Mechanisms of biodiversity between Campylobacter sequence types in a flock of broiler–breeder chickens

Abstract Commercial poultry flocks frequently harbor the dangerous bacterial pathogen Campylobacter. As exclusion efforts frequently fail, there is interest in potential ecologically informed solutions. A long‐term study of Campylobacter sequence types was used to investigate the competitive framework of the Campylobacter metacommunity and understand how multiple sequence types simultaneously co‐occur in a flock of chickens. A combination of matrix and patch‐occupancy models was used to estimate parameters describing the competition, transmission, and mortality of each sequence type. It was found that Campylobacter sequence types form a strong hierarchical framework within a flock of chickens and occupied a broad spectrum of transmission–mortality trade‐offs. Upon further investigation of how biodiversity is thus maintained within the flock, it was found that the demographic capabilities of Campylobacter, such as mortality and transmission, could not explain the broad biodiversity of sequence types seen, suggesting that external factors such as host‐bird health and seasonality are important elements in maintaining biodiversity of Campylobacter sequence types.

ST might persist within a host. We rewrite equation (1) as: where Z t+1 is the (t + 1) th column of Z, and is the Hadamard (element-wise) product. In essence, Z simply acts as a 522 switching mechanism, to switch o the possibility of transitions to a ST that has not yet emerged. This approach carries 523 multiple bene ts. Primarily, the transition matrix now represents the transition probabilities for a ock where all STs are 524 present simultaneously. This inference allows more of the dataset to be utilised, without having to divide our experimental 525 data into multiple regions of di erent sized matrix calculations. A possible limitation to this approach is that it allows 526 inference of competitive outcomes between STs that do not appear at the same time in the original dataset. i.e. it can infer 527 based on the growth abilities of a ST at a later time how it would fare against a ST from an earlier time. While this inference is 528 useful, these limited instances are not experimentally veri able. As such, we do not display these few "assumed" competitive 529 strengths in our results, to avoid confusion.

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Once the best tting P to equation (2) has been found, we may use this P to estimate the associated competition ma-532 trix C. Ulrich et al. (2014) presents such a methodology whereby, assuming homogeneous mixing, the transition matrix P and 533 the competition matrix C are linked by the relationship: for i = j, and where the range of summation in (4) is calculated across the subset considered in the notation P(1, . . . , n). Heuristically, one 536 considers the transition probabilities as the proportional outcomes of all possible competitive interactions. In a four-species 537 system, equations (3) and (4) would de ne: In small systems, the probability of successful transition for each ST could be directly calculated as the proportional 539 23/34 outcome of all possible competitive interactions as given in equations (3) and (4). However, for our system of 20 STs this is 540 computationally impossible, as the size of equation (3) will rapidly balloon for such a large system. Instead we therefore used 541 the approximation approach of Ulrich et al. (2014), utilising the geometric mean of the associated competition values: wherex is the geometric mean of the competition values associated with P i, j .

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Upon testing, we found that this approximation was found to estimate a randomly drawn 20 × 20 test competition matrix 545 with a mean value error < 0.001.

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The above methodology allows us to choose a trial competition matrix, C, convert this to a transition matrix, P via equation

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(5), and then evaluate how well this transition matrix simulates the observed data, A, via equation (2). All that is required 549 now is an approach by which to nd the "best" competition matrix C. As such, we estimate the competition matrix C using Draw random number y from Pois(λ s ).

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Add y to a running tally, Y s , of how many other chickens will be challenged by ST s.  1 -the HDI of C [4,13]. Figure A1 presents the range of the HDIs (upper -lower) in the same format as Figure 3. For the 569 great majority of values, this is < 0.1, save for circumstances when two strains only co-exist very brie y in the experiment 570 duration -strains which are then quickly outcompeted. Uncertainty is very small for competitively superior strains, as would 571 be expected, as more data is available for these strains for which to calculate their competitive capabilities.
572 Figure A1. HDI width magnitudes for the Bayesian posterior distributions of each element of the competition matrix, ordered as presented in Figure 3. Table A1. Median values and upper/lower 95% HDI limits of the posterior distributions of all parameters within the competition matrix, C, as presented in Figure 3. The best-t patch occupancy model parameters presented in Figure 3 result in a wide variety of stochastic evaluations: in 574 some instances a ST may ourish, while in other simulations it may quickly die out, due to random chance. The model was 575 run 100 times, and we present the mean proportion of STs in the ock across these 100 simulations below in Figure A2. We 576 present the results in the same format as Figure 2 to allow direct comparison. Note that the trend seen above of slowly decreasing STs should not be interpreted as an accurate depiction of ST dynamics, 578 rather a representation of probability of persistence to that point in time. ST 1089 for example, is less likely to be maintained 579 in actualisations than ST 1487, but the magnitude of prevalence in these "successful" actualisations is comparable.

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The only considerable di erence seen in the model output compared to the experimental data is the broad proliferation of ST 582 257. In the experimental data shown in Figure 2, ST 257 quickly dies out, and as such there is little data available to infer its 583 competitive strength in Figure 3. We theorise therefore that the model ts to allowing a ST with the least informing data to 584 persist in order to act as a uniform competitive pressure against all STs, since a competition value of 0.5 is assumed against 585 most other STs for which no information was available (the grey squares of Figure 3).