0:00
I'm delighted to take part in the seminar series "Cultures at the Macroscale". Thanks for Andrew, Olivier and Enrico for organising. And I also look very much forward to discussing my research with all you later in February.

0:14
So today, we're going to examine the role of individual and collective memory on the cultural adaptation process. In particular we ask "how do human groups adapt to temporally changing environments"? But this question has already sparked an enormous amount of theoretical and empirical cultural evolution research, resulting in a relatively simple answer: through a combination of innovation and social learning.

0:39
I don't even attempt to define innovation, but in this literature, it is often seen as similar to trial and error experimentation. Importantly, the innovation process leads to the introduction of novel cultural variants into the population, but also possesses intrinsic uncertainties about the adaptiveness, or cost, of social environments. In contrast, social learning is defined as learning through observations that offer interactions with other individuals of the population or its product. Social learning facilitates the spread of (often) adaptive cultural variants in the population, but there is a danger of transmitting outdated information, especially after a moment of change.

1:17
So on the one hand, we have a process that produces novelty of varying quality, and on the other, a process that can help some of those variants to spread, and the population... and allowing the population to adapt to the current environmental conditions. Depending on the stability or instability of the environment—meaning how frequently it changes—the balance between these two processes has to be finely tuned. And that is one of the classical results of the cultural evolutionary literature: that the usefulness of social learning decreases with increasing environmental instability.

1:50
And of course, the opposite is true for innovation. In other words, the average propensity of a population to engage in social learning is high when the environment is stable and will be low when the environment is unstable. And the precise shape of this relationship here depends on the specifics of the model used to derive it. So whether one considers a two environment or K environments scenario, or whether one assumes that only a single variant is adapted to each environment or an unspecified number.

2:21
But let's look at this relationship in a bit more detail. We start with this stable region here. If the environment is relatively stable, then the propensity for social learning is expected to be high, and consequently the propensity for innovation to be low. This makes intuitive sense as social learning in this situation can show its power by facilitating the spread of adaptive cultural variants, so that almost the whole population adopted.... possesses an adaptive solution, leading to very high adaptations at the population level. And also, the situation is characterised by relatively low level of cultural diversity, as social learning has effectively distributed only a small number of maladaptive cultural variants at the same time that propensity for innovation is low.

3:09
So only a very few variants are introduced over some time period, and those variants will likely face in extinction. But what happens when the environment is changing? Now in this situation it is likely that there's no cultural variant that provides some adaptive benefit and the population has to wait until an adaptive variant has been invented. And this waiting time, can be short or longer depending on the complexity of the environment considered. And of course, also, in this waiting period, social learning is completely ineffective as only non-adaptive information can be transmitted. But once an adaptive innovation has been introduced, social learning can… can help spreading it, and consequently, the adaptation level is quickly rising again.

3:59
Now, over time, better and better innovations are introduced, leading the population to a well-adapted state, where the need for further innovations is relatively low. Now, this scenario is well known in the genetics literature, and often called adaptation through de novo innovation. But I would like to briefly mention that it is very likely that the cultural innovation process does not proceed in the same random fashion as a genetic one. So there's a lot of work to be done on how adaption through innovation might be different in the genetic and in the cultural settings. But that would be the topic of a completely different talk. Okay, now let's look at this unstable situation.

4:45
Now, the population propensity for social learning is expected to be low, implying high propensities for innovation. This also makes intuitive sense as now environmental change that happens frequently will increase the probabilities of social learning to transmit outdated information. But due to the high propensity for innovation, the population adaptation level even in stable periods are lower compared to the previous situation. And we also will likely observe typically high number of cultural variants, again, at least compared to the situation of a stable environment.

5:21
But what happens now at an environmental change, in contrast to before, the high propensity for innovation makes it likely that there is already a variant in the population that is adapted to those novel environmental states. So there is no waiting time and social learning can act immediately on help spreading this adaptive variant through the population. So we see a rapid adaptation process. And importantly, the adaptation... population adaptation level does not drop down to zero at the change.

5:56
Again, this scenario is already well known in the genetics literature often called adaptation through standing variation. Now I just would like to repeat it again. Standing variation or adaptations from standing variation leads to a lower adaptation level in stable periods as all cultural variants in the population have to be expressed, but it facilitates rapid adaptation to changing environments.

6:21
And precisely this aspect, that all variants need to be expressed has led us to our research question. In contrast to the genetic case, our human cognition allows for sophisticated cultural memory processes. Very crudely speaking, you're able to recall past experience in our cases means that there is the possibility of remembering cultural variants used in the past together with the adaptation that they provided in the experienced environments. So this question we are going to focus on the following is: "Can memory very crudely defined as the ability to remember past experiences contribute to the efficiency of the cultural and the patient process?"

7:05
This is work done in collaboration with Madeleine Amarr a PhD student in my lab, and Laurel Fogarty. I would like to really stress that Madeleine is really the driving force in this project.

7:15
So we try to solve this question by developing a mathematical framework that is able to incorporate memory, social learning, innovation and environmental change. And we use this model to explore the evolution of social learning and memory, then the environment changes periodically as per definition, memory is only of very little use when the environment changes to a state that has not been seen before.

7:42
So, let me briefly describe the model. It consists of three main components, the environment, the cultural variants, and individuals. For sake of simplification, we assume that the environment has only two states but stress that results do not differ qualitatively if we have K environmental states. Environmental instability is controlled by the parameter PM, which describes the probability of environmental change happening in each time step. Cultural variants are assumed to be adapted to one environmental state only, and they are characterised by their adaptation level which can vary between zero and one. And we assume that our individuals possess a cultural memory. And this cultural memory is comprised of the individual knowledge about used cultural variants, and the adaptation level they have provided in the experienced environments. Further, all individuals are characterised by their inherited propensity to engage in social learning, and their propensity to forget knowledge. I will describe in a second what this... this propensity for, for forgetting is.

8:50
And each time step, we assume that our individuals can accurately infer the environmental state they're in and they have to undergo a couple of steps. First, they have to decide which variant to express to obtain the adaptation level in this time step. To do that they first evaluate the memory, meaning they go through all variants in the memory, and randomly choose a variant from it proportional to the stored adaptation level in this environment. Then they have to decide whether this variant is already good enough or that they would like to engage and learn. And with a probability of one minus the adaptation level of the variants chosen from the memory, an... an individual will engage in learning. And this assumption reflects the fact that there's only a strong need for learning if the chosen variant is not already validated.

9:42
Now, if individuals decide to learn, they engage in social learning for probability, Ej, and innovation with a probability one minus Ej. Social learning occurs through pay-off biased learning and innovation introduces a novel variant where the adaptation level is randomly chosen from interval from zero to one. Now the learned or innovated variant is expressed and added to the individual's memory if it's not already maintained, and if the individual decides to not learn it — simply expressing the variant chosen from the memory. And importantly, we keep a record of how often each variant is expressed by each individual.

10:25
And lastly, our individuals can forget. And forgetting happens with inherited inherited probability for forgetting Phi-J. In the case of for... forgetting, an individual loses one variant contained in its memory. And the variant to be forgotten is chosen inversely proportional to the number of times it has been expressed before.

10:47
So the demographic dynamics of the models resemble that of a Moran. So one individual is chosen for reproduction and one for death, implying a constant population size which we set to 240. That's, of course, random and the individual to reproduce is chosen proportional to the adaptation level of the expressed variant in the last time step.

11:11
When reproducing the individual passes on this propensity for social learning and for forgetting. And this happens, like usually largely faithfully, but with small probabilities, random mutations occur to those propensities as shown by this equation. Further, the reproducing individual transmits its cultural memory — its full cultural memory — to the offspring, but all transmitted... um... variants will only have a count of one in the odds.

11:42
Now, it is important to note here that this intergenerational transmission induced by this vertical social learning is the only way to transmit unexpressed variants meaning potential knowledge about past environments to the next generation.

12:01
Okay, now, repeating this modelling steps many, many times allows us to study the joint evolution of the propensity for social learning, of the propensity for forgetting, and the composition of the individual and population-level memory for different levels of environmental instabilities. Before we do that, let's examine some simpler cases first.

12:21
First we assume phi equal to one for all individuals in the population. And that means that our individuals are not able to create a cultural memory as no variant can be retained, everything is forgotten. And in this no-memory situation, our model reassuringly generates the classical social learning results.

12:44
The many plots here shows the average population propensity for social learning for various levels of environmental instability, characterised by the probability of a change happening in every time step shown here on the x-axis. We start at 0.2 and this already amounts to an average 40 environmental changes per generation. Now we see that the propensity for social learning is decreasing with increasing environmental instability. And of course, the same holds true for the adaptation level.

13:20
But still, let's have a quick look at the time course of the adaptation level for an individual's simulation. We consider a lower environmental instability regime with an average 1 change per 10 generations, and the high environmental instability regime with on average 10 changes per generation. Both figures here shows the same time period of.. um.. 600, timesteps.

13:47
We see the already mentioned trade-off: high propensities for social learning can lead to high adaptation level — high adaptation level for stable periods — but caused the adaptation level to drop to zero after an environmental change. Now, we make it... our individuals pretty easy to innovate a normal adaptive variant and so the waiting time in our situation is relatively short, leading to... to rapid adaptation processes even in this situation.

14:22
High environmental instabilities or high... which which lead to high propensities for innovation, on the other hand, it leads to much lower levels of adaptation for stable periods but allows for rapid adaptation — what is of course favoured when we have a lot of environmental changes happening in in our system.

14:53
So, let's go on and see what memory actually does. But before we go to the to the full-fleshed memory, let's first assume a much simpler scenario where we assume that we just simply remember everything — what we have expressed — meaning we set the forgetting probability to zero for all of our individuals. And this full-memory situation is very interesting as it generates lower adaptation level for low and intermediate levels of environmental instabilities compared to the normal situation.

15:28
So why is if we maintain every learned or innovated variant, they accumulate a large repertoire of var... very different adaptation levels? Now, if we choose a variant from this memory, then we choose quite likely not the best adopted ones, even though the choice is proportional to their adaptation. So keeping everything is not the best idea, especially not for low and intermediate environmental instabilities at the probability of choosing a suboptimal variant is relatively high. Naturally, at the high... for high environmental instability, our full-memory does better than the no-memory situation, simply because the individuals are very likely to express one adaptive variant in any already seen environmental state. The adaptation level is also largely unchanged by the level of environmental instability, because once a large memory has been established, it just simply doesn't matter how frequently the environment is changing anymore. The individuals react with exactly the same.

16:40
I don't want to put too much emphasis on the... on the evolved social learning propensities as we kept the individual memory to a thousand variants. And once this limit is reached, the social learning propensity show a more or less drift-like dynamic.

16:58
Okay, a look at the time cause of the adaptation level for single simulation confirms all our conclusions. We see here — in those two figures — that there's almost no difference in the adaptation levels for any level of environmental instability.

17:14
So summarising. Remembering everything might shield against drops in the adaptation level at the environmental change, but will not result in high average adaptation levels for low or intermediate environmental instabilities.

17:31
Now, finally, let the propensity for forgetting evolve alongside the propensity for social learning. And in this situation, which is shown by a bit the… the yellow lines here, we see that the population adaptation level stays high for all levels of environmental instabilities. And this is achieved with these propensities for social learning and forgetting. Importantly, we see that the propensities for social learning are high for... for all environmental instabilities. And it's notable that only in the case, where we have no environmental change and social learning propensity is is relatively low — but this is simply due to the existence of vertical social learning. At some point the population has invented and learned variants close to the optimum — meaning with an adaptation level of close to one. And those variants are then also transmitted to the next generation through our vertical social learning, resulting in almost no learning events. And as a consequence, there is almost no selective pressure on the system anymore. And this social learning propensities show a more or less adrift like dynamic.

18:49
Okay, but increasing levels of environmental instability, need consistently high propensities for social learning, coupled with decreasing propensities for forgetting to produce a well-adapted population. But before we move on to explore what precise memory structures these propensities for social learning/forgetting actually produced, let's have a look at the adaptation level for a single simulation again.

19:24
And we see that for low environmental instability the memory prevents the drop in the adaptation level to zero at an environment change but still allows the population to um... to be well-adapted and stable periods. And excitingly, the precisely the same is true for high environmental instabilities. So what's the composition of the memory that actually can achieve that?

19:55
First of all, we have seen that the propensity for forgetting is decreasing with increasing environmental stability, which logically resulted for increasing environmental... environmental instabilities — we see slightly larger individual memories. But importantly, those individual memories are still relatively small. So we see that at most, we have, on average, roughly 10 variants in those individual level memories. But I would also like to note that there are some considerable variation on the individual. Now, this small memories prevent the individuals from choosing too often a suboptimal variant, as it was a case in the fu... for the full memory. But they also shield individuals from random forgetting of adaptive variants. So it's... so our our memory need to be finely balanced, to provide the best protection on the ones I prefer getting, but also for the matter of becoming too big so that you have too many errors in choosing a variant from memory.

21:07
But the crucial question now is whether the memory actually contains information about the other environment, even though the population is not in it? And to answer this question, we calculate the probability that the population as a whole has no variant adopted to the other environment at the point of the environmental change. And this is shown by this blue curve here. If we have an environmental stability of 10 to the minus four, which… which amounts to, on average, one change every 50 generations, we see that we have in only 10% of the cases, at least one variant adapted to the other environment in the populational memory. Th.. this probability decreases relatively quickly for increasing environmental instability. For five times 10 to the minus four, which correspond to one change every 10 generations, this probability has already dropped down to... to 50, at 50%. And if we increase our environmental instability even further to 10 to the minus three, which amounts to one change, every five generations, we are all relatively close to zero, meaning that for those environmental instabilities, we do, on average have at least one variant that is adapted to the other environment in the population. But it is even more interesting that those variants which are adapted to this other environment, are only distributed over a very small number of individuals for low and intermediate environmental instabilities and this is shown by this red line here.

22:55
This means the high level of adaptation is achieved not by all individuals having a variant adapted to the other environment, but by a population-level memory generated by just a smallish number of individuals. These individuals that have those variants adapted to the other environment, they can express those variants, and the high social learning propensity produces a rapid spread of those variants results in well-adapted populations in just a few time steps.

23:28
So in summary, if the individual memory is small enough, and at least some memories contains well-adapted variants for the other environment, then it can provide a standing variation that does not lower the population adaptation level in stable periods, but still provides adapted variants in the case of an environmental change. And together with the highest social learning propensity this leads to rapid adaptation to periodically changing environments, which we have seen in the figures before.

24:05
Let me... let me one mention last... a last point about the role of vertical social learning. We observe that vertical social learning is the only way of transmitting unexpressed variance between generation but so far, we only assumed that simply all variants — regardless how good or bad they are — are transmitted. Now, let's assume and let's call it a selective, um... vertical social learning regime, where we only transmit one variant for each environmental state, we have information abound in the memory, and we choose variants probabilistically based on the adaptation level.

24:45
And these are the results shown by this purple line. So we see that the population adaptation level is like even a tiny little bit better. Now I mean, these improvements are small because we are almost close to the maximum, but it... you know, you can see, we still improve the adaptation level slightly by assuming this selective vertical social learning and at the same time our propensities for... for social learning and for forgetting they... they show very similar dynamics, maybe notably that the propensity for forgetting is slightly lower, which is also explainable, because now, at most only two variants are transmitted vertically.

25:37
And you see that, this also is reflected in the individual memory, which is now kind of close to 2.5ish. And excitingly, this individual level of the size of the individual level memory does not change much anymore with environmental instability through our selective vertical learning.

26:03
Lastly, the probability of having no variance... in having no variance of the other en... environment in the population is further decreasing, but the size of the cut... of the collective memory has only changed relatively slightly. So, being selective about what to transmit to the offspring influences the adaptation process positively.

26:30
We can even do better by assuming that the vertically learned variants are sticky. So, we are kind of adding adjectives to social learning. So, so far, we have assumed that every vertically transmitted variant gets only a count of one in the offspring. And so, in principally those variants could be forgotten... forgotten after two times, but maybe assuming some effort on the side of the parents, we increase this initial count to five and this improves... and this improves the adaptation level even more. So we now, it gets really tough to see, but you see, in this green line, that our adaption level is now really close to one to the... to the... to the optimal. And we also see that all other relationships will stay largely unchanged and the probability of having no environment ah sorry, no variant of the other environment in the population is decreasing even further in... for the, you know, the most stable environments.

27:39
So, let me summarise. We are showing that the cognitive capacity for memory can provide a way for keeping information useful in that environmental context in the population without affecting the population level adaption. So in concert with high propensities for social learning, such a carefully crafted memory can generate high levels of adaptation in any environmental instability scenario. And vertical social learning is a means of transmitting those unexpressed variants to the next generation. And selective vertical social learning can further improve the adaptive process. But already random vertical um... social learning provides a needed, but potentially much weaker link, between those generations.

28:28
Now, of course, what I presented today are only some first results from what we think is a pretty fun project based on as simple as possible assumptions. Now on the future, we aim to generalise the model to consider, for example, more complex environments and also cultural variants that can provide benefit to the adopters in more than one environment. Also, we're keen to introduce a production stage so that there's a difference in the resulting adaptation level if they expressed a variant for the first time or the fifth... the 50th time. And then what... this would then naturally lead to the degradation of the quality of the variants, especially if they are very rarely used on population, which hopefully will provide some insights into how unexpressed cultural variants need to be transmitted in order to maintain their usefulness... in order to maintain their information about past environments.

29:28
But as this is work for the future for now, I would like to thank again my and fantastic collaborators, Madeleine Amarr and Laurel Fogarty. And also would like to thank you for listening to this presentation. And as I already said, I look very much forward to discussing this research with you on the... later on January 25. But if you have any question in the meantime, please feel free to drop me an email. Thanks for listening