M. 1992. Life history consequences of nest site choice by the diamondback terrapin, 

malaclemys terrapin. UMI Dissertation Services. Ann Arbor, Michigan. 206pp. 

Sperduto, M., C. Hebert, M. Donlan, and S. Thompson. 1999. (unpublished report) Injury quantification 

and restoration scaling for marine birds killed as a result of the North Cape oil spill. U.S. Fish and 

Wildlife Service. 32pp. 

Tinkle, D.W. , J.D. Congdon and P.C. Rosen. 1981. Nesting frequency and success: implications for the 

demography of painted turtles. Ecology 62: 1426-1432. 

Wilbur, H.M. 1975. The evolutionary and mathematical demography of the turtle Chrysemys picta. 

Ecology 56: 64-77. 

Wood, R. and S. Hales, Personal Communication, 2000-2002. Multiple conversations with diamondback 

terrapin experts from the Wetlands Institute, Stockton State College, New Jersey, regarding the life 

history of terrapins and the potential impacts of oil. 

Wood, R. and S. Hales. 2001. Comparison of northern diamondback terrapin (Malaclemys terrapin 

terrapin) hatching success among variably oiled nesting sites along the Patuxent River following 

the Chalk Point Oil Spill of April 7, 2000. 
1

November 11, 2001 

Norman Meade 

NOAA Damage Assessment Center (N/ORR3) 

1305 East-West Highway 

Room 10357 

Silver Spring, MD 20910 

Dear Norman: 

 The following are my combined comments on two reports, "Acute Mortality of 

Diamondback Terrapins from the Chalk Point Oil Spill" and "Estimate of Total Injury to 

Diamondback Terrapins from the Chalk Point Oil Spill." Both reports address the quantification 

of natural resource injury to terrapins under the 1990 Oil Pollution Act (OPA) following the 

April 2000 Chalk Point oil spill in the Patuxent River. 

 The purpose of the Acute Mortality study was to estimate the direct mortality to 

diamondback terrapins (Malaclemys terrapin) from the oil spill. The goal of the Total Injury 

report was to estimate the number of lost diamondback terrapin years, based on both acute 

mortality and the loss of production of the next generation, following the oil spill. My review of 

these reports addresses the following queries: 

1. Were the assumptions used and the data and methods employed by the investigators 

appropriate for undertaking the stated goals of the study? 

2. Were the methods employed properly implemented? 

3. Do you have suggestions on how to improve the substance and exposition of the report? 

General Statement: 

 My overall assessment of the two reports is that a fair treatment of the situation was given 

considering the absence of thorough knowledge of the disposition of terrapins throughout the 

system and the limited data that were available. In essence, as good a job as possible was done 

with the material available, and the approach used of building scenarios based on known 

biological facts was reasonable and appropriate. To the best of my knowledge the model 

quantifying total lost terrapin years has been properly implemented. A few specific points bear 

mentioning. 

Specific Comments 

Acute Mortality Study 
2

Table 1 – The authors need to be consistent in use of "pipeline break marsh" – if this is a specific 

locality it should be capitalized; need to clarify "notched" on April 30 – does this mean a marked 

animal from a study or an animal injured by a boat? 

page 2 – The point about increased boat traffic is a good one that should be included in the final 

report, as such activities are a consequence of the spill. 

page 3 – The last sentence in first paragraph under Mortality Estimates needs to provide 

confidence limits (range) for the total population estimate. 

page 3 – The most difficult assumption in the acute injury report is the 10%, 2%, and 0.5% 

estimates of mortality. My suggestion is that these be referred to as professional opinions based 

on limited availability of data. The rationale for such an estimate is that higher proportions would 

not be expected because of the minimal number of oiled or dead terrapins found after the spill. 

However, the finding of several individuals affected by the oil spill suggests that at least a small 

proportion of the population was affected, which would presumably be reduced in habitats 

receiving lesser amounts of oil. 

Total Injury Study 

Table 1 – This table needs to be partitioned into two parts (1. Population parameters and 2. 

Parameter values) in order to keep the columns clear and consistent. 

Table 2 -- The citations need to be provided for Wilbur 1975, Tinkle et al. 1981, and Mitchell 

1988. Defining values as both the "mean" and the "average" is confusing as the numbers should 

be the same for either. 

page 5 - The series of assumptions are tedious to follow but seem to be best estimates that are 

accurate within the context of available data on the species for the Patuxent River area. 

page 11 - In the Summary, the maximum of "39 eggs per year" is used in the final calculation. In 

other parts of the reports, both the mean and range have been given. Explanation should be given 

for why the maximum is being used for the potential number of eggs. 

 I hope these comments are useful. Please let me know if you need additional information. 

 

Sincerely, 

J. Whitfield Gibbons 

Professor of Ecology 

Office 803 725-5852 

Email gibbons@srel.edu