Analyzing life history patterns using the Dynamic Energy Budget Integral Projection Model (DEB-IPM)

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Analyzing life history patterns using the

Dynamic Energy Budget Integral Projection

Model (DEB-IPM)

Bachelor Thesis by Iris van Rijn

Student Nr. 12203386

Supervisor: Mw. Dr. I.M. (Isabel) Smallegange

Second assessor: Dr. ir. E.E. (Emiel) van Loon

Date: 31-05-2021

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Abstract

Understanding life history patterns is a great way to predict species responses to change. Two life history patterns are investigated in this research, which are the pace of life and the reproductive strategy axis. Species can range from slow to fast histories and from a semelparous to iteroparous reproductive strategy. Species on different ends of the fast slow continuum respond different to environmental variation. The population size of species with a fast history are more sensitive to reproduction, while those with a slow life history are more sensitive to survival.

These life history patterns have mainly been investigated with demographic models. Since these models lack underlying mechanisms of biological variation, the Dynamic Energy Budget – Integral Projection Model is used. The DEB-IPM integrates the distribution of energy from food supply towards growth and maintenance and offspring. The DEB-IPM calculates three life history quantities for different feeding levels. This way environmental circumstances and food availability are taken into account. With a phylogenetic Principal Component Analyses, The DEB-IPM placed the species on the fast-slow continuum according to theory. Species with a low adult mortality rate ended up at the slow side of the continuum and species with a high mortality rate ended up at the fast end. The reproductive strategy axis however, was not identified due to a lack of parameters that are associated with reproduction. Although the reproductive strategy axis is not found, the DEB-IPM could still provide insight due to the integration of different feeding levels, since a species’ reproductive strategy can be changed with an unexpected food surplus. The DEB-IPM provides important insights for the fast-slow continuum and has great potential for the reproductive strategy axis.

Keywords: integral projection models, perturbation analysis, slow-fast life history continuum, reproductive strategy axis, dynamic energy budget

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1. Introduction

Species around the world face many environmental disturbances, such as habitat loss, agricultural intensification and grazing, that strongly affect population persistence (Williams, Crone, Roulston, Minckley, Packer & Potts 2010). Disturbances are able to change overall community structure, which in turn can ultimately affect community and population dynamics (Fakhry, khazzan & Aljedaani, 2020). How species and populations respond to these disturbances will depend on their behavior, physiology and also the life history of the individuals within these populations (Harmon, Moran & Ives, 2009). Since the frequency and intensity of disturbances are not predictable under different global change scenarios, a general framework for understanding biodiversity response to disturbances is critical (Supp & Ernes, 2014). One analytical framework that could be used to predict responses to disturbances is life history theory (Stearns, 1992).

Life history theory aims to understand how selection shapes organisms to maximize survival and reproductive success (Stearns, 2000). Organisms can be characterized by a range of different life history traits, including the size of an animal at birth, the age or size at which an animal can reproduce, the mortality rate and for example the way it reproduces (Kunz & Orrell, 2004). A combination of these life history traits forms an organism’s life-history strategy. For example, slow life histories are slow developing, long-lived, low fecundity organisms, whereas fast life histories are rapidly developing, short-lived, high fecundity organisms (Stearns, 2000). Besides the fast-slow continuum, life history strategies can also be ranked along an axis of reproductive strategies (Salguero-Gómez et al. 2016). At one extreme there are the highly reproductive, iteroparous species, whereas at the other extreme there are poorly reproductive, semelparous species (Salguero-Gómez et al. 2016). Understanding how life-history strategies are structured is fundamental to our understanding of the evolution, abundance, and distribution of species (Salguero-Gómez et al. 2016).

Understanding and knowing species’ life history strategies can be very beneficial to conservation biologists. For example, species on different ends of the fast slow continuum respond different to environmental variation. The population size of species with a fast history are more sensitive to reproduction (Reynolds, 2003). These species can be seen as more vulnerable to environmental variation, as they also show increasing fluctuations in their population size with increasing environmental variation (Paniw et al., 2018). Species with slow life histories on the other hand, are buffered against environmental variation as their population size less sensitive to reproduction but more sensitive to survival. Contrastingly, slow life history species show higher vulnerability to larger disturbances such as habitat loss due to the long generation time and low fecundity (Reynolds, 2003). By knowing whether a species is on the fast or slow end of the continuum, predictions about responses to change can be made and this way species can be prioritized for conservation.

Predictions about life history strategies along the fast-slow continuum and reproductive strategies axis, have mainly been derived from analyses of demographic population projection models (Salguero-Gómez et al., 2018). From these models one can calculate metrics of population performance, but importantly, these model outcomes are not based on underlying mechanisms of biological variation (Salguero-Gómez et al., 2018). Linking population fluctuations with the underlying demographic processes is essential if we are to develop a better understanding of the fluctuations (van Benthem, Froy, Coulson, Getz, Oli & Ozgul, 2017). The dynamic energy budget integral projection model (DEB-IPM) is such a trait-based demographic model. The DEB-IPM is based on dynamic energy budget theory (Kooijman, 2010). Dynamic Energy Budget theory provides a framework to model the growth and reproduction of individuals as a function of food supply (Kooijman & Metz, 1983). It assumes that energy is either utilized for reproduction or respiration and that the organism is no longer a juvenile as soon as the animal attains a sufficient weight (Kooijman & Metz, 1983). The integration of energy

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5 conservation principles into IPMs permits predictions under novel environmental conditions (Salguero-Gómez et al., 2018).

To see if the combination of life history traits that were priorly found can be understood with the DEB-IPM model, the research question that will be investigated in this paper is:

Can we understand the mechanistic basis of variation in cross-taxonomical patterns in life history speed and reproductive strategy from an energy budget perspective?

The objectives of this project are:

• To parameterize dynamic energy budget integral projection models for a wide range of ectotherm taxa.

• To assess if these taxa can be ranked along a fast slow axis of life history speed and an axis of reproductive strategy.

• To investigate which parameters shows the highest sensitivity to change in each taxa.

To answer the main research question, a functional trait approach is used to explain variation in patterns in life history speed and reproductive strategy for a wide range of ectotherms. The dynamic energy budget theory works best with ectotherms since they do not heat their body to a constant high temperature, but usually follow that of the environment (Kooijman, 1993). Calculating the distribution of energy in an organism is more complex when energy is invested to keep the body temperature fixed at a high level. A previous study that aimed to place species on a fast-slow continuum with the DEB-IPM did not categorize the expected distribution of species on the two axes correctly (Hopman, 2018). For example, the yellow-spotted river turtle (Podocnemis unifilis), was placed at the fast end of the continuum, whereas it is a long-lived and late-maturing organism (Erickson, Journal, Farias & Zuanon 2020). In the research by Hopman (2018), the mortality was not divided in juvenile and adult mortality. A typical, adult female of the yellow-spotted river turtle produces about 550 eggs each reproductive season (Hirth, 1971), which is seen as a fast life history trait. However, estimations show that only 2-3% of hatchlings survive to adulthood (Hirth, 1971). Therefore, it is expected that including juvenile and adult mortality separately, will place the species more accurately along the fast-slow continuum.

Furthermore, in this research a comparison is made between analyses including all DEB-parameters and analyses without the input DEB-parameters. Previous theses on this subject only took the three output parameters (lambda, R0 and generation time) of the DEB-IPM as input for the analyses as opposed to all input parameters and the three output parameters together (Hopman, 2018; Eeltink, 2017). By comparing these two, it can be assessed whether there is a difference in output and if so, which may be more accurate. By adding the division between juvenile and adult mortality and by performing PCA analyses on only derived life history quantities and all DEB-parameters, the correct biological mechanistic foundation can be established to get the most accurate output from the model.

In this project, the species-specific parameters needed are obtained from the DEB-IPM database (Smallegange, 2020). I collected DEB-parameters and data on juvenile and adult mortality for 16 species. The 16 species that are used in this research can be found in Table 1. It is expected that the species with a relatively high survival rate are on the slow side of the continuum and vice-versa (Gaillard et al., 1989). If the results are not as expected, it will still provide insight in the difficulties regarding which processes lead to these life history axes.

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Table 1- List of species researched (All information on habitat type retrieved from: https://animaldiversity.org/)

Common name Latin name Class Habitat type

Australian freshwater crocodile Crocodylus johnsoni Reptilia Freshwater wetlands, billabongs, rivers and creeks Tuatara Sphenodon punctatus Reptilia Offshore islands

Grass snake Natrix natrix Reptilia Open woodland and edge

habitat

Sleepy Lizard Tiliqua rugosa Reptilia Shrublands and desert grasslands to sandy dunes Leatherback turtle Dermochelys coriacea Reptilia Open ocean

three-spined stickleback Gasterosteus aculeatus Actinopterygii Coastal waters or freshwater bodies

porbeagle Lamna nasus Chondrichthyes Offshore fishing banks Snapping turtle Chelydra serpentina Reptilia Water bodies with muddy

bottoms

Yellow mud turtle Kinosternon flavescens Reptilia Smaller ponds with muddy bottoms

Loggerhead sea turtle Caretta caretta Reptilia Coastal waters, coral reefs, salt marches and brackish lagoons the tree dtella Gehyra variegata Reptilia In aboreal trees or between

stones

The eastern fence lizard Sceloporus undulatus Reptilia Grasslands, shrublands, and the edges of pine or hardwood forests.

European bullhead Cottus gobio Actinopterygii In rivers and lakes

Blue shark Prionace glauca Chondrichthyes Pelagic, open-ocean waters, Pacific bluefin tuna Thunnus orientalis Actinopterygii Epipelagic region

Wandering garter snake Thamnophis elegans Reptilia Around lakes and slow flowing streams

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2. Model and methods

2.1 Dynamic Energy Budget Integral Projection Model

The Dynamic Energy Budget Integral Projection model (DEB-IPM) (Smallegange et al. 2017) describes the dynamics of the length number distribution N(L, t) from time t to t + 1, with N as the number of females, by:

Equation 1: N(L,t+1) =

∫

Ω [D(L’,L(t))R(L(t)) + G(L’,L(t))S(L(t))] N(L,t)dL

Where Ω indicates the length of the domain. Equation 1 consists of four functions: the survival function S(L(t)), the growth function G(L’,L(t)), the reproduction function R(L(t)) and the parent-offspring function D(L’,L(t)). Detailed explanations of the four functions can be found in Smallegange (2017), but in short, they are:

(1) The survival function S(L(t)) from equation 1 is explained as the probability that an individual of length L will survive from time t to time t+1

In this function E(Y) is the expected feeding level, which can range from zero (empty gut) to one (full gut). S(L(t)) is 0 when L> Lm E(Y)/κ, which means individuals die from starvation when maintenance requirements are higher than the total amount of assimilated energy. Furthermore, a distinction is made between juveniles and adults since mortalities are often very different. This is incorporated in the function with e-µj_{for survival of juveniles and e}-µa_{for survival of adults.}

(2) The growth function G(L(t)) is the probability that an individual of body length L at year t grows to length L’ at t+1, which follows a Gaussian distribution (Smallegange et al., 2020).

In this equation, E(L(t+1)) = L(t) e−rB+(1−e−rB) Lm •E(Y) and σ2(L(t+1))=(1−e−rB)2 • 𝐿2𝒎 • σ2(Y)

The parameter 𝑟𝐵̇ is the von Beralanffy growth rate and the parameter σ(Y) is the standard deviation of

the expected feeding level. It is assumed that individuals can shrink under starvation conditions (Smallegange et al., 2017).

(3) The reproduction function R(L(t)) provides the number of offspring produced between time t and t+1 by an individual of length L at time t.

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8 Reproduction only takes place when length at puberty (Lp) is reached. Therefore, R(L(t)) is 0 when L<Lp. Furthermore, the number of offspring depends on the maximum reproduction rate (rm) of a female with maximum body length (Lm)

(4) The Parent-Offspring Association (D(L(t)) gives the probability that the offspring of an individual of length L are of length L’ at time t+1

Here, ELb(L(t)) is the expected size of offspring produced by individuals with length L(t) and σ2Lb is the associated variance.

Using Equation 1, one can calculate the derived life history quantities: the population growth rate (λ), the lifetime reproductive success (R0) and generation time (T) for ectothermic species, using species-specific life history traits (Table 3) and individual feeding levels as input parameters (Smallegange et al. 2017). All model calculations were conducted in MATLAB, using a script written by Smallegange et al. (2020). The input parameters for the DEB-IPM and their definitions are given in Table 2.

Table 2: Input parameters of the DEB-IPM

Parameter Definition Unit

κ Fraction of assimilated energy allocated to soma -

Lb Length at birth cm

Lp Length at puberty cm

Lm Maximum length cm

µj Juvenile mortality yr-1

µa Adult mortality yr-1

𝑟

_𝐵

̇

Von bertalanffy growth rate yr-1

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2.2 DEB-IPM parametrization

For each species (Table 1), I parameterized a DEB-IPM using the model parameters presented in Table 2. For most species, κ (assimilated energy allocated to maintenance and growth) was either taken from the dataset from Smallegange (2020), taken from literature or assumed to be 0.8 (Kooijman, 2010). Most values for juvenile and adult mortality (j and a, respectively) were directly taken from literature, but some had to be calculated from other values. This is explained below. All parameter values and references can be found in Table 3.

Calculating mortality rates from yearly survival percentages and yearly survival rates

When percentages of yearly mortality or survival were listed in literature, these were converted to mortality year-1_{. For Crocodylus johnsoni the annual adult survival rate was 95.7% (Tucker, 1997). This} can be rewritten as an annual survival probability P(s) = 0.957. The mortality rate can be calculated with the formula P(s)=exp(-µ). Rewriting the mortality rate as  = -log(P(s)), it returns an annual mortality rate of -log(0.957) = 0.004. This method is also used for juvenile C. johnsoni, for juvenile and adult Gasterosteus aculeatus, for adult Sphenodon punctatus, for juvenile and adult Gehyra variegata and for juvenile and adult Thamnophis elegans.

Calculating the mortality rate from mortality rate values across the life cycle using the geometric mean For the turtles Chelydra serpentine, Kinosternon flavescens and Caretta caretta the mortality rate is calculated by taking the negative logarithm of the geometric mean of the survival rates of different life stages

=-log(GEOMEAN([number1];[number2]; …). In case of C. serpentine, the hatchling survival rate was 0.23 and the juvenile survival rate was 0.678 (Heppell, 1998). The age at maturity for C. serpentine was 16 year (Heppell, 1998). In this case the annual mortality rate was calculated as follows:

= -log √ 0.23 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗

0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678 ∗ 0.678

16

= 0.46.

Averaging different mortality rates values for the same species

Dermochelys coriacea had a juvenile survival proportion of 0.004-0.02 year-1 (_{Eguchi et al., 2006).} Taking the mean (0.012), returns an annual juvenile mortality of  = -log(0.012) = 4.42 year-1_{. For} Sceloporus undulatus the mean of multiple survival rates from different years within the same article

(Ferguson et al., 1980) are used to get both the juvenile and adult mortality rate. Calculating mortality rate from survival till maturity

For the species G. aculeatus, S. punctatus and G. variegata I found juvenile survival rates till maturity (for references see footnotes in Table 3). For these species the juvenile survival rate is calculated with the formula μj = −log (∝√𝑃𝑚), where Pm is the survival probability from newborn to maturity and ∝ is the average age at maturity in years. Taking juvenile G. aculeatus for example, you have a mortality rate from birth to maturation of 99.8% (Ivanova et al., 2016), which can be rewritten as a survival rate of 0.002, and it takes 2 years to mature (Baker et al., 2015). Therefore, the juvenile mortality rate =-log(√0.0022 ), which equals 3.11 per year.

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10 Other ways of calculating the mortality rate

For some species, none of the above approaches could be used. For these species, another method is used. Kitchener et al. (1988) observed an 80% survival for adult G. variegata over three years. I therefore calculated the adult mortality rate as a = 3√0.8 = 0.93 yr-1.

For juvenile Tiliqua rugosa, Bull (1995) scored a a 16% chance of survival of their first year. A total of 42% of those survived a second year, and 62% of those survived a third year. For those 3 years, I therefore calculated the juvenile survival as j = −log⁡(√0.16 ∗ 0.42 ∗ 0.623 ) = 1.06.

The only other parameter which value was not directly taken from literature is the von Bertalanffy growth rate of T. elegans. I imported a von Bertalanffy growth curve of body length (cm) against age (years) (Bronikowski & Arnold, 1999) into graphreader (http://www.graphreader.com/), which reads of the age and correlated size as output in a CSV file. Afterwards, I used an R-studio script (Romeijn, 2021) to calculate the von Bertalanffy growth rate using a nonlinear least-squares estimation procedure, to fit the equation Lb = L∞ – [L∞ – Lb]e- t for

𝑟

_𝐵

̇

against observed growth curves (Bronikowski & Arnold, 1999). The other values that were needed as input were the maximum length of the population, which can be read from the graph and the length at birth. Finally, this resulted in a growth rate of 0.396. After the DEB was parametrized, a high and low feeding level was selected for each species. The low feeding level defines a bad environmental state and was selected for a population growth rate of approximately 0.6. In this state reproduction was negligible. The high feeding level was selected for a population growth rate of approximately 2.0. This defines a good environmental state with high reproduction. A feeding level of 1.0 often resulted in a population growth rate that was much lower than 2.0. Here, the highest population growth rate was taken at E(Y)=1. (Table 5).

2.3 Phylogenetic Principal Component Analysis

To define main axes of life-history strategies, a phylogenetically informed Principal Component Analysis (PCA) was conducted on the life history traits Lb, Lp, Lm, µj, µa,

𝑟

_𝐵

⁡̇and

Rm (Table 2), and the derived life history trait values of lambda, R0 and T of all species, using a slightly adjusted R-script from Paniw et al. (2018b) in R-studio [RStudio Desktop 1.4.1106]. The traits were log-transformed and scaled to µ = 0 and SD = 1 to agree with PCA assumptions. Within the code a phylogenetic tree is made. Then the phylogeny is linked to life-history traits through a modified covariance matrix. Lastly Pagel’s λ is estimated, which is a scaling parameter for the phylogenetic correlation between the species. Pagel’s λ ranges from 0 (no role of phylogeny in determining trait variation) to 1 (trait variation fully explained by phylogeny) (Freckleton et al. 2002). Two axes were kept to explain the variance in life history traits. PC1 describes the largest amount of explained variance of the species, PC2 describes the second largest amount of explained variance of the dataset.

2.4 Perturbation analysis

An elasticity on the log stochastic population growth rate (log(λs)) was conducted in Matlab (MATLAB, version 8.6.0.267246 [R2015b]) to examine the elasticity of λs to perturbation of each of the model parameters Lb, Lp, Lm, Rm,

𝑟

_𝐵

̇

, µj, µa. Each of these life history parameters, were consecutively perturbated, to identify which is the most influential to log(λs). The fraction of assimilated energy allocated to maintenance and growth (κ) was excluded, since this parameter is already included in Lm and Rm. In Matlab, each parameter was perturbed by 1% to calculate the elasticity of log(λs) to that parameter. This was done for both the low and high feeding level for each species.

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3. Results

3.1 DEB-parameters

As input for the DEB-IPM, species-specific parameters needed to be obtained. The results from the literature research are shown in Table 3. Most values for juvenile and adult mortality are not directly obtained from literature but calculated in several ways. This is discussed in section 2.2.

Table 3. Values for the life history parameters for each species. Parameters in top row are: κ, the fraction of assimilated energy allocated to maintenance and growth; Lb, length at birth in cm or mm; Lp, length at puberty in cm or mm; Lm, maximum length in cm or mm; μj, juvenile mortality rate per year; μa, adult mortality rate per year; ṙB, von Bertalanffy growth rate per year; and Rm, maximum reproduction rate per year. Superscript numbers refer to references in footnote. The two blue columns denote the mortality rates for juveniles and adults, which was the focus of this project. The unit of the three length parameters differs between species, but is consistent within one species.

Common name Latin name κ (-)

Lb (cm/mm) Lp (cm/mm) Lm

(cm/mm) µj (yr-1) µa (yr-1) rB (yr-1) Rm (yr-1)

Australian freshwater

crocodile Crocodylus johnsoni 0.971 _24.001 _150.001 _200.001 _0.7830 _0.0431 _0.1011 _13.001

Tuatara Sphenodon punctatus 0.791 _10.501 _45.001 _80.001 _0.2732 _0.0533 _0.0461 _4.501

Grass snake Natrix natrix 0.591 _19.001 _68.001 _190.001 _0.4234 _0.4034 _0.1081 _40.001

Sleepy Lizard Tiliqua rugosa 0.911 _9.001 _23.001 _32.801 _1.0635 _0.1136 _0.4981 _0.881

Leatherback turtle Dermochelys coriacea 0.921 _7.001 _121.001 _175.001 _4.4237 _0.0938 _0.1251 _140.011

three-spined stickleback Gasterosteus aculeatus 0.801 _1.501 _3.501 _8.001 _3.1139 _1.4739 _1.1601 _1500.001

porbeagle Lamna nasus 0.801 _58.001 _200.001 _280.001 _0.1240 _0.2140 _0.1111 _7.501

Snapping turtle Chelydra serpentina 0.802 _27.005 _236.005 _344.005 _0.4611 _0.2111 _0.5505 _12.006

Yellow mud turtle Kinosternon flavescens 0.802 _21.905 _90.005 _117.005 _0.5411 _0.0611 _0.1105 _6.007

Loggerhead sea turtle Caretta caretta 0.802 _5.009 _84.7010 _130.009 _0.2911 _0.3511 _0.7698 _76.5011

the tree dtella Gehyra variegata 0.802 _24.0012 _48.0012 _57.2512 _1.6141 _0.9341 _0.85022 _2.0012

The eastern fence lizard Sceloporus undulatus 0.613 _25.003 _58.003 _80.003 _2.8126 _1.1826 _0.41423 _23.0026

European bullhead Cottus gobio 0.914 _3.0014 _50.0018 _180.0021 _2.1242 _1.8342 _0.40021 _424.0014

Blue shark Prionace glauca 0.802 _45.0015 _201.0019 _383.0015 _0.6419 _0.2319 _0.10024 _33.0027

Pacific bluefin tuna Thunnus orientalis 0.974 _5.004 _150.004 _265.004 _1.2443 _0.1243 _0.17325 _15.4_E₆28

Wandering garter snake Thamnophis elegans 0.802 _187.7016 _400.0016 _700.0020 _1.1129 _0.2944 _0.39645 _14.3529

1_{Smallegange (2020);}2_{assumed 0.8 (Kooijman, 2010);}3_{Kearney (2012)}_;4_{taken from the Add My Pet database (Add-my-pet, 2020);}5_{Shine & Iverson (1995)}_;6 _{Congdon et} al. (1994); 7_{Christiansen & Dunham (1972)}_;8_{Casale et al. (2009)}_;9 _{Marn et al. (2017);}10 _{Casale et al. (2009b);}11 _{Heppell (1998);}12 _{Henle (1990);}14 _{Abdoli et al. (2005);}1 5 Compagno & Leonard (1984) ;16 _{King et al. (2016);}18 _{Fox (2006);}19 _{Campana et al. (2005);}20 _{Sparkman & Palacios (2009);} 21 _{Froese & Pauly (2016);}22 _{Sarre (1998);}23 _{Haenel &} John-Alder (2002);24 _{del Pilar Blanco-Parra et al. (2008);}25 _{Shimose et al. (2009);}26 _{Ferguson et al. (1980);}27 _{Montealegre-Quijano et al. (2014);}28 _{Ashida et al. (2014);}29 _Bronikowski & Arnold (1999) 30 _{Smith (1987);} 31 _{Tucker (1997);} 32 _{Wörner (2009);} 33 _{Mitchell et al. (2009) ;} 34 _{Sewell et al. (2015);} 35 _{Bull (1995);} 36 _{Bull & Baghurst (1998);} 37 _{Eguchi et al.} (2006); 38 _{Rivalan et al. (2005);} 39 _{Ivanova et al. (2016) ;} 40 _{Campana et al. (2001);} 41 _{Kitchener et al. (1988);} 42_{Chaumot et al. (2006);} 43 _{Mangal et al. (2010);} 44 _{Robert et al. (2009).} ;45_{Calculated in R-studio with a graph from Bronikowski & Arnold (1999);}

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3.2 DEB-IPM output for low and high feeding level

The results of the DEB-IPM are presented in table 4 and 5. Table 4 has the derived life history quantities for low feeding level and Table 5 for high feeding level. With all species, lambda and R0 are lower at low feeding level while this varies for generation time. Furthermore, S. undulatus is a notable outlier with the lowest values for lambda at both feeding levels.

Table 4: Derived life history quantities for low feeding level for each species. The derived life history quantities are lambda: population growth rate, R0: lifetime reproductive success and T: generation time.

Table 5: Derived life history quantities for high feeding level for each species. The derived life history quantities are lambda: population growth rate, R0: lifetime reproductive success and T: generation time.

Common name Latin name Feeding level Lambda R0 Generation time

Three spined stickleback G. aculeatus 0.5 1.277 1.683 2.131

The tree dtella G. variegata 0.918367347 0.618573 0.041614 6.618919

European bullhead C. gobio 0.5 0.730549 0.298387 3.851973

The eastern fence lizard S. undulatus 0.765306 0.207377 3.98E-05 6.439355 Wandering garter snake T. elegans 0.62244898 0.602833 2.95E-02 6.962575 Snapping turtle C. serpentina 0.979591837 0.821619212 0.195051084 8.318955868 Loggerhead sea turtle C. caretta 0.663265306 1.077405149 1.517322072 5.592436908 Sleepy lizard T. rugosa 0.775510204 0.663812 0.013355175 10.53273589

Porbeagle L. nasus 0.724 0.945385899 0.168917699 31.6644932

Grass snake N. natrix 0.5 0.871 0.157 13.381

Pacific bluefin tuna T. orientalis 0.571428571 0.743426 0.019383 13.30024

Blue shark P. glauca 0.551020408 0.659907 7.64E-06 28.34453

Yellow mud turtle K. flavescens 0.775510204 0.649586713 3.19E-06 29.33609998 Australian freshwater crocodile C. johnsoni 0.765306122 0.618635562 1.09E-08 38

Tuatara S. punctatus 0.5714 0.8005 0.0000 64.1441

Leatherback turtle D. coriacea 0.714285714 0.642472 1.78E-29 149.6272342

Common name Latin name Feeding level Lambda R0 Generation time

Three spined stickleback G. aculeatus 0.561 2.110 4.929 2.137

The tree dtella G. variegata 1 0.779783 0.181522 6.860101

European bullhead C. gobio 0.836734694 1.963947 6.307275 2.728627 The eastern fence lizard S. undulatus 1 0.40308 0.016101 4.544124

Wandering garter snake T. elegans 1 1.291236 3.885562 5.310126

Snapping turtle C. serpentina 1 0.964869168 0.760468319 7.656590192 Loggerhead sea turtle C. caretta 0.755102041 1.991422 21.70134 4.467415

Sleepy lizard T. rugosa 1 0.924502 0.424636067 10.91105545

Porbeagle L. nasus 1 1.153184 7.952223 14.54778

Grass snake N. natrix 1 1.322 6.765 6.855

Pacific bluefin tuna T. orientalis 0.744897959 1.927122 1357.43 10.99549

Blue shark P. glauca 1 0.9962 0.951806 12.97388

Yellow mud turtle K. flavescens 1 0.946882565 0.142347043 35.7178467 Australian freshwater crocodile C. johnsoni 1 0.935710152 0.009188668 71

Tuatara S. punctatus 1 1.0033 1.1353 38.8281

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Legend for arrows in Figure 1:

3.3.1 Principal Component Analysis

The results of the PCA with all DEB-parameters included is shown in figure 1. In Figure 1A, Ro has a negative correlation with PCA 1, while T correlates positively. PCA axis 2 has a negative correlation with the parameters Rm and µj and a positive correlation with Lb. PCA axis 1 explained 40% and PCA axis 2 explained 20%, altogether 60% of the variation of the life-history traits.

Figure 1B shows a positive correlation of µj with PCA 1 and a negative correlation with Lm and Lp. PCA 2 shows a positive correlation with Lambda and Ro and a negative correlation with T. An explained variation of 39% of PCA 1 and 21% of PCA 2 gives a total of 60% explanation of the variation of the life-history traits at high feeding level.

Figure 1: PCA output for low and high feeding level (all DEB-parameters included)

Without all DEB-parameters, the PCA axes explained a total of 92% of the variation of the life-history traits for low feeding level and a total of 91% for high feeding level (Fig 2). Both high and low feeding level correlate with the same arrows. PCA axis 1 correlates negatively with T and positively with R0. PCA axis 2 correlates negatively with Lambda.

To test the influence of phylogeny on the PCA output, Pagel’s λ is estimated. For both high and low feeding level the outcome was 7.712479e-05 on a scale from 0 to 1 with 0 being no role of phylogeny in determining traits variation.

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Legend for arrows in figure 2:

Figure 2: PCA output for low and high feeding level (input DEB-parameters excluded)

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3.3.2 First PCA axis

The PCA axis that is determined to be the fast-slow continuum is presented for both feeding levels and for with and without DEB-parameters in Figures 3-6. On the left side of the continuum the slow species can be found such as the Leatherback turtle (D. coriacea), on the right side the fast species can be found such as the three-spined stickleback (G. aculeatus). Larger species such as for example the freshwater crocodile (C. johnsoni) are found at the slower side of the continuum, while smaller species such as the tree dtella (G. variegata), who’s snout-vent length reaches 57 mm (Henle, 1990), are at the faster side of the continuum.

The results of the perturbation analysis are visualized between the brackets after each species. These only differ between high and low feeding levels, not between with and without DEB-parameters. The extremities in each figure are almost identical, while there are shifts in the middle between different feeding levels. For the perturbation analysis, most species seem most sensitive to Lp and Lm. There is no shift in sensitivity from the slow to the fast side of the continuum. Furthermore, the only species that are sensitive to mortality are K. flavescens at low feeding level and T. elegans at high feeding level.

Figure 3: Fast-slow continuum for low feeding level, with all parameters included

G. aculeatus (Lm) G. variegata (Lm) C. gobio (Lm) C. caretta (Lp) T. elegans (Lp) C. serpentina (Lp) S. undulatus (Lm) T. rugosa (Lp) N. natrix (Lp) L. nasus (Lp) T. orientalis (Lp) P. glauca (Lp) K. flavescens (mu_juv) C. johnsoni (Lp) S. punctatus (rB) D. coriacea (Lp) -2.5 -1.5 -0.5 0.5 1.5 2.5 Slow Fast

Fast-slow continuum

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Figure 4: Fast-slow continuum for high feeding level, with all parameters included

Figure 5: Fast-slow continuum for low feeding level, without DEB-parameters included

D. coriacea (Lp) S. punctatus (rB) C. johnsoni (Lp) K. flavescens (mu_juv) P. glauca (Lp) L. nasus (Lp) T. orientalis (Lp) N. natrix (Lp) T. rugosa (Lp) C. serpentina (Lp) T. elegans (Lp) G. variegata (Lm) S. undulatus (Lm) C. caretta (Lp) C. gobio (Lm) G. aculeatus (Lm) -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Slow Fast

Fast-slow continuum

Low feeding level - without DEB-parameters

D. coriacea (Lp) C. johnsoni (Lp) S. punctatus (Lm) K. flavescens (Lp) T. rugosa (Lp) P. glauca (Lm) S. undulatus (Lm) L. nasus (Lp) C. serpentina (Lp) G. variegata (Lp) N. natrix (Lp) T. orientalis (Lm) T. elegans (mu_juv) C. caretta (Lm) C. gobio (Lm) G. aculeatus (Lm) -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Slow Fast

Fast-slow continuum

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Figure 6: Fast-slow continuum for high feeding level, without DEB-parameters included

D. coriacea (Lp) C. johnsoni (Lp) K. flavescens (Lp) S. punctatus (Lm) L. nasus (Lp) P. glauca (Lm)T. rugosa (Lp) T. orientalis (Lm) N. natrix (Lp) C. serpentina (Lp) C. caretta (Lm)G. variegata (Lp) T. elegans (mu_juv) C. gobio (Lm) G. aculeatus (Lm) S. undulatus (Lm) -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 Slow Fast

Fast-slow continuum

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3.3.3 Second PCA axis

The second axis of each PCA is visualized in figures 7-10. The parameters between the brackets from the perturbation analysis correspond with the Figures from earlier (3-6). There are larger shifts between the low and high feeding level without DEB-parameters (9&10) than between the low and high feeding level with DEB-parameters (7&8). Figure 7 and 8 do follow a similar distribution with a few changes in the middle, such as an exchange of T. rugosa with C. gobio and L. nasus with T. elegans.

Figure 7: Second axis for low feeding level, with all parameters included

Figure 8: Second axis for high feeding level, with all parameters included

G. aculeatus (Lm) _{D. coriacea (Lp)}T. rugosa (Lp) C. gobio (Lm) T. orientalis (Lp) S. undulatus (Lm) G. variegata (Lm) S. punctatus (rB) C. caretta (Lp) K. flavescens (mu_juv) C. johnsoni (Lp) N. natrix (Lp) P. glauca (Lp) C. serpentina (Lp) L. nasus (Lp) T. elegans (Lp) -2.5 -1.5 -0.5 0.5 1.5 2.5

Second PCA axis

L. nasus (Lp) T. elegans (mu_juv) P. glauca (Lm) C. serpentina (Lp) C. johnsoni (Lp) N. natrix (Lp) K. flavescens (Lp) S. punctatus (Lm) C. caretta (Lm) T. orientalis (Lm) G. variegata (Lp) S. undulatus (Lm) C. gobio (Lm) T. rugosa (Lp) D. coriacea (Lp) G. aculeatus (Lm) -3 -2 -1 0 1 2 3

Second PCA axis

High feeding level Low feeding level

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Figure 9: Second axis for low feeding level, without DEB-parameters included

Figure 10: Second axis for high feeding level, without DEB-parameters included

G. aculeatus (Lm) C. caretta (Lp) L. nasus (Lp) N. natrix (Lp) S. punctatus (rB) C. serpentina (Lp) T. orientalis (Lp) C. gobio (Lm)P. glauca (Lp) K. flavescens (mu_juv) D. coriacea (Lp) T. rugosa (Lp)C. johnsoni (Lp) G. variegata (Lm) T. elegans (Lp) S. undulatus (Lm) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

Second PCA axis

G. aculeatus (Lm) C. caretta (Lm) C. gobio (Lm) T. orientalis (Lm) N. natrix (Lp) T. elegans (mu_juv) D. coriacea (Lp) L. nasus (Lp) S. punctatus (Lm) C. johnsoni (Lp) P. glauca (Lm) K. flavescens (Lp) C. serpentina (Lp) T. rugosa (Lp) G. variegata (Lp) S. undulatus (Lm) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Second PCA axis

Low feeding level - without DEB-parameters

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4. Discussion

This research aimed to find an answer to the question of whether patterns in life history speed and reproductive strategy can be explained from an energy budget perspective. The fast-slow continuum was identified in the results, whereas the reproductive strategy axis could not be identified. For Figure 1B, generation time corresponded with the vertical axis, in contrast with the other figures. Therefore, PCA axis 2 of Figure 1B corresponds with PCA axis 1 in the other figures. Furthermore, differences between the data with and without DEB-parameters are also evident. In the next section, each of the results will be elaborated on.

4.1 Model performance and limitations

The DEB-IPM was used to calculate the derived life history quantities of various species for a low and a high feeding level. Although the values for low and high feeding level were handpicked, they were hard to establish. For example, lambda at the lowest feeding level ranged from 0.20 to 1.27 while the aim was to choose the low feeding level for a lambda between 0.6 and 0.8. S. undulatus reached a lambda of 0.40 at feeding level 1. This is not very accurate since this would mean that the population is not viable. This is probably due to both a high mortality for juveniles and adults. Also, the lifetime reproductive success and generation time for many species resulted in 0 for a large part of the dataset, making it harder to establish a good low and high feeding level.

Furthermore, PCA analyses were conducted on both low and high feeding levels and data with and without DEB parameters incorporated. Firstly, there is a remarkable difference in the explained variance of the axes between Figure 1 and Figure 2. In Figure 1 the explained variance of the data added up to 60% while in Figure 2 it added up to 92%. While the explained variance is higher in Figure 2, the species in the fast-slow continuum and second axis without DEB-parameters seemed more clustered. This possibly has to do with the number of parameters the Figures are based on. When more parameters are taken into account, more variation between the species is included in the data.

In addition, the placing of the species on the axes changed between different feeding levels. The extremities corresponded between the figures, but in the middle, there were many shifts between low and high feeding level. This is an important aspect of the DEB-IPM that is not included in a demographic model. It indicates that not only life history traits provide the necessary information, but also the environment in which the species resides. Although it is difficult to compare the DEB-IPM with demographic models, since there is no comparable study with the same species, this indicates the importance of including the dynamic energy budget.

Lastly, the data from table 3 is gathered from different articles. Therefore, there is no standard way that for example the mortality rates are determined. Environmental circumstances and the time period of the measurements varied a lot between each species and even within one species for juveniles and adults. If there would be one standardized method, results would probably be more accurate since the mortality rate has a high influence on where species are placed at the fast-slow continuum. This could also be improved by comparing or gathering multiple populations from one species to have more certainty about the accuracy of the data.

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4.2.1 Fast-slow continuum

The fast-slow continuum can be recognized in the PCA with age at sexual maturity and generation time at one side, against annual sexual reproduction. This depicts a trade-off between survival and reproduction (Paniw et al., 2018). In figure 1 and 2, generation time is in all cases on the opposite side of R0. Although Paniw et al. (2018) uses different parameters, both annual sexual reproduction and lifetime reproductive success encompass reproduction. Therefore, PCA axis 1 in Figure 1A and Figure 2, and PCA axis 2 in Figure 1B can be interpreted as the fast-slow continuum.

The species in the fast-slow continuum follow a similar distribution in figures 3,4,5 and 6. D. coriacea is in all Figures at the extremity of the slow side while G. aculeatus is at the other

extremity. It was expected that the species with a relatively high mortality rate were on the fast side of the continuum and vice-versa. To a certain extent this corresponds with the Figures, as G. aculeatus, G. variegata, S. undulatus, Cottus gobio and T. elegans are on the fast side of the continuum and all have a very high mortality rate. D. coriacea is an exception, since this species can be found at the slow side. D. coriacea has an extremely high juvenile mortality rate but a very low adult mortality rate. This is presumably the reason why it is at the slow side of the Figure. Other species at the slow side of the continuum are S. punctatus, C. johnsoni and K. flavescens. These all have a very low mortality rate in common (0.05, 0.04 and 0.06 respectively).

Slow life history species also often have low reproduction but offspring of larger size that take longer to mature (Mishra et al., 2017). This suggests that the parameters that also influence the fast-slow continuum are reproduction rate and body size. The species from Table 3 that have few offspring and a significantly higher length at maturity in comparison with their length at birth are C. johnsoni, S. punctatus, Prionace glauca, C. serpentina, K. flavescens, D. coriacea and Lamna nasus. The species in this row that are not found on the expected side based on this theory are C. serpentina and L. nasus. These have in common that their overall mortality rate is higher in comparison with the other species on the slow side. Although juvenile mortality is similar within all species, C. serpentina and L. nasus have higher adult mortality rates. This indicates that the separation of juvenile and adult mortality influences the position of these species on the fast-slow continuum. It placed some of the turtle species (D. coriacea & K. flavescens) on the slow end of the continuum, despite having a high juvenile mortality.

Lastly, it seems that incorporating the DEB-parameters into the PCA, is an easier way to identify which parameters explain the fast-slow continuum. In Figure 1B for example, the arrows for adult mortality, maximum reproduction rate, lambda and the von bertalanffy growth rate correlate with the vertical axis. These are also the parameters that are identified earlier that influence the placing of the species on the axis.

Overall, it showed that the model outputs and the individual parameters correctly placed species on the fast-slow continuum predicted by the life history theory.

4.2.2 Reproductive strategy axis

According to Paniw et al. (2018), the reproductive strategy axis can be determined with positive loadings of the variables R0 and the frequency of reproduction. The frequency of reproduction is not comparable to a parameter that can be found along PCA 2 in Figure 1A and 2 and PCA 1 in Figure 1B. Therefore, these PCA axes cannot be referred to as a reproductive strategy axis. Besides, the

percentage of explained variation is relatively low, which makes it difficult to take any conclusions from it. It is remarkable however, that Figure 9 and 10 almost exactly follow the ascending order of lambda of table 4 and 5, while Figures 7 and 8 do not.

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4.3 Perturbation analysis

The perturbation analysis shows which model parameters each species’ population growth rate (lambda) is the most sensitive for at both feeding levels. For the sensitivity analysis it was expected to notice a shift in the parameters from the slow side to the fast side. There is no distinct shift in the parameter for each species between the low and high feeding level. It is expected that slow life history species are more sensitive for reproduction, while fast life history species are more sensitive for mortality (Smallegange, 2014). These expected results cannot be found in the Figures. The parameters that are found most often in the perturbation analysis are length at puberty, Lp and maximum length, Lm. The maximum length of a species can influence the clutch size. (Frazer & Richardson, 1986) Therefore, this means that the higher the Lp and Lm are, the larger the population growth rate (λ) will be.

None of the species seem to be most sensitive to reproduction in both low and high feeding level. Sensitivity to mortality however, can be found at K. flavescens in low feeding level and T. elegans in high feeding level. Since one of these species is more at the slow side of the continuum and the other is more on the fast side, no conclusions can be drawn from these results.

4.4 Broader context

As stated before, the model was able to place the species on the fast-slow continuum although other methods were used then for example by Salguero-Gómez et al. (2016). The other models from other articles were already able to do so but lacked a mechanistic understanding. These mechanistic understandings are incorporated with trade-offs on where energy is allocated. According to Healy et al. (2019), the position of a species within life history strategy is driven by the acquirement and processing of resources from the environment. This is consistent with the results, as species change their position on the continuum when having a different feeding level. The change of the species along the continuum suggests that means a species is not necessarily classified as a fast or slow species but that this can change according to their circumstances. The DEB-IPM can therefore assess the species’ response situation dependent, which other models are not able to do. For example, when resources are low or circumstances are bad, ‘slow’ species are better in avoiding extinction since they are less vulnerable to such environmental stochastic events. On the other hand, fast life history species are able to grow their population quicker and recover sooner after an event (Allen et al., 2017).

For the reproductive axis, it is clear other parameters are necessary to specify the strategy for each species. However, the DEB-IPM could provide insight due to the different feeding levels that are taken into account when doing calculations. Semelparous species can adapt their reproductive strategy under unexpected circumstances. At high feeding levels, the ‘bonus’ resources that are usually

allocated to growth and maintenance can now be used for a second reproductive event (Hughes, 2017). This trade-off is incorporated in the DEB-IPM and shows the importance of trade-offs in these types of models. When the reproductive axis is specified correctly, the DEB-IPM could predict population fluctuations more accurately due to this aspect under different circumstances.

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4.5 Future research

For future research, it would be interesting to focus on the second PCA axis. Other parameters that refer to reproduction could be added for each species such as the degree of iteroparity, mean clutch size and frequency of reproduction. With addition of these parameters, there is a higher chance of identifying the axis and having a higher explained variation for the second PCA axis. Also, it would be interesting to see if the arrows of the input parameters correlate with the second PCA axis. If so, this would be an easier way of identifying which parameters influence a species reproductive strategy.

5. Conclusion

In this thesis it is researched whether the mechanistic basis of variation in cross-taxonomical patterns can be understood from an energy budget perspective. The first pattern that was expected to be found was the fast-slow continuum. The species that showed a high reproduction rate and high mortality rate were placed on the fast end of the fast-slow continuum, which is in line with life history theory. Some species however, were not found on the continuum as expected based on literature. This mainly has to do with questionable mortality rates from literature and not with the DEB-IPM itself. The other pattern that was expected to be found was a reproductive axis. However, none of the parameters could resemble the parameter necessary to have this axis. Therefore, these is no identification of what the second PCA axis means.

Furthermore, the addition of the DEB-parameters in the PCA analyses, showed a less clustered fast-slow continuum. Although the axis explained less of the variation of the dataset when adding all the DEB-parameters, more information on the species is included into the output. This addition could potentially improve the placing of species on the continuum.

Lastly, feeding level was also a great influence on the species position at the fast-slow continuum. This indicates the importance of integrating dynamic energy budget in a model, which is an aspect that is not taken into account with demographic models. The DEB-IPM could also improve results of the reproductive strategy axis when identified correctly, since the reproductive strategy can be altered when sufficient resources are available. Different feeding levels can therefore alter the distribution on the reproductive axis significantly.

Data Accessibility Statement

The data that support the findings of this study and the used scripts are openly available at: https://github.com/irisvanrijn/BachelorThesis.git

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Acknowledgements

The completion of this study could not have been possible without the expertise of my thesis advisor Dr. Isabel Smallegange. I would like to thank her for the consistent meetings, informative and critical comments and quick replies. I also want to thank my second supervisor Dr. ir. Emiel van Loon for reading and grading my thesis.

Analyzing life history patterns using the Dynamic Energy Budget Integral Projection Model (DEB-IPM)