Evolutionary history partially explains modularity patterns in networks describing species genetic diversity

Juliana José1_{, Marcus A. M. de Aguiar}2_{, Sérgio F. dos Reis}3_{, Paulo R. Guimarães Jr}2,4_. 1_{Pós-graduação em Genética e Biologia Molecular, Instituto de Biologia, Universidade Estadual de}

Campinas, Cx.P.6109, 13083-970, Campinas, São Paulo, Brasil. +55(19)3521-6279. E-mail: [email protected]

2 _{Instituto de Física Gleb Wataghin and Instituto de Biologia, UNICAMP, 13083-970, Campinas,}

SP, Brazil.

3 _{Departamento de Parasitologia, Instituto de Biologia, Universidade Estadual de Campinas,}

Cx.P.6109, 13083-970, Campinas, São Paulo, Brasil. +55(19)3521-6279.

4 _{Department of Ecology and Evolutionary Biology, University of California, Santa Cruz, CA,}

95064, U.S.A.

Key words: heterozygosity, population genetics, macroevolution, taxonomy, spectral

analysis, simulated annealing.

Abstract. We studied for the first time species genetic diversity (SGD) with network

approach. SGD networks are highly modular and have non-random structural patterns. Within modules species are organized according to similar levels of genetic diversity and this modular structure is partially explained by species evolutionary history. Our results suggest that organizing processes acting at the species level are influencing the genetic diversity we observe in current species. The approach introduced here may be useful to detect patterns of similar SGD within taxa.

Introduction

In the past decade, the description of natural, technological and social systems has benefited from the network approach, in which the system elements are described as nodes and the interactions between elements are depicted as links (Albert and Barabasi 2002; Amaral and Ottino 2004; Proulx et al. 2005). The network approach was especially useful to detect modularity, that is, the existence of cohesive groups of interacting elements forming subunits within the networks (Wattz and Strogatz 1998; Guimera and Amaral 2005). Different organizing processes operating in the system will lead to different network patterns. Therefore, the structural patterns observed in a network may allow us to infer the underlying processes operating in the system (Albert and Barabasi 2002).

In biology, the use of analytical methods based on the network approach has been used to describe different biological levels of organization, from cell metabolism to entire ecosystems (Barabasi and Oltvai 2004; Montoya et al. 2006; Williams et al. 2002). In this context, modularity was observed in distinct biological systems, including metabolism (Ravasz et al. 2002), reproductive (Fortuna et al. 2008), competitive (Araujo et al. 2008) and social (Guimarães et al. 2007) interactions between individuals within animal populations, and species interactions (Olesen et al. 2007; Guimarães et al. 2007b, Melian and Bascompte 2004). In all these systems, the detection of modular patterns was useful to reveal some organizing processes operating in the system. For example, the modular structure observed in food webs may be the result of ecological and evolutionary processes, leading to some groups of species sharing more similar prey assemblages than with other species (Melian and Bascompte 2004).

Species vary not only in their degree of similarity with respect to their feeding habits, but also in all other biological attributes, including morphology, physiology and

genetics. Hence, network analysis may help to detect the occurrence of discrete groups of species according to a given biological attribute. For instance, species varies highly in the amount of genetic diversity and this variation can be structured in groups of species (Nevo 1978; Nevo et al. 1984; Ward et al. 1992).

Genetic diversity is a central concept in evolutionary biology and an important trait

for the population genetics and conservation biology. The importance of genetic diversity rest on the assumption that the reservoir of genetic variability acts as hedge against extinction (Dobzhansky 1939), and thus is an important requisite for evolutionary change (Lewontin 2002). Species genetic diversity has been linked to many other species traits (Nevo et al. 1984, Frankham 1996, Spielman et al. 2004, Bazin et al. 2006). However, the importance of evolutionary history shaping species genetic diversity has been neglected (José et al. in press).

Differences in the amount of genetic diversity between groups of species may be a result of the species’ evolutionary history (Ward et al. 1992, José et al. in press). In addiction, closely related species usually resemble each other in their biological attributes more than do non-closely related species (Felsenstein 1985, Cheverud et al. 1985, Bloomberg and Garland 2002). Therefore, we would expect that closely related species would share more similar levels of genetic diversity.

Here, we described for the first time different groups of species as networks in which nodes represent species and edges connect pairs of species that show similar levels of genetic diversity. We analyzed some basic aspects of network structure, with special attention to patterns of modularity. Whenever modularity emerges, we tested if modules are associated with discrete evolutionary groups.

Methods

Our dataset includes a wide variety of distinct taxonomic groups: Molluscs (Littorinidae, Patelloidea, and Planorbidae), Crustaceans (Gammaridae and Decapoda), Insects (Drosophila, Hemiptera, Hymenoptera and Lepidoptera), Reptiles (Squamata), and Mammals (Carnivora, Primata and Rodentia), amounting to13 groups. We compiled from literature the estimates of genetic diversity, measured as expected heterozygosity (known as genetic diversity) (Wright 1931). Our dataset include species from database of Nevo (1978), Nevo et al. (1983) and Ward et al. (1992), and is available upon request.

For each taxonomic group, we create a matrix

W

describing the genetic diversity similarity within a given animal group. In this matrix, the element is wij = 1 H

(

i
Hj

)

, in

which Hi is the expected heterozygosity for the species

i

and

H

j is the expected

heterozygosity for the species j. We defined the adjacency matrix

A

as A =

TW, in

which

T is an operator acting on each element

w

ij in such way that the value one is

assigned whenever

w

_ij

> T

in which

T

is a threshold value and zero otherwise (Costa 2004). In our study we defined

T

as the mean genetic diversity similarity.

The general structure of a complex network can be described by the distribution of eigenvalues of

A

(Aguiar and Bar-Yam 2005). Thus, we described the general structure of the thirteen species genetic diversity networks (SGD networks) through spectral analysis. The smoothed density of eigenvalues of the square matrix is defined as



_

_{( )}

=

1

N

_i





(  

i

)

S

in which

i are the eigenvalues, and

N

is the total number of species in the network.
E is

a normalized Gaussian whose width

controls the smoothness of density function. If
is

No documento Evolução da variabilidade genetica : separando os fatores que determinam a variabilidade das especies (páginas 76-80)