Complex Adaptive Systems in Biology

Have you ever taken a moment to look at an anthill? It is a fascinating sight. There are hundreds of small ants working towards one goal: maintaining the wellness and propagation of the offspring. They are intrinsically organized into various committees. These sub-communities have specialized tasks such as caring for young, nest building and foraging etc. (Leitner, 2019). Though they all work towards the same goal overall, each hierarchical community contributes in a different way. The ant network is an example of a complex system. Now imagine if the ants’ food supply becomes extinct. To maintain the wellness of their community, they must adapt the chain of sub-communities to fit their new needs. The anthill now is known as a complex adaptive system (CAS). Complex adaptive systems are found across many fields and are often used to understand how patterns of interaction arise (Hartvigsen, 1998; Preise, 2018). It provides an understanding of how small scale local interactions produce macroscopic changes on a larger scale (Hartvigsen, 1998). 

As the name sounds, CAS can be hard to define. It is an abstract concept with many moving parts. In general, CAS can be defined through understanding three main properties: diverse and individual in its components, local interactions within those components and a self-organizing property that uses the outcomes of interactions to determine their replication (Levin, 1998). Individual working groups, interacting with other groups creating a network of interactions that seem to be one working entity, such an anthill. There is no global controller but rather each hierarchical level controls itself (Levin, 1998). If one component becomes disrupted, there is a chain reaction of feedback events. For example, when one of the plant species in a food web becomes extinct, it initially affects the herbivores, but that effect inevitably impacts carnivores as well (Carmichael, 2019; Levin, 2013). It produces a wave effect. Through the next three examples, we hope to clear up what CAS is and how complexity plays a role in biology.


Though complex adaptive systems in biology differ in many ways, most have one starting point. That starting point is genes. It is the first deterministic entity of all further behaviour. But why are genes the foundation of most biological complex adaptive systems?

Genetic Selection and Phylogenetic Classification 

Genes are the first level of selection for replication and enhancement of traits. John Holland, one of the early investigators of CAS, introduced the “never get there” phenomenon (Holland, 1992). As environments continue to change, the whole system is always in a novel surrounding (Holland, 1992). Thus, CAS are always far from optimal conditions, so they "never get there" (Holland, 1992). They are constantly evolving to exhibit new behavior patterns. Although the environment is important for evolution, the genes are what propagates to the next generation (Levin, 1998). So, the genes are the key to the adaptive nature described in the "never get there" phenomenon. Adaptation occurs through the process of natural selection and it requires no global control (Morange, 2001). For example, a study used gene markers to determine the ancestral relationship between Caninae species (Zrzavý, 2018). Each species of the Caninae is its own CAS within the larger CAS of the ecosystem. The ancestral relationships show how the species complex system has adapted over time (Hinchliff, 2015). They can classify each species system based on their genes which is reflected in their behaviors and morphology (Provata, 2014). Though natural selection chooses specific behaviours to pass on, it is the gene that propagates to the next generation. This is because animals diverge from their ancestors through genetic changes (Provata, 2014). Hence, the gene is the foundation of the fundamental principle of replication and enhancement of CAS.

Genetic Interactions 

Genes interact at an individual level but influence all further global levels beyond them. Genes participate in localized interactions in a very complex manner. For example, when a gene is “knocked out”, it may not have drastic effects on the organism because the other genes could compensate for its loss (Morange, 2001). Many genes have developed adaptations to protect the destruction of the complex system. But some genetic interactions can also produce negative effects because they can lead to fitness defects (Kuzmin, 2018). For example, synthetic lethality is when two mutations that are not lethal on their own occur at the same time inducing an inviable organism (Kuzmin, 2018). In this case, the gene determines the fitness of the individual. These two gene interactions show the influence of the local gene interactions on the observable traits of the individual. Then those individuals interact with other individuals forming populations, communities, ecosystems, and biomes. But the basis of local interactions that influences the rest of the hierarchy are the genes themselves which induces a global effect.

Genetic Diversity

Genes are also the foundation of many biological CAS because they are the vehicle of variation (Hughes, 2008). Diversity is what fuels selective processes in natural selection. (Page, 2010). Variation allows for one individual to outcompete others and thus, enhance the population's gene pool (Page, 2010). Genetic diversity also has important ecological consequences because it influences processes such as productivity, competition, communal structure, and energy flow (Morange, 2001). These consequences occur across the population, community, and even ecosystem hierarchical levels (Hughes, 2008). At the population level, genes create variation within species through random mutation events, heredity patterns, RNA editing, and gene regulation (Lynch, 2003). Spliceosomes in genes also induce great variation in gene expression (Karamysheva, 2015). Spliceosomes act like scissors and cut mRNA, which is the blueprint for protein formation, in a variety of different ways (Karamysheva, 2015). The ways in which these mRNAs are cut can be precursors for disease formation within cells and tissues such as cancer (Karamysheva, 2015). The variation within the cutting of mRNA is determinant of the disease trait and how it interacts with other systems such as proteins and cells. Each gene variation will interact differently with the environment and thus drive the adaptive change in the system. This makes genes a foundational component of CAS. 

Genetics has allowed for the interpretation of how many behaviours and biological patterns adapt. Genes are the key to CAS because they are the underlying mechanism in diversity, selection, and interactions. They can be used as a model for finding parallels in similarity in other fields. They are the key to adoption in CAS and thus should be deemed as determinants of complexity in biology. 


Early discussions of human anatomy assumed that singular and simple factors led to the vast changes within a body. However, there is a growing awareness that individual factors do not independently affect the body; instead, they work in conjunction with each other to varying degrees. Bioarchaeology is one such field that seeks to understand how factors such as diet, lifestyle, and sex affect anatomical development through an evolutionary perspective. Researchers are now understanding that the human body is a complex adaptive system that responds to environmental and biological conditions (Wells & Stock, 2020). This section of the literature review will discuss how three factors—diet, sex and lifestyle—influence human anatomy by looking at early farmers. 


Human diets changed from lots of animal proteins into a mix of carbohydrates with some low-quality proteins (Macintosh et al, 2016). They began to harvest cereals and grasses as those were the plants growing around them (Leonard et al, 2010). Less protein meant that these early humans had reduced bone and muscle growth, resulting in a lower body mass and strength (Macintosh et al, 2016; Little, 2020). Bones such as the tibia—the shins—and femur—the thigh bone—were the main areas that became smaller (Bridges et al, 2000). Cranial bones also got smaller, and there were additional changes to their brains’ shape and proportions. Interestingly, studies in Europe have found the opposite, where the rapid increase in quality of life made them grow taller (Rosenstock et al, 2019). Maturation and puberty also began earlier, limiting their growth in favour of increasing reproductive rates. Instead of developing for longer, they had longer fertile years and faster reproduction. Species that live under intense environmental changes or stressors will increase their fertility to counteract the high death rates (Macintosh et al, 2016). Finally, a higher carbohydrate intake would not provide enough energy for processes such as fat and muscle build-up, leading to a smaller stature (Piontek & Vancata, 2012).

A side effect of eating mostly carbohydrates meant that tooth decay or caries were more prevalent (Clement, 2013). Carbohydrates fall under two categories; simple sugars, like in fruits, or complex sugars, such in grains. Without practising any dental hygiene, the sugar would stay longer in the mouth. These will then combine with the mouth's bacteria and salivary enzymes. These become plaques that adhere to teeth, eventually dissolving the protective enamel. Also, early farmers did not eat enough high-quality proteins, further enabling plaque development. Another contributing factor to developing caries is underdeveloped enamel or enamel hypoplasia. Early maturation meant that the enamel would not be as thick as in hunter-gatherers. Less enamel means that the teeth would wear out quicker and be weaker (Karsten, 2014; Nicklisch et al, 2016).

Neolithic humans also ingested simple sugars by drinking milk after the domestication of sheep and goats (Leonard et al, 2010). Farming crops means that there are seasons without any food, so early farmers would have started to supplement the diet year-round. By watching other species, such as dogs and cats, suckle humans learned how to milk farm animals. The ancestor of cows—aurochs—were also undergoing domestication at this time and eventually became a source of meat and milk to farmers. Milk contains sugars in the form of lactose and is digested with the help of an enzyme called lactase. Most species have a gene that turns off lactase enzymes and decreases their desire to drink milk as adults. However, these farmers underwent selection to maintain lactase throughout the lifecycle. This is known as lactase persistence or tolerance and is the reason that modern humans can eat dairy products (Chessa et al, 2011; Helmer et al, 2007).

Biological Sex

Maintenance of these farm animals and food processing are assumed to be two of the main roles of Neolithic women. To reach this conclusion, scientists compared Middle Age and Neolithic female farmers. Both groups performed similar activities on the farm and had similar bone structures (Larsen et al, 2019; Vick, 2005). For instance, grinding using a saddle quern takes 5 hours of manual labour, which caused an increased humeral—upper arm bone—strength (Larsen et al, 2019). Increases in upper bone strength were also seen in Neolithic females. The saddle quern and other similar tools were also used by Neolithic farmers. Therefore, scientists can assume that Neolithic women performed similar roles. The relatively sedentary roles women performed also explain bone weakness in the lower limbs and reduced motility. Interestingly, women did not show large changes to their body mass or strength relative to the men (Macintosh et al, 2017). One explanation is that women made artifacts, such as pottery, along with some foraging in the hunter-gatherer communities. Those movements may have been similar to the Neolithic women; thereby maintaining the muscle and bone mass.

Historically, men were the hunters of the community. During the last Ice Age, men would hunt large mammals such as mammoths. Once the Ice Age ended, humans began to hunt smaller animals, like deer and pigs. Then, most hunting stopped when they became farmers. At every stage, a larger size became more evolutionarily unfavourable (Tarli & Repetto, 1986). The size difference between males and females continued to decrease until men were only a fifth larger than females. In comparison, gorillas—one of the humans’ most related species—are three times as large as female gorillas. Increased metabolic demands, low protein diets and advancements in technology meant that the larger male body size was too hard to maintain. Thus, there was a marked decrease in body size that was closer to that of females (Wells & Stock, 2020; Little, 2020; Tarli & Repetto, 1986).

Where women saw a drastic change in their bodies was in the frequency of fertility periods. Female humans that live in urban centers are fertile year-round. In contrast, female farmers experience periods of higher fertility. The growing season increases reproductive success, and the opposite occurs in the winter (Bailey et al, 2008; Haandrikman & van Wissen, 2008). This occurs because significant weight loss results in decreased ovarian function. Reproduction is a non-essential function, so the body transfers energy elsewhere (Page et al, 2016; Panter-Brick et al, 1993). These trends are seen globally, which reinforces the same pattern in early farmers (Bailey et al, 2008; Haandrikman & van Wissen, 2008; Panter-Brick et al, 1993) Pregnancy, ovulation and periods of starvation cause hormonal fluctuations (Lukacs, 2011). For instance, increased estrogen levels during pregnancy would decrease the production and quality of saliva (Lukacs & Largaespada, 2006). If saliva is not circulating enough, the bacteria stays in the mouth for longer (Bergdahl, 2002; Lukacs, 2011). In addition, women are more likely to increase carbohydrate intake during these periods. Cultural notions that a woman should be larger heightened the sugar intake. It was a sign of prosperity. As a result, the cultural and biological conditions also negatively affected their dental health by allowing more caries to form (Lukacs, 1996; Malomo & Nthholang, 2018).

Culture also impacts the role women had in a family. The Neolithic is when scientists first see monogamy. Burial sites show skeletons of nuclear families together. Traditional roles of inheritance are seen here with the male holding the wealth and lands. Women were then expected to migrate between the territories. Migration between areas helps make a species more adaptable through a process called gene flow, where genes are transferred from one group to another. It creates diversity; a necessary factor for a species to adapt to their environment. Because farming was physically and mentally difficult, increasing their adaptability means that they are more likely to survive. The genetic variability was passed down from the mother, making the entire species more durable (Rasteiro & Chikhi, 2013).


Cultural ideas also affected the way that Neolithic farmers lived (Rasteiro & Chikhi, 2013). Farming pushed farmers to live in denser and larger communities than as hunter-gatherers. Males no longer had to compete with other males for women or territory, further diminishing the need for a large body size. Moreover, the first instances of monogamy occurred, thereby lowering the demands of sexual selection on males (Luyer et al, 2016). For the community, it meant that infection rates increased (Page et al, 2016). Interestingly, early European populations showed higher rate of infection because of their rapid agriculturalization. Agricultural communities were already established in the Near East, so European farmers would have built on the existing technology.

Not only were Neolithic farms living closer to each other, but they also began to domesticate animals and cut down forests for land (Yerkes et al, 2012). Domesticating wild animals introduced new parasites into the population (Karsten et al, 2014. That is why researchers must wear masks when contacting some Amazonian Indigenous groups. The parasites within urban humans could kill these people (Walker & Hill, 2015). Deforestation would also introduce new parasites. A modern-day example is the increasing prevalence of Lyme disease. Due to deforestation, more rats are moving into urban spaces, bringing tics with them (Wood et al, 1992)

While researchers cannot determine the effects of stressors with a skeleton, they can use skeletal lesions as a measure of disease. These include underdeveloped enamel and a reduction in sexual dimorphism—differences between the sexes. Prior examples show that many Neolithic farms had these lesions (Milner, 2019; Wood et al, 1992). For instance, skeletons that showed more enamel hypoplasia also died younger (Boldsen, 2006). An explanation is that early farmers exhibited instances of malnutrition. Malnutrition causes a weaker immune system and allows for more damage to the bones. Instances of tuberculosis and scurvy were found in mass graves, showing that diseases were a problem for these populations (Nicklisch et al 2012; Pósa et al, 2015; Snoody et al, 2017). The only humans to survive needed to have a strong immune system and the ability to adapt (Page et al, 2016).

Living close to others was not all bad for these farmers. Decreased male-to-male competition would foster the growth of communities. Religion and art begin to form. Pottery, sculptures such as the Venus of Willendorf and other artifacts were made and buried with the dead. Plasters of skulls were even made to preserve the dead. Advancements in culture meant that there was more aid when an individual needed help. Together, they could work against stressors. For modern humans, it reinforces that these aspects of culture are important for an individual’s well-being (German, n.d.).


The interaction between mathematics and biology highlight the importance of analyzing phenomena from an interdisciplinary perspective. This is where the discipline of Complex Adaptive Systems (CAS) comes in. This new concept is defined as any system that allows interactions between fields. CAS is key to achieve an all-rounded understanding of different phenomena, and this section will focus on how applied mathematics allows for a better understanding of biology.

Branching processes: how long can you go?

Mathematical models can simplify biological assumptions, keeping them manageable as they represent the intricate dynamics of a system (Korsbo & Jönsson, 2020; Longo & Soto, 2016), and branching processes represent an example. This concept states that an entity will exist in a certain time and space, and will eventually be replaced by others that will continue the lineage in a similar or different direction (Kimmel & Axelrod, 2015). This idea can be applied to a cell (Míguez, 2015; Macken & Perelson, 1985), or a noble family (Albertsen, 1995) where we can ask the same question -where will the lineage come to a halt? There are two possibilities to be considered: either the conditions are such that no progeny occurs, or reproduction takes place giving rise to new variables which will keep diverging away from one another… until when?

This is the question asked by Dr. Geoff Wild in his paper “Inclusive Fitness from Multitype Branching Process” (Wild, 2011). Dr. Wild developed models that represent how likely a mutant allele is to go extinct in a random context. His models allow him to include different variables that will take place in such an adverse setting. The model also accounts for different scenarios that can take place per generation, and the genetic and behavioural factors at play. It becomes exceedingly difficult to keep track of these factors and their interplay. But, as Dr. Wild stated, “All math details can get summarized easily with coefficients of relatedness, you can have alleles distributed in a population in a complicated way. Nevertheless, it boils down to coefficients of identity by descent”. This highlights how math can aid us to make simplify the complicated world around us. Mathematics becomes a language through which we can read biology in a way where all the interactions taking place are clearly outlined. In this context, it is simplifying the writing and interpretation of a game with too many players present. By doing so, it promotes a better understanding of biological systems, which is what CAS aims to achieve.

The regulation of the sex-ratio: a story of natural selection and mathematical models

Mathematics help us to determine whether a finding or observation has biological importance, or if it happened by chance alone (Nanjundiah, 2003; Lovell, 2013). A decade after Darwin argued that natural selection was responsible for the sex-ratio of communities, Carl Düsing turned this theory into mathematical models (Edwards, 2000). Dr. Düsing wrote, “if there is a shortage of individuals of one sex then more young ones of that sex will be produced” and provided mathematical evidence that this would be the case regardless of isolated cases who defied the rule (Edwards, 2000).

Dr. Wild explored the same topic as Dr. Düring, but added some variables: what do the sex ratios look like when helpers stay at the nest (Wild, 2006)? Even in controlled conditions, a mutation or anomaly could arise that makes the sex-ratio behaviour of the focal individual exceptional. To determine the reliability of the observation, a local and a population wide average sex-ratio behaviour average were calculated by Dr. Wild. By comparing an isolated case against measured averages the reliability of the observation is established and allows for a concluding statement about the functioning of the biological system. The shift from the theoretical description of the influence of natural selection on sex-ratio (Edwards, 1998). towards a mathematical representation allowed for the establishment of patterns (Eberhart-Phillips et al, 2017). Once these are developed, complexity can be introduced into the model, since the foundation upon which to build is already there (Reed, 2015). Dr. Düring’s mathematization of visual trends in biology paved the road for major developments in evolutionary biology (Argasinski, 2013), inspiring scientists such as Fisher (Edwards, 1998).

Dr. Wild used the words “evolving, improving, highly coupled” to describe CAS. In the same way that this discipline creates a self-propelling machinery fueled by the collaboration between different fields, the mathematical representation of the sex-ratio opened the doors for a better understanding of disciplines such as population genetics and developmental biology, encouraging their development.

Promiscuity and the evolution of cooperative breed: the limitations of words when describing biological phenomena

 In his paper “Promiscuity and the evolution of cooperative breed”, Dr. Wild explains that verbalization can underestimate the complexity found in the biological field, and mathematics are needed to comprehend all possible interactions and outcomes of a process (Leggett et al, 2012). This study assumes the simplest setting to explore the consequences of promiscuity on community relatedness. Even so, there are several actions taking place: mating, birth, dispersal, helping, and competition for vacant patches. All these factors are affecting one another by turning these empirical observations into variables it is possible to comprehend the trends and patterns that result (Reed, 2015; Colon-Berlingeri & Burrowes, 2011). Even for the simplest scenario, the factors under consideration cannot only be outlined verbally: it needs mathematization. Each combination of variables produces several outcomes depending on the value of coefficients such as relatedness, and given their continuous nature, subtle changes can have an impact on the resulting interaction (Leggett et al, 2012; Colon-Berlingeri & Burrowes, 2011). This is an example of a non-visible factor at play that would be unable to be accounted for in a theoretical argument. In this case as in many others, math is providing the necessary tools to describe certain intricate interactions in nature that a verbal description could not deliver.

Mathematics allowed us to communicate, classify, and represent massive amounts of datasets through which we could analyze and comprehend phenomena around us. It can do so by simplifying the interaction of several variables and modeling their subsequent ramifications, such as branching processes. It can also be a way to account for non-visible factors and other outcomes too complex for verbalization. Additionally, it will help us tell the rule from the exception apart. CAS sheds light upon the necessity for fields to interact with one another, and through the aforementioned examples following the word of Dr. Wild, it becomes evident that mathematics fulfills an essential role in framing observations and experiments (Longo & Soto, 2016).


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Created by M. Aletta, V. Ravinder, A. Umasuthan, December 14, 2020 (Seminar in Biology 4920F CEL)