ONLINE RESOURCE 1
Growth models
Non-linear regression was used with four commonly used growth models (von Bertalanffy;
Gompertz; Richards; a Logistic model; Table 1). The best growth model was firstly identified for males
and females separately by considering the entire sampling period (8 years). Starting with the AICc values
(i.e., the AIC values corrected for small sample size), we calculated the Akaike weights (wi), which
indicated the probability of each model being the best model among the four model candidates (Burnham
and Anderson 2002).
The model that best described males’ population growth when considering the whole study
period was the von Bertalanffy model (48%), followed by the Gompertz model (29%). Conversely,
females showed the opposite result as the Gompertz model was the most supported (43% probability),
followed by the von Bertalanffy model (30%; Table 2). Comparisons between the growth patterns of
males and females were made using the von Bertalanffy model since this model obtained the highest
mean probability for both males and females (averaged probability: Bertalanffy = 39%, Gompertz =
36%). Additionally, selection of the von Bertalanffy model enhanced the comparability of the results of
our work as it is the most widely used model to describe chelonians population growth (Zivkov et al.
2007; Macale et al. 2009). The calculated parameters using the growth curves between sexes appear in
Table 3.
TABLE 1.- For known age models, the dependent variable is carapace length at age t (CL), S∞ is
asymptotic size, b is a parameter associated with the amount of growth remaining, and k is the growth
rate. For the Richard’s model, n is a curve shape parameter. For the interval analogues, the parameters are
the same, although the dependent variable is carapace length at recapture (CL2), CL1 is carapace length at
the initial capture, and t is the interval between captures in years. This table has been created with
modifications from Dodd and Dreslik (2007).
Model
Known age
Interval analogue
Von Bertalanffy1
S∞ (1 - b𝑒 −𝑘𝑡 )
CL2=S∞ - (S∞ - CL1) 𝑒 −𝑘𝑡
Gompertz
S∞ 𝑒 b𝑒
−𝑘𝑡
CL2=S∞ 𝑒 log(CL1/S∞) 𝑒
−𝑘𝑡
Richards
S∞ (1 − b𝑒 −𝑘𝑡 )1/𝑛
CL2=S∞ (1 + (( CL1/S∞ )1/𝑛 – 1) 𝑒 −𝑘𝑡 )𝑛
Logistic2
S∞ ⁄(1 − b𝑒 −𝑘𝑡 )
CL2 = CL1 S∞ ⁄( CL1 + (S∞ − CL1)𝑒 −𝑘𝑡 )
1 - Interval analogue derived by Fabens (1965).
2 - Interval analogue derived by Schoener and Schoener (1978).
TABLE 2-. Growth model parameters and inter-model comparisons using an information-theoretic
approach for females (n=80) and males (n=96). n = shape parameter of the growth model; S∞ =
asymptotic size; k = growth rate; AICc = Akaike information criterion corrected for small sample size;
ΔAICc = AICc differences; wi =model probability;
Model
n
S∞
k
AICc
ΔAICc
wi
Females
Betarlanffy
161.84 0.106
475.55
0.71
0.30
Gompertz
158.01 0.147
474.84
0
0.43
159.15 0.131
476.43
1.59
0.19
156.54 0.178
478.41
3.57
0.07
Betarlanffy
121.27 0.155
485.84
0
0.48
Gompertz
120.52 0.195
486.89
1.05
0.29
120.96 0.168
487.48
1.64
0.21
120.21 0.227
492.64
6.8
0.02
Richards
2.455*
Logistic
Males
Richards
Logistic
1.48*
(*) Calculated from the model as appears in the table 1.
TABLE 3.- . Fire-related changes in von Bertalanffy growth parameters for males and female Testudo
graeca. S∞ = asymptotic size; k = growth rate
Females
Males
S∞
CI
k
CI
S∞
CI
k
CI
Global
161.84
±8.23
0.106
±0.032
121.27
±2.83
0.156
±0.034
Pre-fire
158.26
±7.66
0.145
±0.048
118.23
±4.24
0.228
±0.078
Post-fire
165.61
±14.86
0.086
±0.040
125.04
±4.45
0.112
±0.032
REFERENCES.
Burnham KP, Anderson DR (2002) Model Selection and Multimodel Inference: A Practical InformationTheoretic Approach, 2nd ed. Springer-Verlag.
Dodd CK Jr, Dreslik MJ (2007) Habitat disturbances differentially affect individual growth rates in a
long-lived turtle. J Zool 275:18-25.
Fabens AJ (1965) Properties and fitting of the von Bertalanffy growth curve. Growth 29, 265–289.
Macale D, Scalici M, Venchi A (2009) Growth, mortality, and longevity of the Egyptian tortoise Testudo
kleinmanni Lortet, 1883. Isr J of Ecol Evol 55 (2): 133-147.
Schoener TW, Schoener A (1978) Estimating and interpreting body-size growth in some Anolis lizards.
Copeia 1978, 390–405.
Zivkov M, Ivanchev I, Raikova-Petrova G, Trichkova T (2007) First data on the population structure,
growth rate and ontogenetic allometry of the tortoise Testudo hermanni in eastern Stara Planina
(Bulgaria) - Comptes Rendus de L’Academie Bulgare des Sciences 60 (9): 1015-1022.