We calculated daily energy requirements for birds under field conditions as M =  2.5, where W is the weight of an average insectivorous bird on coffee farms . We calculated the weight of an average insectivorous bird by averaging body masses of 33 insectivorous resident and migrant bird species reported to consume CBB on Jamaican and Costa Rican coffee farms , or predicted to consume CBB based on morphology and diet breadth . Sherry et al. found that CBB made up 5%–10% of the diet of three Neotropical migratory warblers by number of individuals consumed; we used these percentages to estimate how many calories, and therefore how many CBB, birds potentially eat. Avian consumption rate of CBB was constant, with even effort across the coffee season. For avian densities, we used estimates from Karp et al. of 3 to 14 birds per ha, because these densities include known CBB predators on coffee farms in Costa Rica.Parameters for our Leslie matrix for coffee berry borers are broadly consistent with expectations and general knowledge . For example, our conversion of fecundity to a daily value, F1 = 1.341, is consistent with published literature stating that 1–2 eggs are laid per day by CBB . Model projections showed that across a 185-day CBB breeding period starting at the point of first ovipositing, an initial population size of 100 female dispersers would produce 1.3 million offspring, resulting in a new adult population of 70,245 females . Assuming  99% of colonizing females successfully bore and oviposit in a coffee cherry on Day 0, the first generation of new dispersing females does not appear until day 37. At Day 38, the adult population begins to increase, and continues to do so exponentially.The daily growth rate of this population converged on 1.042. Sensitivity analysis revealed that survival of adult females had the largest impact on overall population growth , followed by daily survival of pupa , juveniles , eggs and larvae and dispersing females . In addition to modeling growth with 100 initial colonists , grow bag for tomato we projected the population growth of low and high starting populations calculated from observed weekly alcohol-lure trap catches during peak dispersal .

Comparing the three population projections, peak number of dispersers at Day 185 varied considerably, with 162, 3259, and 8768 daily dispersers for low, medium, and high colonizing populations, respectively. In the high population projection, the adult population toward the end of the growing season reached over 18,800 individuals. Note that because these are density-independent models, the number of CBB does not depend on plant density. However, the impacts of the CBB population on yield would depend on coffee plant density. To reduce the final adult population by 50%, the daily survival rate of dispersing females would have to be reduced from 0.99602 to 0.83202. This change represents a 16.4% reduction in daily survival when dispersing. The number of CBB that birds need to eat to reduce the adult population at this rate was driven by the initial population size as a straight line, y = 79.23 N0 . At medium starting population , birds need to consume 7628 CBB during the borer breeding season, while at high starting population , about 20,500 dispersing CBB must be consumed by birds. Daily consumption rates by birds would have to increase over time as the CBB population grows and could vary from 15 to 750 CBB being consumed a day, depending on starting population size . Overall, we calculated that for every female CBB in the initial colonization, birds need to consume 79 CBB to reduce the end of season population by half.We estimated that the caloric content of a 195 μg adult CBB to be 1.09 calories per gram dry weight, or 0.00109 kcal. At 5%–10% of a bird’s daily diet based on number of prey items, birds would consume <7 CBB per day. This represents 0.03%–0.05% of daily caloric requirements of our average insectivorous bird. At these feeding rates, our models suggest that by the time of peak dispersal, 4, 88, and 236 birds are required at low, medium, and high starting population sizes, respectively, to reduce CBB populations by 50% on day 185 .Our model suggests that avian predation is likely to be effective at reducing CBB populations by 50% only during small infestations , or during the early stages of larger infestations .

Birds appear unable to successfully suppress medium and large infestations because the number of CBB that need to be eaten in a season requires higher bird densities than are reported in the literature. Karp et al. estimated 4–12 birds/ha of species that are confirmed or suspected CBB predators. Flocks of migratory birds on coffee farms are estimated at 19/ha and 24/ha , but these values are also short of our estimates of necessary densities for suppressing larger CBB outbreaks. One caveat to our conclusions is that our calculations were based on CBB accounting for 5%–10% of a bird’s daily diet . This assumption meant birds would only eat a set maximum of 7 CBB per day. Sherry et al. reported up to 116 CBB in the stomach contents of a single warbler, suggesting under certain circumstances in the field, birds eat more CBB. Generalist insectivores, particularly Neotropical migrants, have flexible foraging preferences and would likely feed opportunistically on CBB in response to dramatic dispersal peaks. Therefore, birds might be expected to increase feeding rates as CBB disperser abundances increase, though it may depend on the relative abundances of other prey. Better data on CBB consumption rates by birds under different circumstances would improve our estimates of the circumstances under which birds can control CBB populations. A second caveat is that bird densities used in the model may not represent the potential for CBB control because bird densities depend on the structure of the agricultural landscape, which the current model does not consider. On coffee farms, birds are more abundant when native tree cover is highest and natural forests are close by . Across tropical and temperate regions, the propensity for birds to forage on farms, and thus exert pressure on agricultural pests, is correlated with the physical complexity and diversity of the agroecosystem . For example, birds make more frequent foraging trips to apple orchards with high native tree coverage . In alfalfa fields, edge habitat complexity supports greater avian richness leading to lower pest abundances . Under some circumstances, the density of birds foraging in certain areas may behigher than average densities would imply, leading to greater control potential than our models suggest.

More generally, our CBB population model is density independent and assumes environmental conditions and sufficient resources to allow CBB populations to increase without restriction. As a result, our model is limited, as it does not consider localized effects of weather and temperature fluctuations on CBB developmental time , nor characteristics of coffee farms that influence both CBB infestation and bird density. We assumed maximal capacity for CBB population growth and used estimates of bird densities from the literature that only included birds known to consume CBB, perhaps underestimating the potential for avian control. Models are an important tool for estimating population dynamics, but as with any species, the growth potential for CBB and availability of its predators, is context dependent. Our study echoes Kendall et al.’s conclusion that, grow bag for blueberry plants even though errors in model construction are common, these seldom change qualitative conclusions. From our population matrix, CBB daily growth rate converged on λdaily = 1.042 around day 124, with an observed rate of population change across the entire coffee-growing season of 705 . Our λdaily is higher than Mariño et al.’s reported lambda of 1.32 over  50– 56 days, which corresponds to λdaily ≈ 1.006 . Part of this discrepancy may come from the fact that Marino et al. combined vital rates across life stages with different time steps. Nonetheless, both models are consistent in predicting rapidly growing populations. Observed CBB population growth rates are similar to ours: Baker, Barrera, & Rivas, calculated a 1.067 growth rate in wild populations and RuizCardenas and Baker reported 1.047 in CBB reared in laboratory settings. In their sensitivity analysis, Mariño et al. reported that adult female survival, and transitions from larva to pupa and pupa to juvenile had high sensitivity in contributing to population growth rate, with adult survival the highest . We found a similar peak sensitivity value for female adult survival in our matrix , supporting the idea that CBB population growth is most sensitive to adult survival rate. Interestingly, dispersal survival from our matrix was estimated to have low impact on population growth , even though this life stage is when CBB are vulnerable to bird predation. Thus, our analysis superficially suggests that population control once CBB are established should focus on reducing adult survival rather than on trapping dispersing females , if the same impact on numbers could be achieved. However, dispersing females are much more accessible to control methods like spraying fungal bioinsecticide than are adult females, which are inside the coffee cherries, so despite the tremendous difference in sensitivity values, management of an established population is likely to be more cost effective by continuing to focus on dispersing females . Population models specific to CBB have been criticized for not being representative of wild populations, since more generations are estimated through modeling than are observed in field studies . We analyzed CBB population growth using a deterministic model, with an even distribution of dispersal and a fixed predation pressure. While CBB dispersal is continuous, there can be dramatic intraseasonal peaks in numbers that were not captured by our model . In addition, reported longevity of female CBB varies widely from 55 to 380 days, though some studies looked at CBB reared on artificial diet . Refinements of survival in natural settings would, therefore, improve models of CBB population growth, and the potential for control by birds. If field data on CBB vital rate stochasticity become available, and bird densities opportunistically increase during CBB peak numbers, it could affect our conclusions about the capacity of birds to control larger CBB outbreaks. Based on our analyses, there is a population density of CBB above which their capacity to produce more adults exceeds the ability of birds to control their numbers, at least to limit the population size by 50%. This positive density-dependent relationship between population growth and density is an Allee effect , and escape from predation is one mechanism for this phenomenon . In general, predator-driven Allee effects can occur when predators are the main driver of prey dynamics and when predators are generalists as are insectivorous Neotropical migrants . Additionally, predators can exert strong pressure when prey availability is not temporally or spatially limited—a potential limiting factor in the coffee system, since CBB are only available to birds during dispersal. Variation in starting population size is likely dependent on how recently CBB have colonized in an area, timing of trapping , the size of the farm , and the extent to which farmers used control measures the previous year . We found that only under very low initial population sizes of CBB could birds be expected to suppress pest numbers by 50%. We note that earlier, stronger CBB suppression by birds would lead to lower infestation numbers later in the coffee season, but this might require selective foraging by birds, depending on relative abundances of other prey species. In conclusion, our models suggest that birds can control CBB under some circumstances, depending on the relative size of the starting CBB population and existing local bird density. To put this idea into practice it is important to remember that managing farms for bird habitat does not always result in pest reduction. Birds may not prey on the pest of interest or birds might cause pest numbers in increase by preying on insect predators that normally regulates the pest population . Aside from predators, pest species are also impacted by the agricultural environment directly . In fact, on coffee farms where bird densities are higher in shade, CBB infestations are also higher , possibly because CBB native range is in humid, shade forests of Africa . It is important that future modeling include such habitat-specific factors to understand Our research helps quantify the densities under which birds have the potential to control CBB populations.