Philippa Kaur

New wave: Petar Puškarić used yeast isolated from the Adriatic Sea to make a beer that he named Morski Kukumar (Sea Cucumber).Credit: Marin Ordulj

Petar Puškarić is an engineer, ecologist and head of beer production at LAB Split, a craft brewery in Split, Croatia. He graduated with a master’s degree from the department of marine studies at the University of Split last year, after successfully making a beer from Candida famata, a yeast that can be isolated from sea water. He now hopes to brew this sea-yeast beer commercially. He speaks to Nature about some of the challenges in going from dissertation to commercialization.How did your marine-yeast beer come about?I’ve had an interest in brewing beer for a long time, and started brewing as a hobby when I was a student. During a marine-microbiology lecture as part of my undergraduate degree in ecology, my mentor Marin Ordulj and I started to talk about marine yeasts, and one question led to another. We wondered whether sea yeast could ferment beer.We researched the literature and could not find anyone who had made a beer with a yeast isolated from the sea. Perhaps we could become the first to do so? The idea stayed with me for a few years as I continued my degree and moved on to my master’s course. When I came to choose my dissertation topic, I decided it was time to put the idea to the test. I discussed things with Marin, and he agreed to help me plan an experiment. By then, I was working part-time at the LAB Split brewery, so I had some brewing experience to bring to our investigations.Our first task was to isolate yeasts from the sea. We then tested the fermentation abilities of the isolated yeasts and grew cultures from the most promising samples. Finally, we used those cultures to brew beer.How did you manage your time between brewing and your degree?I wasn’t overorganized, but I always made sure to be disciplined and to do whatever was needed as tasks came along. I kept active outside work as well, continuing to play as a mandolinist in an orchestra, for example.I didn’t think too strictly about my career, and made time to do the things I enjoyed. I’d recommend that other students also try to enjoy life and spend as much time as possible with friends. After all, life is not just about building a career. I was lucky in proposing a graduate topic that I found interesting and that my mentor liked: that helped me through the duller and more difficult moments.What was the hardest part of the process?The biggest problem was created by marine bacteria, which would outgrow the yeast colonies and thus make the isolation of yeast more difficult. We tackled this problem by using selective nutrient media, which inhibit the growth of bacteria. Eventually, this resulted in pure yeast cultures.What did the beer taste like?The first beer tasting after all that research, thinking and anticipation was really exciting. We noted clove and fruit aromas and a slightly sour tone. It didn’t carry the taste of the sea; the flavour was closest to that of sour beer.What impact do you hope this work will have?The beer is an exciting product of my graduate work, but I also hope that my thesis will encourage others to explore in more detail the yeasts in the Adriatic Sea, and to realize their potential in ecology, medicine and nutrition. Split is on the Adriatic coast and I like the idea that we’re contributing in some small way to protecting that coastline.Sea Cucumber, as we’ve named the beer, might not help much directly in that regard, but I do hope that it could raise awareness about how many useful things there are in the sea.Are you planning on taking the sea yeast further in your career?Any experience in microbiology helps in the food industry. Sea yeast might turn out to be useful in brewing, but we have to consider the finances and infrastructure we’d need to support its use commercially. For now, we’re concentrating on brewing more standard beers. In the future, I hope to brew some of my own recipes, whether Sea Cucumber or something else. I would definitely like to combine brewing with the search for new yeasts that can be used not only in beer making, but in other industries as well. More

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PreliminariesTo unify all the five classes of two-by-two games, Yamamoto et al.35 introduced the weightlifting game. In this game, each player either cooperates or defects in carrying a weight. Players who carry the weight pay a cost, (cge 0). The weight is successfully lifted with probability ({p}_{i}), where (i=mathrm{0,1},2) is the total number of cooperators and ({p}_{i}) increases with the number of cooperators (i). If the cooperators succeed, both players receive a benefit (b >0). However, in case of failure, both players gain nothing. The pay-off of the cooperators is (b{p}_{i}-c), and the pay-off of the defectors is (b{p}_{i}) (Table 2). In terms of the parameters (Delta {p}_{1}={p}_{1}-{p}_{0}) and (Delta {p}_{2}={p}_{2}-{p}_{1}), which represents the increase in the probability of success due to an additional cooperator, the following inequalities are obtained for the pay-offs (R, T, S), and (P) (Table 1):

(i)

(Delta {p}_{1} >c/b) for (S >P),

(ii)

(Delta {p}_{2} >c/b) for (R >T), and

(iii)

(Delta {p}_{1}+Delta {p}_{2} >c/b) for (R >P).

Table 2 Pay-off table of two-person weightlifting game.Full size tablePD satisfies only (iii), CH satisfies (i) and (iii), SH satisfies (ii) and (iii), DT satisfies none of the three conditions, and CT satisfies all three. In 2021, Chiba et al.1 studied the evolution of cooperation in society by incorporating environmental value in the weightlifting game. They found that the evolution of cooperation seems to follow a DT to DT trajectory, which can explain the rise and fall of human societies.The ({varvec{n}})-player weightlifting gameIn this study, we generalize the weightlifting game to (n)-players. Suppose (n) self-interested and rational individuals selected from a population of infinite size. The (n) players are asked to lift a weight. Each individual (or player) can decide to either carry the weight (cooperate, (C)) or not carry/pretend to carry the weight (defect, (D)). Players who decide to carry the weight can either succeed or fail. The probability of successful weightlifting is denoted by ({p}_{i}), (i=mathrm{0,1},dots ,n), where (i) indicates the number of cooperators (henceforth, (i) always represents the number of cooperators). The probability of success increases with the number of individuals cooperating, and it may remain less than unity even if all (n) individuals cooperate. Players who decide to carry the weight pay a cost, (cge 0), regardless of the outcome, while those who defect need not pay anything. If the cooperators succeed, all (n) individuals receive a benefit (bge 0). There is no penalty for failure. We use the expected gains/losses of the players as the pay-off. If there are (i-1) cooperative players, then the pay-off of (j) is ({B}_{C}left(iright)=b{p}_{i}-c) when (j) cooperates and ({B}_{D}left(i-1right)=b{p}_{i-1}) when (j) defects. The number of cooperators differs by one, since in ({B}_{C}left(iright)), there is an additional cooperator, which is (j) him- or herself. To decide whether to cooperate or defect, all players weigh their expected gain and rationally choose the option with the highest expected gain. The graphical outline of this game is illustrated in Fig. 1 (see also Supplementary Figure S1 for the flow of the game). The pay-off table for a four-player game is shown as an example in Table 3. Here, player (1) is the innermost row (strategies are listed in the second column of the table), player (2) is the innermost column (strategies are listed in the second row of the table), and the succeeding players take the succeeding rows or columns (we enter the first player as a row player and the following player as a column player and continue in this order). Each cell represents players’ pay-offs, with the first component being the pay-off for the first player, the second for the second player, and so on. For instance, consider the entry in the first row and third column, where players (1, 2) and (3) cooperate but player (4) defects. The pay-offs of players (1) to (3) are ({B}_{C}(3)), while the pay-off of player (4) is ({B}_{D}left(3right)). In the above example, there are as many row players as column players because the number of players is even. However, we can have one more player in the rows than in the columns if there is an odd number of players.Figure 1A schematic diagram of the n-player weightlifting game. In this game, players decide whether to cooperate or defect in carrying the weight. Cooperators need to pay a cost. The weightlifting can either succeed or fail. In case of success, all players receive a benefit. In case of failure, all players receive nothing. The player’s pay-off depends on the benefit, cost and probability of success. Each player decides whether to cooperate or defect so as to maximize the expected gain.Full size imageTable 3 Pay-off table of four-player weightlifting game.Full size tableNash equilibrium and pareto optimal strategiesHere we present the Nash equilibrium and Pareto optimal strategies of the (n)-player weightlifting game in terms of the cost-to-benefit ratio (c/b) and probability of success ({p}_{i}). The Nash equilibrium consists of the best responses of each player. Players have no incentive to deviate from this strategy profile since deviation will not increase an individual’s pay-off if the other players maintain the same strategy. If ({B}_{C}(i)ge {B}_{D}(i-1)), the best response of player (j) is to cooperate, but if ({B}_{C}(i)le {B}_{D}(i-1)), the best response is to defect.We have (Delta {p}_{i}={p}_{i}-{p}_{i-1}ge 0) for the increase in the probability of success because the probability ({p}_{i}) increases with the number of cooperators (i). It is convenient to divide cases depending on whether (Delta {p}_{i} >c/b) or (Delta {p}_{i} More

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